Stability Analysis of Interconnected Fuzzy Systems Using the Fuzzy Lyapunov Method
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Ken Yeh
2010-01-01
Full Text Available The fuzzy Lyapunov method is investigated for use with a class of interconnected fuzzy systems. The interconnected fuzzy systems consist of J interconnected fuzzy subsystems, and the stability analysis is based on Lyapunov functions. Based on traditional Lyapunov stability theory, we further propose a fuzzy Lyapunov method for the stability analysis of interconnected fuzzy systems. The fuzzy Lyapunov function is defined in fuzzy blending quadratic Lyapunov functions. Some stability conditions are derived through the use of fuzzy Lyapunov functions to ensure that the interconnected fuzzy systems are asymptotically stable. Common solutions can be obtained by solving a set of linear matrix inequalities (LMIs that are numerically feasible. Finally, simulations are performed in order to verify the effectiveness of the proposed stability conditions in this paper.
Application of Lyapunov's Second Method in the Stability Analysis of ...
African Journals Online (AJOL)
In this paper, Lyapunov's method for determining the stability of non-linear systems under dynamic states is presented. The paper highlights a practical application of the method to investigate the stability of crude oil/natural gas separation process. Mathematical state models for the separation process, used in the ...
Lyapunov vs. geometrical stability analysis of the Kepler and the restricted three body problems
International Nuclear Information System (INIS)
Yahalom, A.; Levitan, J.; Lewkowicz, M.; Horwitz, L.
2011-01-01
In this Letter we show that although the application of standard Lyapunov analysis predicts that completely integrable Kepler motion is unstable, the geometrical analysis of Horwitz et al. predicts the observed stability. This seems to us to provide evidence for both the incompleteness of the standard Lyapunov analysis and the strength of the geometrical analysis. Moreover, we apply this approach to the three body problem in which the third body is restricted to move on a circle of large radius which induces an adiabatic time dependent potential on the second body. This causes the second body to move in a very interesting and intricate but periodic trajectory; however, the standard Lyapunov analysis, as well as methods based on the parametric variation of curvature associated with the Jacobi metric, incorrectly predict chaotic behavior. The geometric approach predicts the correct stable motion in this case as well. - Highlights: → Lyapunov analysis predicts Kepler motion to be unstable. → Geometrical analysis predicts the observed stability. → Lyapunov analysis predicts chaotic behavior in restricted three body problem. → The geometric approach predicts the correct stable motion in restricted three body problem.
Stability analysis of polynomial fuzzy models via polynomial fuzzy Lyapunov functions
Bernal Reza, Miguel Ángel; Sala, Antonio; JAADARI, ABDELHAFIDH; Guerra, Thierry-Marie
2011-01-01
In this paper, the stability of continuous-time polynomial fuzzy models by means of a polynomial generalization of fuzzy Lyapunov functions is studied. Fuzzy Lyapunov functions have been fruitfully used in the literature for local analysis of Takagi-Sugeno models, a particular class of the polynomial fuzzy ones. Based on a recent Taylor-series approach which allows a polynomial fuzzy model to exactly represent a nonlinear model in a compact set of the state space, it is shown that a refinemen...
Global stability analysis of epidemiological models based on Volterra–Lyapunov stable matrices
International Nuclear Information System (INIS)
Liao Shu; Wang Jin
2012-01-01
Highlights: ► Global dynamics of high dimensional dynamical systems. ► A systematic approach for global stability analysis. ► Epidemiological models of environment-dependent diseases. - Abstract: In this paper, we study the global dynamics of a class of mathematical epidemiological models formulated by systems of differential equations. These models involve both human population and environmental component(s) and constitute high-dimensional nonlinear autonomous systems, for which the global asymptotic stability of the endemic equilibria has been a major challenge in analyzing the dynamics. By incorporating the theory of Volterra–Lyapunov stable matrices into the classical method of Lyapunov functions, we present an approach for global stability analysis and obtain new results on some three- and four-dimensional model systems. In addition, we conduct numerical simulation to verify the analytical results.
Lyapunov stability analysis of magnetohydrodynamic plasma equilibria with axisymmetric toroidal flow
International Nuclear Information System (INIS)
Almaguer, J.A.; Hameiri, E.; Herrera, J.; Holm, D.D.
1988-01-01
Lyapunov stability conditions for ideal magnetohydrodynamic (MHD) plasmas with mass flow in axisymmetric toroidal geometry are determined in the Eulerian representation. Axisymmetric equilibrium solutions of ideal MHD are associated to critical points of a nonlinearly conserved Lyapunov functional consisting of the sum of the total energy and the following flux-weighted quantities: the circulation along field lines, the angular momentum, the toroidal flux, and the mass content within each flux tube. Conditions sufficient for Lyapunov stability of these equilibria against axisymmetric perturbations are found by taking advantage of the Hamiltonian formalism for ideal MHD. In particular [see Eq. (60)], it is sufficient for Lyapunov stability under linearized dynamics that an axisymmetric equilibrium be subsonic in the appropriate rotating frame, lie in the first elliptic regime of the Bernoulli--Grad--Shafranov (BGS) system of equations, and satisfy one additional, more complicated, condition. Effects of boundary conditions, nonlinearity, and three-dimensionality on MHD stability are also discussed
International Nuclear Information System (INIS)
Burande, Chandrakant S.; Bhalekar, Anil A.
2005-01-01
The thermodynamic stability of a few representative elementary chemical reactions proceeding at finite rates has been investigated using the recently proposed thermodynamic Lyapunov function and following the steps of Lyapunov's second method (also termed as the direct method) of stability of motion. The thermodynamic Lyapunov function; L s , used herein is the excess rate of entropy production in the thermodynamic perturbation space, which thereby inherits the dictates of the second law of thermodynamics. This Lyapunov function is not the same as the excess entropy rate that one encounters in thermodynamic (irreversible) literature. The model chemical conversions studied in this presentation are A+B→v x X and A+B↔ν x X. For the sake of simplicity, the thermal effects of chemical reactions have been considered as not adding to the perturbation as our main aim was to demonstrate how one should use systematically the proposed thermodynamic Lyapunov function following the steps of Lyapunov's second method of stability of motion. The domains of thermodynamic stability under the constantly acting small disturbances, thermodynamic asymptotic stability and thermodynamic instability in these model systems get established
Hall magnetohydrodynamics: Conservation laws and Lyapunov stability
International Nuclear Information System (INIS)
Holm, D.D.
1987-01-01
Hall electric fields produce circulating mass flow in confined ideal-fluid plasmas. The conservation laws, Hamiltonian structure, equilibrium state relations, and Lyapunov stability conditions are presented here for ideal Hall magnetohydrodynamics (HMHD) in two and three dimensions. The approach here is to use the remarkable array of nonlinear conservation laws for HMHD that follow from its Hamiltonian structure in order to construct explicit Lyapunov functionals for the HMHD equilibrium states. In this way, the Lyapunov stability analysis provides classes of HMHD equilibria that are stable and whose linearized initial-value problems are well posed (in the sense of possessing continuous dependence on initial conditions). Several examples are discussed in both two and three dimensions
International Nuclear Information System (INIS)
Druzhinina, O V; Shestakov, A A
2002-01-01
A generalized direct Lyapunov method is put forward for the study of stability and attraction in general time systems of the following types: the classical dynamical system in the sense of Birkhoff, the general system in the sense of Zubov, the general system in the sense of Seibert, the general system with delay, and the general 'input-output' system. For such systems, with the help of generalized Lyapunov functions with respect to two filters, two quasifilters, or two filter bases, necessary and sufficient conditions for stability and attraction are obtained under minimal assumptions about the mathematical structure of the general system
Lyapunov stability robust analysis and robustness design for linear continuous-time systems
Luo, J.S.; Johnson, A.; Bosch, van den P.P.J.
1995-01-01
The linear continuous-time systems to be discussed are described by state space models with structured time-varying uncertainties. First, the explicit maximal perturbation bound for maintaining quadratic Lyapunov stability of the closed-loop systems is presented. Then, a robust design method is
A Lyapunov method for stability analysis of piecewise-affine systems over non-invariant domains
Rubagotti, Matteo; Zaccarian, Luca; Bemporad, Alberto
2016-05-01
This paper analyses stability of discrete-time piecewise-affine systems, defined on possibly non-invariant domains, taking into account the possible presence of multiple dynamics in each of the polytopic regions of the system. An algorithm based on linear programming is proposed, in order to prove exponential stability of the origin and to find a positively invariant estimate of its region of attraction. The results are based on the definition of a piecewise-affine Lyapunov function, which is in general discontinuous on the boundaries of the regions. The proposed method is proven to lead to feasible solutions in a broader range of cases as compared to a previously proposed approach. Two numerical examples are shown, among which a case where the proposed method is applied to a closed-loop system, to which model predictive control was applied without a-priori guarantee of stability.
Large-Signal Lyapunov-Based Stability Analysis of DC/AC Inverters and Inverter-Based Microgrids
Kabalan, Mahmoud
Microgrid stability studies have been largely based on small-signal linearization techniques. However, the validity and magnitude of the linearization domain is limited to small perturbations. Thus, there is a need to examine microgrids with large-signal nonlinear techniques to fully understand and examine their stability. Large-signal stability analysis can be accomplished by Lyapunov-based mathematical methods. These Lyapunov methods estimate the domain of asymptotic stability of the studied system. A survey of Lyapunov-based large-signal stability studies showed that few large-signal studies have been completed on either individual systems (dc/ac inverters, dc/dc rectifiers, etc.) or microgrids. The research presented in this thesis addresses the large-signal stability of droop-controlled dc/ac inverters and inverter-based microgrids. Dc/ac power electronic inverters allow microgrids to be technically feasible. Thus, as a prelude to examining the stability of microgrids, the research presented in Chapter 3 analyzes the stability of inverters. First, the 13 th order large-signal nonlinear model of a droop-controlled dc/ac inverter connected to an infinite bus is presented. The singular perturbation method is used to decompose the nonlinear model into 11th, 9th, 7th, 5th, 3rd and 1st order models. Each model ignores certain control or structural components of the full order model. The aim of the study is to understand the accuracy and validity of the reduced order models in replicating the performance of the full order nonlinear model. The performance of each model is studied in three different areas: time domain simulations, Lyapunov's indirect method and domain of attraction estimation. The work aims to present the best model to use in each of the three domains of study. Results show that certain reduced order models are capable of accurately reproducing the performance of the full order model while others can be used to gain insights into those three areas of
Directory of Open Access Journals (Sweden)
Eklas Hossain
2017-11-01
Full Text Available To mitigate the microgrid instability despite the presence of dense Constant Power Load (CPL loads in the system, a number of compensation techniques have already been gone through extensive research, proposed, and implemented around the world. In this paper, a storage based load side compensation technique is used to enhance stability of microgrids. Besides adopting this technique here, Sliding Mode Controller (SMC and Lyapunov Redesign Controller (LRC, two of the most prominent nonlinear control techniques, are individually implemented to control microgrid system stability with desired robustness. CPL power is then varied to compare robustness of these two control techniques. This investigation revealed the better performance of the LRC system compared to SMC to retain stability in microgrid with dense CPL load. All the necessary results are simulated in Matlab/Simulink platform for authentic verification. Reasons behind inferior SMC performance and ways to mitigate that are also discussed. Finally, the effectiveness of SMC and LRC systems to attain stability in real microgrids is verified by numerical analysis.
International Nuclear Information System (INIS)
Verdu, G.; Ginestar, D.; Bovea, M.D.; Jimenez, P.; Pena, J.; Munoz-Cobo, J.L.
1997-01-01
The dynamics reconstruction techniques have been applied to systems as BWRs with a big amount of noise. The success of this methodology was limited due to the noise in the signals. Recently, new techniques have been introduced for short and noisy data sets based on a global fit of the signal by means of orthonormal polynomials. In this paper, we revisit these ideas in order to adapt them for the analysis of the neutronic power signals to characterize the stability regime of BWR reactors. To check the performance of the methodology, we have analyzed simulated noisy signals, observing that the method works well, even with a big amount of noise. Also, we have analyzed experimental signals from Ringhals 1 BWR. In this case, the reconstructed phase space for the system is not very good. A modal decomposition treatment for the signals is proposed producing signals with better behaviour. (author)
Hossain, Eklas; Perez, Ron; Padmanaban, Sanjeevikumar; Mihet-Popa, Lucian; Blaabjerg, Frede; Ramachandaramurthy, Vigna K.
2017-01-01
To mitigate the microgrid instability despite the presence of dense Constant Power Load (CPL) loads in the system, a number of compensation techniques have already been gone through extensive research, proposed, and implemented around the world. In this paper, a storage based load side compensation technique is used to enhance stability of microgrids. Besides adopting this technique here, Sliding Mode Controller (SMC) and Lyapunov Redesign Controller (LRC), two of the most prominent nonlinear...
Lyapunov functionals and stability of stochastic functional differential equations
Shaikhet, Leonid
2013-01-01
Stability conditions for functional differential equations can be obtained using Lyapunov functionals. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations describes the general method of construction of Lyapunov functionals to investigate the stability of differential equations with delays. This work continues and complements the author’s previous book Lyapunov Functionals and Stability of Stochastic Difference Equations, where this method is described for discrete- and continuous-time difference equations. The text begins with a description of the peculiarities of deterministic and stochastic functional differential equations. There follow basic definitions for stability theory of stochastic hereditary systems, and a formal procedure of Lyapunov functionals construction is presented. Stability investigation is conducted for stochastic linear and nonlinear differential equations with constant and distributed delays. The proposed method is used for stability investigation of di...
Stability of time-delay systems via Lyapunov functions
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Carlos F. Alastruey
2002-01-01
Full Text Available In this paper, a Lyapunov function candidate is introduced for multivariable systems with inner delays, without assuming a priori stability for the nondelayed subsystem. By using this Lyapunov function, a controller is deduced. Such a controller utilizes an input–output description of the original system, a circumstance that facilitates practical applications of the proposed approach.
Lyapunov functionals and stability of stochastic difference equations
Shaikhet, Leonid
2011-01-01
This book offers a general method of Lyapunov functional construction which lets researchers analyze the degree to which the stability properties of differential equations are preserved in their difference analogues. Includes examples from physical systems.
Directory of Open Access Journals (Sweden)
A. V. Stepanov
2014-01-01
Full Text Available A development of the direct Lyapunov method for the analysis of transient stability of a system of synchronous generators based on the determination of non- stable equilibria on a multidimensional sphere.We consider the problem of transient stability analysis for a system of synchronous generators under the action of strong perturbations. The aim of our work is to develop methods to analyze a transient stability of the system of synchronous generators, which allow getting trustworthy results on reserve transient stability under different perturbations. For the analysis of transient stability, we use the direct Lyapunov method.One of the problems for this method application is to find the Lypunov function that well reflects the properties of a parallel system of synchronous generators. The most reliable results were obtained when the analysis of transient stability was performed with a Lyapunov function of energy type. Another problem for application of the direct Lyapunov method is to determine the critical value of the Lyapunov function, which requires finding the non-stable equilibria of the system. Determination of the non-stable equilibria requires studying the Lyapunov function in a multidimensional space in a neighborhood of a stable equilibrium for the post-breakdown system; this is a complicated non-linear problem.In the paper, we propose a method for determination of the non-stable equilibria on a multidimensional sphere. The method is based on a search of a minimum of the Lyapunov function on a multidimensional sphere the center of which is a stable equilibrium. Our method allows, comparing with the other, e.g., gradient methods, reliable finding a non-stable equilibrium and calculating the critical value. The reliability of our method is proved by numerical experiments. The developed methods and a program realized in a MATLAB package can be recommended for design of a post-breakdown control system of synchronous generators or as a
Geodesic stability, Lyapunov exponents, and quasinormal modes
International Nuclear Information System (INIS)
Cardoso, Vitor; Miranda, Alex S.; Berti, Emanuele; Witek, Helvi; Zanchin, Vilson T.
2009-01-01
Geodesic motion determines important features of spacetimes. Null unstable geodesics are closely related to the appearance of compact objects to external observers and have been associated with the characteristic modes of black holes. By computing the Lyapunov exponent, which is the inverse of the instability time scale associated with this geodesic motion, we show that, in the eikonal limit, quasinormal modes of black holes in any dimensions are determined by the parameters of the circular null geodesics. This result is independent of the field equations and only assumes a stationary, spherically symmetric and asymptotically flat line element, but it does not seem to be easily extendable to anti-de Sitter spacetimes. We further show that (i) in spacetime dimensions greater than four, equatorial circular timelike geodesics in a Myers-Perry black-hole background are unstable, and (ii) the instability time scale of equatorial null geodesics in Myers-Perry spacetimes has a local minimum for spacetimes of dimension d≥6.
Stability of dynamical systems on the role of monotonic and non-monotonic Lyapunov functions
Michel, Anthony N; Liu, Derong
2015-01-01
The second edition of this textbook provides a single source for the analysis of system models represented by continuous-time and discrete-time, finite-dimensional and infinite-dimensional, and continuous and discontinuous dynamical systems. For these system models, it presents results which comprise the classical Lyapunov stability theory involving monotonic Lyapunov functions, as well as corresponding contemporary stability results involving non-monotonicLyapunov functions.Specific examples from several diverse areas are given to demonstrate the applicability of the developed theory to many important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, and artificial neural networks. The authors cover the following four general topics: - Representation and modeling of dynamical systems of the types described above - Presentation of Lyapunov and Lagrange stability theory for dynamical sy...
International Nuclear Information System (INIS)
Souza, Fernando O.; Palhares, Reinaldo M.; Ekel, Petr Ya.
2009-01-01
This paper deals with the stability analysis of delayed uncertain Cohen-Grossberg neural networks (CGNN). The proposed methodology consists in obtaining new robust stability criteria formulated as linear matrix inequalities (LMIs) via the Lyapunov-Krasovskii theory. Particularly one stability criterion is derived from the selection of a parameter-dependent Lyapunov-Krasovskii functional, which allied with the Gu's discretization technique and a simple strategy that decouples the system matrices from the functional matrices, assures a less conservative stability condition. Two computer simulations are presented to support the improved theoretical results.
Non Lyapunov stability of a constant spatially developing 2-D gas flow
Balint, Agneta M.; Balint, Stefan; Tanasie, Loredana
2017-01-01
Different types of stabilities (global, local) and instabilities (global absolute, local convective) of the constant spatially developing 2-D gas flow are analyzed in a particular phase space of continuously differentiable functions, endowed with the usual algebraic operations and the topology generated by the uniform convergence on the plane. For this purpose the Euler equations linearized at the constant flow are used. The Lyapunov stability analysis was presented in [1] and this paper is a continuation of [1].
Lyapunov analysis: from dynamical systems theory to applications
Cencini, Massimo; Ginelli, Francesco
2013-06-01
The study of deterministic laws of evolution has characterized the development of science since Newton's times. Chaos, namely the manifestation of irregular and unpredictable dynamics (not random but look random [1]), entered the debate on determinism at the end of the 19th century with the discovery of sensitivity to initial conditions, meaning that small infinitesimal differences in the initial state might lead to dramatic differences at later times. Poincaré [2, 3] was the first to realize that solutions of the three-body problem are generically highly sensitive to initial conditions. At about the same time, this property was recognized in geodesic flows with negative curvature by Hadamard [4]. One of the first experimental observations of chaos, as understood much later, was when irregular noise was heard by Van der Pol in 1927 [5] while studying a periodically forced nonlinear oscillator. Nevertheless, it was only with the advent of digital computing that chaos started to attract the interest of the wider scientific community. After the pioneering investigation of ergodicity in a chain of nonlinear oscillators by Fermi, Pasta and Ulam in 1955 [6], it was in the early 1960s that the numerical studies of Lorenz [7] and Hénon and Heiles [8] revealed that irregular and unpredictable motions are a generic feature of low-dimensional nonlinear deterministic systems. The existence and onset of chaos was then rigorously analyzed in several systems. While an exhaustive list of such mathematical proofs is beyond the scope of this preface, one should mention the contributions of Kolmogorov [9, 10], Chirikov [11], Smale [12], Ruelle and Takens [13], Li and Yorke [14] and Feigenbaum [15]. The characteristic Lyapunov exponents introduced by Oseledets in 1968 [16] are the fundamental quantities for measuring the sensitivity to initial conditions. Oseledets' work generalized the concept of Lyapunov stability to irregular trajectories building upon earlier studies of Birkhoff
Parameter-dependent PWQ Lyapunov function stability criteria for uncertain piecewise linear systems
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Morten Hovd
2018-01-01
Full Text Available The calculation of piecewise quadratic (PWQ Lyapunov functions is addressed in view of stability analysis of uncertain piecewise linear dynamics. As main contribution, the linear matrix inequality (LMI approach proposed in (Johansson and Rantzer, 1998 for the stability analysis of PWL and PWA dynamics is extended to account for parametric uncertainty based on a improved relaxation technique. The results are applied for the analysis of a Phase Locked Loop (PLL benchmark and the ability to guarantee a stability region in the parameter space well beyond the state of the art is demonstrated.
Lyapunov functions and global stability for SIR and SEIR models with age-dependent susceptibility
Korobeinikov, Andrei; Melnik, Andrey V.
2013-01-01
We consider global asymptotic properties for the SIR and SEIR age structured models for infectious diseases where the susceptibility depends on the age. Using the direct Lyapunov method with Volterra type Lyapunov functions, we establish conditions for the global stability of a unique endemic steady state and the infection-free steady state.
Lyapunov stability and thermal stability of partially relaxed fluids and plasmas
International Nuclear Information System (INIS)
Elsaesser, K.; Spiess, P.
1996-01-01
The relation between the Lyapunov stability of a Hamiltonian system and the thermal stability of a fluid whose temperature is controlled from outside is explored: The free energy as a functional of the correct variables (specific volume, local entropy, and some Clebsch potentials of the velocity) may serve as a Lyapunov functional, depending on the open-quote open-quote Casimirs close-quote close-quote as exchanged quantities. For a multi-species plasma one obtains a sufficient condition for stability: γ(v 2 /c 2 s )-1 s the sound speed. Some features of partially relaxed (T=const) cylindrical plasmas are also discussed. copyright 1996 American Institute of Physics
Lyapunov stability of ideal compressible and incompressible fluid equilibria in three dimensions
International Nuclear Information System (INIS)
Holm, D.D.
1985-08-01
Linearized stability of ideal compressible and incompressible fluid equilibria in three dimensions is analyzed using Lyapunov's direct method. An action principle is given for the Eulerian and Lagrangian fluid descriptions and the family of constants of motion due to symmetry under fluid-particle relabelling is derived in the form of Ertel's theorem for each description. In an augmented Euleriah description, the steady equilibrium flows of these two fluids theories are identified as critical points of the conserved Lyapunov functionals defined by the sum, H + C, of the energy H, and the Ertel constants of motion, C. It turns out that unconditional linear Lyapunov stability of these flows in the norm provided by the second variation of H + C is precluded by vortex-particle stretching, even for otherwise shear-stable flows. Conditional Lyapunov stability of these flows is discussed. 24 refs
Lyapunov Based Estimation of Flight Stability Boundary under Icing Conditions
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Binbin Pei
2017-01-01
Full Text Available Current fight boundary of the envelope protection in icing conditions is usually defined by the critical values of state parameters; however, such method does not take the interrelationship of each parameter and the effect of the external disturbance into consideration. This paper proposes constructing the stability boundary of the aircraft in icing conditions through analyzing the region of attraction (ROA around the equilibrium point. Nonlinear icing effect model is proposed according to existing wind tunnel test results. On this basis, the iced polynomial short period model can be deduced further to obtain the stability boundary under icing conditions using ROA analysis. Simulation results for a series of icing severity demonstrate that, regardless of the icing severity, the boundary of the calculated ROA can be treated as an estimation of the stability boundary around an equilibrium point. The proposed methodology is believed to be a promising way for ROA analysis and stability boundary construction of the aircraft in icing conditions, and it will provide theoretical support for multiple boundary protection of icing tolerant flight.
Piecewise quadratic Lyapunov functions for stability verification of approximate explicit MPC
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Morten Hovd
2010-04-01
Full Text Available Explicit MPC of constrained linear systems is known to result in a piecewise affine controller and therefore also piecewise affine closed loop dynamics. The complexity of such analytic formulations of the control law can grow exponentially with the prediction horizon. The suboptimal solutions offer a trade-off in terms of complexity and several approaches can be found in the literature for the construction of approximate MPC laws. In the present paper a piecewise quadratic (PWQ Lyapunov function is used for the stability verification of an of approximate explicit Model Predictive Control (MPC. A novel relaxation method is proposed for the LMI criteria on the Lyapunov function design. This relaxation is applicable to the design of PWQ Lyapunov functions for discrete-time piecewise affine systems in general.
Lyapunov stability and its application to systems of ordinary differential equations
Kennedy, E. W.
1979-01-01
An outline and a brief introduction to some of the concepts and implications of Lyapunov stability theory are presented. Various aspects of the theory are illustrated by the inclusion of eight examples, including the Cartesian coordinate equations of the two-body problem, linear and nonlinear (Van der Pol's equation) oscillatory systems, and the linearized Kustaanheimo-Stiefel element equations for the unperturbed two-body problem.
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Hui Ye
2017-01-01
Full Text Available This paper investigates the problem of global stabilization for a class of switched nonlinear systems using multiple Lyapunov functions (MLFs. The restrictions on nonlinearities are neither linear growth condition nor Lipschitz condition with respect to system states. Based on adding a power integrator technique, we design homogeneous state feedback controllers of all subsystems and a switching law to guarantee that the closed-loop system is globally asymptotically stable. Finally, an example is given to illustrate the validity of the proposed control scheme.
Sliding Mode Controller and Lyapunov Redesign Controller to Improve Microgrid Stability
DEFF Research Database (Denmark)
Hossain, Eklas; Perez, Ron; Padmanaban, Sanjeevikumar
2017-01-01
technique is used to enhance stability of microgrids. Besides adopting this technique here, Sliding Mode Controller (SMC) and Lyapunov Redesign Controller (LRC), two of the most prominent nonlinear control techniques, are individually implemented to control microgrid system stability with desired robustness....... CPL power is then varied to compare robustness of these two control techniques. This investigation revealed the better performance of the LRC system compared to SMC to retain stability in microgrid with dense CPL load. All the necessary results are simulated in Matlab/Simulink platform for authentic......To mitigate the microgrid instability despite the presence of dense Constant Power Load (CPL) loads in the system, a number of compensation techniques have already been gone through extensive research, proposed, and implemented around the world. In this paper, a storage based load side compensation...
Balint, Stefan; Balint, Agneta M.
2017-01-01
Different types of stabilities (global, local) and instabilities (global absolute, local convective) of the constant spatially developing 1-D gas flow are analyzed in the phase space of continuously differentiable functions, endowed with the usual algebraic operations and the topology generated by the uniform convergence on the real axis. For this purpose the Euler equations linearized at the constant flow are used. The Lyapunov stability analysis was presented in [1] and this paper is a continuation of [1].
Lyapunov-based Stability of Feedback Interconnections of Negative Imaginary Systems
Ghallab, Ahmed G.
2017-10-19
Feedback control systems using sensors and actuators such as piezoelectric sensors and actuators, micro-electro-mechanical systems (MEMS) sensors and opto-mechanical sensors, are allowing new advances in designing such high precision technologies. The negative imaginary control systems framework allows for robust control design for such high precision systems in the face of uncertainties due to unmodelled dynamics. The stability of the feedback interconnection of negative imaginary systems has been well established in the literature. However, the proofs of stability feedback interconnection which are used in some previous papers have a shortcoming due to a matrix inevitability issue. In this paper, we provide a new and correct Lyapunov-based proof of one such result and show that the result is still true.
Lyapunov-based Stability of Feedback Interconnections of Negative Imaginary Systems
Ghallab, Ahmed G.; Mabrok, Mohamed; Petersen, Ian R.
2017-01-01
Feedback control systems using sensors and actuators such as piezoelectric sensors and actuators, micro-electro-mechanical systems (MEMS) sensors and opto-mechanical sensors, are allowing new advances in designing such high precision technologies. The negative imaginary control systems framework allows for robust control design for such high precision systems in the face of uncertainties due to unmodelled dynamics. The stability of the feedback interconnection of negative imaginary systems has been well established in the literature. However, the proofs of stability feedback interconnection which are used in some previous papers have a shortcoming due to a matrix inevitability issue. In this paper, we provide a new and correct Lyapunov-based proof of one such result and show that the result is still true.
Blanchini, Franco; Giordano, G.
2017-01-01
For a vast class of dynamical networks, including chemical reaction networks (CRNs) with monotonic reaction rates, the existence of a polyhedral Lyapunov function (PLF) implies structural (i.e., parameter-free) local stability. Global structural stability is ensured under the additional
Analysis of Human Standing Balance by Largest Lyapunov Exponent
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Kun Liu
2015-01-01
Full Text Available The purpose of this research is to analyse the relationship between nonlinear dynamic character and individuals’ standing balance by the largest Lyapunov exponent, which is regarded as a metric for assessing standing balance. According to previous study, the largest Lyapunov exponent from centre of pressure time series could not well quantify the human balance ability. In this research, two improvements were made. Firstly, an external stimulus was applied to feet in the form of continuous horizontal sinusoidal motion by a moving platform. Secondly, a multiaccelerometer subsystem was adopted. Twenty healthy volunteers participated in this experiment. A new metric, coordinated largest Lyapunov exponent was proposed, which reflected the relationship of body segments by integrating multidimensional largest Lyapunov exponent values. By using this metric in actual standing performance under sinusoidal stimulus, an obvious relationship between the new metric and the actual balance ability was found in the majority of the subjects. These results show that the sinusoidal stimulus can make human balance characteristics more obvious, which is beneficial to assess balance, and balance is determined by the ability of coordinating all body segments.
A Lyapunov Stability Theory-Based Control Strategy for Three-Level Shunt Active Power Filter
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Yijia Cao
2017-01-01
Full Text Available The three-phase three-wire neutral-point-clamped shunt active power filter (NPC-SAPF, which most adopts classical closed-loop feedback control methods such as proportional-integral (PI, proportional-resonant (PR and repetitive control, can only output 1st–25th harmonic currents with 10–20 kHz switching frequency. The reason for this is that the controller design must make a compromise between system stability and harmonic current compensation ability under the condition of less than 20 kHz switching frequency. To broaden the bandwidth of the compensation current, a Lyapunov stability theory-based control strategy is presented in this paper for NPC-SAPF. The proposed control law is obtained by constructing the switching function on the basis of the mathematical model and the Lyapunov candidate function, which can avoid introducing closed-loop feedback control and keep the system globally asymptotically stable. By means of the proposed method, the NPC-SAPF has compensation ability for the 1st–50th harmonic currents, the total harmonic distortion (THD and each harmonic content of grid currents satisfy the requirements of IEEE Standard 519-2014. In order to verify the superiority of the proposed control strategy, stability conditions of the proposed strategy and the representative PR controllers are compared. The simulation results in MATLAB/Simulink (MathWorks, Natick, MA, USA and the experimental results obtained on a 6.6 kVA NPC-SAPF laboratory prototype validate the proposed control strategy.
International Nuclear Information System (INIS)
Look, Nicole; Arellano, Christopher J.; Grabowski, Alena M.; Kram, Rodger; McDermott, William J.; Bradley, Elizabeth
2013-01-01
In this paper, we study dynamic stability during running, focusing on the effects of speed, and the use of a leg prosthesis. We compute and compare the maximal Lyapunov exponents of kinematic time-series data from subjects with and without unilateral transtibial amputations running at a wide range of speeds. We find that the dynamics of the affected leg with the running-specific prosthesis are less stable than the dynamics of the unaffected leg and also less stable than the biological legs of the non-amputee runners. Surprisingly, we find that the center-of-mass dynamics of runners with two intact biological legs are slightly less stable than those of runners with amputations. Our results suggest that while leg asymmetries may be associated with instability, runners may compensate for this effect by increased control of their center-of-mass dynamics
Lyapunov stability and poisson structure of the thermal TDHF and RPA equations
International Nuclear Information System (INIS)
Balian, R.; Veneroni, M.
1989-01-01
The thermal TDHF equation is analyzed in the Liouville representation of quantum mechanics, where the matrix elements of the single-particle (s.p) density ρ behave as classical dynamical variables. By introducing the Lie--Poisson bracket associated with the unitary group of the s.p. Hilbert space, we show that TDHF has a Hamiltonian, but non-canonical, classical form. Within this Poisson structure, either the s.p. energy or the s.p. grand potential Ω(ρ) act as a Hamilton function. The Lyapunov stability of both the TDHF and RPA equations around a HF state then follows, since the HF approximation for thermal equilibrium is determined by minimizing Ω(ρ). The RPA matrix in the Liouville space is expressed as the product of the Poisson tensor with the HF stability matrix, interpreted as a metric tensor generated by the entropy. This factorization displays the roles of the energy and entropy terms arising from Ω(ρ) in the RPA dynamics, and it helps to construct the RPA modes. Several extensions are considered. copyright 1989 Academic Press, Inc
Lyapunov stability and Poisson structure of the thermal TDHF and RPA equations
International Nuclear Information System (INIS)
Veneroni, M.; Balian, R.
1989-01-01
The thermal TDHF equation is analyzed in the Liouville representation of quantum mechanics, where the matrix elements of the single-particle (s.p.) density ρ behave as classical dynamical variables. By introducing the Lie-Poisson bracket associated with the unitary group of the s.p. Hilbert space, we show that TDHF has a hamiltonian, but non-canonical, classical form. Within this Poisson structure, either the s.p. energy or the s.p. grand potential Ω(ρ) act as a Hamilton function. The Lyapunov stability of both the TDHF and RPA equations around a HF state then follows, since the HF approximation for thermal equilibrium is determined by minimizing Ω(ρ). The RPA matrix in the Liouville space is expressed as the product of the Poisson tensor with the HF stability matrix, interpreted as a metric tensor generated by the entropy. This factorization displays the roles of the energy and entropy terms arising from Ω(ρ) in the RPA dynamics, and it helps to construct the RPA modes. Several extensions are considered
Kumar, Rajesh; Srivastava, Smriti; Gupta, J R P
2017-03-01
In this paper adaptive control of nonlinear dynamical systems using diagonal recurrent neural network (DRNN) is proposed. The structure of DRNN is a modification of fully connected recurrent neural network (FCRNN). Presence of self-recurrent neurons in the hidden layer of DRNN gives it an ability to capture the dynamic behaviour of the nonlinear plant under consideration (to be controlled). To ensure stability, update rules are developed using lyapunov stability criterion. These rules are then used for adjusting the various parameters of DRNN. The responses of plants obtained with DRNN are compared with those obtained when multi-layer feed forward neural network (MLFFNN) is used as a controller. Also, in example 4, FCRNN is also investigated and compared with DRNN and MLFFNN. Robustness of the proposed control scheme is also tested against parameter variations and disturbance signals. Four simulation examples including one-link robotic manipulator and inverted pendulum are considered on which the proposed controller is applied. The results so obtained show the superiority of DRNN over MLFFNN as a controller. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Hu, D. L.; Liu, X. B.
Both periodic loading and random forces commonly co-exist in real engineering applications. However, the dynamic behavior, especially dynamic stability of systems under parametric periodic and random excitations has been reported little in the literature. In this study, the moment Lyapunov exponent and stochastic stability of binary airfoil under combined harmonic and non-Gaussian colored noise excitations are investigated. The noise is simplified to an Ornstein-Uhlenbeck process by applying the path-integral method. Via the singular perturbation method, the second-order expansions of the moment Lyapunov exponent are obtained, which agree well with the results obtained by the Monte Carlo simulation. Finally, the effects of the noise and parametric resonance (such as subharmonic resonance and combination additive resonance) on the stochastic stability of the binary airfoil system are discussed.
International Nuclear Information System (INIS)
Ignat'yev, A O
2003-01-01
A system of ordinary differential equations with impulse action at fixed moments of time is considered. The system is assumed to have the zero solution. It is shown that the existence of a corresponding Lyapunov function is a necessary and sufficient condition for the uniform asymptotic stability of the zero solution. Restrictions on perturbations of the right-hand sides of differential equations and impulse actions are obtained under which the uniform asymptotic stability of the zero solution of the 'unperturbed' system implies the uniform asymptotic stability of the zero solution of the 'perturbed' system
Barreira, Luís
2017-01-01
This book offers a self-contained introduction to the theory of Lyapunov exponents and its applications, mainly in connection with hyperbolicity, ergodic theory and multifractal analysis. It discusses the foundations and some of the main results and main techniques in the area, while also highlighting selected topics of current research interest. With the exception of a few basic results from ergodic theory and the thermodynamic formalism, all the results presented include detailed proofs. The book is intended for all researchers and graduate students specializing in dynamical systems who are looking for a comprehensive overview of the foundations of the theory and a sample of its applications.
International Nuclear Information System (INIS)
Takeuchi, Kazumasa A; Chaté, Hugues
2013-01-01
We show, using covariant Lyapunov vectors in addition to standard Lyapunov analysis, that there exists a set of collective Lyapunov modes in large chaotic systems exhibiting collective dynamics. Associated with delocalized Lyapunov vectors, they act collectively on the trajectory and hence characterize the instability of its collective dynamics. We further develop, for globally coupled systems, a connection between these collective modes and the Lyapunov modes in the corresponding Perron–Frobenius equation. We thereby address the fundamental question of the effective dimension of collective dynamics and discuss the extensivity of chaos in the presence of collective dynamics. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)
New zero-input overflow stability proofs based on Lyapunov theory
Werter, M.J.; Ritzerfeld, J.H.F.
1989-01-01
The authors demonstrate some proofs of zero-input overflow-oscillation suppression in recursive digital filters. The proofs are based on the second method of Lyapunov. For second-order digital filters with complex conjugated poles, the state describes a trajectory in the phase plane, spiraling
Using largest Lyapunov exponent to confirm the intrinsic stability of boiling water reactors
International Nuclear Information System (INIS)
Gavilian-Moreno, Carlos; Espinosa-Paredes, Gilberto
2016-01-01
The aim of this paper is the study of instability state of boiling water reactors with a method based in largest Lyapunov exponents (LLEs). Detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the LLE. Lyapunov exponents quantify the exponential divergence of initially close state-space trajectories and estimate the amount of chaos in a system. This method was applied to a set of signals from several nuclear power plant (NPP) reactors under commercial operating conditions that experienced instabilities events, apparently each of a different nature. Laguna Verde and Forsmark NPPs with in-phase instabilities, and Cofrentes NPP with out-of-phases instability. This study presents the results of intrinsic instability in the boiling water reactors of three NPPs. In the analyzed cases the limit cycle was not reached, which implies that the point of equilibrium exerts influence and attraction on system evolution
Using largest Lyapunov exponent to confirm the intrinsic stability of boiling water reactors
Energy Technology Data Exchange (ETDEWEB)
Gavilian-Moreno, Carlos [Iberdrola Generacion, S.A., Cofrentes Nuclear Power Plant, Project Engineering Department, Paraje le Plano S/N, Valencia (Spain); Espinosa-Paredes, Gilberto [Area de ingeniera en Recursos Energeticos, Universidad Autonoma Metropolitana-Iztapalapa, Mexico city (Mexico)
2016-04-15
The aim of this paper is the study of instability state of boiling water reactors with a method based in largest Lyapunov exponents (LLEs). Detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the LLE. Lyapunov exponents quantify the exponential divergence of initially close state-space trajectories and estimate the amount of chaos in a system. This method was applied to a set of signals from several nuclear power plant (NPP) reactors under commercial operating conditions that experienced instabilities events, apparently each of a different nature. Laguna Verde and Forsmark NPPs with in-phase instabilities, and Cofrentes NPP with out-of-phases instability. This study presents the results of intrinsic instability in the boiling water reactors of three NPPs. In the analyzed cases the limit cycle was not reached, which implies that the point of equilibrium exerts influence and attraction on system evolution.
Using Largest Lyapunov Exponent to Confirm the Intrinsic Stability of Boiling Water Reactors
Directory of Open Access Journals (Sweden)
Carlos J. Gavilán-Moreno
2016-04-01
Full Text Available The aim of this paper is the study of instability state of boiling water reactors with a method based in largest Lyapunov exponents (LLEs. Detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the LLE. Lyapunov exponents quantify the exponential divergence of initially close state-space trajectories and estimate the amount of chaos in a system. This method was applied to a set of signals from several nuclear power plant (NPP reactors under commercial operating conditions that experienced instabilities events, apparently each of a different nature. Laguna Verde and Forsmark NPPs with in-phase instabilities, and Cofrentes NPP with out-of-phases instability. This study presents the results of intrinsic instability in the boiling water reactors of three NPPs. In the analyzed cases the limit cycle was not reached, which implies that the point of equilibrium exerts influence and attraction on system evolution.
Ma, Junhai; Ren, Wenbo; Zhan, Xueli
2017-04-01
Based on the study of scholars at home and abroad, this paper improves the three-dimensional IS-LM model in macroeconomics, analyzes the equilibrium point of the system and stability conditions, focuses on the parameters and complex dynamic characteristics when Hopf bifurcation occurs in the three-dimensional IS-LM macroeconomics system. In order to analyze the stability of limit cycles when Hopf bifurcation occurs, this paper further introduces the first Lyapunov coefficient to judge the limit cycles, i.e. from a practical view of the business cycle. Numerical simulation results show that within the range of most of the parameters, the limit cycle of 3D IS-LM macroeconomics is stable, that is, the business cycle is stable; with the increase of the parameters, limit cycles becomes unstable, and the value range of the parameters in this situation is small. The research results of this paper have good guide significance for the analysis of macroeconomics system.
Crauel, Hans; Eckmann, Jean-Pierre
1991-01-01
Since the predecessor to this volume (LNM 1186, Eds. L. Arnold, V. Wihstutz)appeared in 1986, significant progress has been made in the theory and applications of Lyapunov exponents - one of the key concepts of dynamical systems - and in particular, pronounced shifts towards nonlinear and infinite-dimensional systems and engineering applications are observable. This volume opens with an introductory survey article (Arnold/Crauel) followed by 26 original (fully refereed) research papers, some of which have in part survey character. From the Contents: L. Arnold, H. Crauel: Random Dynamical Systems.- I.Ya. Goldscheid: Lyapunov exponents and asymptotic behaviour of the product of random matrices.- Y. Peres: Analytic dependence of Lyapunov exponents on transition probabilities.- O. Knill: The upper Lyapunov exponent of Sl (2, R) cocycles:Discontinuity and the problem of positivity.- Yu.D. Latushkin, A.M. Stepin: Linear skew-product flows and semigroups of weighted composition operators.- P. Baxendale: Invariant me...
ORIGINAL ARTICLE Stability Analysis of Delayed Cournot Model in ...
African Journals Online (AJOL)
HP
and Lyapunov method of nonlinear stability analysis are employed. It is ascertained ... and the rival player makes decision without delay, it leads to instability of the dynamic system at ... phenomena such as economic growth, prediction and ...
On the Lyapunov stability of a plane parallel convective flow of a binary mixture
Directory of Open Access Journals (Sweden)
Giuseppe Mulone
1991-05-01
Full Text Available The nonlinear stability of plane parallel convective flows of a binary fluid mixture in the Oberbeck-Boussinesq scheme is studied in the stress-free boundary case. Nonlinear stability conditions independent of Reynolds number are proved.
Directory of Open Access Journals (Sweden)
Coşkun Yakar
2010-01-01
Full Text Available The qualitative behavior of a perturbed fractional-order differential equation with Caputo's derivative that differs in initial position and initial time with respect to the unperturbed fractional-order differential equation with Caputo's derivative has been investigated. We compare the classical notion of stability to the notion of initial time difference stability for fractional-order differential equations in Caputo's sense. We present a comparison result which again gives the null solution a central role in the comparison fractional-order differential equation when establishing initial time difference stability of the perturbed fractional-order differential equation with respect to the unperturbed fractional-order differential equation.
Lyapunov exponents and smooth ergodic theory
Barreira, Luis
2001-01-01
This book is a systematic introduction to smooth ergodic theory. The topics discussed include the general (abstract) theory of Lyapunov exponents and its applications to the stability theory of differential equations, stable manifold theory, absolute continuity, and the ergodic theory of dynamical systems with nonzero Lyapunov exponents (including geodesic flows). The authors consider several non-trivial examples of dynamical systems with nonzero Lyapunov exponents to illustrate some basic methods and ideas of the theory. This book is self-contained. The reader needs a basic knowledge of real analysis, measure theory, differential equations, and topology. The authors present basic concepts of smooth ergodic theory and provide complete proofs of the main results. They also state some more advanced results to give readers a broader view of smooth ergodic theory. This volume may be used by those nonexperts who wish to become familiar with the field.
Generalized decompositions of dynamic systems and vector Lyapunov functions
Ikeda, M.; Siljak, D. D.
1981-10-01
The notion of decomposition is generalized to provide more freedom in constructing vector Lyapunov functions for stability analysis of nonlinear dynamic systems. A generalized decomposition is defined as a disjoint decomposition of a system which is obtained by expanding the state-space of a given system. An inclusion principle is formulated for the solutions of the expansion to include the solutions of the original system, so that stability of the expansion implies stability of the original system. Stability of the expansion can then be established by standard disjoint decompositions and vector Lyapunov functions. The applicability of the new approach is demonstrated using the Lotka-Volterra equations.
International Nuclear Information System (INIS)
Guerrieri, A.
2009-01-01
In this report the largest Lyapunov characteristic exponent of a high dimensional atmospheric global circulation model of intermediate complexity has been estimated numerically. A sensitivity analysis has been carried out by varying the equator-to-pole temperature difference, the space resolution and the value of some parameters employed by the model. Chaotic and non-chaotic regimes of circulation have been found. [it
Directory of Open Access Journals (Sweden)
Seung Kwan Song
2016-10-01
Full Text Available We present two control strategies for an oscillating water column-wave energy converter (OWC-WEC in the time domain. We consider a fixed OWC-WEC on the open sea with an impulse turbine module. This system mainly consists of a chamber, turbine and electric generator. For the time domain analysis, all of the conversion stages considering mutualities among them should be analyzed based on the Newtonian mechanics. According to the analysis of Newtonian mechanics, the hydrodynamics of wave energy absorption in the chamber and the turbine aerodynamic performance are directly coupled and share the internal air pressure term via the incompressible air assumption. The turbine aerodynamics and the dynamics of the electric generator are connected by torque load through the rotor shaft, which depends on an electric terminal load that acts as a control input. The proposed control strategies are an instant maximum turbine efficiency tracking control and a constant angular velocity of the turbine rotor control methods. Both are derived by Lyapunov stability analysis. Numerical simulations are carried out under irregular waves with various heights and periods in the time domain, and the results with the controllers are analyzed. We then compare these results with simulations carried out in the absence of the control strategy in order to prove the performance of the controllers.
Greenwood, Nigel J C; Gunton, Jenny E
2014-07-01
This study demonstrated the novel application of a "machine-intelligent" mathematical structure, combining differential game theory and Lyapunov-based control theory, to the artificial pancreas to handle dynamic uncertainties. Realistic type 1 diabetes (T1D) models from the literature were combined into a composite system. Using a mixture of "black box" simulations and actual data from diabetic medical histories, realistic sets of diabetic time series were constructed for blood glucose (BG), interstitial fluid glucose, infused insulin, meal estimates, and sometimes plasma insulin assays. The problem of underdetermined parameters was side stepped by applying a variant of a genetic algorithm to partial information, whereby multiple candidate-personalized models were constructed and then rigorously tested using further data. These formed a "dynamic envelope" of trajectories in state space, where each trajectory was generated by a hypothesis on the hidden T1D system dynamics. This dynamic envelope was then culled to a reduced form to cover observed dynamic behavior. A machine-intelligent autonomous algorithm then implemented game theory to construct real-time insulin infusion strategies, based on the flow of these trajectories through state space and their interactions with hypoglycemic or near-hyperglycemic states. This technique was tested on 2 simulated participants over a total of fifty-five 24-hour days, with no hypoglycemic or hyperglycemic events, despite significant uncertainties from using actual diabetic meal histories with 10-minute warnings. In the main case studies, BG was steered within the desired target set for 99.8% of a 16-hour daily assessment period. Tests confirmed algorithm robustness for ±25% carbohydrate error. For over 99% of the overall 55-day simulation period, either formal controller stability was achieved to the desired target or else the trajectory was within the desired target. These results suggest that this is a stable, high
Grzybowski, J. M. V.; Macau, E. E. N.; Yoneyama, T.
2017-05-01
This paper presents a self-contained framework for the stability assessment of isochronal synchronization in networks of chaotic and limit-cycle oscillators. The results were based on the Lyapunov-Krasovskii theorem and they establish a sufficient condition for local synchronization stability of as a function of the system and network parameters. With this in mind, a network of mutually delay-coupled oscillators subject to direct self-coupling is considered and then the resulting error equations are block-diagonalized for the purpose of studying their stability. These error equations are evaluated by means of analytical stability results derived from the Lyapunov-Krasovskii theorem. The proposed approach is shown to be a feasible option for the investigation of local stability of isochronal synchronization for a variety of oscillators coupled through linear functions of the state variables under a given undirected graph structure. This ultimately permits the systematic identification of stability regions within the high-dimensionality of the network parameter space. Examples of applications of the results to a number of networks of delay-coupled chaotic and limit-cycle oscillators are provided, such as Lorenz, Rössler, Cubic Chua's circuit, Van der Pol oscillator and the Hindmarsh-Rose neuron.
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Mokaedi V. Lekgari
2014-01-01
Full Text Available We investigate random-time state-dependent Foster-Lyapunov analysis on subgeometric rate ergodicity of continuous-time Markov chains (CTMCs. We are mainly concerned with making use of the available results on deterministic state-dependent drift conditions for CTMCs and on random-time state-dependent drift conditions for discrete-time Markov chains and transferring them to CTMCs.
Lyapunov functions for the fixed points of the Lorenz model
International Nuclear Information System (INIS)
Bakasov, A.A.; Govorkov, B.B. Jr.
1992-11-01
We have shown how the explicit Lyapunov functions can be constructed in the framework of a regular procedure suggested and completed by Lyapunov a century ago (''method of critical cases''). The method completely covers all practically encountering subtle cases of stability study for ordinary differential equations when the linear stability analysis fails. These subtle cases, ''the critical cases'', according to Lyapunov, include both bifurcations of solutions and solutions of systems with symmetry. Being properly specialized and actually powerful in case of ODE's, this Lyapunov's method is formulated in simple language and should attract a wide interest of the physical audience. The method leads to inevitable construction of the explicit Lyapunov function, takes automatically into account the Fredholm alternative and avoids infinite step calculations. Easy and apparent physical interpretation of the Lyapunov function as a potential or as a time-dependent entropy provides one with more details about the local dynamics of the system at non-equilibrium phase transition points. Another advantage is that this Lyapunov's method consists of a set of very detailed explicit prescriptions which allow one to easy programmize the method for a symbolic processor. The application of the Lyapunov theory for critical cases has been done in this work to the real Lorenz equations and it is shown, in particular, that increasing σ at the Hopf bifurcation point suppresses the contribution of one of the variables to the destabilization of the system. The relation of the method to contemporary methods and its place among them have been clearly and extensively discussed. Due to Appendices, the paper is self-contained and does not require from a reader to approach results published only in Russian. (author). 38 refs
International Nuclear Information System (INIS)
Ginelli, Francesco; Politi, Antonio; Chaté, Hugues; Livi, Roberto
2013-01-01
Recent years have witnessed a growing interest in covariant Lyapunov vectors (CLVs) which span local intrinsic directions in the phase space of chaotic systems. Here, we review the basic results of ergodic theory, with a specific reference to the implications of Oseledets’ theorem for the properties of the CLVs. We then present a detailed description of a ‘dynamical’ algorithm to compute the CLVs and show that it generically converges exponentially in time. We also discuss its numerical performance and compare it with other algorithms presented in the literature. We finally illustrate how CLVs can be used to quantify deviations from hyperbolicity with reference to a dissipative system (a chain of Hénon maps) and a Hamiltonian model (a Fermi–Pasta–Ulam chain). This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)
Directory of Open Access Journals (Sweden)
Rui Wang
2014-01-01
Full Text Available A modified multiple structural changes model is built to test structural breaks of the financial system based on calculating the largest Lyapunov exponents of the financial time series. Afterwards, the Lorenz system is used as a simulation example to inspect the new model. As the Lorenz system has strong nonlinearity, the verification results show that the new model has good capability in both finding the breakpoint and revealing the changes in nonlinear characteristics of the time series. The empirical study based on the model used daily data from the S&P 500 stock index during the global financial crisis from 2005 to 2012. The results provide four breakpoints of the period, which divide the contagion into four stages: stationary, local outbreak, global outbreak, and recovery period. An additional significant result is the obvious chaos characteristic difference in the largest Lyapunov exponents and the standard deviation at various stages, particularly at the local outbreak stage.
Robust lyapunov controller for uncertain systems
Laleg-Kirati, Taous-Meriem
2017-02-23
Various examples of systems and methods are provided for Lyapunov control for uncertain systems. In one example, a system includes a process plant and a robust Lyapunov controller configured to control an input of the process plant. The robust Lyapunov controller includes an inner closed loop Lyapunov controller and an outer closed loop error stabilizer. In another example, a method includes monitoring a system output of a process plant; generating an estimated system control input based upon a defined output reference; generating a system control input using the estimated system control input and a compensation term; and adjusting the process plant based upon the system control input to force the system output to track the defined output reference. An inner closed loop Lyapunov controller can generate the estimated system control input and an outer closed loop error stabilizer can generate the system control input.
International Nuclear Information System (INIS)
Tasso, H.
1993-04-01
For a system of van der Pol-like oscillators, Lyapunov functions valid in the greater part of phase space are given. They allow a finite region of attraction to be defined. Any attractor has to be within the rigorously estimated bounds. Under a special choice of the interaction matrices the attractive region can be squeezed to zero. In this case the asymptotic behaviour is given by a conservative system of nonlinear oscillators which acts as attractor. Though this system does not possess, in general, a Hamiltonian formulation, Gibbs statistics is possible due to the proof of a Liouville theorem and the existence of a positive invariant or 'shell' condition. The 'canonical' distribution on the attractor is remarkably simple despite nonlinearities. Finally the connection of the van der Pol-like system and of the attractive region with turbulence and fluctuation spectra in fluids and plasmas is discussed. (orig.)
Stability Analysis for Car Following Model Based on Control Theory
International Nuclear Information System (INIS)
Meng Xiang-Pei; Li Zhi-Peng; Ge Hong-Xia
2014-01-01
Stability analysis is one of the key issues in car-following theory. The stability analysis with Lyapunov function for the two velocity difference car-following model (for short, TVDM) is conducted and the control method to suppress traffic congestion is introduced. Numerical simulations are given and results are consistent with the theoretical analysis. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
2010-05-14
Mikhailovich Lyapunov is discussed. Main attention is focused on the first Lyapunov method. LYAPUNOV BUNDLES IN CYCLIC FEEDBACK SYSTEMS WITH DELAYS George ...Lyapunov frequently discussed this problem with Henry Poincare (1854-1912) and George Darwin (1845 - 1912). They both considered the "pear-form" figure as... Cantor -type set. Neither can the existence of such systems be excluded. The results we present are discussed in a joint paper with K. Bjerkloev. МЕТОДЫ А.М
DEFF Research Database (Denmark)
Eriksson, Robert
2014-01-01
The stability of an interconnected ac/dc system is affected by disturbances occurring in the system. Disturbances, such as three-phase faults, may jeopardize the rotor-angle stability and, thus, the generators fall out of synchronism. The possibility of fast change of the injected powers...... by the multiterminal dc grid can, by proper control action, enhance this stability. This paper proposes a new time optimal control strategy for the injected power of multiterminal dc grids to enhance the rotor-angle stability. The controller is time optimal, since it reduces the impact of a disturbance as fast...
Relative Lyapunov Center Bifurcations
DEFF Research Database (Denmark)
Wulff, Claudia; Schilder, Frank
2014-01-01
Relative equilibria (REs) and relative periodic orbits (RPOs) are ubiquitous in symmetric Hamiltonian systems and occur, for example, in celestial mechanics, molecular dynamics, and rigid body motion. REs are equilibria, and RPOs are periodic orbits of the symmetry reduced system. Relative Lyapunov...... center bifurcations are bifurcations of RPOs from REs corresponding to Lyapunov center bifurcations of the symmetry reduced dynamics. In this paper we first prove a relative Lyapunov center theorem by combining recent results on the persistence of RPOs in Hamiltonian systems with a symmetric Lyapunov...... center theorem of Montaldi, Roberts, and Stewart. We then develop numerical methods for the detection of relative Lyapunov center bifurcations along branches of RPOs and for their computation. We apply our methods to Lagrangian REs of the N-body problem....
Stability analysis of linear switching systems with time delays
International Nuclear Information System (INIS)
Li Ping; Zhong Shouming; Cui Jinzhong
2009-01-01
The issue of stability analysis of linear switching system with discrete and distributed time delays is studied in this paper. An appropriate switching rule is applied to guarantee the stability of the whole switching system. Our results use a Riccati-type Lyapunov functional under a condition on the time delay. So, switching systems with mixed delays are developed. A numerical example is given to illustrate the effectiveness of our results.
Stability analysis for cellular neural networks with variable delays
International Nuclear Information System (INIS)
Zhang Qiang; Wei Xiaopeng; Xu Jin
2006-01-01
Some sufficient conditions for the global exponential stability of cellular neural networks with variable delay are obtained by means of a method based on delay differential inequality. The method, which does not make use of Lyapunov functionals, is simple and effective for the stability analysis of neural networks with delay. Some previously established results in the literature are shown to be special cases of the presented result
Uniting Control Lyapunov and Control Barrier Functions
Romdlony, Zakiyullah; Jayawardhana, Bayu
2014-01-01
In this paper, we propose a nonlinear control design for solving the problem of stabilization with guaranteed safety. The design is based on the merging of a Control Lyapunov Function and a Control Barrier Function. The proposed control method allows us to combine the design of a stabilizer based on
International Nuclear Information System (INIS)
Zamani, Najmeh; Ataei, Mohammad; Niroomand, Mehdi
2015-01-01
Highlights: • Applying nonlinear analysis of complex dynamics displayed by current-mode controlled boost converter. • The ramp compensation method is used to control bifurcation and chaos in these converters based on bifurcation diagram and Lyapunov exponents assignment. • A discrete-time iterative nonlinear mapping model has been derived by inserting the ramp compensation parameter in the dynamical equations of the system. • A design methodology for chaos control is provided in this converter based on Lyapunov exponents assignment in desired values theoretically by proper selection of compensator slope. • Practical results are provided to confirm the theoretical analysis and simulations. - Abstract: Nonlinear analysis of complex dynamics displayed by current mode dc–dc converter and idea of Lyapunov exponents assignment by ramp compensator in order to control chaotic behavior is proposed in this article. A discrete-time iterative nonlinear mapping model is derived. The occurrence of the complex behaviors of bifurcation and chaos generated by varying the circuit parameters are investigated through numerical analysis and software implementation of the circuit. Next, in order to control bifurcation and chaos in these converters, the ramp compensation method is used. By inserting the ramp compensation parameter in the dynamical equations of the system, these complex behaviors are examined theoretically and numerically as well. It is proved that through this method, the stable period-one operation of the converter can be extended. By evaluating the Lyapunov exponents (LEs) of the system, the impact of the slope on the location of LEs are determined analytically. This leads to a design methodology for control of chaos in this converter based on LEs assignment in desired values by proper selection of compensator slope. By developing an experimental set up, practical results are obtained to confirm the theoretical analysis and simulations.
Stability Analysis of Fractional-Order Nonlinear Systems with Delay
Directory of Open Access Journals (Sweden)
Yu Wang
2014-01-01
Full Text Available Stability analysis of fractional-order nonlinear systems with delay is studied. We propose the definition of Mittag-Leffler stability of time-delay system and introduce the fractional Lyapunov direct method by using properties of Mittag-Leffler function and Laplace transform. Then some new sufficient conditions ensuring asymptotical stability of fractional-order nonlinear system with delay are proposed firstly. And the application of Riemann-Liouville fractional-order systems is extended by the fractional comparison principle and the Caputo fractional-order systems. Numerical simulations of an example demonstrate the universality and the effectiveness of the proposed method.
Lyapunov, attractors and exponents
International Nuclear Information System (INIS)
Oliveira, C.R. de.
1987-01-01
Based on the fundamental principles of statistical mechanics and ergodic theory a definition is given to atractor, as an invariant measure. Many results which reinforce this definition are demonstrated. Chaos is related to the presence of an atractor with entropy above zero. The role of Lyapunov exponents is analyzed. (A.C.A.S.) [pt
International Nuclear Information System (INIS)
Park, Ju H.
2007-01-01
This paper considers the robust stability analysis of cellular neural networks with discrete and distributed delays. Based on the Lyapunov stability theory and linear matrix inequality (LMI) technique, a novel stability criterion guaranteeing the global robust convergence of the equilibrium point is derived. The criterion can be solved easily by various convex optimization algorithms. An example is given to illustrate the usefulness of our results
Application of linearized model to the stability analysis of the pressurized water reactor
International Nuclear Information System (INIS)
Li Haipeng; Huang Xiaojin; Zhang Liangju
2008-01-01
A Linear Time-Invariant model of the Pressurized Water Reactor is formulated through the linearization of the nonlinear model. The model simulation results show that the linearized model agrees well with the nonlinear model under small perturbation. Based upon the Lyapunov's First Method, the linearized model is applied to the stability analysis of the Pressurized Water Reactor. The calculation results show that the methodology of linearization to stability analysis is conveniently feasible. (authors)
International Nuclear Information System (INIS)
Wen Zhen; Sun Jitao
2009-01-01
In this paper, we investigate the existence and uniqueness of equilibrium point for delayed Cohen-Grossberg bidirectional associative memory (BAM) neural networks with impulses, based on nonsmooth analysis method. And we give the criteria of global exponential stability of the unique equilibrium point for the delayed BAM neural networks with impulses using Lyapunov method. The new sufficient condition generalizes and improves the previously known results. Finally, we present examples to illustrate that our results are effective.
Fixed-Time Stability Analysis of Permanent Magnet Synchronous Motors with Novel Adaptive Control
Directory of Open Access Journals (Sweden)
Maoxing Liu
2017-01-01
Full Text Available We firstly investigate the fixed-time stability analysis of uncertain permanent magnet synchronous motors with novel control. Compared with finite-time stability where the convergence rate relies on the initial permanent magnet synchronous motors state, the settling time of fixed-time stability can be adjusted to desired values regardless of initial conditions. Novel adaptive stability control strategy for the permanent magnet synchronous motors is proposed, with which we can stabilize permanent magnet synchronous motors within fixed time based on the Lyapunov stability theory. Finally, some simulation and comparison results are given to illustrate the validity of the theoretical results.
Robinett III, Rush D
2011-01-01
Nonlinear Powerflow Control Design presents an innovative control system design process motivated by renewable energy electric grid integration problems. The concepts developed result from the convergence of three research and development goals: • to create a unifying metric to compare the value of different energy sources – coal-burning power plant, wind turbines, solar photovoltaics, etc. – to be integrated into the electric power grid and to replace the typical metric of costs/profit; • to develop a new nonlinear control tool that applies power flow control, thermodynamics, and complex adaptive systems theory to the energy grid in a consistent way; and • to apply collective robotics theories to the creation of high-performance teams of people and key individuals in order to account for human factors in controlling and selling power into a distributed, decentralized electric power grid. All three of these goals have important concepts in common: exergy flow, limit cycles, and balance between compe...
Stability Analysis of Neural Networks-Based System Identification
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Talel Korkobi
2008-01-01
Full Text Available This paper treats some problems related to nonlinear systems identification. A stability analysis neural network model for identifying nonlinear dynamic systems is presented. A constrained adaptive stable backpropagation updating law is presented and used in the proposed identification approach. The proposed backpropagation training algorithm is modified to obtain an adaptive learning rate guarantying convergence stability. The proposed learning rule is the backpropagation algorithm under the condition that the learning rate belongs to a specified range defining the stability domain. Satisfying such condition, unstable phenomena during the learning process are avoided. A Lyapunov analysis leads to the computation of the expression of a convenient adaptive learning rate verifying the convergence stability criteria. Finally, the elaborated training algorithm is applied in several simulations. The results confirm the effectiveness of the CSBP algorithm.
Improved asymptotic stability analysis for uncertain delayed state neural networks
International Nuclear Information System (INIS)
Souza, Fernando O.; Palhares, Reinaldo M.; Ekel, Petr Ya.
2009-01-01
This paper presents a new linear matrix inequality (LMI) based approach to the stability analysis of artificial neural networks (ANN) subject to time-delay and polytope-bounded uncertainties in the parameters. The main objective is to propose a less conservative condition to the stability analysis using the Gu's discretized Lyapunov-Krasovskii functional theory and an alternative strategy to introduce slack matrices. Two computer simulations examples are performed to support the theoretical predictions. Particularly, in the first example, the Hopf bifurcation theory is used to verify the stability of the system when the origin falls into instability. The second example is presented to illustrate how the proposed approach can provide better stability performance when compared to other ones in the literature
Sampled-Data Control of Spacecraft Rendezvous with Discontinuous Lyapunov Approach
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Zhuoshi Li
2013-01-01
Full Text Available This paper investigates the sampled-data stabilization problem of spacecraft relative positional holding with improved Lyapunov function approach. The classical Clohessy-Wiltshire equation is adopted to describe the relative dynamic model. The relative position holding problem is converted into an output tracking control problem using sampling signals. A time-dependent discontinuous Lyapunov functionals approach is developed, which will lead to essentially less conservative results for the stability analysis and controller design of the corresponding closed-loop system. Sufficient conditions for the exponential stability analysis and the existence of the proposed controller are provided, respectively. Finally, a simulation result is established to illustrate the effectiveness of the proposed control scheme.
Multiscale Lyapunov exponent for 2-microlocal functions
International Nuclear Information System (INIS)
Dhifaoui, Zouhaier; Kortas, Hedi; Ammou, Samir Ben
2009-01-01
The Lyapunov exponent is an important indicator of chaotic dynamics. Using wavelet analysis, we define a multiscale representation of this exponent which we demonstrate the scale-wise dependence for functions belonging to C x 0 s,s ' spaces. An empirical study involving simulated processes and financial time series corroborates the theoretical findings.
Stability analysis of delayed genetic regulatory networks with stochastic disturbances
Energy Technology Data Exchange (ETDEWEB)
Zhou Qi, E-mail: zhouqilhy@yahoo.com.c [School of Automation, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu (China); Xu Shengyuan [School of Automation, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu (China); Chen Bing [Institute of Complexity Science, Qingdao University, Qingdao 266071, Shandong (China); Li Hongyi [Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin 150001 (China); Chu Yuming [Department of Mathematics, Huzhou Teacher' s College, Huzhou 313000, Zhejiang (China)
2009-10-05
This Letter considers the problem of stability analysis of a class of delayed genetic regulatory networks with stochastic disturbances. The delays are assumed to be time-varying and bounded. By utilizing Ito's differential formula and Lyapunov-Krasovskii functionals, delay-range-dependent and rate-dependent (rate-independent) stability criteria are proposed in terms of linear matrices inequalities. An important feature of the proposed results is that all the stability conditions are dependent on the upper and lower bounds of the delays. Another important feature is that the obtained stability conditions are less conservative than certain existing ones in the literature due to introducing some appropriate free-weighting matrices. A simulation example is employed to illustrate the applicability and effectiveness of the proposed methods.
Stability analysis of embedded nonlinear predictor neural generalized predictive controller
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Hesham F. Abdel Ghaffar
2014-03-01
Full Text Available Nonlinear Predictor-Neural Generalized Predictive Controller (NGPC is one of the most advanced control techniques that are used with severe nonlinear processes. In this paper, a hybrid solution from NGPC and Internal Model Principle (IMP is implemented to stabilize nonlinear, non-minimum phase, variable dead time processes under high disturbance values over wide range of operation. Also, the superiority of NGPC over linear predictive controllers, like GPC, is proved for severe nonlinear processes over wide range of operation. The necessary conditions required to stabilize NGPC is derived using Lyapunov stability analysis for nonlinear processes. The NGPC stability conditions and improvement in disturbance suppression are verified by both simulation using Duffing’s nonlinear equation and real-time using continuous stirred tank reactor. Up to our knowledge, the paper offers the first hardware embedded Neural GPC which has been utilized to verify NGPC–IMP improvement in realtime.
Stability Analysis of a Microgrid System based on Inverter-Interfaced Distributed Generators
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CUSIDO, J.
2013-08-01
Full Text Available This paper presents a phase-plane trajectory analysis and the appliance of Lyapunov's methodology to evaluate the stability limits of a small signal model of a Microgrid system. The work done is based on a non-linear tool and several computer simulations. The study indicates how to analyze a Microgrid system that is subjected to a severe transient disturbance by using its large signal model without the necessity of the small signal analysis as it is commonly applied.
Containment vessel stability analysis
International Nuclear Information System (INIS)
Harstead, G.A.; Morris, N.F.; Unsal, A.I.
1983-01-01
The stability analysis for a steel containment shell is presented herein. The containment is a freestanding shell consisting of a vertical cylinder with a hemispherical dome. It is stiffened by large ring stiffeners and relatively small longitudinal stiffeners. The containment vessel is subjected to both static and dynamic loads which can cause buckling. These loads must be combined prior to their use in a stability analysis. The buckling loads were computed with the aid of the ASME Code case N-284 used in conjunction with general purpose computer codes and in-house programs. The equations contained in the Code case were used to compute the knockdown factors due to shell imperfections. After these knockdown factors were applied to the critical stress states determined by freezing the maximum dynamic stresses and combining them with other static stresses, a linear bifurcation analysis was carried out with the aid of the BOSOR4 program. Since the containment shell contained large penetrations, the Code case had to be supplemented by a local buckling analysis of the shell area surrounding the largest penetration. This analysis was carried out with the aid of the NASTRAN program. Although the factor of safety against buckling obtained in this analysis was satisfactory, it is claimed that the use of the Code case knockdown factors are unduly conservative when applied to the analysis of buckling around penetrations. (orig.)
Stability analysis for stochastic BAM nonlinear neural network with delays
Lv, Z. W.; Shu, H. S.; Wei, G. L.
2008-02-01
In this paper, stochastic bidirectional associative memory neural networks with constant or time-varying delays is considered. Based on a Lyapunov-Krasovskii functional and the stochastic stability analysis theory, we derive several sufficient conditions in order to guarantee the global asymptotically stable in the mean square. Our investigation shows that the stochastic bidirectional associative memory neural networks are globally asymptotically stable in the mean square if there are solutions to some linear matrix inequalities(LMIs). Hence, the global asymptotic stability of the stochastic bidirectional associative memory neural networks can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed global asymptotic stability criteria.
Stability analysis for stochastic BAM nonlinear neural network with delays
International Nuclear Information System (INIS)
Lv, Z W; Shu, H S; Wei, G L
2008-01-01
In this paper, stochastic bidirectional associative memory neural networks with constant or time-varying delays is considered. Based on a Lyapunov-Krasovskii functional and the stochastic stability analysis theory, we derive several sufficient conditions in order to guarantee the global asymptotically stable in the mean square. Our investigation shows that the stochastic bidirectional associative memory neural networks are globally asymptotically stable in the mean square if there are solutions to some linear matrix inequalities(LMIs). Hence, the global asymptotic stability of the stochastic bidirectional associative memory neural networks can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed global asymptotic stability criteria
Linear and nonlinear stability analysis, associated to experimental fast reactors. Part 2
International Nuclear Information System (INIS)
Amorim, E.S. do; Moura Neto, C. de; Rosa, M.A.P.
1980-07-01
The nonlinear effects in fast reactors kinetics and their stability are studied. The Lyapunov criteria and the Lurie-Letov functions for nonlinear systems were established and simulated. Small oscillations were studied by a Fourier analysis to clarify particular aspects of feedback and load functions in fast reactor at zero power, or/and in normal power level. The results were in agreement with the experimental data existing in the literature. (E.G.) [pt
On the existence of polynomial Lyapunov functions for rationally stable vector fields
DEFF Research Database (Denmark)
Leth, Tobias; Wisniewski, Rafal; Sloth, Christoffer
2018-01-01
This paper proves the existence of polynomial Lyapunov functions for rationally stable vector fields. For practical purposes the existence of polynomial Lyapunov functions plays a significant role since polynomial Lyapunov functions can be found algorithmically. The paper extents an existing result...... on exponentially stable vector fields to the case of rational stability. For asymptotically stable vector fields a known counter example is investigated to exhibit the mechanisms responsible for the inability to extend the result further....
Nolinear stability analysis of nuclear reactors : expansion methods for stability domains
International Nuclear Information System (INIS)
Yang, Chae Yong
1992-02-01
Two constructive methods for estimating asymptotic stability domains of nonlinear reactor models are developed in this study: an improved Chang and Thorp's method based on expansion of a Lyapunov function and a new method based on expansion of any positive definite function. The methods are established on the concept of stability definitions of Lyapunov itself. The first method provides a sequence of stability regions that eventually approaches the exact stability domain, but requires many expansions in order to obtain the entire stability region because the starting Lyapunov function usually corresponds to a small stability region and because most dynamic systems are stiff. The second method (new method) requires only a positive definite function and thus it is easy to come up with a starting region. From a large starting region, the entire stability region is estimated effectively after sufficient iterations. It is particularly useful for stiff systems. The methods are applied to several nonlinear reactor models known in the literature: one-temperature feedback model, two-temperature feedback model, and xenon dynamics model, and the results are compared. A reactor feedback model for a pressurized water reactor (PWR) considering fuel and moderator temperature effects is developed and the nonlinear stability regions are estimated for the various values of design parameters by using the new method. The steady-state properties of the nonlinear reactor system are analyzed via bifurcation theory. The analysis of nonlinear phenomena is carried out for the various forms of reactivity feedback coefficients that are both temperature- (or power-) independent and dependent. If one of two temperature coefficients is positive, unstable limit cycles or multiplicity of the steady-state solutions appear when the other temperature coefficient exceeds a certain critical value. As an example, even though the fuel temperature coefficient is negative, if the moderator temperature
A variational approach to Lyapunov type inequalities from ODEs to PDEs
Cañada, Antonio
2015-01-01
This book highlights the current state of Lyapunov-type inequalities through a detailed analysis. Aimed toward researchers and students working in differential equations and those interested in the applications of stability theory and resonant systems, the book begins with an overview Lyapunov’s original results and moves forward to include prevalent results obtained in the past ten years. Detailed proofs and an emphasis on basic ideas are provided for different boundary conditions for ordinary differential equations, including Neumann, Dirichlet, periodic, and antiperiodic conditions. Novel results of higher eigenvalues, systems of equations, partial differential equations as well as variational approaches are presented. To this respect, a new and unified variational point of view is introduced for the treatment of such problems and a systematic discussion of different types of boundary conditions is featured. Various problems make the study of Lyapunov-type inequalities of interest to those in pure and ...
Robust lyapunov controller for uncertain systems
Laleg-Kirati, Taous-Meriem; Elmetennani, Shahrazed
2017-01-01
Various examples of systems and methods are provided for Lyapunov control for uncertain systems. In one example, a system includes a process plant and a robust Lyapunov controller configured to control an input of the process plant. The robust
Lyapunov equation for infinite-dimensional discrete bilinear systems
International Nuclear Information System (INIS)
Costa, O.L.V.; Kubrusly, C.S.
1991-03-01
Mean-square stability for discrete systems requires that uniform convergence is preserved between input and state correlation sequences. Such a convergence preserving property holds for an infinite-dimensional bilinear system if and only if the associate Lyapunov equation has a unique strictly positive solution. (author)
Stability analysis of impulsive parabolic complex networks
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Wang Jinliang, E-mail: wangjinliang1984@yahoo.com.cn [Science and Technology on Aircraft Control Laboratory, School of Automation Science and Electrical Engineering, Beihang University, XueYuan Road, No. 37, HaiDian District, Beijing 100191 (China); Wu Huaining [Science and Technology on Aircraft Control Laboratory, School of Automation Science and Electrical Engineering, Beihang University, XueYuan Road, No. 37, HaiDian District, Beijing 100191 (China)
2011-11-15
Highlights: > Two impulsive parabolic complex network models are proposed. > The global exponential stability of impulsive parabolic complex networks are considered. > The robust global exponential stability of impulsive parabolic complex networks are considered. - Abstract: In the present paper, two kinds of impulsive parabolic complex networks (IPCNs) are considered. In the first one, all nodes have the same time-varying delay. In the second one, different nodes have different time-varying delays. Using the Lyapunov functional method combined with the inequality techniques, some global exponential stability criteria are derived for the IPCNs. Furthermore, several robust global exponential stability conditions are proposed to take uncertainties in the parameters of the IPCNs into account. Finally, numerical simulations are presented to illustrate the effectiveness of the results obtained here.
Stability analysis of impulsive parabolic complex networks
International Nuclear Information System (INIS)
Wang Jinliang; Wu Huaining
2011-01-01
Highlights: → Two impulsive parabolic complex network models are proposed. → The global exponential stability of impulsive parabolic complex networks are considered. → The robust global exponential stability of impulsive parabolic complex networks are considered. - Abstract: In the present paper, two kinds of impulsive parabolic complex networks (IPCNs) are considered. In the first one, all nodes have the same time-varying delay. In the second one, different nodes have different time-varying delays. Using the Lyapunov functional method combined with the inequality techniques, some global exponential stability criteria are derived for the IPCNs. Furthermore, several robust global exponential stability conditions are proposed to take uncertainties in the parameters of the IPCNs into account. Finally, numerical simulations are presented to illustrate the effectiveness of the results obtained here.
Construction of Lyapunov Function for Dissipative Gyroscopic System
International Nuclear Information System (INIS)
Xu Wei; Ao Ping; Yuan Bo
2011-01-01
We introduce a force decomposition to construct a potential function in deterministic dynamics described by ordinary differential equations in the context of dissipative gyroscopic systems. Such a potential function serves as the corresponding Lyapunov function for the dynamics, hence it gives both quantitative and qualitative descriptions for stability of motion. As an example we apply our force decomposition to a four-dimensional dissipative gyroscopic system. We explicitly obtain the potential function for all parameter regimes in the linear limit, including those regimes where the Lyapunov function was previously believed not to exist. (general)
Stability analysis of hybrid-driven underwater glider
Niu, Wen-dong; Wang, Shu-xin; Wang, Yan-hui; Song, Yang; Zhu, Ya-qiang
2017-10-01
Hybrid-driven underwater glider is a new type of unmanned underwater vehicle, which combines the advantages of autonomous underwater vehicles and traditional underwater gliders. The autonomous underwater vehicles have good maneuverability and can travel with a high speed, while the traditional underwater gliders are highlighted by low power consumption, long voyage, long endurance and good stealth characteristics. The hybrid-driven underwater gliders can realize variable motion profiles by their own buoyancy-driven and propeller propulsion systems. Stability of the mechanical system determines the performance of the system. In this paper, the Petrel-II hybrid-driven underwater glider developed by Tianjin University is selected as the research object and the stability of hybrid-driven underwater glider unitedly controlled by buoyancy and propeller has been targeted and evidenced. The dimensionless equations of the hybrid-driven underwater glider are obtained when the propeller is working. Then, the steady speed and steady glide path angle under steady-state motion have also been achieved. The steady-state operating conditions can be calculated when the hybrid-driven underwater glider reaches the desired steady-state motion. And the steadystate operating conditions are relatively conservative at the lower bound of the velocity range compared with the range of the velocity derived from the method of the composite Lyapunov function. By calculating the hydrodynamic coefficients of the Petrel-II hybrid-driven underwater glider, the simulation analysis has been conducted. In addition, the results of the field trials conducted in the South China Sea and the Danjiangkou Reservoir of China have been presented to illustrate the validity of the analysis and simulation, and to show the feasibility of the method of the composite Lyapunov function which verifies the stability of the Petrel-II hybrid-driven underwater glider.
Using genetic programming to find Lyapunov functions
Soute, I.A.C.; Molengraft, van de M.J.G.; Angelis, G.Z.; Ryan, C; Spector, L.
2001-01-01
In this paper Genetic Programming is used to find Lyapunov functions for (non)linear dif ferential equations of autonomous systems. As Lyapunov functions can be difficult to find, we use OP to make the decisions concerning the form of the Lyapunov function. As an e5cample two systems are taken to
Stability analysis of nonlinear systems with slope restricted nonlinearities.
Liu, Xian; Du, Jiajia; Gao, Qing
2014-01-01
The problem of absolute stability of Lur'e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.
Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities
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Xian Liu
2014-01-01
Full Text Available The problem of absolute stability of Lur’e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.
Lyapunov Functions and Solutions of the Lyapunov Matrix Equation for Marginally Stable Systems
DEFF Research Database (Denmark)
Kliem, Wolfhard; Pommer, Christian
2000-01-01
We consider linear systems of differential equations $I \\ddot{x}+B \\dot{x}+C{x}={0}$ where $I$ is the identity matrix and $B$ and $C$ are general complex $n$ x $n$ matrices. Our main interest is to determine conditions for complete marginalstability of these systems. To this end we find solutions...... of the Lyapunov matrix equation and characterize the set of matrices $(B, C)$ which guarantees marginal stability. The theory is applied to gyroscopic systems, to indefinite damped systems, and to circulatory systems, showing how to choose certain parameter matrices to get sufficient conditions for marginal...... stability.Comparison is made with some known results for equations with real system matrices.Moreover more general cases are investigated and several examples are given....
Lyapunov Function Synthesis - Algorithm and Software
DEFF Research Database (Denmark)
Leth, Tobias; Sloth, Christoffer; Wisniewski, Rafal
2016-01-01
In this paper we introduce an algorithm for the synthesis of polynomial Lyapunov functions for polynomial vector fields. The Lyapunov function is a continuous piecewisepolynomial defined on simplices, which compose a collection of simplices. The algorithm is elaborated and crucial features are ex...
International Nuclear Information System (INIS)
Valtonen, K.
1990-01-01
The objective of this study has been to examine TVO-I oscillation incident, which occured in February 22.1987 and to find out safety implications of oscillations in ATWS incidents. Calculations have been performed with RAMONA-3B and TRAB codes. RAMONA-3B is a BWR transient analysis code with three-dimencional neutron kinetics and nonequilibrium, nonhomogeneous thermal hydraulics. TRAB code is a one-dimencional BWR transient code which uses methods similar to RAMONA-3B. The results have shown that both codes are capable of analyzing of the oscillation incidents. Both out-of-phase and in-phase oscillations are possible. If the reactor scram fails (ATWS) during oscillations the severe fuel failures are always possible and the reactor core may exceed the prompt criticality
Directory of Open Access Journals (Sweden)
Leonardo-Alonso MartÃnez Rivera
2015-10-01
Full Text Available Resumen: Determinar la estabilidad de los controladores, ya sea mediante simulaciones o mediante tÃ©cnicas analÃticas, es vital en su diseÃ±o e implantaciÃ³n. El mÃ©todo analÃtico de estabilidad en el sentido de Lyapunov requiere encontrar una funciÃ³n candidata, como criterio suficiente pero no necesario para tal fin. Esta funciÃ³n candidata es elusiva para los controladores borrosos. Se propone, como posible soluciÃ³n a este problema, cuantificar la estabilidad de los controladores borrosos mediante el exponente de Lyapunov (EL calculado numÃ©ricamente. Las series de tiempo de la cuales se calculan los exponentes de Lyapunov son obtenidas de la salida de diversos controladores borrosos tipo Mamdani en lazo cerrado con la dinÃ¡mica de la planta no lineal estabilizada en una regiÃ³n de operaciÃ³n admisible. Los experimentos fueron llevados al cabo mediante la implantaciÃ³n del mÃ©todo numÃ©rico en la plataforma MATLAB, integrÃ¡ndolo con datos provenientes de la simulaciÃ³n de diversos controladores borrosos. La planta a controlar es el sistema carro-pÃ©ndulo invertido modelado con la formulaciÃ³n Euler Lagrange. En cada experimento se obtuvo la serie de tiempo correspondiente a la seÃ±al de control y se calculÃ³ el exponente de Lyapunov. Aunque se observan variaciones en magnitud, el exponente calculado resulta negativo en todos los casos. Esto indica que los controladores difusos tipo Mamdani empleados son sistemas disipativos. Como trabajo futuro se esboza el empleo del EL en control adaptable. Abstract: In order to design and implement any type of controller, their stability analysis is pivotal. At this regard, Lyapunov's analytical method consists in finding a candidate function as a sufficient but not necessary condition to validate the stability of the controller. In the case of fuzzy controllers such a candidate function is not always found, leading to an uncertainty about their stability. To
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Zhixiong Zhong
2013-01-01
Full Text Available The stability analysis and stabilization of Takagi-Sugeno (T-S fuzzy delta operator systems with time-varying delay are investigated via an input-output approach. A model transformation method is employed to approximate the time-varying delay. The original system is transformed into a feedback interconnection form which has a forward subsystem with constant delays and a feedback one with uncertainties. By applying the scaled small gain (SSG theorem to deal with this new system, and based on a Lyapunov Krasovskii functional (LKF in delta operator domain, less conservative stability analysis and stabilization conditions are obtained. Numerical examples are provided to illustrate the advantages of the proposed method.
Directory of Open Access Journals (Sweden)
Hamed Kharrati
2012-01-01
Full Text Available This study presents an improved model and controller for nonlinear plants using polynomial fuzzy model-based (FMB systems. To minimize mismatch between the polynomial fuzzy model and nonlinear plant, the suitable parameters of membership functions are determined in a systematic way. Defining an appropriate fitness function and utilizing Taylor series expansion, a genetic algorithm (GA is used to form the shape of membership functions in polynomial forms, which are afterwards used in fuzzy modeling. To validate the model, a controller based on proposed polynomial fuzzy systems is designed and then applied to both original nonlinear plant and fuzzy model for comparison. Additionally, stability analysis for the proposed polynomial FMB control system is investigated employing Lyapunov theory and a sum of squares (SOS approach. Moreover, the form of the membership functions is considered in stability analysis. The SOS-based stability conditions are attained using SOSTOOLS. Simulation results are also given to demonstrate the effectiveness of the proposed method.
Soriano, Diogo C.; Santos, Odair V. dos; Suyama, Ricardo; Fazanaro, Filipe I.; Attux, Romis
2018-03-01
This work has a twofold aim: (a) to analyze an alternative approach for computing the conditional Lyapunov exponent (λcmax) aiming to evaluate the synchronization stability between nonlinear oscillators without solving the classical variational equations for the synchronization error dynamical system. In this first framework, an analytic reference value for λcmax is also provided in the context of Duffing master-slave scenario and precisely evaluated by the proposed numerical approach; (b) to apply this technique to the study of synchronization stability in chaotic Hindmarsh-Rose (HR) neuronal models under uni- and bi-directional resistive coupling and different excitation bias, which also considered the root mean square synchronization error, information theoretic measures and asymmetric transfer entropy in order to offer a better insight of the synchronization phenomenon. In particular, statistical and information theoretical measures were able to capture similarity increase between the neuronal oscillators just after a critical coupling value in accordance to the largest conditional Lyapunov exponent behavior. On the other hand, transfer entropy was able to detect neuronal emitter influence even in a weak coupling condition, i.e. under the increase of conditional Lyapunov exponent and apparently desynchronization tendency. In the performed set of numerical simulations, the synchronization measures were also evaluated for a two-dimensional parameter space defined by the neuronal coupling (emitter to a receiver neuron) and the (receiver) excitation current. Such analysis is repeated for different feedback couplings as well for different (emitter) excitation currents, revealing interesting characteristics of the attained synchronization region and conditions that facilitate the emergence of the synchronous behavior. These results provide a more detailed numerical insight of the underlying behavior of a HR in the excitation and coupling space, being in accordance
Bilinear Approximate Model-Based Robust Lyapunov Control for Parabolic Distributed Collectors
Elmetennani, Shahrazed
2016-11-09
This brief addresses the control problem of distributed parabolic solar collectors in order to maintain the field outlet temperature around a desired level. The objective is to design an efficient controller to force the outlet fluid temperature to track a set reference despite the unpredictable varying working conditions. In this brief, a bilinear model-based robust Lyapunov control is proposed to achieve the control objectives with robustness to the environmental changes. The bilinear model is a reduced order approximate representation of the solar collector, which is derived from the hyperbolic distributed equation describing the heat transport dynamics by means of a dynamical Gaussian interpolation. Using the bilinear approximate model, a robust control strategy is designed applying Lyapunov stability theory combined with a phenomenological representation of the system in order to stabilize the tracking error. On the basis of the error analysis, simulation results show good performance of the proposed controller, in terms of tracking accuracy and convergence time, with limited measurement even under unfavorable working conditions. Furthermore, the presented work is of interest for a large category of dynamical systems knowing that the solar collector is representative of physical systems involving transport phenomena constrained by unknown external disturbances.
Zhang, Xinxin; Niu, Peifeng; Ma, Yunpeng; Wei, Yanqiao; Li, Guoqiang
2017-10-01
This paper is concerned with the stability analysis issue of fractional-order impulsive neural networks. Under the one-side Lipschitz condition or the linear growth condition of activation function, the existence of solution is analyzed respectively. In addition, the existence, uniqueness and global Mittag-Leffler stability of equilibrium point of the fractional-order impulsive neural networks with one-side Lipschitz condition are investigated by the means of contraction mapping principle and Lyapunov direct method. Finally, an example with numerical simulation is given to illustrate the validity and feasibility of the proposed results. Copyright © 2017 Elsevier Ltd. All rights reserved.
PATRIMONIAL ANALYSIS OF FINANCIAL STABILITY
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GABRIELA CORINA SLUSARIUC
2011-01-01
Full Text Available Patrimonial analysis of financial stability is realized with the help of some indicator determined on the balance: working capital; required working capital and net treasury. These indicators are determined and presented in evolution at two companies with different situations, and there are given conclusions and suggestions concerning achieving and maintaining the financial equilibrium or initiating corrective measures in time, before the imbalance would take irrecoverable forms.
Lyapunov vectors and assimilation in the unstable subspace: theory and applications
International Nuclear Information System (INIS)
Palatella, Luigi; Carrassi, Alberto; Trevisan, Anna
2013-01-01
Based on a limited number of noisy observations, estimation algorithms provide a complete description of the state of a system at current time. Estimation algorithms that go under the name of assimilation in the unstable subspace (AUS) exploit the nonlinear stability properties of the forecasting model in their formulation. Errors that grow due to sensitivity to initial conditions are efficiently removed by confining the analysis solution in the unstable and neutral subspace of the system, the subspace spanned by Lyapunov vectors with positive and zero exponents, while the observational noise does not disturb the system along the stable directions. The formulation of the AUS approach in the context of four-dimensional variational assimilation (4DVar-AUS) and the extended Kalman filter (EKF-AUS) and its application to chaotic models is reviewed. In both instances, the AUS algorithms are at least as efficient but simpler to implement and computationally less demanding than their original counterparts. As predicted by the theory when error dynamics is linear, the optimal subspace dimension for 4DVar-AUS is given by the number of positive and null Lyapunov exponents, while the EKF-AUS algorithm, using the same unstable and neutral subspace, recovers the solution of the full EKF algorithm, but dealing with error covariance matrices of a much smaller dimension and significantly reducing the computational burden. Examples of the application to a simplified model of the atmospheric circulation and to the optimal velocity model for traffic dynamics are given. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)
Lyapunov Functions to Caputo Fractional Neural Networks with Time-Varying Delays
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Ravi Agarwal
2018-05-01
Full Text Available One of the main properties of solutions of nonlinear Caputo fractional neural networks is stability and often the direct Lyapunov method is used to study stability properties (usually these Lyapunov functions do not depend on the time variable. In connection with the Lyapunov fractional method we present a brief overview of the most popular fractional order derivatives of Lyapunov functions among Caputo fractional delay differential equations. These derivatives are applied to various types of neural networks with variable coefficients and time-varying delays. We show that quadratic Lyapunov functions and their Caputo fractional derivatives are not applicable in some cases when one studies stability properties. Some sufficient conditions for stability of equilibrium of nonlinear Caputo fractional neural networks with time dependent transmission delays, time varying self-regulating parameters of all units and time varying functions of the connection between two neurons in the network are obtained. The cases of time varying Lipschitz coefficients as well as nonLipschitz activation functions are studied. We illustrate our theory on particular nonlinear Caputo fractional neural networks.
Lyapunov Orbits in the Jupiter System Using Electrodynamic Tethers
Bokelmann, Kevin; Russell, Ryan P.; Lantoine, Gregory
2013-01-01
Various researchers have proposed the use of electrodynamic tethers for power generation and capture from interplanetary transfers. The effect of tether forces on periodic orbits in Jupiter-satellite systems are investigated. A perturbation force is added to the restricted three-body problem model and a series of simplifications allows development of a conservative system that retains the Jacobi integral. Expressions are developed to find modified locations of equilibrium positions. Modified families of Lyapunov orbits are generated as functions of tether size and Jacobi integral. Zero velocity curves and stability analyses are used to evaluate the dynamical properties of tether-modified orbits.
Design of Connectivity Preserving Flocking Using Control Lyapunov Function
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Bayu Erfianto
2016-01-01
Full Text Available This paper investigates cooperative flocking control design with connectivity preserving mechanism. During flocking, interagent distance is measured to determine communication topology of the flocks. Then, cooperative flocking motion is built based on cooperative artificial potential field with connectivity preserving mechanism to achieve the common flocking objective. The flocking control input is then obtained by deriving cooperative artificial potential field using control Lyapunov function. As a result, we prove that our flocking protocol establishes group stabilization and the communication topology of multiagent flocking is always connected.
Directory of Open Access Journals (Sweden)
A. Berbey
2014-04-01
Full Text Available Resumen: En este trabajo, se propone un nuevo índice basado en el método directo de Lyapunov para el diseño de un algoritmo de reprogramación en tiempo real para líneas de metro. En este estudio se utiliza una versión modificada de un modelo de espacio de estados en tiempo real discreto, que considera los efectos de saturación en la línea de metro. Una vez que el modelo de espacio de estados se ha obtenido, el método directo de Lyapunov se aplica con el fin de analizar la estabilidad del sistema de la línea de metro. Como resultado de este análisis no sólo se propone un nuevo índice de estabilidad, sino también la creación de tres zonas de estabilidad para indicar el estado actual del sistema. Finalmente, se presenta un nuevo algoritmo que permite la reprogramación del calendario de los trenes en tiempo real en presencia de perturbaciones medianas. Abstract: A new Lyapunov-based index for designing a rescheduling algorithm in real time for metro lines has been proposed in this paper. A modified real time discrete space state model which considers saturation effects in the metro line has been utilized in this study. Once the space state model has been obtained, the direct method of Lyapunov is applied in order to analyze the stability of the metro line system. As a result of this analysis not only a new stability index is proposed, but also the establishment of three stability zones to indicate the current state of the system. Finally, a new algorithm which allows the rescheduling of the timetable in the real time of the trains under presence of medium disturbances has been presented. Palabras clave: Sistema de metro, estabilidad de Lyapunov, planificación en tiempo real, Keywords: Metro system, Lyapunov stability, real time planning, traffic regulation
Jeong, Peter Inuk
Synthetic jet (SJ) control of a low-Reynolds number, unsteady, compressible, viscous flow over a NACA 65-(1)412 airfoil, typical for unmanned air vehicles and gas turbines, has been investigated computationally. A particular focus was placed in the development and control of Lagrangian Coherent Structures (LCS) and the associated Finite-Time Lyapunov Exponent (FTLE) fields. The FTLE fields quantitatively measure of the repulsion rate in forward-time and the attraction rate in backward-time, and provide a unique perspective on effective flow control. A Discontinuous-Galerkin (DG) methods, high-fidelity Navier-Stokes solver performs direct numerical simulation (DNS) of the airfoil flow. Three SJ control strategies have been investigated: immediately downstream of flow separation, normal to the separated shear layer; near the leading edge, normal to the airfoil suction side; near the trailing edge, normal to the airfoil pressure side. A finite difference algorithm computes the FTLE from DNS velocity data. A baseline flow without SJ control is compared to SJ actuated flows. The baseline flow forms a regular, time-periodic, asymmetric von Karman vortex street in the wake. The SJ downstream of flow separation increases recirculation region vorticity and reduces the effective angle of attack. This decreases the time-averaged lift by 2:98% and increases the time-averaged drag by 5:21%. The leading edge SJ produces small vortices that deflect the shear layer downwards, and decreases the effective angle of attack. This reduces the time-averaged lift by 1:80%, and the time-averaged drag by 1:84%. The trailing edge SJ produces perturbations that add to pressure side vortices without affecting global flow characteristics. The time-averaged lift decreases by 0:47%, and the time-averaged drag increases by 0:20%. For all SJ cases, the aerodynamic performance is much more dependent on changes to the pressure distribution than changes to the skin friction distribution. No proposed
Discrete-time recurrent neural networks with time-varying delays: Exponential stability analysis
International Nuclear Information System (INIS)
Liu, Yurong; Wang, Zidong; Serrano, Alan; Liu, Xiaohui
2007-01-01
This Letter is concerned with the analysis problem of exponential stability for a class of discrete-time recurrent neural networks (DRNNs) with time delays. The delay is of the time-varying nature, and the activation functions are assumed to be neither differentiable nor strict monotonic. Furthermore, the description of the activation functions is more general than the recently commonly used Lipschitz conditions. Under such mild conditions, we first prove the existence of the equilibrium point. Then, by employing a Lyapunov-Krasovskii functional, a unified linear matrix inequality (LMI) approach is developed to establish sufficient conditions for the DRNNs to be globally exponentially stable. It is shown that the delayed DRNNs are globally exponentially stable if a certain LMI is solvable, where the feasibility of such an LMI can be easily checked by using the numerically efficient Matlab LMI Toolbox. A simulation example is presented to show the usefulness of the derived LMI-based stability condition
A survey of quantum Lyapunov control methods.
Cong, Shuang; Meng, Fangfang
2013-01-01
The condition of a quantum Lyapunov-based control which can be well used in a closed quantum system is that the method can make the system convergent but not just stable. In the convergence study of the quantum Lyapunov control, two situations are classified: nondegenerate cases and degenerate cases. For these two situations, respectively, in this paper the target state is divided into four categories: the eigenstate, the mixed state which commutes with the internal Hamiltonian, the superposition state, and the mixed state which does not commute with the internal Hamiltonian. For these four categories, the quantum Lyapunov control methods for the closed quantum systems are summarized and analyzed. Particularly, the convergence of the control system to the different target states is reviewed, and how to make the convergence conditions be satisfied is summarized and analyzed.
Statistical-mechanical formulation of Lyapunov exponents
International Nuclear Information System (INIS)
Tanase-Nicola, Sorin; Kurchan, Jorge
2003-01-01
We show how the Lyapunov exponents of a dynamic system can, in general, be expressed in terms of the free energy of a (non-Hermitian) quantum many-body problem. This puts their study as a problem of statistical mechanics, whose intuitive concepts and techniques of approximation can hence be borrowed
Evaluating Lyapunov exponent spectra with neural networks
International Nuclear Information System (INIS)
Maus, A.; Sprott, J.C.
2013-01-01
Highlights: • Cross-correlation is employed to remove spurious Lyapunov exponents from a spectrum. • Neural networks are shown to accurately model Lyapunov exponent spectra. • Neural networks compare favorably to local linear fits in modeling Lyapunov exponents. • Numerical experiments are performed with time series of varying length and noise. • Methods perform reasonably well on discrete time series. -- Abstract: A method using discrete cross-correlation for identifying and removing spurious Lyapunov exponents when embedding experimental data in a dimension greater than the original system is introduced. The method uses a distribution of calculated exponent values produced by modeling a single time series many times or multiple instances of a time series. For this task, global models are shown to compare favorably to local models traditionally used for time series taken from the Hénon map and delayed Hénon map, especially when the time series are short or contaminated by noise. An additional merit of global modeling is its ability to estimate the dynamical and geometrical properties of the original system such as the attractor dimension, entropy, and lag space, although consideration must be taken for the time it takes to train the global models
Inertia theorems for operator Lyapunov inequalities
Sasane, AJ; Curtain, RF
2001-01-01
We study operator Lyapunov inequalities and equations for which the infinitesimal generator is not necessarily stable, but it satisfies the spectrum decomposition assumption and it has at most finitely many unstable eigenvalues. Moreover, the input or output operators are not necessarily bounded,
Zhang, Tie-Yan; Zhao, Yan; Xie, Xiang-Peng
2012-12-01
This paper is concerned with the problem of stability analysis of nonlinear Roesser-type two-dimensional (2D) systems. Firstly, the fuzzy modeling method for the usual one-dimensional (1D) systems is extended to the 2D case so that the underlying nonlinear 2D system can be represented by the 2D Takagi—Sugeno (TS) fuzzy model, which is convenient for implementing the stability analysis. Secondly, a new kind of fuzzy Lyapunov function, which is a homogeneous polynomially parameter dependent on fuzzy membership functions, is developed to conceive less conservative stability conditions for the TS Roesser-type 2D system. In the process of stability analysis, the obtained stability conditions approach exactness in the sense of convergence by applying some novel relaxed techniques. Moreover, the obtained result is formulated in the form of linear matrix inequalities, which can be easily solved via standard numerical software. Finally, a numerical example is also given to demonstrate the effectiveness of the proposed approach.
International Nuclear Information System (INIS)
Zhang Tie-Yan; Zhao Yan; Xie Xiang-Peng
2012-01-01
This paper is concerned with the problem of stability analysis of nonlinear Roesser-type two-dimensional (2D) systems. Firstly, the fuzzy modeling method for the usual one-dimensional (1D) systems is extended to the 2D case so that the underlying nonlinear 2D system can be represented by the 2D Takagi—Sugeno (TS) fuzzy model, which is convenient for implementing the stability analysis. Secondly, a new kind of fuzzy Lyapunov function, which is a homogeneous polynomially parameter dependent on fuzzy membership functions, is developed to conceive less conservative stability conditions for the TS Roesser-type 2D system. In the process of stability analysis, the obtained stability conditions approach exactness in the sense of convergence by applying some novel relaxed techniques. Moreover, the obtained result is formulated in the form of linear matrix inequalities, which can be easily solved via standard numerical software. Finally, a numerical example is also given to demonstrate the effectiveness of the proposed approach. (general)
An algorithm for constructing Lyapunov functions
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Sigurdur Freyr Hafstein
2007-08-01
Full Text Available In this monograph we develop an algorithm for constructing Lyapunov functions for arbitrary switched dynamical systems $dot{mathbf{x}} = mathbf{f}_sigma(t,mathbf{x}$, possessing a uniformly asymptotically stable equilibrium. Let $dot{mathbf{x}}=mathbf{f}_p(t,mathbf{x}$, $pinmathcal{P}$, be the collection of the ODEs, to which the switched system corresponds. The number of the vector fields $mathbf{f}_p$ on the right-hand side of the differential equation is assumed to be finite and we assume that their components $f_{p,i}$ are $mathcal{C}^2$ functions and that we can give some bounds, not necessarily close, on their second-order partial derivatives. The inputs of the algorithm are solely a finite number of the function values of the vector fields $mathbf{f}_p$ and these bounds. The domain of the Lyapunov function constructed by the algorithm is only limited by the size of the equilibrium's region of attraction. Note, that the concept of a Lyapunov function for the arbitrary switched system $dot{mathbf{x}} = mathbf{f}_sigma(t,mathbf{x}$ is equivalent to the concept of a common Lyapunov function for the systems $dot{mathbf{x}}=mathbf{f}_p(t,mathbf{x}$, $pinmathcal{P}$, and that if $mathcal{P}$ contains exactly one element, then the switched system is just a usual ODE $dot{mathbf{x}}=mathbf{f}(t,mathbf{x}$. We give numerous examples of Lyapunov functions constructed by our method at the end of this monograph.
A statistical approach to estimate the LYAPUNOV spectrum in disc brake squeal
Oberst, S.; Lai, J. C. S.
2015-01-01
The estimation of squeal propensity of a brake system from the prediction of unstable vibration modes using the linear complex eigenvalue analysis (CEA) in the frequency domain has its fair share of successes and failures. While the CEA is almost standard practice for the automotive industry, time domain methods and the estimation of LYAPUNOV spectra have not received much attention in brake squeal analyses. One reason is the challenge in estimating the true LYAPUNOV exponents and their discrimination against spurious ones in experimental data. A novel method based on the application of the ECKMANN-RUELLE matrices is proposed here to estimate LYAPUNOV exponents by using noise in a statistical procedure. It is validated with respect to parameter variations and dimension estimates. By counting the number of non-overlapping confidence intervals for LYAPUNOV exponent distributions obtained by moving a window of increasing size over bootstrapped same-length estimates of an observation function, a dispersion measure's width is calculated and fed into a BAYESIAN beta-binomial model. Results obtained using this method for benchmark models of white and pink noise as well as the classical HENON map indicate that true LYAPUNOV exponents can be isolated from spurious ones with high confidence. The method is then applied to accelerometer and microphone data obtained from brake squeal tests. Estimated LYAPUNOV exponents indicate that the pad's out-of-plane vibration behaves quasi-periodically on the brink to chaos while the microphone's squeal signal remains periodic.
Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation
Maschke, Bernhard M.J.; Ortega, Romeo; Schaft, Arjan J. van der
1998-01-01
It is well known that the total energy is a suitable Lyapunov function to study the stability of the trivial equilibrium of an isolated standard Hamiltonian system. In many practical instances, however, the system is in interaction with its environment through some constant forcing terms. This gives
Interpolation of polytopic control Lyapunov functions for discrete–time linear systems
Nguyen, T.T.; Lazar, M.; Spinu, V.; Boje, E.; Xia, X.
2014-01-01
This paper proposes a method for interpolating two (or more) polytopic control Lyapunov functions (CLFs) for discrete--time linear systems subject to polytopic constraints, thereby combining different control objectives. The corresponding interpolated CLF is used for synthesis of a stabilizing
Stability and response bounds of non-conservative linear systems
DEFF Research Database (Denmark)
Pommer, Christian
2003-01-01
For a linear system of second order differential equations the stability is studied by Lyapunov's direct method. The Lyapunov matrix equation is solved and a sufficient condition for stability is expressed by the system matrices. For a system which satisfies the condition for stability the Lyapunov...
Stability analysis and stabilization strategies for linear supply chains
Nagatani, Takashi; Helbing, Dirk
2004-04-01
Due to delays in the adaptation of production or delivery rates, supply chains can be dynamically unstable with respect to perturbations in the consumption rate, which is known as “bull-whip effect”. Here, we study several conceivable production strategies to stabilize supply chains, which is expressed by different specifications of the management function controlling the production speed in dependence of the stock levels. In particular, we will investigate, whether the reaction to stock levels of other producers or suppliers has a stabilizing effect. We will also demonstrate that the anticipation of future stock levels can stabilize the supply system, given the forecast horizon τ is long enough. To show this, we derive linear stability conditions and carry out simulations for different control strategies. The results indicate that the linear stability analysis is a helpful tool for the judgement of the stabilization effect, although unexpected deviations can occur in the non-linear regime. There are also signs of phase transitions and chaotic behavior, but this remains to be investigated more thoroughly in the future.
The Multivariate Largest Lyapunov Exponent as an Age-Related Metric of Quiet Standing Balance
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Kun Liu
2015-01-01
Full Text Available The largest Lyapunov exponent has been researched as a metric of the balance ability during human quiet standing. However, the sensitivity and accuracy of this measurement method are not good enough for clinical use. The present research proposes a metric of the human body’s standing balance ability based on the multivariate largest Lyapunov exponent which can quantify the human standing balance. The dynamic multivariate time series of ankle, knee, and hip were measured by multiple electrical goniometers. Thirty-six normal people of different ages participated in the test. With acquired data, the multivariate largest Lyapunov exponent was calculated. Finally, the results of the proposed approach were analysed and compared with the traditional method, for which the largest Lyapunov exponent and power spectral density from the centre of pressure were also calculated. The following conclusions can be obtained. The multivariate largest Lyapunov exponent has a higher degree of differentiation in differentiating balance in eyes-closed conditions. The MLLE value reflects the overall coordination between multisegment movements. Individuals of different ages can be distinguished by their MLLE values. The standing stability of human is reduced with the increment of age.
Almost sure exponential stability of stochastic fuzzy cellular neural networks with delays
International Nuclear Information System (INIS)
Zhao Hongyong; Ding Nan; Chen Ling
2009-01-01
This paper is concerned with the problem of exponential stability analysis for fuzzy cellular neural network with delays. By constructing suitable Lyapunov functional and using stochastic analysis we present some sufficient conditions ensuring almost sure exponential stability for the network. Moreover, an example is given to demonstrate the advantages of our method.
Riemannian theory of Hamiltonian chaos and Lyapunov exponents
Casetti, Lapo; Clementi, Cecilia; Pettini, Marco
1996-12-01
A nonvanishing Lyapunov exponent λ1 provides the very definition of deterministic chaos in the solutions of a dynamical system; however, no theoretical mean of predicting its value exists. This paper copes with the problem of analytically computing the largest Lyapunov exponent λ1 for many degrees of freedom Hamiltonian systems as a function of ɛ=E/N, the energy per degree of freedom. The functional dependence λ1(ɛ) is of great interest because, among other reasons, it detects the existence of weakly and strongly chaotic regimes. This aim, the analytic computation of λ1(ɛ), is successfully reached within a theoretical framework that makes use of a geometrization of Newtonian dynamics in the language of Riemannian differential geometry. An alternative point of view about the origin of chaos in these systems is obtained independently of the standard explanation based on homoclinic intersections. Dynamical instability (chaos) is here related to curvature fluctuations of the manifolds whose geodesics are natural motions and is described by means of the Jacobi-Levi-Civita equation (JLCE) for geodesic spread. In this paper it is shown how to derive from the JLCE an effective stability equation. Under general conditions, this effective equation formally describes a stochastic oscillator; an analytic formula for the instability growth rate of its solutions is worked out and applied to the Fermi-Pasta-Ulam β model and to a chain of coupled rotators. Excellent agreement is found between the theoretical prediction and numeric values of λ1(ɛ) for both models.
Local Lyapunov exponents for dissipative continuous systems
International Nuclear Information System (INIS)
Grond, Florian; Diebner, Hans H.
2005-01-01
We analyze a recently proposed algorithm for computing Lyapunov exponents focusing on its capability to calculate reliable local values for chaotic attractors. The averaging process of local contributions to the global measure becomes interpretable, i.e. they are related to the local topological structure in phase space. We compare the algorithm with the commonly used Wolf algorithm by means of analyzing correlations between coordinates of the chaotic attractor and local values of the Lyapunov exponents. The correlations for the new algorithm turn out to be significantly stronger than those for the Wolf algorithm. Since the usage of scalar measures to capture complex structures can be questioned we discuss these entities along with a more phenomenological description of scatter plots
International Nuclear Information System (INIS)
Huang He; Qu Yuzhong; Li Hanxiong
2005-01-01
With the development of intelligent control, switched systems have been widely studied. Here we try to introduce some ideas of the switched systems into the field of neural networks. In this Letter, a class of switched Hopfield neural networks with time-varying delay is investigated. The parametric uncertainty is considered and assumed to be norm bounded. Firstly, the mathematical model of the switched Hopfield neural networks is established in which a set of Hopfield neural networks are used as the individual subsystems and an arbitrary switching rule is assumed; Secondly, robust stability analysis for such switched Hopfield neural networks is addressed based on the Lyapunov-Krasovskii approach. Some criteria are given to guarantee the switched Hopfield neural networks to be globally exponentially stable for all admissible parametric uncertainties. These conditions are expressed in terms of some strict linear matrix inequalities (LMIs). Finally, a numerical example is provided to illustrate our results
A Dynamic Analysis for an Anaerobic Digester: Stability and Bifurcation Branches
Directory of Open Access Journals (Sweden)
Alejandro Rincón
2014-01-01
Full Text Available This work presents a dynamic analysis for an anaerobic digester, supported on the analytical application of the indirect Lyapunov method. The mass-balance model considered is based on two biological reaction pathways and involves both Monod and Haldane representations of the specific biomass growth rates. The dilution rate, the influent concentration of chemical oxygen demand (COD, and the influent concentration of volatile fatty acids (VFA are considered as stability parameters. Several characteristics are determined analytically for the normal operation equilibrium point: (i equilibrium coordinates, (ii parameter conditions that lead to positive values of the equilibrium state variables, (iii parameter conditions for locally stable nature of the equilibrium, (iv coordinates for the local bifurcation points—fold and transcritical—, and (v coordinates of the crossing between bifurcation points. These factors are computed analytically and explicitly as expressions of the dilution rate and the influent concentrations of COD and VFA.
High beta and second stability region transport and stability analysis
International Nuclear Information System (INIS)
Hughes, M.H.; Phillps, M.W.; Todd, A.M.M.; Krishnaswami, J.; Hartley, R.
1992-09-01
This report describes ideal and resistive studies of high-beta plasmas and of the second stability region. Emphasis is focused on ''supershot'' plasmas in TFIR where MHD instabilities are frequently observed and which spoil their confinement properties. Substantial results are described from the analysis of these high beta poloidal plasmas. During these studies, initial pressure and safety factor profiles were obtained from the TRANSP code, which is used extensively to analyze experimental data. Resistive MBD stability studies of supershot equilibria show that finite pressure stabilization of tearing modes is very strong in these high βp plasmas. This has prompted a detailed re-examination of linear tearing mode theory in which we participated in collaboration with Columbia University and General Atomics. This finite pressure effect is shown to be highly sensitive to small scale details of the pressure profile. Even when an ad hoc method of removing this stabilizing mechanism is implemented, however, it is shown that there is only superficial agreement between resistive MBD stability computation and the experimental data. While the mode structures observed experimentally can be found computationally, there is no convincing correlation with the experimental observations when the computed results are compared with a large set of supershot data. We also describe both the ideal and resistive stability properties of TFIR equilibria near the transition to the second region. It is shown that the highest β plasmas, although stable to infinite-n ideal ballooning modes, can be unstable to the so called ''infernal'' modes associated with small shear. The sensitivity of these results to the assumed pressure and current density profiles is discussed. Finally, we describe results from two collaborative studies with PPPL. The first involves exploratory studies of the role of the 1/1 mode in tokamaks and, secondly, a study of sawtooth stabilization using ICRF
High beta and second stability region transport and stability analysis
International Nuclear Information System (INIS)
1990-01-01
This document summarizes progress made on the research of high beta and second region transport and stability. In the area second stability region studies we report on an investigation of the possibility of second region access in the center of TFTR ''supershots.'' The instabilities found may coincide with experimental observation. Significant progress has been made on the resistive stability properties of high beta poloidal ''supershot'' discharges. For these studies profiles were taken from the TRANSP transport analysis code which analyzes experimental data. Invoking flattening of the pressure profile on mode rational surfaces causes tearing modes to persist into the experimental range of interest. Further, the experimental observation of the modes seems to be consistent with the predictions of the MHD model. In addition, code development in several areas has proceeded
Improved result on stability analysis of discrete stochastic neural networks with time delay
International Nuclear Information System (INIS)
Wu Zhengguang; Su Hongye; Chu Jian; Zhou Wuneng
2009-01-01
This Letter investigates the problem of exponential stability for discrete stochastic time-delay neural networks. By defining a novel Lyapunov functional, an improved delay-dependent exponential stability criterion is established in terms of linear matrix inequality (LMI) approach. Meanwhile, the computational complexity of the newly established stability condition is reduced because less variables are involved. Numerical example is given to illustrate the effectiveness and the benefits of the proposed method.
Stability and Bifurcation Analysis of a Three-Species Food Chain Model with Fear
Panday, Pijush; Pal, Nikhil; Samanta, Sudip; Chattopadhyay, Joydev
In the present paper, we investigate the impact of fear in a tri-trophic food chain model. We propose a three-species food chain model, where the growth rate of middle predator is reduced due to the cost of fear of top predator, and the growth rate of prey is suppressed due to the cost of fear of middle predator. Mathematical properties such as equilibrium analysis, stability analysis, bifurcation analysis and persistence have been investigated. We also describe the global stability analysis of the equilibrium points. Our numerical simulations reveal that cost of fear in basal prey may exhibit bistability by producing unstable limit cycles, however, fear in middle predator can replace unstable limit cycles by a stable limit cycle or a stable interior equilibrium. We observe that fear can stabilize the system from chaos to stable focus through the period-halving phenomenon. We conclude that chaotic dynamics can be controlled by the fear factors. We apply basic tools of nonlinear dynamics such as Poincaré section and maximum Lyapunov exponent to identify the chaotic behavior of the system.
Power system stability modelling, analysis and control
Sallam, Abdelhay A
2015-01-01
This book provides a comprehensive treatment of the subject from both a physical and mathematical perspective and covers a range of topics including modelling, computation of load flow in the transmission grid, stability analysis under both steady-state and disturbed conditions, and appropriate controls to enhance stability.
Adaptive Fuzzy-Lyapunov Controller Using Biologically Inspired Swarm Intelligence
Directory of Open Access Journals (Sweden)
Alejandro Carrasco Elizalde
2008-01-01
Full Text Available The collective behaviour of swarms produces smarter actions than those achieved by a single individual. Colonies of ants, flocks of birds and fish schools are examples of swarms interacting with their environment to achieve a common goal. This cooperative biological intelligence is the inspiration for an adaptive fuzzy controller developed in this paper. Swarm intelligence is used to adjust the parameters of the membership functions used in the adaptive fuzzy controller. The rules of the controller are designed using a computing-with-words approach called Fuzzy-Lyapunov synthesis to improve the stability and robustness of an adaptive fuzzy controller. Computing-with-words provides a powerful tool to manipulate numbers and symbols, like words in a natural language.
A Lyapunov theory based UPFC controller for power flow control
Energy Technology Data Exchange (ETDEWEB)
Zangeneh, Ali; Kazemi, Ahad; Hajatipour, Majid; Jadid, Shahram [Center of Excellence for Power Systems Automation and Operation, Iran University of Science and Technology, Tehran (Iran)
2009-09-15
Unified power flow controller (UPFC) is the most comprehensive multivariable device among the FACTS controllers. Capability of power flow control is the most important responsibility of UPFC. According to high importance of power flow control in transmission lines, the proper controller should be robust against uncertainty and disturbance and also have suitable settling time. For this purpose, a new controller is designed based on the Lyapunov theory and its stability is also evaluated. The Main goal of this paper is to design a controller which enables a power system to track reference signals precisely and to be robust in the presence of uncertainty of system parameters and disturbances. The performance of the proposed controller is simulated on a two bus test system and compared with a conventional PI controller. The simulation results show the power and accuracy of the proposed controller. (author)
MHD stability analysis of helical system plasmas
International Nuclear Information System (INIS)
Nakamura, Yuji
2000-01-01
Several topics of the MHD stability studies in helical system plasmas are reviewed with respect to the linear and ideal modes mainly. Difference of the method of the MHD stability analysis in helical system plasmas from that in tokamak plasmas is emphasized. Lack of the cyclic (symmetric) coordinate makes an analysis more difficult. Recent topic about TAE modes in a helical system is also described briefly. (author)
Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach
Nasiri, Alireza; Nguang, Sing Kiong; Swain, Akshya; Almakhles, Dhafer
2018-02-01
This paper deals with the problem of designing a controller for a class of discrete-time nonlinear systems which is represented by discrete-time polynomial fuzzy model. Most of the existing control design methods for discrete-time fuzzy polynomial systems cannot guarantee their Lyapunov function to be a radially unbounded polynomial function, hence the global stability cannot be assured. The proposed control design in this paper guarantees a radially unbounded polynomial Lyapunov functions which ensures global stability. In the proposed design, state feedback structure is considered and non-convexity problem is solved by incorporating an integrator into the controller. Sufficient conditions of stability are derived in terms of polynomial matrix inequalities which are solved via SOSTOOLS in MATLAB. A numerical example is presented to illustrate the effectiveness of the proposed controller.
Cessna Citation X Business Aircraft Eigenvalue Stability – Part2: Flight Envelope Analysis
Directory of Open Access Journals (Sweden)
Yamina BOUGHARI
2017-12-01
Full Text Available Civil aircraft flight control clearance is a time consuming, thus an expensive process in the aerospace industry. This process has to be investigated and proved to be safe for thousands of combinations in terms of speeds, altitudes, gross weights, Xcg / weight configurations and angles of attack. Even in this case, a worst-case condition that could lead to a critical situation might be missed. To address this problem, models that are able to describe an aircraft’s dynamics by taking into account all uncertainties over a region within a flight envelope have been developed using Linear Fractional Representation. In order to investigate the Cessna Citation X aircraft Eigenvalue Stability envelope, the Linear Fractional Representation models are implemented using the speeds and the altitudes as varying parameters. In this paper Part 2, the aircraft longitudinal eigenvalue stability is analyzed in a continuous range of flight envelope with varying parameter of True airspeed and altitude, instead of a single point, like classical methods. This is known as the aeroelastic stability envelope, required for civil aircraft certification as given by the Circular Advisory “Aeroelastic Stability Substantiation of Transport Category Airplanes AC No: 25.629-18”. In this new methodology the analysis is performed in time domain based on Lyapunov stability and solved by convex optimization algorithms by using the linear matrix inequalities to evaluate the eigenvalue stability, which is reduced to search for the negative eigenvalues in a region of flight envelope. It can also be used to study the stability of a system during an arbitrary motion from one point to another in the flight envelope. A whole aircraft analysis results’ for its entire envelope are presented in the form of graphs, thus offering good readability, and making them easily exploitable.
Regeneration cycle and the covariant Lyapunov vectors in a minimal wall turbulence.
Inubushi, Masanobu; Takehiro, Shin-ichi; Yamada, Michio
2015-08-01
Considering a wall turbulence as a chaotic dynamical system, we study regeneration cycles in a minimal wall turbulence from the viewpoint of orbital instability by employing the covariant Lyapunov analysis developed by [F. Ginelli et al. Phys. Rev. Lett. 99, 130601 (2007)]. We divide the regeneration cycle into two phases and characterize them with the local Lyapunov exponents and the covariant Lyapunov vectors of the Navier-Stokes turbulence. In particular, we show numerically that phase (i) is dominated by instabilities related to the sinuous mode and the streamwise vorticity, and there is no instability in phase (ii). Furthermore, we discuss a mechanism of the regeneration cycle, making use of an energy budget analysis.
Lyapunov exponents for infinite dimensional dynamical systems
Mhuiris, Nessan Mac Giolla
1987-01-01
Classically it was held that solutions to deterministic partial differential equations (i.e., ones with smooth coefficients and boundary data) could become random only through one mechanism, namely by the activation of more and more of the infinite number of degrees of freedom that are available to such a system. It is only recently that researchers have come to suspect that many infinite dimensional nonlinear systems may in fact possess finite dimensional chaotic attractors. Lyapunov exponents provide a tool for probing the nature of these attractors. This paper examines how these exponents might be measured for infinite dimensional systems.
The stability analysis of non-topological solitons in gauge theory and in electrodynamics
International Nuclear Information System (INIS)
Chakrabarti, S.
1982-08-01
The Lyapunov stability analysis of the nontopological soliton solution in the many-charge Qsub(i) Synge Model in non-Abelian SU(2)xU(1) symmetry with the presence of gauge fields is considered. It is shown that in the presence of the subsidiary condition of fixation of charges μsub(i)νsub(i)delta Qsub(i)=0 the necessary condition for stability of the soliton solution (periodic in time with parameters νsub(i)) is defined by the inequality: μsub(i,k) (deltaQsub(i) 0 /deltaνsub(k)) - νsub(i)νsub(k)<0. This condition holds for any Lagrangian density with second-order time derivatives in the presence of gauge fields. This result is extended to the stability analysis of a scalar soliton with electromagnetic field in U(1) symmetry, and it is shown that, in this case, the necessary condition reduces to deltaQsub(i)/deltaν<0. (author)
Stability analysis by ERATO code
International Nuclear Information System (INIS)
Tsunematsu, Toshihide; Takeda, Tatsuoki; Matsuura, Toshihiko; Azumi, Masafumi; Kurita, Gen-ichi
1979-12-01
Problems in MHD stability calculations by ERATO code are described; which concern convergence property of results, equilibrium codes, and machine optimization of ERATO code. It is concluded that irregularity on a convergence curve is not due to a fault of the ERATO code itself but due to inappropriate choice of the equilibrium calculation meshes. Also described are a code to calculate an equilibrium as a quasi-inverse problem and a code to calculate an equilibrium as a result of a transport process. Optimization of the code with respect to I/O operations reduced both CPU time and I/O time considerably. With the FACOM230-75 APU/CPU multiprocessor system, the performance is about 6 times as high as with the FACOM230-75 CPU, showing the effectiveness of a vector processing computer for the kind of MHD computations. This report is a summary of the material presented at the ERATO workshop 1979(ORNL), supplemented with some details. (author)
Stability analysis of free piston Stirling engines
Bégot, Sylvie; Layes, Guillaume; Lanzetta, François; Nika, Philippe
2013-03-01
This paper presents a stability analysis of a free piston Stirling engine. The model and the detailed calculation of pressures losses are exposed. Stability of the machine is studied by the observation of the eigenvalues of the model matrix. Model validation based on the comparison with NASA experimental results is described. The influence of operational and construction parameters on performance and stability issues is exposed. The results show that most parameters that are beneficial for machine power seem to induce irregular mechanical characteristics with load, suggesting that self-sustained oscillations could be difficult to maintain and control.
Stability Analysis of the Embankment Model
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G.S. Gopalakrishna
2009-01-01
Full Text Available In analysis of embankment model affected by dynamic force, employment of shaking table is a scientific way in assessment of earthquake behavior. This work focused on saturated loose sandy foundation and enbankment. The results generated through the pore pressure sensors indicated pore water pressure playing main role in creation of liquefaction and stability of the system, and also revealed deformation, settlement, liquefaction intensity and time stability of system in direct correlation with the strength and characteristics of soil. One of the economical methods in stabilization of soil foundation is improvement of some part soil foundation.
Stability analysis of zigzag boron nitride nanoribbons
Energy Technology Data Exchange (ETDEWEB)
Rai, Hari Mohan, E-mail: rai.2208@gmail.com; Late, Ravikiran; Saxena, Shailendra K.; Kumar, Rajesh; Sagdeo, Pankaj R. [Indian Institute of Technology, Indore –452017 (India); Jaiswal, Neeraj K. [Discipline of Physics, PDPM- Indian Institute of Information Technology, Design and Manufacturing, Jabalpur – 482005 (India); Srivastava, Pankaj [Computational Nanoscience and Technology Lab. (CNTL), ABV- Indian Institute of Information Technology and Management, Gwalior – 474015 (India)
2015-05-15
We have explored the structural stability of bare and hydrogenated zigzag boron nitride nanoribbons (ZBNNRs). In order to investigate the structural stability, we calculate the cohesive energy for bare, one-edge and both edges H-terminated ZBNNRs with different widths. It is found that the ZBNNRs with width Nz=8 are energetically more favorable than the lower-width counterparts (Nz<8). Bare ZBNNRs have been found energetically most stable as compared to the edge terminated ribbons. Our analysis reveals that the structural stability is a function of ribbon-width and it is not affected significantly by the type of edge-passivation (one-edge or both-edges)
Nonlinear stability of Gardner breathers
Alejo, Miguel A.
2018-01-01
We show that breather solutions of the Gardner equation, a natural generalization of the KdV and mKdV equations, are H2 (R) stable. Through a variational approach, we characterize Gardner breathers as minimizers of a new Lyapunov functional and we study the associated spectral problem, through (i) the analysis of the spectrum of explicit linear systems (spectral stability), and (ii) controlling degenerated directions by using low regularity conservation laws.
Stability Analysis of a Voltage-Based Controller for Robot Manipulators
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Jorge Orrante-Sakanassi
2013-01-01
Full Text Available A voltage-based control scheme for robot manipulators has been presented in recent literature, where feedback linearization is applied in the electrical equations of the DC motors in order to cancel the electrical current terms. However, in this paper we show that this control technique generates a system of the form Ex = Ax + Bu, where E is a singular matrix, that is to say, a generalized state-space system or singular system. This paper introduces a formal stability analysis of the respective system by considering the state-space equation as a singular system. Furthermore, in order to avoid the singularity of the closed-loop system, modified voltage-based control schemes are proposed, whose Lyapunov stability analyses conclude semiglobal asymptotic stability for the set-point control case and uniform boundedness of the solutions and semiglobal convergence of the position, as well as velocity errors for the tracking control case. The proposed control systems are simulated for the tracking and set-point cases using the CICESE Pelican robot driven by DC motors.
A New Approach to the Method of Lyapunov Functionals and Its Applications
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Yunguo Jin
2013-01-01
Full Text Available We show some results which can replace the graph theory used to construct global Lyapunov functions in some coupled systems of differential equations. We present an example of an epidemic model with stage structure and latency spreading in a heterogeneous host population and obtain a more general threshold for the extinction and persistence of a disease. Using some results obtained by mathematical induction and suitable Lyapunov functionals, we prove the global stability of the endemic equilibrium. For some coupled systems of differential equations, by a similar approach to the discussion of the epidemic model, the conditions of threshold property or global stability can be established without the assumption that the relative matrix is irreducible.
Stability analysis of fuzzy parametric uncertain systems.
Bhiwani, R J; Patre, B M
2011-10-01
In this paper, the determination of stability margin, gain and phase margin aspects of fuzzy parametric uncertain systems are dealt. The stability analysis of uncertain linear systems with coefficients described by fuzzy functions is studied. A complexity reduced technique for determining the stability margin for FPUS is proposed. The method suggested is dependent on the order of the characteristic polynomial. In order to find the stability margin of interval polynomials of order less than 5, it is not always necessary to determine and check all four Kharitonov's polynomials. It has been shown that, for determining stability margin of FPUS of order five, four, and three we require only 3, 2, and 1 Kharitonov's polynomials respectively. Only for sixth and higher order polynomials, a complete set of Kharitonov's polynomials are needed to determine the stability margin. Thus for lower order systems, the calculations are reduced to a large extent. This idea has been extended to determine the stability margin of fuzzy interval polynomials. It is also shown that the gain and phase margin of FPUS can be determined analytically without using graphical techniques. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.
Linear stability analysis of heated parallel channels
International Nuclear Information System (INIS)
Nourbakhsh, H.P.; Isbin, H.S.
1982-01-01
An analyis is presented of thermal hydraulic stability of flow in parallel channels covering the range from inlet subcooling to exit superheat. The model is based on a one-dimensional drift velocity formulation of the two phase flow conservation equations. The system of equations is linearized by assuming small disturbances about the steady state. The dynamic response of the system to an inlet flow perturbation is derived yielding the characteristic equation which predicts the onset of instabilities. A specific application is carried out for homogeneous and regional uniformly heated systems. The particular case of equal characteristic frequencies of two-phase and single phase vapor region is studied in detail. The D-partition method and the Mikhailov stability criterion are used for determining the marginal stability boundary. Stability predictions from the present analysis are compared with the experimental data from the solar test facility. 8 references
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O. M. Kwon
2012-01-01
Full Text Available The purpose of this paper is to investigate the delay-dependent stability analysis for discrete-time neural networks with interval time-varying delays. Based on Lyapunov method, improved delay-dependent criteria for the stability of the networks are derived in terms of linear matrix inequalities (LMIs by constructing a suitable Lyapunov-Krasovskii functional and utilizing reciprocally convex approach. Also, a new activation condition which has not been considered in the literature is proposed and utilized for derivation of stability criteria. Two numerical examples are given to illustrate the effectiveness of the proposed method.
On global exponential stability of high-order neural networks with time-varying delays
International Nuclear Information System (INIS)
Zhang Baoyong; Xu Shengyuan; Li Yongmin; Chu Yuming
2007-01-01
This Letter investigates the problem of stability analysis for a class of high-order neural networks with time-varying delays. The delays are bounded but not necessarily differentiable. Based on the Lyapunov stability theory together with the linear matrix inequality (LMI) approach and the use of Halanay inequality, sufficient conditions guaranteeing the global exponential stability of the equilibrium point of the considered neural networks are presented. Two numerical examples are provided to demonstrate the effectiveness of the proposed stability criteria
On global exponential stability of high-order neural networks with time-varying delays
Energy Technology Data Exchange (ETDEWEB)
Zhang Baoyong [School of Automation, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu (China)]. E-mail: baoyongzhang@yahoo.com.cn; Xu Shengyuan [School of Automation, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu (China)]. E-mail: syxu02@yahoo.com.cn; Li Yongmin [School of Automation, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu (China) and Department of Mathematics, Huzhou Teacher' s College, Huzhou 313000, Zhejiang (China)]. E-mail: ymlwww@163.com; Chu Yuming [Department of Mathematics, Huzhou Teacher' s College, Huzhou 313000, Zhejiang (China)
2007-06-18
This Letter investigates the problem of stability analysis for a class of high-order neural networks with time-varying delays. The delays are bounded but not necessarily differentiable. Based on the Lyapunov stability theory together with the linear matrix inequality (LMI) approach and the use of Halanay inequality, sufficient conditions guaranteeing the global exponential stability of the equilibrium point of the considered neural networks are presented. Two numerical examples are provided to demonstrate the effectiveness of the proposed stability criteria.
Phase space reconstruction and estimation of the largest Lyapunov exponent for gait kinematic data
Energy Technology Data Exchange (ETDEWEB)
Josiński, Henryk [Silesian University of Technology, Akademicka 16, 44-100 Gliwice (Poland); Świtoński, Adam [Polish-Japanese Institute of Information Technology, Aleja Legionów 2, 41-902 Bytom (Poland); Silesian University of Technology, Akademicka 16, 44-100 Gliwice (Poland); Michalczuk, Agnieszka; Wojciechowski, Konrad [Polish-Japanese Institute of Information Technology, Aleja Legionów 2, 41-902 Bytom (Poland)
2015-03-10
The authors describe an example of application of nonlinear time series analysis directed at identifying the presence of deterministic chaos in human motion data by means of the largest Lyapunov exponent. The method was previously verified on the basis of a time series constructed from the numerical solutions of both the Lorenz and the Rössler nonlinear dynamical systems.
Lyapunov spectra of density fluctuations in TBR-1
International Nuclear Information System (INIS)
Oiwa, N.N.; Fidler-Ferrara, N.
1993-01-01
The results for the Lyapunov exponents associated with density fluctuations measured by Langmuir probes placed in the scrape-off layer of the Tokamak TBR-1 are reported. By a judicious use of the Sano-Sawada and Eckmann-Ruelle algorithms conclusive values for the positive Lyapunov exponents for most of the analysed signals are used showing evidences of chaotic behavior. (author)
A stability analysis of ventilated boiling channels
International Nuclear Information System (INIS)
Taleyarkhan, R.P.; Podowski, M.Z.; Lahey, R.T. Jr.
1986-01-01
A mathematical model has been developed for the linear stability analysis of a system of ventilated parallel boiling channels. This model accounts for subcooled boiling, an arbitrary heat flux distribution, distributed and local hydraulic losses, heated wall dynamics, slip flow, turbulent mixing and arbitrary flow paths for transverse ventilation. The digital computer program MAZDA-NF was written for numerical evaluation of the mathematical model. Comparison of MAZDA-NF results with those obtained form both a closed form analytical solution and experiment, showed good agreement. A parametric study revealed that such phenomena as subcooled boiling, the transverse coupling between channels (due to cross-flow and mixing) and power skewing can have a significant impact on predicted stability margins. An analysis of an advanced BWR fuel, of the ASEA-ATOM SVEA design, has indicated that transverse ventilation may considerably improve channel stability. (orig.)
Analysis of Chatter Stability in Facing
Kebdani, S.; Sahli, A.; Rahmani, O.; Boutchicha, D.; Belarbi, A.
This study attempts to develop a chatter model for predicting chatter stability conditions in hard turning. A linear model is developed by introducing non-uniform load distribution on a tool tip to account for the flank wear effect. Stability analysis based on the root locus method and the harmonic balance method is conducted to determine a critical stability parameter. To validate the model, a series of experiment is carried out to determine the stability limits as well as certain characteristic parameters for facing and straight turning. Chatter in hard turning has the feature that the critical stability limits increase very rapidly when the cutting speed is higher than 13 rev sec-1 for all feed directions. The main contributions of the study are threefold. First, chatter-free cutting conditions are predicted and can be used as a guideline for designing tools and machines. Second, the characteristics of chatter in hard turning, which is observed for the first time, helps to broaden our physical understanding of the interactions between the tool and the workpiece in hard turning. Third, experimental stability limits for different flank wear can contribute to lead more reasonable ways to consider the flank wear effect in chatter models of hard turning. Based on these contributions, the proposed linear chatter model will support to improve the productivity in many manufacturing processes. In addition, the chatter experimental data will be useful to develop other chatter models in hard turning.
Full spectrum of Lyapunov exponents in gauge field theories
International Nuclear Information System (INIS)
Biro, T.S.; Markum, H.; Pullirsch, R.
2003-01-01
Full text: Results are presented for the full spectrum of Lyapunov exponents of the compact U(1) gauge system in classical field theory. Instead of the determination of the largest Lyapunov exponent by the rescaling method we now use the monodromy matrix approach. The Lyapunov spectrum L i is expressed in terms of the eigenvalues Λ i of the monodromy matrix M. In the confinement phase the eigenvalues lie on either the real or on the imaginary axes. This is a nice illustration of a strange attractor of a chaotic system. Positive Lyapunov exponents eject the trajectories from oscillating orbits provided by the imaginary eigenvalues. Negative Lyapunov exponents attract the trajectories keeping them confined in the basin. Latest studies concern the time (in)dependence of the monodromy matrix. Further, we show that monopoles are created and annihilated in pairs as a function of real time in access to a fixed average monopole number. (author)
Stability analysis of cylinders with circular cutouts
Almroth, B. O.; Brogan, F. A.; Marlowe, M. B.
1973-01-01
The stability of axially compressed cylinders with circular cutouts is analyzed numerically. An extension of the finite-difference method is used which removes the requirement that displacement components be defined in the directions of the grid lines. The results of this nonlinear analysis are found to be in good agreement with earlier experimental results.
High beta and second stability region transport and stability analysis
International Nuclear Information System (INIS)
1991-01-01
This document describes ideal and resistive MHD studies of high-beta plasmas and of the second stability region. Significant progress is reported on the resistive stability properties of high beta poloidal ''supershot'' discharges. For these studies initial profiles were taken from the TRANSP code which is used extensively to analyze experimental data. When an ad hoc method of removing the finite pressure stabilization of tearing modes is implemented it is shown that there is substantial agreement between MHD stability computation and experiment. In particular, the mode structures observed experimentally are consistent with the predictions of the resistive MHD model. We also report on resistive stability near the transition to the second region in TFTR. Tearing modes associated with a nearby infernal mode may explain the increase in MHD activity seen in high beta supershots and which impede the realization of Q∼1. We also report on a collaborative study with PPPL involving sawtooth stabilization with ICRF
On the angle between the first and second Lyapunov vectors in spatio-temporal chaos
International Nuclear Information System (INIS)
Pazó, D; López, J M; Rodríguez, M A
2013-01-01
In a dynamical system the first Lyapunov vector (LV) is associated with the largest Lyapunov exponent and indicates—at any point on the attractor—the direction of maximal growth in tangent space. The LV corresponding to the second largest Lyapunov exponent generally points in a different direction, but tangencies between both vectors can in principle occur. Here we find that the probability density function (PDF) of the angle ψ spanned by the first and second LVs should be expected to be approximately symmetric around π/4 and to peak at 0 and π/2. Moreover, for small angles we uncover a scaling law for the PDF Q of ψ l = ln ψ with the system size L: Q(ψ l ) = L −1/2 f(ψ l L −1/2 ). We give a theoretical argument that justifies this scaling form and also explains why it should be universal (irrespective of the system details) for spatio-temporal chaos in one spatial dimension. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)
Directory of Open Access Journals (Sweden)
Yan-Ke Du
2013-09-01
Full Text Available We study a class of discrete-time bidirectional ring neural network model with delay. We discuss the asymptotic stability of the origin and the existence of Neimark-Sacker bifurcations, by analyzing the corresponding characteristic equation. Employing M-matrix theory and the Lyapunov functional method, global asymptotic stability of the origin is derived. Applying the normal form theory and the center manifold theorem, the direction of the Neimark-Sacker bifurcation and the stability of bifurcating periodic solutions are obtained. Numerical simulations are given to illustrate the main results.
Stability analysis of rubblemound breakwater using ANN
Digital Repository Service at National Institute of Oceanography (India)
Mandal, S.; Rao, S.; Manjunath, Y.R.; Kim, D.H.
relation is not clear. In more practical terms networks are non-linear modeling tools and they can be used to model complex relationship between input and output system. Earlier applications of neural networks for stability analysis of rubble mound.... WORKING PRINCIPLE OF NEURAL NETWORK The feed forward neural networks have ability to approximate any continuous function or complex phenomena into a simple one. The working of neural network as described below. A feed forward neural network as shown...
Advanced Lyapunov control of a novel laser beam tracking system
Nikulin, Vladimir V.; Sofka, Jozef; Skormin, Victor A.
2005-05-01
Laser communication systems developed for mobile platforms, such as satellites, aircraft, and terrain vehicles, require fast wide-range beam-steering devices to establish and maintain a communication link. Conventionally, the low-bandwidth, high-steering-range part of the beam-positioning task is performed by gimbals that inherently constitutes the system bottleneck in terms of reliability, accuracy and dynamic performance. Omni-WristTM, a novel robotic sensor mount capable of carrying a payload of 5 lb and providing a full 180-deg hemisphere of azimuth/declination motion is known to be free of most of the deficiencies of gimbals. Provided with appropriate controls, it has the potential to become a new generation of gimbals systems. The approach we demonstrate describes an adaptive controller enabling Omni-WristTM to be utilized as a part of a laser beam positioning system. It is based on a Lyapunov function that ensures global asymptotic stability of the entire system while achieving high tracking accuracy. The proposed scheme is highly robust, does not require knowledge of complex system dynamics, and facilitates independent control of each channel by full decoupling of the Omni-WristTM dynamics. We summarize the basic algorithm and demonstrate the results obtained in the simulation environment.
Directory of Open Access Journals (Sweden)
S. S. Askar
2017-01-01
Full Text Available Many researchers have used quadratic utility function to study its influences on economic games with product differentiation. Such games include Cournot, Bertrand, and a mixed-type game called Cournot-Bertrand. Within this paper, a cubic utility function that is derived from a constant elasticity of substitution production function (CES is introduced. This cubic function is more desirable than the quadratic one besides its amenability to efficiency analysis. Based on that utility a two-dimensional Cournot duopoly game with horizontal product differentiation is modeled using a discrete time scale. Two different types of games are studied in this paper. In the first game, firms are updating their output production using the traditional bounded rationality approach. In the second game, firms adopt Puu’s mechanism to update their productions. Puu’s mechanism does not require any information about the profit function; instead it needs both firms to know their production and their profits in the past time periods. In both scenarios, an explicit form for the Nash equilibrium point is obtained under certain conditions. The stability analysis of Nash point is considered. Furthermore, some numerical simulations are carried out to confirm the chaotic behavior of Nash equilibrium point. This analysis includes bifurcation, attractor, maximum Lyapunov exponent, and sensitivity to initial conditions.
Nonlinear physical systems spectral analysis, stability and bifurcations
Kirillov, Oleg N
2013-01-01
Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems.Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynam
Using Covariant Lyapunov Vectors to Understand Spatiotemporal Chaos in Fluids
Paul, Mark; Xu, Mu; Barbish, Johnathon; Mukherjee, Saikat
2017-11-01
The spatiotemporal chaos of fluids present many difficult and fascinating challenges. Recent progress in computing covariant Lyapunov vectors for a variety of model systems has made it possible to probe fundamental ideas from dynamical systems theory including the degree of hyperbolicity, the fractal dimension, the dimension of the inertial manifold, and the decomposition of the dynamics into a finite number of physical modes and spurious modes. We are interested in building upon insights such as these for fluid systems. We first demonstrate the power of covariant Lyapunov vectors using a system of maps on a lattice with a nonlinear coupling. We then compute the covariant Lyapunov vectors for chaotic Rayleigh-Bénard convection for experimentally accessible conditions. We show that chaotic convection is non-hyperbolic and we quantify the spatiotemporal features of the spectrum of covariant Lyapunov vectors. NSF DMS-1622299 and DARPA/DSO Models, Dynamics, and Learning (MoDyL).
On some properties of the discrete Lyapunov exponent
International Nuclear Information System (INIS)
Amigo, Jose M.; Kocarev, Ljupco; Szczepanski, Janusz
2008-01-01
One of the possible by-products of discrete chaos is the application of its tools, in particular of the discrete Lyapunov exponent, to cryptography. In this Letter we explore this question in a very general setting
Stability Analysis and Stabilization of Miduk Heap Leaching Structure, Iran
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Mehdi Amini
2013-06-01
Full Text Available To construct copper heap leaching structures, a stepped heap of ore is placed over an isolated sloping surface and then washed with sulphuric acid. The isolated bed of such a heap consists of some natural and geosynthetic layers. Shear strength parameters between these layers are low, so they form the possible sliding surfaces of the heaps. Economic and environmental considerations call for studying such slides. In this study, firstly, results of the laboratory tests carried on the materials of the heap leaching structures bed are presented. Then, the instability mechanisms of such structures are investigated and proper approaches are summarized for their stabilization. Finally, stability of the Miduk copper heap is evaluated as a case history, and appropriate approaches and their effects are discussed for its stabilization.
A Lyapunov based approach to energy maximization in renewable energy technologies
Iyasere, Erhun
system. The controller tracks a desired array voltage, designed online using an incremental conductance extremum-seeking algorithm, by varying the duty cycle of the switching converter. The stability of the control algorithm is demonstrated by means of Lyapunov analysis. Representative numerical results demonstrate that the grid power system can be controlled to track the maximum power point of the photovoltaic array panel in varying atmospheric conditions. Additionally, the performance of the proposed strategy is compared to the typical maximum power point tracking (MPPT) method of perturb and observe (P&O), where the converter dynamics are ignored, and is shown to yield better results.
Lyapunov-based control of limit cycle oscillations in uncertain aircraft systems
Bialy, Brendan
Store-induced limit cycle oscillations (LCO) affect several fighter aircraft and is expected to remain an issue for next generation fighters. LCO arises from the interaction of aerodynamic and structural forces, however the primary contributor to the phenomenon is still unclear. The practical concerns regarding this phenomenon include whether or not ordnance can be safely released and the ability of the aircrew to perform mission-related tasks while in an LCO condition. The focus of this dissertation is the development of control strategies to suppress LCO in aircraft systems. The first contribution of this work (Chapter 2) is the development of a controller consisting of a continuous Robust Integral of the Sign of the Error (RISE) feedback term with a neural network (NN) feedforward term to suppress LCO behavior in an uncertain airfoil system. The second contribution of this work (Chapter 3) is the extension of the development in Chapter 2 to include actuator saturation. Suppression of LCO behavior is achieved through the implementation of an auxiliary error system that features hyperbolic functions and a saturated RISE feedback control structure. Due to the lack of clarity regarding the driving mechanism behind LCO, common practice in literature and in Chapters 2 and 3 is to replicate the symptoms of LCO by including nonlinearities in the wing structure, typically a nonlinear torsional stiffness. To improve the accuracy of the system model a partial differential equation (PDE) model of a flexible wing is derived (see Appendix F) using Hamilton's principle. Chapters 4 and 5 are focused on developing boundary control strategies for regulating the bending and twisting deformations of the derived model. The contribution of Chapter 4 is the construction of a backstepping-based boundary control strategy for a linear PDE model of an aircraft wing. The backstepping-based strategy transforms the original system to a exponentially stable system. A Lyapunov-based stability
Milanović, Jovica V
2017-08-13
Future power systems will be significantly different compared with their present states. They will be characterized by an unprecedented mix of a wide range of electricity generation and transmission technologies, as well as responsive and highly flexible demand and storage devices with significant temporal and spatial uncertainty. The importance of probabilistic approaches towards power system stability analysis, as a subsection of power system studies routinely carried out by power system operators, has been highlighted in previous research. However, it may not be feasible (or even possible) to accurately model all of the uncertainties that exist within a power system. This paper describes for the first time an integral approach to probabilistic stability analysis of power systems, including small and large angular stability and frequency stability. It provides guidance for handling uncertainties in power system stability studies and some illustrative examples of the most recent results of probabilistic stability analysis of uncertain power systems.This article is part of the themed issue 'Energy management: flexibility, risk and optimization'. © 2017 The Author(s).
Airfoil stall interpreted through linear stability analysis
Busquet, Denis; Juniper, Matthew; Richez, Francois; Marquet, Olivier; Sipp, Denis
2017-11-01
Although airfoil stall has been widely investigated, the origin of this phenomenon, which manifests as a sudden drop of lift, is still not clearly understood. In the specific case of static stall, multiple steady solutions have been identified experimentally and numerically around the stall angle. We are interested here in investigating the stability of these steady solutions so as to first model and then control the dynamics. The study is performed on a 2D helicopter blade airfoil OA209 at low Mach number, M 0.2 and high Reynolds number, Re 1.8 ×106 . Steady RANS computation using a Spalart-Allmaras model is coupled with continuation methods (pseudo-arclength and Newton's method) to obtain steady states for several angles of incidence. The results show one upper branch (high lift), one lower branch (low lift) connected by a middle branch, characterizing an hysteresis phenomenon. A linear stability analysis performed around these equilibrium states highlights a mode responsible for stall, which starts with a low frequency oscillation. A bifurcation scenario is deduced from the behaviour of this mode. To shed light on the nonlinear behavior, a low order nonlinear model is created with the same linear stability behavior as that observed for that airfoil.
Estabilización del Péndulo Invertido Sobre Dos Ruedas mediante el método de Lyapunov
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O. Octavio Gutiérrez Frías
2013-01-01
Full Text Available Resumen: En este trabajo, se presenta un controlador no lineal para estabilizar el sistema Péndulo Invertido Sobre Dos Ruedas. Como primera etapa la estrategia de control, se basa en una linealización parcial por realimentación, para posteriormente proponer una función candidata de Lyapunov en combinación con el principio de invariancia de LaSalle con el fin de obtener el controlador esta- bilizador. El sistema en lazo cerrado obtenido es asintóticamente estable localmente alrededor del punto de equilibrio inestable, con un dominio de atracción calculable. Abstract: In this paper, a nonlinear controller is presented for the stabilization of the two wheels inverted pendulum. The control strategy is based on partial feedback linealization, in first stage and then a suitable function Lyapunov in conjunction with LaSalle's invariance principle is formed to obtain a stabilizing feedback controller. The obtained closed-loop system is locally asymptotically stable around its unstable equilibrium point, with a computable domain of attraction. Palabras clave: Sistema Subactuado, Péndulo Invertido Sobre Dos Ruedas, Método de Lyapunov, Control No Lineal, Keywords: Under Actuated System, Two Wheels Inverted Pendulum, Lyapunov Approach, Non-Linear Control
Stability analysis of cylindrical Vlasov equilibria
International Nuclear Information System (INIS)
Short, R.W.
1979-01-01
A general method of stability analysis is described which may be applied to a large class of such problems, namely those which are described dynamically by the Vlasov equation, and geometrically by cylindrical symmetry. The method is presented for the simple case of the Vlasov-Poisson (electrostatic) equations, and the results are applied to a calculation of the lower-hybrid-drift instability in a plasma with a rigid rotor distribution function. The method is extended to the full Vlasov-Maxwell (electromagnetic) equations. These results are applied to a calculation of the instability of the extraordinary electromagnetic mode in a relativistic E-layer interacting with a background plasma
Stability analysis of cylindrical Vlasov equilibria
International Nuclear Information System (INIS)
Short, R.W.
1979-01-01
A general method of stability analysis is described which may be applied to a large class of such problems, namely those which are described dynamically by the Vlasov equation, and geometrically by clindrical symmetry. The method is presented for the simple case of the Vlasov-Poisson (electrostatic) equations, and the results are applied to a calculation of the lower-hybrid-drift instability in a plasma with a rigid rotor distribution function. The method is extended to the full Vlasov-Maxwell (electromagnetic) equations. These results are applied to a calculation of the instability of the extraordinary electromagnetic mode in a relativistic E-layer interacting with a background plasma
Directory of Open Access Journals (Sweden)
Liang QU
2017-06-01
Full Text Available Icing is one of the crucial factors that could pose great threat to flight safety, and thus research on stability and stability region of aircraft safety under icing conditions is significant for control and flight. Nonlinear dynamical equations and models of aerodynamic coefficients of an aircraft are set up in this paper to study the stability and stability region of the aircraft under an icing condition. Firstly, the equilibrium points of the iced aircraft system are calculated and analyzed based on the theory of differential equation stability. Secondly, according to the correlation theory about equilibrium points and the stability region, this paper estimates the multidimensional stability region of the aircraft, based on which the stability regions before and after icing are compared. Finally, the results are confirmed by the time history analysis. The results can give a reference for stability analysis and envelope protection of the nonlinear system of an iced aircraft.
New stability and stabilization for switched neutral control systems
International Nuclear Information System (INIS)
Xiong Lianglin; Zhong Shouming; Ye Mao; Wu Shiliang
2009-01-01
This paper concerns stability and stabilization issues for switched neutral systems and presents new classes of piecewise Lyapunov functionals and multiple Lyapunov functionals, based on which, two new switching rules are introduced to stabilize the neutral systems. One switching rule is designed from the solution of the so-called Lyapunov-Metzler linear matrix inequalities. The other is based on the determination of average dwell time computed from a new class of linear matrix inequalities (LMIs). And then, state-feedback control is derived for the switched neutral control system mainly based on the state switching rules. Finally, three examples are given to demonstrate the effectiveness of the proposed method.
Dynamic stability analysis of fractional order leaky integrator echo state neural networks
Pahnehkolaei, Seyed Mehdi Abedi; Alfi, Alireza; Tenreiro Machado, J. A.
2017-06-01
The Leaky integrator echo state neural network (Leaky-ESN) is an improved model of the recurrent neural network (RNN) and adopts an interconnected recurrent grid of processing neurons. This paper presents a new proof for the convergence of a Lyapunov candidate function to zero when time tends to infinity by means of the Caputo fractional derivative with order lying in the range (0, 1). The stability of Fractional-Order Leaky-ESN (FO Leaky-ESN) is then analyzed, and the existence, uniqueness and stability of the equilibrium point are provided. A numerical example demonstrates the feasibility of the proposed method.
Global exponential stability analysis on impulsive BAM neural networks with distributed delays
Li, Yao-Tang; Yang, Chang-Bo
2006-12-01
Using M-matrix and topological degree tool, sufficient conditions are obtained for the existence, uniqueness and global exponential stability of the equilibrium point of bidirectional associative memory (BAM) neural networks with distributed delays and subjected to impulsive state displacements at fixed instants of time by constructing a suitable Lyapunov functional. The results remove the usual assumptions that the boundedness, monotonicity, and differentiability of the activation functions. It is shown that in some cases, the stability criteria can be easily checked. Finally, an illustrative example is given to show the effectiveness of the presented criteria.
Directory of Open Access Journals (Sweden)
L.F.P. Franca
2003-01-01
Full Text Available This contribution presents an investigation on noise sensitivity of some of the most disseminated techniques employed to estimate Lyapunov exponents from time series. Since noise contamination is unavoidable in cases of data acquisition, it is important to recognize techniques that could be employed for a correct identification of chaos. State space reconstruction and the determination of Lyapunov exponents are carried out to investigate the response of a nonlinear pendulum. Signals are generated by numerical integration of the mathematical model, selecting a single variable of the system as a time series. In order to simulate experimental data sets, a random noise is introduced in the signal. Basically, the analyses of periodic and chaotic motions are carried out. Results obtained from mathematical model are compared with the one obtained from time series analysis, evaluating noise sensitivity. This procedure allows the identification of the best techniques to be employed in the analysis of experimental data.
International Nuclear Information System (INIS)
Ali, M. Syed
2011-01-01
In this paper, the global stability of Takagi—Sugeno (TS) uncertain stochastic fuzzy recurrent neural networks with discrete and distributed time-varying delays (TSUSFRNNs) is considered. A novel LMI-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of TSUSFRNNs. The proposed stability conditions are demonstrated through numerical examples. Furthermore, the supplementary requirement that the time derivative of time-varying delays must be smaller than one is removed. Comparison results are demonstrated to show that the proposed method is more able to guarantee the widest stability region than the other methods available in the existing literature. (general)
Voltage stability analysis using a modified continuation load flow ...
African Journals Online (AJOL)
This paper addresses the rising problem of identifying the voltage stability limits of load buses in a power system and how to optimally place capacitor banks for voltage stability improvement. This paper uses the concept of the continuation power flow analysis used in voltage stability analysis. It uses the modified ...
Stability analysis of multiple-robot control systems
Wen, John T.; Kreutz, Kenneth
1989-01-01
In a space telerobotic service scenario, cooperative motion and force control of multiple robot arms are of fundamental importance. Three paradigms to study this problem are proposed. They are distinguished by the set of variables used for control design. They are joint torques, arm tip force vectors, and an accelerated generalized coordinate set. Control issues related to each case are discussed. The latter two choices require complete model information, which presents practical modeling, computational, and robustness problems. Therefore, focus is on the joint torque control case to develop relatively model independent motion and internal force control laws. The rigid body assumption allows the motion and force control problems to be independently addressed. By using an energy motivated Lyapunov function, a simple proportional derivative plus gravity compensation type of motion control law is always shown to be stabilizing. The asymptotic convergence of the tracing error to zero requires the use of a generalized coordinate with the contact constraints taken into account. If a non-generalized coordinate is used, only convergence to a steady state manifold can be concluded. For the force control, both feedforward and feedback schemes are analyzed. The feedback control, if proper care has been taken, exhibits better robustness and transient performance.
Truck Roll Stability Data Collection and Analysis
Energy Technology Data Exchange (ETDEWEB)
Stevens, SS
2001-07-02
The principal objective of this project was to collect and analyze vehicle and highway data that are relevant to the problem of truck rollover crashes, and in particular to the subset of rollover crashes that are caused by the driver error of entering a curve at a speed too great to allow safe completion of the turn. The data are of two sorts--vehicle dynamic performance data, and highway geometry data as revealed by vehicle behavior in normal driving. Vehicle dynamic performance data are relevant because the roll stability of a tractor trailer depends both on inherent physical characteristics of the vehicle and on the weight and distribution of the particular cargo that is being carried. Highway geometric data are relevant because the set of crashes of primary interest to this study are caused by lateral acceleration demand in a curve that exceeds the instantaneous roll stability of the vehicle. An analysis of data quality requires an evaluation of the equipment used to collect the data because the reliability and accuracy of both the equipment and the data could profoundly affect the safety of the driver and other highway users. Therefore, a concomitant objective was an evaluation of the performance of the set of data-collection equipment on the truck and trailer. The objective concerning evaluation of the equipment was accomplished, but the results were not entirely positive. Significant engineering apparently remains to be done before a reliable system can be fielded. Problems were identified with the trailer to tractor fiber optic connector used for this test. In an over-the-road environment, the communication between the trailer instrumentation and the tractor must be dependable. In addition, the computer in the truck must be able to withstand the rigors of the road. The major objective--data collection and analysis--was also accomplished. Using data collected by instruments on the truck, a ''bad-curve'' database can be generated. Using
BWR stability analysis at Brookhaven National Laboratory
International Nuclear Information System (INIS)
Wulff, W.; Cheng, H.S.; Mallen, A.N.; Rohatgi, U.S.
1991-01-01
Following the unexpected, but safely terminated, power and flow oscillations in the LaSalle-2 Boiling Water Reactor (BWR) on March 9, 1988, the Nuclear Regulatory Commission (NRC) Offices of Nuclear Reactor Regulation (NRR) and of Analysis and Evaluation of Operational Data (AEOD) requested that the Office of Nuclear Regulatory Research (RES) carry out BWR stability analyses, centered around fourteen specific questions. Ten of the fourteen questions address BWR stability issues in general and are dealt with in this paper. The other four questions address local, out-of-phase oscillations and matters of instrumentation; they fall outside the scope of the work reported here. It was the purpose of the work documented in this report to answer ten of the fourteen NRC-stipulated questions. Nine questions are answered by analyzing the LaSalle-2 instability and related BWR transients with the BNL Engineering Plant Analyzer (EPA) and by performing an uncertainty assessment of the EPA predictions. The tenth question is answered on the basis of first principles. The ten answers are summarized
Nonparallel linear stability analysis of unconfined vortices
Herrada, M. A.; Barrero, A.
2004-10-01
Parabolized stability equations [F. P. Bertolotti, Th. Herbert, and P. R. Spalart, J. Fluid. Mech. 242, 441 (1992)] have been used to study the stability of a family of swirling jets at high Reynolds numbers whose velocity and pressure fields decay far from the axis as rm-2 and r2(m-2), respectively [M. Pérez-Saborid, M. A. Herrada, A. Gómez-Barea, and A. Barrero, J. Fluid. Mech. 471, 51 (2002)]; r is the radial distance and m is a real number in the interval 0
The Analysis Stability of Anchor Retaining Wall
International Nuclear Information System (INIS)
Benamara, F. Z.; Belabed, L
2011-01-01
The construction of anchored retaining walls reach every day in the field of Civil Engineering especially in public works. Their dimensioning and stability are the axes of research for geotechnical. The rule is to reduce the active forces of the slide and increase the effective normal stress on the rupture surface. So that, we anchored tied-back (constituted by steel cables) in the stable ground located under the failure surface and we apply at the top a traction force. This effort can be distributed over the ground surface by means of small plates or massive reinforced concrete. The study of the stability of anchored retaining wall was also performed by using software GEO4. Many cases can be solved using analytical solutions available in the group GEO4 program, but for our standard model solution studied analytically proved unsatisfactory so we used a numerical analysis based on the method of finite element in this program. The results obtained by numerical study were interpreted to identify the precision numerical predictions. Moreover these methods were useful and economics in the realization of reinforced slopes by tied-buck. (author)
OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS.
Ott, William; Rivas, Mauricio A; West, James
2015-12-01
Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝ N using a 'typical' nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C 1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time- T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence).
Anisotropies in magnetic field evolution and local Lyapunov exponents
International Nuclear Information System (INIS)
Tang, X.Z.; Boozer, A.H.
2000-01-01
The natural occurrence of small scale structures and the extreme anisotropy in the evolution of a magnetic field embedded in a conducting flow is interpreted in terms of the properties of the local Lyapunov exponents along the various local characteristic (un)stable directions for the Lagrangian flow trajectories. The local Lyapunov exponents and the characteristic directions are functions of Lagrangian coordinates and time, which are completely determined once the flow field is specified. The characteristic directions that are associated with the spatial anisotropy of the problem, are prescribed in both Lagrangian and Eulerian frames. Coordinate transformation techniques are employed to relate the spatial distributions of the magnetic field, the induced current density, and the Lorentz force, which are usually followed in Eulerian frame, to those of the local Lyapunov exponents, which are naturally defined in Lagrangian coordinates
Universality in chaos: Lyapunov spectrum and random matrix theory
Hanada, Masanori; Shimada, Hidehiko; Tezuka, Masaki
2018-02-01
We propose the existence of a new universality in classical chaotic systems when the number of degrees of freedom is large: the statistical property of the Lyapunov spectrum is described by random matrix theory. We demonstrate it by studying the finite-time Lyapunov exponents of the matrix model of a stringy black hole and the mass-deformed models. The massless limit, which has a dual string theory interpretation, is special in that the universal behavior can be seen already at t =0 , while in other cases it sets in at late time. The same pattern is demonstrated also in the product of random matrices.
Lyapunov exponent of the random frequency oscillator: cumulant expansion approach
International Nuclear Information System (INIS)
Anteneodo, C; Vallejos, R O
2010-01-01
We consider a one-dimensional harmonic oscillator with a random frequency, focusing on both the standard and the generalized Lyapunov exponents, λ and λ* respectively. We discuss the numerical difficulties that arise in the numerical calculation of λ* in the case of strong intermittency. When the frequency corresponds to a Ornstein-Uhlenbeck process, we compute analytically λ* by using a cumulant expansion including up to the fourth order. Connections with the problem of finding an analytical estimate for the largest Lyapunov exponent of a many-body system with smooth interactions are discussed.
Universality in chaos: Lyapunov spectrum and random matrix theory.
Hanada, Masanori; Shimada, Hidehiko; Tezuka, Masaki
2018-02-01
We propose the existence of a new universality in classical chaotic systems when the number of degrees of freedom is large: the statistical property of the Lyapunov spectrum is described by random matrix theory. We demonstrate it by studying the finite-time Lyapunov exponents of the matrix model of a stringy black hole and the mass-deformed models. The massless limit, which has a dual string theory interpretation, is special in that the universal behavior can be seen already at t=0, while in other cases it sets in at late time. The same pattern is demonstrated also in the product of random matrices.
ANALYSIS AND OPTIMISATION OF DYNAMIC STABILITY OF MOBILE WORKING MACHINES
Directory of Open Access Journals (Sweden)
Peter BIGOŠ
2014-09-01
Full Text Available This paper describes an investigation of the dynamic stability, which is specified for the mobile working machines. There are presented the basic theoretical principles of the stability theory together with an introduction of two illustrative examples of the dynamic stability analysis.
International Nuclear Information System (INIS)
Ali, M. Syed
2014-01-01
In this paper, the global asymptotic stability problem of Markovian jumping stochastic Cohen—Grossberg neural networks with discrete and distributed time-varying delays (MJSCGNNs) is considered. A novel LMI-based stability criterion is obtained by constructing a new Lyapunov functional to guarantee the asymptotic stability of MJSCGNNs. Our results can be easily verified and they are also less restrictive than previously known criteria and can be applied to Cohen—Grossberg neural networks, recurrent neural networks, and cellular neural networks. Finally, the proposed stability conditions are demonstrated with numerical examples
Shah, Neerav
2011-01-01
The Magnetospheric MultiScale Mission (MMS) is scheduled to launch in late 2014. Its primary goal is to discover the fundamental plasma physics processes of reconnection in the Earth's magnetosphere. Each of the four MMS spacecraft is spin-stabilized at a nominal rate of 3 RPM. Traditional spin-stabilized spacecraft have used a number of separate modes to control nutation, spin rate, and precession. To reduce the number of modes and simplify operations, the Delta-H control mode is designed to accomplish nutation control, spin rate control, and precession control simultaneously. A nonlinear design technique, Lyapunov's method, is used to design the Delta-H control mode. A global spin rate controller selected as the baseline controller for MMS, proved to be insufficient due to an ambiguity in the attitude. Lyapunov's design method was used to solve this ambiguity, resulting in a controller that meets the design goals. Simulation results show the advantage of the pointing and rate controller for maneuvers larger than 90 deg and provide insight into the performance of this controller.
On global stability criterion for neural networks with discrete and distributed delays
International Nuclear Information System (INIS)
Park, Ju H.
2006-01-01
Based on the Lyapunov functional stability analysis for differential equations and the linear matrix inequality (LMI) optimization approach, a new delay-dependent criterion for neural networks with discrete and distributed delays is derived to guarantee global asymptotic stability. The criterion is expressed in terms of LMIs, which can be solved easily by various convex optimization algorithms. Some numerical examples are given to show the effectiveness of proposed method
International Nuclear Information System (INIS)
Lou, X.; Cui, B.
2008-01-01
In this paper we consider the problem of exponential stability for recurrent neural networks with multiple time varying delays and reaction-diffusion terms. The activation functions are supposed to be bounded and globally Lipschitz continuous. By means of Lyapunov functional, sufficient conditions are derived, which guarantee global exponential stability of the delayed neural network. Finally, a numerical example is given to show the correctness of our analysis. (author)
Design of Connectivity Preserving Flocking Using Control Lyapunov Function
Erfianto, Bayu; Bambang, Riyanto T.; Hindersah, Hilwadi; Muchtadi-Alamsyah, Intan
2016-01-01
This paper investigates cooperative flocking control design with connectivity preserving mechanism. During flocking, interagent distance is measured to determine communication topology of the flocks. Then, cooperative flocking motion is built based on cooperative artificial potential field with connectivity preserving mechanism to achieve the common flocking objective. The flocking control input is then obtained by deriving cooperative artificial potential field using control Lyapunov functio...
Reliability Analysis of Dynamic Stability in Waves
DEFF Research Database (Denmark)
Søborg, Anders Veldt
2004-01-01
exhibit sufficient characteristics with respect to slope at zero heel (GM value), maximum leverarm, positive range of stability and area below the leverarm curve. The rule-based requirements to calm water leverarm curves are entirely based on experience obtained from vessels in operation and recorded......The assessment of a ship's intact stability is traditionally based on a semi-empirical deterministic concept that evaluates the characteristics of ship's calm water restoring leverarm curves. Today the ship is considered safe with respect to dynamic stability if its calm water leverarm curves...... accidents in the past. The rules therefore only leaves little room for evaluation and improvement of safety of a ship's dynamic stability. A few studies have evaluated the probability of ship stability loss in waves using Monte Carlo simulations. However, since this probability may be in the order of 10...
Stability of fundamental couplings: A global analysis
Martins, C. J. A. P.; Pinho, A. M. M.
2017-01-01
Astrophysical tests of the stability of fundamental couplings are becoming an increasingly important probe of new physics. Motivated by the recent availability of new and stronger constraints we update previous works testing the consistency of measurements of the fine-structure constant α and the proton-to-electron mass ratio μ =mp/me (mostly obtained in the optical/ultraviolet) with combined measurements of α , μ and the proton gyromagnetic ratio gp (mostly in the radio band). We carry out a global analysis of all available data, including the 293 archival measurements of Webb et al. and 66 more recent dedicated measurements, and constraining both time and spatial variations. While nominally the full data sets show a slight statistical preference for variations of α and μ (at up to two standard deviations), we also find several inconsistencies between different subsets, likely due to hidden systematics and implying that these statistical preferences need to be taken with caution. The statistical evidence for a spatial dipole in the values of α is found at the 2.3 sigma level. Forthcoming studies with facilities such as ALMA and ESPRESSO should clarify these issues.
Remarks on boiling water reactor stability analysis. Pt. 2. Stability monitoring
Energy Technology Data Exchange (ETDEWEB)
Lange, Carsten; Hennig, Dieter; Hurtado, Antonio [Technische Univ. Dresden (Germany). Chair of Hydrogen and Nuclear Energy; Schuster, Roland [Kernkraftwerk Brunsbuettel GmbH und Co. oHG, Brunsbuettel (Germany); Lukas, Bernard [EnBW Kernkraft GmbH, Philippsburg (Germany). Kernkraftwerk Philippsburg; Aguirre, Carlos [Kernkraftwerk Leibstadt AG, Aargau (Switzerland)
2012-12-15
In part 1 of this article we explained the partly relative complex solution manifold of the differential equations describing the stability behaviour of a BWR, in particular the coexistence of different types of solutions, such as the coexistence of unstable limit cycles and stable fixed points are of interest from the operational safety point of view. The part 2 is devoted to the surveillance of the stability behaviour. We summarize some stability monitoring methods and suggest to support stability tests by RAM-ROM analyses in order to reveal in advance the stability 'landscape' of the BWR in a parameter region high sensitive for appearing of linear unstable states. The analysis of an especial stability test, performed at NPP Leibstadt (KKL), makes it clear that the measurement results can only be interpreted by application of bifurcation analysis. (orig.)
International Nuclear Information System (INIS)
Hennig, D.; Nechvatal, L.
1996-09-01
The report describes the PSI stability analysis methodology and the validation of this methodology based on the international OECD/NEA BWR stability benchmark task. In the frame of this work, the stability properties of some operation points of the NPP Ringhals 1 have been analysed and compared with the experimental results. (author) figs., tabs., 45 refs
Stability Analysis of an HIV/AIDS Dynamics Model with Drug Resistance
Directory of Open Access Journals (Sweden)
Qianqian Li
2012-01-01
Full Text Available A mathematical model of HIV/AIDS transmission incorporating treatment and drug resistance was built in this study. We firstly calculated the threshold value of the basic reproductive number (R0 by the next generation matrix and then analyzed stability of two equilibriums by constructing Lyapunov function. When R0<1, the system was globally asymptotically stable and converged to the disease-free equilibrium. Otherwise, the system had a unique endemic equilibrium which was also globally asymptotically stable. While an antiretroviral drug tried to reduce the infection rate and prolong the patients’ survival, drug resistance was neutralizing the effects of treatment in fact.
Longo, Alessia; Federolf, Peter; Haid, Thomas; Meulenbroek, Ruud
2018-06-01
In many daily jobs, repetitive arm movements are performed for extended periods of time under continuous cognitive demands. Even highly monotonous tasks exhibit an inherent motor variability and subtle fluctuations in movement stability. Variability and stability are different aspects of system dynamics, whose magnitude may be further affected by a cognitive load. Thus, the aim of the study was to explore and compare the effects of a cognitive dual task on the variability and local dynamic stability in a repetitive bimanual task. Thirteen healthy volunteers performed the repetitive motor task with and without a concurrent cognitive task of counting aloud backwards in multiples of three. Upper-body 3D kinematics were collected and postural reconfigurations-the variability related to the volunteer's postural change-were determined through a principal component analysis-based procedure. Subsequently, the most salient component was selected for the analysis of (1) cycle-to-cycle spatial and temporal variability, and (2) local dynamic stability as reflected by the largest Lyapunov exponent. Finally, end-point variability was evaluated as a control measure. The dual cognitive task proved to increase the temporal variability and reduce the local dynamic stability, marginally decrease endpoint variability, and substantially lower the incidence of postural reconfigurations. Particularly, the latter effect is considered to be relevant for the prevention of work-related musculoskeletal disorders since reduced variability in sustained repetitive tasks might increase the risk of overuse injuries.
CAREM-25 Steam Generator Stability Analysis
International Nuclear Information System (INIS)
Rabiti, A.; Delmastro, D.
2003-01-01
In this work the stability of a once-through CAREM-25 steam generator is analyzed.A fix nodes numerical model, that allows the modelling of the liquid, two-phase and superheated steam zones, is implemented.This model was checked against a mobile finite elements model under saturated steam conditions at the channel exit and a good agreement was obtained.Finally the stability of a CAREM steam generator is studied and the range of in let restrictions that a assure the system stability is analyzed
Angle Stability Analysis for Voltage-Controlled Converters
DEFF Research Database (Denmark)
Lin, Hengwei; Jia, Chenxi; Guerrero, Josep M.
2017-01-01
a criterion to analyze the quasi-steady angle stability and the direct current (DC) side stability for VSCs. The operating limit and the angle instability mechanism are revealed, which is generally applicable to the voltage-controlled converters. During the analysis, the influence of the parameters on angle...... stability is studied. Further, the difference on instability mechanism between power electronic converters and synchronous generators are explained in detail. Finally, experiment results with corrective actions verify the analysis....
On a program manifold's stability of one contour automatic control systems
Zumatov, S. S.
2017-12-01
Methodology of analysis of stability is expounded to the one contour systems automatic control feedback in the presence of non-linearities. The methodology is based on the use of the simplest mathematical models of the nonlinear controllable systems. Stability of program manifolds of one contour automatic control systems is investigated. The sufficient conditions of program manifold's absolute stability of one contour automatic control systems are obtained. The Hurwitz's angle of absolute stability was determined. The sufficient conditions of program manifold's absolute stability of control systems by the course of plane in the mode of autopilot are obtained by means Lyapunov's second method.
Lyapunov matrices approach to the parametric optimization of time-delay systems
Directory of Open Access Journals (Sweden)
Duda Józef
2015-09-01
Full Text Available In the paper a Lyapunov matrices approach to the parametric optimization problem of time-delay systems with a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of Lyapunov functional for the initial function of the time-delay system. The Lyapunov functional is determined by means of the Lyapunov matrix
Lyapunov exponent for aging process in induction motor
Bayram, Duygu; Ünnü, Sezen Yıdırım; Şeker, Serhat
2012-09-01
Nonlinear systems like electrical circuits and systems, mechanics, optics and even incidents in nature may pass through various bifurcations and steady states like equilibrium point, periodic, quasi-periodic, chaotic states. Although chaotic phenomena are widely observed in physical systems, it can not be predicted because of the nature of the system. On the other hand, it is known that, chaos is strictly dependent on initial conditions of the system [1-3]. There are several methods in order to define the chaos. Phase portraits, Poincaré maps, Lyapunov Exponents are the most common techniques. Lyapunov Exponents are the theoretical indicator of the chaos, named after the Russian mathematician Aleksandr Lyapunov (1857-1918). Lyapunov Exponents stand for the average exponential divergence or convergence of nearby system states, meaning estimating the quantitive measure of the chaotic attractor. Negative numbers of the exponents stand for a stable system whereas zero stands for quasi-periodic systems. On the other hand, at least if one of the exponents is positive, this situation is an indicator of the chaos. For estimating the exponents, the system should be modeled by differential equation but even in that case mathematical calculation of Lyapunov Exponents are not very practical and evaluation of these values requires a long signal duration [4-7]. For experimental data sets, it is not always possible to acquire the differential equations. There are several different methods in literature for determining the Lyapunov Exponents of the system [4, 5]. Induction motors are the most important tools for many industrial processes because they are cheap, robust, efficient and reliable. In order to have healthy processes in industrial applications, the conditions of the machines should be monitored and the different working conditions should be addressed correctly. To the best of our knowledge, researches related to Lyapunov exponents and electrical motors are mostly
Stability Analysis for HIFiRE Experiments
Li, Fei; Choudhari, Meelan M.; Chang, Chau-Lyan; White, Jeffery A.; Kimmel, Roger; Adamczak, David; Borg, Matthew; Stanfield, Scott; Smith, Mark S.
2012-01-01
The HIFiRE-1 flight experiment provided a valuable database pertaining to boundary layer transition over a 7-degree half-angle, circular cone model from supersonic to hypersonic Mach numbers, and a range of Reynolds numbers and angles of attack. This paper reports selected findings from the ongoing computational analysis of the measured in-flight transition behavior. Transition during the ascent phase at nearly zero degree angle of attack is dominated by second mode instabilities except in the vicinity of the cone meridian where a roughness element was placed midway along the length of the cone. The growth of first mode instabilities is found to be weak at all trajectory points analyzed from the ascent phase. For times less than approximately 18.5 seconds into the flight, the peak amplification ratio for second mode disturbances is sufficiently small because of the lower Mach numbers at earlier times, so that the transition behavior inferred from the measurements is attributed to an unknown physical mechanism, potentially related to step discontinuities in surface height near the locations of a change in the surface material. Based on the time histories of temperature and/or heat flux at transducer locations within the aft portion of the cone, the onset of transition correlated with a linear N-factor, based on parabolized stability equations, of approximately 13.5. Due to the large angles of attack during the re-entry phase, crossflow instability may play a significant role in transition. Computations also indicate the presence of pronounced crossflow separation over a significant portion of the trajectory segment that is relevant to transition analysis. The transition behavior during this re-entry segment of HIFiRE-1 flight shares some common features with the predicted transition front along the elliptic cone shaped HIFiRE-5 flight article, which was designed to provide hypersonic transition data for a fully 3D geometric configuration. To compare and contrast the
Adaptive control of nonlinear in parameters chaotic system via Lyapunov exponents placement
Energy Technology Data Exchange (ETDEWEB)
Ayati, Moosa [Department of Electrical Engineering, K.N. Toosi University of Technology, Sayyed Khandan Bridge, Shariati Street, Tehran (Iran, Islamic Republic of)], E-mail: Ayati@dena.kntu.ac.ir; Khaki-Sedigh, Ali [Department of Electrical Engineering, K.N. Toosi University of Technology, Sayyed Khandan Bridge, Shariati Street, Tehran (Iran, Islamic Republic of)], E-mail: sedigh@kntu.ac.ir
2009-08-30
This paper proposes a new method for the adaptive control of nonlinear in parameters (NLP) chaotic systems. A method based on Lagrangian of a cost function is used to identify the parameters of the system. Estimation results are used to calculate the Lyapunov exponents adaptively. Finally, the Lyapunov exponents placement method is used to assign the desired Lyapunov exponents of the closed loop system.
Adaptive control of nonlinear in parameters chaotic system via Lyapunov exponents placement
International Nuclear Information System (INIS)
Ayati, Moosa; Khaki-Sedigh, Ali
2009-01-01
This paper proposes a new method for the adaptive control of nonlinear in parameters (NLP) chaotic systems. A method based on Lagrangian of a cost function is used to identify the parameters of the system. Estimation results are used to calculate the Lyapunov exponents adaptively. Finally, the Lyapunov exponents placement method is used to assign the desired Lyapunov exponents of the closed loop system.
Directory of Open Access Journals (Sweden)
Zejian Zhang
2013-01-01
Full Text Available This paper discusses the stability and stabilization problem for uncertain T-S fuzzy systems with time-varying state and input delays. A new augmented Lyapunov function with an additional triple-integral term and different membership functions of the fuzzy models and fuzzy controllers are introduced to derive the stability criterion, which is less conservative than the existing results. Moreover, a new flexibility design method is also provided. Some numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed method.
Song, Qiankun; Yu, Qinqin; Zhao, Zhenjiang; Liu, Yurong; Alsaadi, Fuad E
2018-07-01
In this paper, the boundedness and robust stability for a class of delayed complex-valued neural networks with interval parameter uncertainties are investigated. By using Homomorphic mapping theorem, Lyapunov method and inequality techniques, sufficient condition to guarantee the boundedness of networks and the existence, uniqueness and global robust stability of equilibrium point is derived for the considered uncertain neural networks. The obtained robust stability criterion is expressed in complex-valued LMI, which can be calculated numerically using YALMIP with solver of SDPT3 in MATLAB. An example with simulations is supplied to show the applicability and advantages of the acquired result. Copyright © 2018 Elsevier Ltd. All rights reserved.
Linear stability analysis of supersonic axisymmetric jets
Directory of Open Access Journals (Sweden)
Zhenhua Wan
2014-01-01
Full Text Available Stabilities of supersonic jets are examined with different velocities, momentum thicknesses, and core temperatures. Amplification rates of instability waves at inlet are evaluated by linear stability theory (LST. It is found that increased velocity and core temperature would increase amplification rates substantially and such influence varies for different azimuthal wavenumbers. The most unstable modes in thin momentum thickness cases usually have higher frequencies and azimuthal wavenumbers. Mode switching is observed for low azimuthal wavenumbers, but it appears merely in high velocity cases. In addition, the results provided by linear parabolized stability equations show that the mean-flow divergence affects the spatial evolution of instability waves greatly. The most amplified instability waves globally are sometimes found to be different from that given by LST.
Exploring the Lyapunov instability properties of high-dimensional atmospheric and climate models
De Cruz, Lesley; Schubert, Sebastian; Demaeyer, Jonathan; Lucarini, Valerio; Vannitsem, Stéphane
2018-05-01
The stability properties of intermediate-order climate models are investigated by computing their Lyapunov exponents (LEs). The two models considered are PUMA (Portable University Model of the Atmosphere), a primitive-equation simple general circulation model, and MAOOAM (Modular class="text">Arbitrary-Order Ocean-Atmosphere Model), a quasi-geostrophic coupled ocean-class="text">atmosphere model on a β-plane. We wish to investigate the effect of the different levels of filtering on the instabilities and dynamics of the atmospheric flows. Moreover, we assess the impact of the oceanic coupling, the dissipation scheme, and the resolution on the spectra of LEs. The PUMA Lyapunov spectrum is computed for two different values of the meridional temperature gradient defining the Newtonian forcing to the temperature field. The increase in the gradient gives rise to a higher baroclinicity and stronger instabilities, corresponding to a larger dimension of the unstable manifold and a larger first LE. The Kaplan-Yorke dimension of the attractor increases as well. The convergence rate of the rate function for the large deviation law of the finite-time Lyapunov exponents (FTLEs) is fast for all exponents, which can be interpreted as resulting from the absence of a clear-cut atmospheric timescale separation in such a model. The MAOOAM spectra show that the dominant atmospheric instability is correctly represented even at low resolutions. However, the dynamics of the central manifold, which is mostly associated with the ocean dynamics, is not fully resolved because of its associated long timescales, even at intermediate orders. As expected, increasing the mechanical atmosphere-ocean coupling coefficient or introducing a turbulent diffusion parametrisation reduces the Kaplan-Yorke dimension and Kolmogorov-Sinai entropy. In all considered configurations, we are not yet in the regime in which one can robustly define large deviation laws describing the statistics of the FTLEs. This
Stability and chaos of LMSER PCA learning algorithm
International Nuclear Information System (INIS)
Lv Jiancheng; Y, Zhang
2007-01-01
LMSER PCA algorithm is a principal components analysis algorithm. It is used to extract principal components on-line from input data. The algorithm has both stability and chaotic dynamic behavior under some conditions. This paper studies the local stability of the LMSER PCA algorithm via a corresponding deterministic discrete time system. Conditions for local stability are derived. The paper also explores the chaotic behavior of this algorithm. It shows that the LMSER PCA algorithm can produce chaos. Waveform plots, Lyapunov exponents and bifurcation diagrams are presented to illustrate the existence of chaotic behavior of this algorithm
Stability analysis of artificial synthetic overweight elements
International Nuclear Information System (INIS)
Zhou Jian
1990-01-01
Stability of artificial synthetic overweight elements has been analysed theoretically using a diagram of nuclear stability. It is indicated that overweight nucleus can be synthesized only when a certain amount of neutrons participate simultaneously in the synthesis. The maximum number of protons in overweight elements is 1002. The proton number of 'extreme overweight' elements of which the neutron star is possibly composed is in the range from 326 to 1002. It is expected that the mass number of the stable overweight elements with proton number 114 is in the range from 299 to 315
An analysis for crack layer stability
Sehanobish, K.; Botsis, J.; Moet, A.; Chudnovsky, A.
1986-01-01
The problem of uncontrolled crack propagation and crack arrest is considered with respect to crack layer (CL) translational stability. CL propagation is determined by the difference between the energy release rate and the amount of energy required for material transformation, and necessary and sufficient conditions for CL instability are derived. CL propagation in polystyrene is studied for two cases. For the case of remotely applied fixed load fatigue, the sufficient condition of instability is shown to be met before the necessary condition, and the necessary condition controls the stability. For the fixed displacement case, neither of the instability conditions are met, and CL propagation remains stable, resulting in crack arrest.
Methods of stability analysis in nonlinear mechanics
International Nuclear Information System (INIS)
Warnock, R.L.; Ruth, R.D.; Gabella, W.; Ecklund, K.
1989-01-01
We review our recent work on methods to study stability in nonlinear mechanics, especially for the problems of particle accelerators, and compare our ideals to those of other authors. We emphasize methods that (1) show promise as practical design tools, (2) are effective when the nonlinearity is large, and (3) have a strong theoretical basis. 24 refs., 2 figs., 2 tabs
Lyapunov exponents a tool to explore complex dynamics
Pikovsky, Arkady
2016-01-01
Lyapunov exponents lie at the heart of chaos theory, and are widely used in studies of complex dynamics. Utilising a pragmatic, physical approach, this self-contained book provides a comprehensive description of the concept. Beginning with the basic properties and numerical methods, it then guides readers through to the most recent advances in applications to complex systems. Practical algorithms are thoroughly reviewed and their performance is discussed, while a broad set of examples illustrate the wide range of potential applications. The description of various numerical and analytical techniques for the computation of Lyapunov exponents offers an extensive array of tools for the characterization of phenomena such as synchronization, weak and global chaos in low and high-dimensional set-ups, and localization. This text equips readers with all the investigative expertise needed to fully explore the dynamical properties of complex systems, making it ideal for both graduate students and experienced researchers...
Quantum synchronization in an optomechanical system based on Lyapunov control.
Li, Wenlin; Li, Chong; Song, Heshan
2016-06-01
We extend the concepts of quantum complete synchronization and phase synchronization, which were proposed in A. Mari et al., Phys. Rev. Lett. 111, 103605 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.103605, to more widespread quantum generalized synchronization. Generalized synchronization can be considered a necessary condition or a more flexible derivative of complete synchronization, and its criterion and synchronization measure are proposed and analyzed in this paper. As examples, we consider two typical generalized synchronizations in a designed optomechanical system. Unlike the effort to construct a special coupling synchronization system, we purposefully design extra control fields based on Lyapunov control theory. We find that the Lyapunov function can adapt to more flexible control objectives, which is more suitable for generalized synchronization control, and the control fields can be achieved simply with a time-variant voltage. Finally, the existence of quantum entanglement in different generalized synchronizations is also discussed.
Lyapunov exponent and criticality in the Hamiltonian mean field model
Filho, L. H. Miranda; Amato, M. A.; Rocha Filho, T. M.
2018-03-01
We investigate the dependence of the largest Lyapunov exponent (LLE) of an N-particle self-gravitating ring model at equilibrium with respect to the number of particles and its dependence on energy. This model has a continuous phase-transition from a ferromagnetic to homogeneous phase, and we numerically confirm with large scale simulations the existence of a critical exponent associated to the LLE, although at variance with the theoretical estimate. The existence of strong chaos in the magnetized state evidenced by a positive Lyapunov exponent is explained by the coupling of individual particle oscillations to the diffusive motion of the center of mass of the system and also results in a change of the scaling of the LLE with the number of particles. We also discuss thoroughly for the model the validity and limits of the approximations made by a geometrical model for their analytic estimate.
Global exponential stability of BAM neural networks with time-varying delays: The discrete-time case
Raja, R.; Marshal Anthoni, S.
2011-02-01
This paper deals with the problem of stability analysis for a class of discrete-time bidirectional associative memory (BAM) neural networks with time-varying delays. By employing the Lyapunov functional and linear matrix inequality (LMI) approach, a new sufficient conditions is proposed for the global exponential stability of discrete-time BAM neural networks. The proposed LMI based results can be easily checked by LMI control toolbox. Moreover, an example is also provided to demonstrate the effectiveness of the proposed method.
Lyapunov exponent and topological entropy plateaus in piecewise linear maps
International Nuclear Information System (INIS)
Botella-Soler, V; Oteo, J A; Ros, J; Glendinning, P
2013-01-01
We consider a two-parameter family of piecewise linear maps in which the moduli of the two slopes take different values. We provide numerical evidence of the existence of some parameter regions in which the Lyapunov exponent and the topological entropy remain constant. Analytical proof of this phenomenon is also given for certain cases. Surprisingly however, the systems with that property are not conjugate as we prove by using kneading theory. (paper)
Lyapunov functions for a dengue disease transmission model
International Nuclear Information System (INIS)
Tewa, Jean Jules; Dimi, Jean Luc; Bowong, Samuel
2009-01-01
In this paper, we study a model for the dynamics of dengue fever when only one type of virus is present. For this model, Lyapunov functions are used to show that when the basic reproduction ratio is less than or equal to one, the disease-free equilibrium is globally asymptotically stable, and when it is greater than one there is an endemic equilibrium which is also globally asymptotically stable.
Lyapunov functions for a dengue disease transmission model
Energy Technology Data Exchange (ETDEWEB)
Tewa, Jean Jules [Department of Mathematics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde (Cameroon)], E-mail: tewa@univ-metz.fr; Dimi, Jean Luc [Department of Mathematics, Faculty of Science, University Marien Ngouabi, P.O. Box 69, Brazzaville (Congo, The Democratic Republic of the)], E-mail: jldimi@yahoo.fr; Bowong, Samuel [Department of Mathematics and Computer Science, Faculty of Science, University of Douala, P.O. Box 24157, Douala (Cameroon)], E-mail: samuelbowong@yahoo.fr
2009-01-30
In this paper, we study a model for the dynamics of dengue fever when only one type of virus is present. For this model, Lyapunov functions are used to show that when the basic reproduction ratio is less than or equal to one, the disease-free equilibrium is globally asymptotically stable, and when it is greater than one there is an endemic equilibrium which is also globally asymptotically stable.
Dynamic analysis of stochastic bidirectional associative memory neural networks with delays
International Nuclear Information System (INIS)
Zhao Hongyong; Ding Nan
2007-01-01
In this paper, stochastic bidirectional associative memory neural networks model with delays is considered. By constructing Lyapunov functionals, and using stochastic analysis method and inequality technique, we give some sufficient criteria ensuring almost sure exponential stability, pth exponential stability and mean value exponential stability. The obtained criteria can be used as theoretic guidance to stabilize neural networks in practical applications when stochastic noise is taken into consideration
Modeling, Stability Analysis and Active Stabilization of Multiple DC-Microgrids Clusters
DEFF Research Database (Denmark)
Shafiee, Qobad; Dragicevic, Tomislav; Vasquez, Juan Carlos
2014-01-01
), and more especially during interconnection with other MGs, creating dc MG clusters. This paper develops a small signal model for dc MGs from the control point of view, in order to study stability analysis and investigate effects of CPLs and line impedances between the MGs on stability of these systems....... This model can be also used to synthesis and study dynamics of control loops in dc MGs and also dc MG clusters. An active stabilization method is proposed to be implemented as a dc active power filter (APF) inside the MGs in order to not only increase damping of dc MGs at the presence of CPLs but also...... to improve their stability while connecting to the other MGs. Simulation results are provided to evaluate the developed models and demonstrate the effectiveness of proposed active stabilization technique....
Mathematical modelling and linear stability analysis of laser fusion cutting
International Nuclear Information System (INIS)
Hermanns, Torsten; Schulz, Wolfgang; Vossen, Georg; Thombansen, Ulrich
2016-01-01
A model for laser fusion cutting is presented and investigated by linear stability analysis in order to study the tendency for dynamic behavior and subsequent ripple formation. The result is a so called stability function that describes the correlation of the setting values of the process and the process’ amount of dynamic behavior.
Linear and nonlinear stability analysis, associated to experimental fast reactors
International Nuclear Information System (INIS)
Amorim, E.S. do; Moura Neto, C. de; Rosa, M.A.P.
1980-07-01
Phenomena associated to the physics of fast neutrons were analysed by linear and nonlinear Kinetics with arbitrary feedback. The theoretical foundations of linear kinetics and transfer functions aiming at the analysis of fast reactors stability, are established. These stability conditions were analitically proposed and investigated by digital and analogic programs. (E.G.) [pt
Mathematical modelling and linear stability analysis of laser fusion cutting
Energy Technology Data Exchange (ETDEWEB)
Hermanns, Torsten; Schulz, Wolfgang [RWTH Aachen University, Chair for Nonlinear Dynamics, Steinbachstr. 15, 52047 Aachen (Germany); Vossen, Georg [Niederrhein University of Applied Sciences, Chair for Applied Mathematics and Numerical Simulations, Reinarzstr.. 49, 47805 Krefeld (Germany); Thombansen, Ulrich [RWTH Aachen University, Chair for Laser Technology, Steinbachstr. 15, 52047 Aachen (Germany)
2016-06-08
A model for laser fusion cutting is presented and investigated by linear stability analysis in order to study the tendency for dynamic behavior and subsequent ripple formation. The result is a so called stability function that describes the correlation of the setting values of the process and the process’ amount of dynamic behavior.
Stability analysis in tachyonic potential chameleon cosmology
International Nuclear Information System (INIS)
Farajollahi, H.; Salehi, A.; Tayebi, F.; Ravanpak, A.
2011-01-01
We study general properties of attractors for tachyonic potential chameleon scalar-field model which possess cosmological scaling solutions. An analytic formulation is given to obtain fixed points with a discussion on their stability. The model predicts a dynamical equation of state parameter with phantom crossing behavior for an accelerating universe. We constrain the parameters of the model by best fitting with the recent data-sets from supernovae and simulated data points for redshift drift experiment generated by Monte Carlo simulations
Stability analysis in tachyonic potential chameleon cosmology
Energy Technology Data Exchange (ETDEWEB)
Farajollahi, H.; Salehi, A.; Tayebi, F.; Ravanpak, A., E-mail: hosseinf@guilan.ac.ir, E-mail: a.salehi@guilan.ac.ir, E-mail: ftayebi@guilan.ac.ir, E-mail: aravanpak@guilan.ac.ir [Department of Physics, University of Guilan, Rasht (Iran, Islamic Republic of)
2011-05-01
We study general properties of attractors for tachyonic potential chameleon scalar-field model which possess cosmological scaling solutions. An analytic formulation is given to obtain fixed points with a discussion on their stability. The model predicts a dynamical equation of state parameter with phantom crossing behavior for an accelerating universe. We constrain the parameters of the model by best fitting with the recent data-sets from supernovae and simulated data points for redshift drift experiment generated by Monte Carlo simulations.
Stability analysis for downflow in heated channels
International Nuclear Information System (INIS)
Sampaio, P.A.B. de.
1985-01-01
Stability and flow distribution are analysed for downflow in heated channels. It is shown that at low flow rates instabilities associated with the buoyancy forces may appear. A computer code in FORTRAN language to determine downflow distribution among n heated channels is presented. The model used to calculate downflow distribution and the onset of instability is compared with experiments performed in a test section with two parallel channels. (Author) [pt
MHD stability analysis of ELMs in MAST
International Nuclear Information System (INIS)
Saarelma, S; Hender, T C; Kirk, A; Meyer, H; Wilson, H R; Team, MAST
2007-01-01
In this paper, edge stability analyses of the MAST tokamak plasmas are presented. The analyses show that the experimental equilibrium prior to an edge localized mode (ELM) is unstable against very narrow peeling modes with low growth rate. When the edge pressure gradient becomes steeper, wider peeling-ballooning modes with larger growth rate become unstable. These modes are the likely triggers of ELMs. In the analyses the required pressure increase for destabilization is sensitive to how the X-point is modelled in the equilibrium reconstruction. A 'sharp' X-point approximation is more stable against the peeling-ballooning modes than a 'round' one. An experimental ELM-free single null plasma is significantly more stable against the peeling-ballooning modes than the double null plasma, but this is unlikely to be directly due to the single null geometry but rather due to the different plasma profiles. Sheared toroidal rotation is able to stabilize the peeling-ballooning modes. This suggests the following model for the ELM triggering: the rotation shear keeps the edge stable until the pressure gradient has sufficiently exceeded the stability boundary for the static plasma. When the mode becomes unstable, it starts to grow, ties the flux surfaces together and flattens the rotation profile. This further destabilizes the edge plasma leading to an ELM crash
Stability analysis of impulsive functional differential equations
Stamova, Ivanka
2009-01-01
This book is devoted to impulsive functional differential equations which are a natural generalization of impulsive ordinary differential equations (without delay) and of functional differential equations (without impulses). At the present time the qualitative theory of such equationsis under rapid development. After a presentation of the fundamental theory of existence, uniqueness and continuability of solutions, a systematic development of stability theory for that class of problems is given which makes the book unique. It addresses to a wide audience such as mathematicians, applied research
Stability analysis of host dynamics for hiv
Geetha, V.; Balamuralitharan, S.
2018-04-01
The phenomenon of disease modeling can be easily accomplished through mathematical framework. In this paper the transmission of disease in human is represented mathematically as a nonlinear system. We think about the components of the Human Immunodeficiency Virus (HIV) among the beginning periods of illness. Throughout this paper we have determined those logical representation of a three-compartmental HIV demonstrate for their stability evaluation. We tend to likewise explore the stimulating behavior of the model and acquire those Steady states for the disease-free and the endemic agreement. The framework can be evaluated by reproduction number R0. We additionally clarify the numerical recreation and their outcomes.
Advances in power system modelling, control and stability analysis
Milano, Federico
2016-01-01
Advances in Power System Modelling, Control and Stability Analysis captures the variety of new methodologies and technologies that are changing the way modern electric power systems are modelled, simulated and operated.
Genotype x environment interaction and stability analysis for yield ...
African Journals Online (AJOL)
etc
2015-05-06
. Combined analysis of variance (ANOVA) for yield and yield components revealed highly significant .... yield stability among varieties, multi-location trials with ... Mean grain yield (kg/ha) of 17 Kabuli-type chickpea genotypes ...
stability analysis of ssss thin rectangular plate using multi
African Journals Online (AJOL)
user
The stability analysis of all four edges simply supported (SSSS) thin ... average percentage difference of K – values from two previous works and the present study when compared with ... freedom eigen value problem of the elastic buckling of.
Stability Analysis of a Reaction-Diffusion System Modeling Atherogenesis
Ibragimov, Akif; Ritter, Laura; Walton, Jay R.
2010-01-01
This paper presents a linear, asymptotic stability analysis for a reaction-diffusionconvection system modeling atherogenesis, the initiation of atherosclerosis, as an inflammatory instability. Motivated by the disease paradigm articulated by Ross
Yield stability analysis of pearl millet hybrids in Nigeria
African Journals Online (AJOL)
hope&shola
2006-02-02
.] was ... Genotype x environment interaction was observed, a large component of which was accounted ... The importance of evaluating many potential genotypes .... Pooled analysis of variance for stability of grain yield (t/ha).
Liu, Hongjian; Wang, Zidong; Shen, Bo; Huang, Tingwen; Alsaadi, Fuad E
2018-06-01
This paper is concerned with the globally exponential stability problem for a class of discrete-time stochastic memristive neural networks (DSMNNs) with both leakage delays as well as probabilistic time-varying delays. For the probabilistic delays, a sequence of Bernoulli distributed random variables is utilized to determine within which intervals the time-varying delays fall at certain time instant. The sector-bounded activation function is considered in the addressed DSMNN. By taking into account the state-dependent characteristics of the network parameters and choosing an appropriate Lyapunov-Krasovskii functional, some sufficient conditions are established under which the underlying DSMNN is globally exponentially stable in the mean square. The derived conditions are made dependent on both the leakage and the probabilistic delays, and are therefore less conservative than the traditional delay-independent criteria. A simulation example is given to show the effectiveness of the proposed stability criterion. Copyright © 2018 Elsevier Ltd. All rights reserved.
Stability Analysis and H∞ Model Reduction for Switched Discrete-Time Time-Delay Systems
Directory of Open Access Journals (Sweden)
Zheng-Fan Liu
2014-01-01
Full Text Available This paper is concerned with the problem of exponential stability and H∞ model reduction of a class of switched discrete-time systems with state time-varying delay. Some subsystems can be unstable. Based on the average dwell time technique and Lyapunov-Krasovskii functional (LKF approach, sufficient conditions for exponential stability with H∞ performance of such systems are derived in terms of linear matrix inequalities (LMIs. For the high-order systems, sufficient conditions for the existence of reduced-order model are derived in terms of LMIs. Moreover, the error system is guaranteed to be exponentially stable and an H∞ error performance is guaranteed. Numerical examples are also given to demonstrate the effectiveness and reduced conservatism of the obtained results.
International Nuclear Information System (INIS)
Cao Jinde; Ho, Daniel W.C.
2005-01-01
In this paper, global asymptotic stability is discussed for neural networks with time-varying delay. Several new criteria in matrix inequality form are given to ascertain the uniqueness and global asymptotic stability of equilibrium point for neural networks with time-varying delay based on Lyapunov method and Linear Matrix Inequality (LMI) technique. The proposed LMI approach has the advantage of considering the difference of neuronal excitatory and inhibitory efforts, which is also computationally efficient as it can be solved numerically using recently developed interior-point algorithm. In addition, the proposed results generalize and improve previous works. The obtained criteria also combine two existing conditions into one generalized condition in matrix form. An illustrative example is also given to demonstrate the effectiveness of the proposed results
Stabilization analysis of Euler-Bernoulli beam equation with locally distributed disturbance
Directory of Open Access Journals (Sweden)
Pengcheng HAN
2017-12-01
Full Text Available In order to enrich the system stability theory of the control theories, taking Euler-Bernoulli beam equation as the research subject, the stability of Euler-Bernoulli beam equation with locally distributed disturbance is studied. A feedback controller based on output is designed to reduce the effects of the disturbances. The well-posedness of the nonlinear closed-loop system is investigated by the theory of maximal monotone operator, namely the existence and uniqueness of solutions for the closed-loop system. An appropriate state space is established, an appropriate inner product is defined, and a non-linear operator satisfying this state space is defined. Then, the system is transformed into the form of evolution equation. Based on this, the existence and uniqueness of solutions for the closed-loop system are proved. The asymptotic stability of the system is studied by constructing an appropriate Lyapunov function, which proves the asymptotic stability of the closed-loop system. The result shows that designing proper anti-interference controller is the foundation of investigating the system stability, and the research of the stability of Euler-bernoulli beam equation with locally distributed disturbance can prove the asymptotic stability of the system. This method can be extended to study the other equations such as wave equation, Timoshenko beam equation, Schrodinger equation, etc.
Lyapunov-based distributed control of the safety-factor profile in a tokamak plasma
International Nuclear Information System (INIS)
Bribiesca Argomedo, Federico; Witrant, Emmanuel; Prieur, Christophe; Brémond, Sylvain; Nouailletas, Rémy; Artaud, Jean-François
2013-01-01
A real-time model-based controller is developed for the tracking of the distributed safety-factor profile in a tokamak plasma. Using relevant physical models and simplifying assumptions, theoretical stability and robustness guarantees were obtained using a Lyapunov function. This approach considers the couplings between the poloidal flux diffusion equation, the time-varying temperature profiles and an independent total plasma current control. The actuator chosen for the safety-factor profile tracking is the lower hybrid current drive, although the results presented can be easily extended to any non-inductive current source. The performance and robustness of the proposed control law is evaluated with a physics-oriented simulation code on Tore Supra experimental test cases. (paper)
Detection of the onset of numerical chaotic instabilities by lyapunov exponents
Directory of Open Access Journals (Sweden)
Alicia Serfaty De Markus
2001-01-01
Full Text Available It is commonly found in the fixed-step numerical integration of nonlinear differential equations that the size of the integration step is opposite related to the numerical stability of the scheme and to the speed of computation. We present a procedure that establishes a criterion to select the largest possible step size before the onset of chaotic numerical instabilities, based upon the observation that computational chaos does not occur in a smooth, continuous way, but rather abruptly, as detected by examining the largest Lyapunov exponent as a function of the step size. For completeness, examination of the bifurcation diagrams with the step reveals the complexity imposed by the algorithmic discretization, showing the robustness of a scheme to numerical instabilities, illustrated here for explicit and implicit Euler schemes. An example of numerical suppression of chaos is also provided.
Lyapunov-based decentralized control of a rougher flotation phenomenological simulator
International Nuclear Information System (INIS)
Benaskeur, A.R.; Desbiens, A.
1999-01-01
In this paper a new approach to decentralized control of linear two-by-two plants is presented. The novelty lies in the use of a modified control function of Lyapunov and the introduction of an integral action in each manipulated variable, to ensure zero tracking errors. An appropriate choice of the regulated errors, allows the elimination of the cross terms in the obtained backstepping-based multivariable controller. It will be proven that if the H ∞ -norm of the plant interaction quotient is less than one, the centralized controller can be split up into two independent scalar output feedback regulators. Under these conditions, the global stability and zero tracking errors will still be guaranteed. The developed scheme is successfully applied to the control of a rougher flotation phenomenological simulator. (author)
Finite-time analysis of global projective synchronization on coloured ...
Indian Academy of Sciences (India)
A novel finite-time analysis is given to investigate the global projective synchronization on coloured networks. Some less conservative conditions are derived by utilizing finite-time control techniques and Lyapunov stability theorem. In addition, two illustrative numerical simulations are provided to verify the effectiveness of ...
Effect of parameter calculation in direct estimation of the Lyapunov exponent in short time series
Directory of Open Access Journals (Sweden)
A. M. López Jiménez
2002-01-01
Full Text Available The literature about non-linear dynamics offers a few recommendations, which sometimes are divergent, about the criteria to be used in order to select the optimal calculus parameters in the estimation of Lyapunov exponents by direct methods. These few recommendations are circumscribed to the analysis of chaotic systems. We have found no recommendation for the estimation of λ starting from the time series of classic systems. The reason for this is the interest in distinguishing variability due to a chaotic behavior of determinist dynamic systems of variability caused by white noise or linear stochastic processes, and less in the identification of non-linear terms from the analysis of time series. In this study we have centered in the dependence of the Lyapunov exponent, obtained by means of direct estimation, of the initial distance and the time evolution. We have used generated series of chaotic systems and generated series of classic systems with varying complexity. To generate the series we have used the logistic map.
Single-shell tank interim stabilization risk analysis
International Nuclear Information System (INIS)
Basche, A.D.
1998-01-01
The purpose of the Single-Shell Tank (SST) Interim Stabilization Risk Analysis is to provide a cost and schedule risk analysis of HNF-2358, Rev. 1, Single-Shell Tank Interim Stabilization Project Plan (Project Plan) (Ross et al. 1998). The analysis compares the required cost profile by fiscal year (Section 4.2) and revised schedule completion date (Section 4.5) to the Project Plan. The analysis also evaluates the executability of the Project Plan and recommends a path forward for risk mitigation
Nastac, Gabriel; Labahn, Jeffrey W.; Magri, Luca; Ihme, Matthias
2017-09-01
Metrics used to assess the quality of large-eddy simulations commonly rely on a statistical assessment of the solution. While these metrics are valuable, a dynamic measure is desirable to further characterize the ability of a numerical simulation for capturing dynamic processes inherent in turbulent flows. To address this issue, a dynamic metric based on the Lyapunov exponent is proposed which assesses the growth rate of the solution separation. This metric is applied to two turbulent flow configurations: forced homogeneous isotropic turbulence and a turbulent jet diffusion flame. First, it is shown that, despite the direct numerical simulation (DNS) and large-eddy simulation (LES) being high-dimensional dynamical systems with O (107) degrees of freedom, the separation growth rate qualitatively behaves like a lower-dimensional dynamical system, in which the dimension of the Lyapunov system is substantially smaller than the discretized dynamical system. Second, a grid refinement analysis of each configuration demonstrates that as the LES filter width approaches the smallest scales of the system the Lyapunov exponent asymptotically approaches a plateau. Third, a small perturbation is superimposed onto the initial conditions of each configuration, and the Lyapunov exponent is used to estimate the time required for divergence, thereby providing a direct assessment of the predictability time of simulations. By comparing inert and reacting flows, it is shown that combustion increases the predictability of the turbulent simulation as a result of the dilatation and increased viscosity by heat release. The predictability time is found to scale with the integral time scale in both the reacting and inert jet flows. Fourth, an analysis of the local Lyapunov exponent is performed to demonstrate that this metric can also determine flow-dependent properties, such as regions that are sensitive to small perturbations or conditions of large turbulence within the flow field. Finally
Continuation of probability density functions using a generalized Lyapunov approach
Energy Technology Data Exchange (ETDEWEB)
Baars, S., E-mail: s.baars@rug.nl [Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, P.O. Box 407, 9700 AK Groningen (Netherlands); Viebahn, J.P., E-mail: viebahn@cwi.nl [Centrum Wiskunde & Informatica (CWI), P.O. Box 94079, 1090 GB, Amsterdam (Netherlands); Mulder, T.E., E-mail: t.e.mulder@uu.nl [Institute for Marine and Atmospheric research Utrecht, Department of Physics and Astronomy, Utrecht University, Princetonplein 5, 3584 CC Utrecht (Netherlands); Kuehn, C., E-mail: ckuehn@ma.tum.de [Technical University of Munich, Faculty of Mathematics, Boltzmannstr. 3, 85748 Garching bei München (Germany); Wubs, F.W., E-mail: f.w.wubs@rug.nl [Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, P.O. Box 407, 9700 AK Groningen (Netherlands); Dijkstra, H.A., E-mail: h.a.dijkstra@uu.nl [Institute for Marine and Atmospheric research Utrecht, Department of Physics and Astronomy, Utrecht University, Princetonplein 5, 3584 CC Utrecht (Netherlands); School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY (United States)
2017-05-01
Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining probability density functions of systems of stochastic partial differential equations near fixed points, under a small noise approximation. Key innovation is the efficient solution of a generalized Lyapunov equation using an iterative method involving low-rank approximations. We apply and illustrate the capabilities of the method using a problem in physical oceanography, i.e. the occurrence of multiple steady states of the Atlantic Ocean circulation.
Abstraction of continuous dynamical systems utilizing lyapunov functions
DEFF Research Database (Denmark)
Sloth, Christoffer; Wisniewski, Rafael
2010-01-01
This paper considers the development of a method for abstracting continuous dynamical systems by timed automata. The method is based on partitioning the state space of dynamical systems with invariant sets, which form cells representing locations of the timed automata. To enable verification...... of the dynamical system based on the abstraction, conditions for obtaining sound, complete, and refinable abstractions are set up. It is proposed to partition the state space utilizing sub-level sets of Lyapunov functions, since they are positive invariant sets. The existence of sound abstractions for Morse......-Smale systems and complete and refinable abstractions for linear systems are shown....
Stability analysis of a heated channel cooled by supercritical water
International Nuclear Information System (INIS)
Magni, M. C.; Delmastro, D. F; Marcel, C. P
2009-01-01
A simple model to study thermal-hydraulic stability of a heated cannel under supercritical conditions is presented. Single cannel stability analysis for the SCWR (Supercritical Water Cooled Reactor) design was performed. The drastic change of fluid density in the reactor core of a SCWR may induce DWO (Density Wave Oscillations) similar to those observed in BWRs. Due to the similarities between subcritical and supercritical systems we may treat the supercritical fluid as a pseudo two-phase system. Thus, we may extend the modeling approach often used for boiling flow stability analysis to supercritical pressure operation conditions. The model developed in this work take into account three regions: a heavy fluid region, similar to an incompressible liquid; a zone where a heavy fluid and a light fluid coexist, similar to two-phase mixture; and a light fluid region which behaves like superheated steam. It was used the homogeneous equilibrium model (HEM) for the pseudo boiling zone, and the ideal gas model for the pseudo superheated steam zone. System stability maps were obtained using linear stability analysis in the frequency domain. Two possible instability mechanisms are observed: DWO and excursive Ledinegg instabilities. Also, a sensitivity analysis showed that frictions in pseudo superheated steam zone, together with acceleration effect, are the most destabilizing effects. On the other hand, frictions in pseudo liquid zone are the most important stabilizing effect. [es
Stability analysis of the Ghana Research Reactor-1 (GHARR-1)
International Nuclear Information System (INIS)
Della, R.; Alhassan, E.; Adoo, N.A.; Bansah, C.Y.; Nyarko, B.J.B.; Akaho, E.H.K.
2013-01-01
Highlights: • We developed a theoretical model to study the stability of the Ghana Research Reactor-1. • The neutronics transfer function was described by the point kinetics model for a single group of delayed neutrons. • The thermal hydraulics transfer function was based on the modified lumped parameter concept. • A computer code, RESA (REactor Stability Analysis) was developed. • Results show that the closed-loop transfer function was stable and well damped for variable operating power levels. - Abstract: A theoretical model has been developed to study the stability of the Ghana Research Reactor one (GHARR-1). The closed-loop transfer function of GHARR-1 was established based on the model, which involved the neutronics and the thermal hydraulics transfer functions. The reactor kinetics was described by the point kinetics model for a single group of delayed neutrons, whilst the thermal hydraulics transfer function was based on the modified lumped parameter concept. The inherent internal feedback effect due to the fuel and the coolant was represented by the fuel temperature coefficient and the moderator temperature coefficient respectively. A computer code, RESA (REactor Stability Analysis), entirely in Java was developed based on the model for systems analysis. Stability analysis of the open-loop transfer function of GHARR-1 based on the Nyquist criterion and Bode diagrams using RESA, has shown that the closed-loop transfer function was marginally stable for variable operating power levels. The relative stability margins of GHARR-1 were also identified
Solar Dynamic Power System Stability Analysis and Control
Momoh, James A.; Wang, Yanchun
1996-01-01
The objective of this research is to conduct dynamic analysis, control design, and control performance test of solar power system. Solar power system consists of generation system and distribution network system. A bench mark system is used in this research, which includes a generator with excitation system and governor, an ac/dc converter, six DDCU's and forty-eight loads. A detailed model is used for modeling generator. Excitation system is represented by a third order model. DDCU is represented by a seventh order system. The load is modeled by the combination of constant power and constant impedance. Eigen-analysis and eigen-sensitivity analysis are used for system dynamic analysis. The effects of excitation system, governor, ac/dc converter control, and the type of load on system stability are discussed. In order to improve system transient stability, nonlinear ac/dc converter control is introduced. The direct linearization method is used for control design. The dynamic analysis results show that these controls affect system stability in different ways. The parameter coordination of controllers are recommended based on the dynamic analysis. It is concluded from the present studies that system stability is improved by the coordination of control parameters and the nonlinear ac/dc converter control stabilize system oscillation caused by the load change and system fault efficiently.
Linear stability analysis in a solid-propellant rocket motor
Energy Technology Data Exchange (ETDEWEB)
Kim, K.M.; Kang, K.T.; Yoon, J.K. [Agency for Defense Development, Taejon (Korea, Republic of)
1995-10-01
Combustion instability in solid-propellant rocket motors depends on the balance between acoustic energy gains and losses of the system. The objective of this paper is to demonstrate the capability of the program which predicts the standard longitudinal stability using acoustic modes based on linear stability analysis and T-burner test results of propellants. Commercial ANSYS 5.0A program can be used to calculate the acoustic characteristic of a rocket motor. The linear stability prediction was compared with the static firing test results of rocket motors. (author). 11 refs., 17 figs.
Contributions to fuzzy polynomial techniques for stability analysis and control
Pitarch Pérez, José Luis
2014-01-01
The present thesis employs fuzzy-polynomial control techniques in order to improve the stability analysis and control of nonlinear systems. Initially, it reviews the more extended techniques in the field of Takagi-Sugeno fuzzy systems, such as the more relevant results about polynomial and fuzzy polynomial systems. The basic framework uses fuzzy polynomial models by Taylor series and sum-of-squares techniques (semidefinite programming) in order to obtain stability guarantees...
Stability Analysis for Operation of DG Units in Smart Grids
DEFF Research Database (Denmark)
Pouresmaeil, Edris; Shaker, Hamid Reza; Mehrasa, Majid
2015-01-01
This paper presents a multifunction control strategy for the stable operation of Distributed Generation (DG) units during grid integration. The proposed control model is based on Direct Lyapunov Control (DLC) theory and provides a stable region for the appropriate operation of DG units during grid....... Application of this concept can guarantee to reduce the stress on the grid during the energy demand peak. Simulation results are presented to demonstrate the proficiency and performance of the proposed DLC technique in DG technology....
Non linear stability analysis of parallel channels with natural circulation
Energy Technology Data Exchange (ETDEWEB)
Mishra, Ashish Mani; Singh, Suneet, E-mail: suneet.singh@iitb.ac.in
2016-12-01
Highlights: • Nonlinear instabilities in natural circulation loop are studied. • Generalized Hopf points, Sub and Supercritical Hopf bifurcations are identified. • Bogdanov–Taken Point (BT Point) is observed by nonlinear stability analysis. • Effect of parameters on stability of system is studied. - Abstract: Linear stability analysis of two-phase flow in natural circulation loop is quite extensively studied by many researchers in past few years. It can be noted that linear stability analysis is limited to the small perturbations only. It is pointed out that such systems typically undergo Hopf bifurcation. If the Hopf bifurcation is subcritical, then for relatively large perturbation, the system has unstable limit cycles in the (linearly) stable region in the parameter space. Hence, linear stability analysis capturing only infinitesimally small perturbations is not sufficient. In this paper, bifurcation analysis is carried out to capture the non-linear instability of the dynamical system and both subcritical and supercritical bifurcations are observed. The regions in the parameter space for which subcritical and supercritical bifurcations exist are identified. These regions are verified by numerical simulation of the time-dependent, nonlinear ODEs for the selected points in the operating parameter space using MATLAB ODE solver.
Stability and Hopf bifurcation analysis of a new system
International Nuclear Information System (INIS)
Huang Kuifei; Yang Qigui
2009-01-01
In this paper, a new chaotic system is introduced. The system contains special cases as the modified Lorenz system and conjugate Chen system. Some subtle characteristics of stability and Hopf bifurcation of the new chaotic system are thoroughly investigated by rigorous mathematical analysis and symbolic computations. Meanwhile, some numerical simulations for justifying the theoretical analysis are also presented.
Delay-slope-dependent stability results of recurrent neural networks.
Li, Tao; Zheng, Wei Xing; Lin, Chong
2011-12-01
By using the fact that the neuron activation functions are sector bounded and nondecreasing, this brief presents a new method, named the delay-slope-dependent method, for stability analysis of a class of recurrent neural networks with time-varying delays. This method includes more information on the slope of neuron activation functions and fewer matrix variables in the constructed Lyapunov-Krasovskii functional. Then some improved delay-dependent stability criteria with less computational burden and conservatism are obtained. Numerical examples are given to illustrate the effectiveness and the benefits of the proposed method.
Periodic oscillation and exponential stability of delayed CNNs
Cao, Jinde
2000-05-01
Both the global exponential stability and the periodic oscillation of a class of delayed cellular neural networks (DCNNs) is further studied in this Letter. By applying some new analysis techniques and constructing suitable Lyapunov functionals, some simple and new sufficient conditions are given ensuring global exponential stability and the existence of periodic oscillatory solution of DCNNs. These conditions can be applied to design globally exponentially stable DCNNs and periodic oscillatory DCNNs and easily checked in practice by simple algebraic methods. These play an important role in the design and applications of DCNNs.
On exponential stability and periodic solutions of CNNs with delays
Cao, Jinde
2000-03-01
In this Letter, the author analyses further problems of global exponential stability and the existence of periodic solutions of cellular neural networks with delays (DCNNs). Some simple and new sufficient conditions are given ensuring global exponential stability and the existence of periodic solutions of DCNNs by applying some new analysis techniques and constructing suitable Lyapunov functionals. These conditions have important leading significance in the design and applications of globally stable DCNNs and periodic oscillatory DCNNs and are weaker than those in the earlier works [Phys. Rev. E 60 (1999) 3244], [J. Comput. Syst. Sci. 59 (1999)].
International Nuclear Information System (INIS)
Fernandez, P.; Wang, Q.
2017-01-01
We investigate the impact of numerical discretization on the Lyapunov spectrum of separated flow simulations. The two-dimensional chaotic flow around the NACA 0012 airfoil at a low Reynolds number and large angle of attack is considered to that end. Time, space and accuracy-order refinement studies are performed to examine each of these effects separately. Numerical results show that the time discretization has a small impact on the dynamics of the system, whereas the spatial discretization can dramatically change them. Also, the finite-time Lyapunov exponents associated to unstable modes are shown to be positively skewed, and quasi-homoclinic tangencies are observed in the attractor of the system. The implications of these results on flow physics and sensitivity analysis of chaotic flows are discussed.
Fernandez, P.; Wang, Q.
2017-12-01
We investigate the impact of numerical discretization on the Lyapunov spectrum of separated flow simulations. The two-dimensional chaotic flow around the NACA 0012 airfoil at a low Reynolds number and large angle of attack is considered to that end. Time, space and accuracy-order refinement studies are performed to examine each of these effects separately. Numerical results show that the time discretization has a small impact on the dynamics of the system, whereas the spatial discretization can dramatically change them. Also, the finite-time Lyapunov exponents associated to unstable modes are shown to be positively skewed, and quasi-homoclinic tangencies are observed in the attractor of the system. The implications of these results on flow physics and sensitivity analysis of chaotic flows are discussed.
Stability and Control of Large-Scale Dynamical Systems A Vector Dissipative Systems Approach
Haddad, Wassim M
2011-01-01
Modern complex large-scale dynamical systems exist in virtually every aspect of science and engineering, and are associated with a wide variety of physical, technological, environmental, and social phenomena, including aerospace, power, communications, and network systems, to name just a few. This book develops a general stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems, and presents the most complete treatment on vector Lyapunov function methods, vector dissipativity theory, and decentralized control architectures. Large-scale dynami
International Nuclear Information System (INIS)
Ge Zhengming; Chang Chingming
2009-01-01
By applying pure error dynamics and elaborate nondiagonal Lyapunov function, the nonlinear generalized synchronization is studied in this paper. Instead of current mixed error dynamics in which master state variables and slave state variables are presented, the nonlinear generalized synchronization can be obtained by pure error dynamics without auxiliary numerical simulation. The elaborate nondiagonal Lyapunov function is applied rather than current monotonous square sum Lyapunov function deeply weakening the powerfulness of Lyapunov direct method. Both autonomous and nonautonomous double Mathieu systems are used as examples with numerical simulations.
Pyrosequencing Based Microbial Community Analysis of Stabilized Mine Soils
Park, J. E.; Lee, B. T.; Son, A.
2015-12-01
Heavy metals leached from exhausted mines have been causing severe environmental problems in nearby soils and groundwater. Environmental mitigation was performed based on the heavy metal stabilization using Calcite and steel slag in Korea. Since the soil stabilization only temporarily immobilizes the contaminants to soil matrix, the potential risk of re-leaching heavy metal still exists. Therefore the follow-up management of stabilized soils and the corresponding evaluation methods are required to avoid the consequent contamination from the stabilized soils. In this study, microbial community analysis using pyrosequencing was performed for assessing the potential leaching of the stabilized soils. As a result of rarefaction curve and Chao1 and Shannon indices, the stabilized soil has shown lower richness and diversity as compared to non-contaminated negative control. At the phyla level, as the degree of contamination increases, most of phyla decreased with only exception of increased proteobacteria. Among proteobacteria, gamma-proteobacteria increased against the heavy metal contamination. At the species level, Methylobacter tundripaludum of gamma-proteobacteria showed the highest relative portion of microbial community, indicating that methanotrophs may play an important role in either solubilization or immobilization of heavy metals in stabilized soils.
Stability Analysis for a Multi-Camera Photogrammetric System
Directory of Open Access Journals (Sweden)
Ayman Habib
2014-08-01
Full Text Available Consumer-grade digital cameras suffer from geometrical instability that may cause problems when used in photogrammetric applications. This paper provides a comprehensive review of this issue of interior orientation parameter variation over time, it explains the common ways used for coping with the issue, and describes the existing methods for performing stability analysis for a single camera. The paper then points out the lack of coverage of stability analysis for multi-camera systems, suggests a modification of the collinearity model to be used for the calibration of an entire photogrammetric system, and proposes three methods for system stability analysis. The proposed methods explore the impact of the changes in interior orientation and relative orientation/mounting parameters on the reconstruction process. Rather than relying on ground truth in real datasets to check the system calibration stability, the proposed methods are simulation-based. Experiment results are shown, where a multi-camera photogrammetric system was calibrated three times, and stability analysis was performed on the system calibration parameters from the three sessions. The proposed simulation-based methods provided results that were compatible with a real-data based approach for evaluating the impact of changes in the system calibration parameters on the three-dimensional reconstruction.
Probabilistic approaches for geotechnical site characterization and slope stability analysis
Cao, Zijun; Li, Dianqing
2017-01-01
This is the first book to revisit geotechnical site characterization from a probabilistic point of view and provide rational tools to probabilistically characterize geotechnical properties and underground stratigraphy using limited information obtained from a specific site. This book not only provides new probabilistic approaches for geotechnical site characterization and slope stability analysis, but also tackles the difficulties in practical implementation of these approaches. In addition, this book also develops efficient Monte Carlo simulation approaches for slope stability analysis and implements these approaches in a commonly available spreadsheet environment. These approaches and the software package are readily available to geotechnical practitioners and alleviate them from reliability computational algorithms. The readers will find useful information for a non-specialist to determine project-specific statistics of geotechnical properties and to perform probabilistic analysis of slope stability.
Static Voltage Stability Analysis by Using SVM and Neural Network
Directory of Open Access Journals (Sweden)
Mehdi Hajian
2013-01-01
Full Text Available Voltage stability is an important problem in power system networks. In this paper, in terms of static voltage stability, and application of Neural Networks (NN and Supported Vector Machine (SVM for estimating of voltage stability margin (VSM and predicting of voltage collapse has been investigated. This paper considers voltage stability in power system in two parts. The first part calculates static voltage stability margin by Radial Basis Function Neural Network (RBFNN. The advantage of the used method is high accuracy in online detecting the VSM. Whereas the second one, voltage collapse analysis of power system is performed by Probabilistic Neural Network (PNN and SVM. The obtained results in this paper indicate, that time and number of training samples of SVM, are less than NN. In this paper, a new model of training samples for detection system, using the normal distribution load curve at each load feeder, has been used. Voltage stability analysis is estimated by well-know L and VSM indexes. To demonstrate the validity of the proposed methods, IEEE 14 bus grid and the actual network of Yazd Province are used.
Global robust exponential stability analysis for interval recurrent neural networks
International Nuclear Information System (INIS)
Xu Shengyuan; Lam, James; Ho, Daniel W.C.; Zou Yun
2004-01-01
This Letter investigates the problem of robust global exponential stability analysis for interval recurrent neural networks (RNNs) via the linear matrix inequality (LMI) approach. The values of the time-invariant uncertain parameters are assumed to be bounded within given compact sets. An improved condition for the existence of a unique equilibrium point and its global exponential stability of RNNs with known parameters is proposed. Based on this, a sufficient condition for the global robust exponential stability for interval RNNs is obtained. Both of the conditions are expressed in terms of LMIs, which can be checked easily by various recently developed convex optimization algorithms. Examples are provided to demonstrate the reduced conservatism of the proposed exponential stability condition
Stability Analysis of Nonuniform Rectangular Beams Using Homotopy Perturbation Method
Directory of Open Access Journals (Sweden)
Seval Pinarbasi
2012-01-01
Full Text Available The design of slender beams, that is, beams with large laterally unsupported lengths, is commonly controlled by stability limit states. Beam buckling, also called “lateral torsional buckling,” is different from column buckling in that a beam not only displaces laterally but also twists about its axis during buckling. The coupling between twist and lateral displacement makes stability analysis of beams more complex than that of columns. For this reason, most of the analytical studies in the literature on beam stability are concentrated on simple cases: uniform beams with ideal boundary conditions and simple loadings. This paper shows that complex beam stability problems, such as lateral torsional buckling of rectangular beams with variable cross-sections, can successfully be solved using homotopy perturbation method (HPM.
A Lyapunov Function Based Remedial Action Screening Tool Using Real-Time Data
Energy Technology Data Exchange (ETDEWEB)
Mitra, Joydeep [Michigan State Univ., East Lansing, MI (United States); Ben-Idris, Mohammed [Univ. of Nevada, Reno, NV (United States); Faruque, Omar [Florida State Univ., Tallahassee, FL (United States); Backhaus, Scott [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Deb, Sidart [LCG Consulting, Los Altos, CA (United States)
2016-03-30
This report summarizes the outcome of a research project that comprised the development of a Lyapunov function based remedial action screening tool using real-time data (L-RAS). The L-RAS is an advanced computational tool that is intended to assist system operators in making real-time redispatch decisions to preserve power grid stability. The tool relies on screening contingencies using a homotopy method based on Lyapunov functions to avoid, to the extent possible, the use of time domain simulations. This enables transient stability evaluation at real-time speed without the use of massively parallel computational resources. The project combined the following components. 1. Development of a methodology for contingency screening using a homotopy method based on Lyapunov functions and real-time data. 2. Development of a methodology for recommending remedial actions based on the screening results. 3. Development of a visualization and operator interaction interface. 4. Testing of screening tool, validation of control actions, and demonstration of project outcomes on a representative real system simulated on a Real-Time Digital Simulator (RTDS) cluster. The project was led by Michigan State University (MSU), where the theoretical models including homotopy-based screening, trajectory correction using real-time data, and remedial action were developed and implemented in the form of research-grade software. Los Alamos National Laboratory (LANL) contributed to the development of energy margin sensitivity dynamics, which constituted a part of the remedial action portfolio. Florida State University (FSU) and Southern California Edison (SCE) developed a model of the SCE system that was implemented on FSU's RTDS cluster to simulate real-time data that was streamed over the internet to MSU where the L-RAS tool was executed and remedial actions were communicated back to FSU to execute stabilizing controls on the simulated system. LCG Consulting developed the visualization
Advances in Computational Stability Analysis of Composite Aerospace Structures
International Nuclear Information System (INIS)
Degenhardt, R.; Araujo, F. C. de
2010-01-01
European aircraft industry demands for reduced development and operating costs. Structural weight reduction by exploitation of structural reserves in composite aerospace structures contributes to this aim, however, it requires accurate and experimentally validated stability analysis of real structures under realistic loading conditions. This paper presents different advances from the area of computational stability analysis of composite aerospace structures which contribute to that field. For stringer stiffened panels main results of the finished EU project COCOMAT are given. It investigated the exploitation of reserves in primary fibre composite fuselage structures through an accurate and reliable simulation of postbuckling and collapse. For unstiffened cylindrical composite shells a proposal for a new design method is presented.
Power system small signal stability analysis and control
Mondal, Debasish; Sengupta, Aparajita
2014-01-01
Power System Small Signal Stability Analysis and Control presents a detailed analysis of the problem of severe outages due to the sustained growth of small signal oscillations in modern interconnected power systems. The ever-expanding nature of power systems and the rapid upgrade to smart grid technologies call for the implementation of robust and optimal controls. Power systems that are forced to operate close to their stability limit have resulted in the use of control devices by utility companies to improve the performance of the transmission system against commonly occurring power system
Nonlinear stability of ideal fluid equilibria
International Nuclear Information System (INIS)
Holm, D.D.
1988-01-01
The Lyapunov method for establishing stability is related to well- known energy principles for nondissipative dynamical systems. A development of the Lyapunov method for Hamiltonian systems due to Arnold establishes sufficient conditions for Lyapunov stability by using the energy plus other conserved quantities, together with second variations and convexity estimates. When treating the stability of ideal fluid dynamics within the Hamiltonian framework, a useful class of these conserved quantities consists of the Casimir functionals, which Poisson-commute with all functionals of the dynamical fluid variables. Such conserved quantities, when added to the energy, help to provide convexity estimates that bound the growth of perturbations. These convexity estimates, in turn, provide norms necessary for establishing Lyapunov stability under the nonlinear evolution. In contrast, the commonly used second variation or spectral stability arguments only prove linearized stability. As ideal fluid examples, in these lectures we discuss planar barotropic compressible fluid dynamics, the three-dimensional hydrostatic Boussinesq model, and a new set of shallow water equations with nonlinear dispersion due to Basdenkov, Morosov, and Pogutse[1985]. Remarkably, all three of these samples have the same Hamiltonian structure and, thus, possess the same Casimir functionals upon which their stability analyses are based. We also treat stability of modified quasigeostrophic flow, a problem whose Hamiltonian structure and Casimirs closely resemble Arnold's original example. Finally, we discuss some aspects of conditional stability and the applicability of Arnold's development of the Lyapunov technique. 100 refs
International Nuclear Information System (INIS)
Li Chuandong; Liao Xiaofeng; Zhang Rong
2005-01-01
For bi-directional associative memory (BAM) neural networks (NNs) with different constant or time-varying delays, the problems of determining the exponential stability and estimating the exponential convergence rate are investigated in this paper. An approach combining the Lyapunov-Krasovskii functional with the linear matrix inequality (LMI) is taken to study the problems, which provide bounds on the interconnection matrix and the activation functions, so as to guarantee the system's exponential stability. Some criteria for the exponential stability, which give information on the delay-dependent property, are derived. The results obtained in this paper provide one more set of easily verified guidelines for determining the exponential stability of delayed BAM (DBAM) neural networks, which are less conservative and less restrictive than the ones reported so far in the literature. Some typical examples are presented to show the application of the criteria obtained in this paper
Narimani, Mohammand; Lam, H K; Dilmaghani, R; Wolfe, Charles
2011-06-01
Relaxed linear-matrix-inequality-based stability conditions for fuzzy-model-based control systems with imperfect premise matching are proposed. First, the derivative of the Lyapunov function, containing the product terms of the fuzzy model and fuzzy controller membership functions, is derived. Then, in the partitioned operating domain of the membership functions, the relations between the state variables and the mentioned product terms are represented by approximated polynomials in each subregion. Next, the stability conditions containing the information of all subsystems and the approximated polynomials are derived. In addition, the concept of the S-procedure is utilized to release the conservativeness caused by considering the whole operating region for approximated polynomials. It is shown that the well-known stability conditions can be special cases of the proposed stability conditions. Simulation examples are given to illustrate the validity of the proposed approach.
High beta and second stability region transport and stability analysis. Final report
Energy Technology Data Exchange (ETDEWEB)
Hughes, M.H.; Phillips, M.W.
1996-01-01
This report describes MHD equilibrium and stability studies carried out at Northrop Grumman`s Advanced Technology and Development Center during the period March 1 to December 31, 1995. Significant progress is reported in both ideal and resistive MHD modeling of TFTR plasmas. Specifically, attention is concentrated on analysis of Advanced Tokamak experiments at TFTR involving plasmas in which the q-profiles were non-monotonic.
A Hyperchaotic Attractor with Multiple Positive Lyapunov Exponents
International Nuclear Information System (INIS)
Guo-Si, Hu
2009-01-01
There are many hyperchaotic systems, but few systems can generate hyperchaotic attractors with more than three PLEs (positive Lyapunov exponents). A new hyperchaotic system, constructed by adding an approximate time-delay state feedback to a five-dimensional hyperchaotic system, is presented. With the increasing number of phase-shift units used in this system, the number of PLEs also steadily increases. Hyperchaotic attractors with 25 PLEs can be generated by this system with 32 phase-shift units. The sum of the PLEs will reach the maximum value when 23 phase-shift units are used. A simple electronic circuit, consisting of 16 operational amplifiers and two analogy multipliers, is presented for confirming hyperchaos of order 5, i.e., with 5 PLEs
Stability Analysis for Hybrid Automata Using Conservative Gains
Langerak, Romanus; Engell, S.; Guegen, H.; Polderman, Jan W.; Krilavicius, T.; Zaytoon, J.
2003-01-01
This paper presents a stability analysis approach for a class of hybrid automata. It is assumed that the dynamics in each location of the hybrid automaton is linear and asymptotically stable, and that the guards on the transitions are hyperplanes in the state space. For each pair of ingoing and
Yield evaluation and stability analysis in newly selected `KSA' cotton ...
African Journals Online (AJOL)
Yield evaluation and stability analysis in newly selected `KSA' cotton cultivars in Western Kenya. R M Opondo, G A Ombakho. Abstract. (African Crop Science Journal, 1997 5(2): 119-126). http://dx.doi.org/10.4314/acsj.v5i2.27854 · AJOL African Journals Online. HOW TO USE AJOL... for Researchers · for Librarians ...
The analysis of Stability reliability of Qian Tang River seawall
Wu, Xue-Xiong
2017-11-01
Qiantang River seawall due to high water soaking pond by foreshore scour, encountered during the low tide prone slope overall instability. Considering the seawall beach scour in front of random change, using the simplified Bishop method, combined with the variability of soil mechanics parameters, calculation and analysis of Qiantang River Xiasha seawall segments of the overall stability.
Stability Analysis for Multi-Parameter Linear Periodic Systems
DEFF Research Database (Denmark)
Seyranian, A.P.; Solem, Frederik; Pedersen, Pauli
1999-01-01
This paper is devoted to stability analysis of general linear periodic systems depending on real parameters. The Floquet method and perturbation technique are the basis of the development. We start out with the first and higher-order derivatives of the Floquet matrix with respect to problem...
A tutorial on incremental stability analysis using contraction theory
DEFF Research Database (Denmark)
Jouffroy, Jerome; Fossen, Thor I.
2010-01-01
This paper introduces a methodology for dierential nonlinear stability analysis using contraction theory (Lohmiller and Slotine, 1998). The methodology includes four distinct steps: the descriptions of two systems to be compared (the plant and the observer in the case of observer convergence...... on several simple examples....
Experimental bifurcation analysis of an impact oscillator – Determining stability
DEFF Research Database (Denmark)
Bureau, Emil; Schilder, Frank; Elmegård, Michael
2014-01-01
We propose and investigate three different methods for assessing stability of dynamical equilibrium states during experimental bifurcation analysis, using a control-based continuation method. The idea is to modify or turn off the control at an equilibrium state and study the resulting behavior...
Stability analysis for a general age-dependent vaccination model
International Nuclear Information System (INIS)
El Doma, M.
1995-05-01
An SIR epidemic model of a general age-dependent vaccination model is investigated when the fertility, mortality and removal rates depends on age. We give threshold criteria of the existence of equilibriums and perform stability analysis. Furthermore a critical vaccination coverage that is sufficient to eradicate the disease is determined. (author). 12 refs
Stabilization diagrams using operational modal analysis and sliding filters
DEFF Research Database (Denmark)
Olsen, Peter; Juul, Martin Ørum Ørhem; Tarpø, Marius Glindtvad
2017-01-01
This paper presents a filtering technique for doing effective operational modal analysis. The result of the filtering method is construction of stabilization diagram that clearly separates physical poles from spurious noise poles needed for unbiased fitting. A band pass filter is moved slowly over...
stability analysis of food barley genotypes in northern ethiopia
African Journals Online (AJOL)
ACSS
interaction and stability for barley grain yield and yield related traits in the growing ... that the environments were diverse; causing most of the variation in grain yield. ... component axes IPCA1, IPCA2 and IPCA3, which explained 58.06, 27.11 and ..... AMMI analysis of variance for grain yield (t ha-1) of food barley genotypes ...
Transient stability analysis of a distribution network with distributed generators
Xyngi, I.; Ishchenko, A.; Popov, M.; Sluis, van der L.
2009-01-01
This letter describes the transient stability analysis of a 10-kV distribution network with wind generators, microturbines, and CHP plants. The network being modeled in Matlab/Simulink takes into account detailed dynamic models of the generators. Fault simulations at various locations are
Stability Analysis of Static Slip-Energy Recovery Drive via ...
African Journals Online (AJOL)
The stability of the sub synchronous static slip energy recovery scheme for the speed control of slip-ring induction motor is presented. A set of nonlinear differential equations which describe the system dynamics are derived and linearized about an operating point using perturbation technique. The Eigenvalue analysis of the ...
Lyapunov Functions, Stationary Distributions, and Non-equilibrium Potential for Reaction Networks
DEFF Research Database (Denmark)
Anderson, David F; Craciun, Gheorghe; Gopalkrishnan, Manoj
2015-01-01
We consider the relationship between stationary distributions for stochastic models of reaction systems and Lyapunov functions for their deterministic counterparts. Specifically, we derive the well-known Lyapunov function of reaction network theory as a scaling limit of the non-equilibrium potent...
A sampling approach to constructing Lyapunov functions for nonlinear continuous–time systems
Bobiti, R.V.; Lazar, M.
2016-01-01
The problem of constructing a Lyapunov function for continuous-time nonlinear dynamical systems is tackled in this paper via a sampling-based approach. The main idea of the sampling-based method is to verify a Lyapunov-type inequality for a finite number of points (known state vectors) in the
Directory of Open Access Journals (Sweden)
Li Qiu
2013-01-01
unified Markov jump model. The random time delays and packet dropouts existed in feedback communication link are modeled by two independent Markov chains; the resulting closed-loop system is described by a new Markovian jump linear system (MJLS with Markov delays. Sufficient conditions of the stochastic stability for NCSs is obtained by constructing a novel Lyapunov functional, and the mode-dependent output feedback controller design method is presented based on linear matrix inequality (LMI technique. A numerical example is given to illustrate the effectiveness of the proposed method.
Aeroelastic stability analysis of a Darrieus wind turbine
Popelka, D.
1982-02-01
An aeroelastic stability analysis was developed for predicting flutter instabilities on vertical axis wind turbines. The analytical model and mathematical formulation of the problem are described as well as the physical mechanism that creates flutter in Darrieus turbines. Theoretical results are compared with measured experimental data from flutter tests of the Sandia 2 Meter turbine. Based on this comparison, the analysis appears to be an adequate design evaluation tool.
Aeroelastic stability analysis of a Darrieus wind turbine
Energy Technology Data Exchange (ETDEWEB)
Popelka, D.
1982-02-01
An aeroelastic stability analysis has been developed for predicting flutter instabilities on vertical axis wind turbines. The analytical model and mathematical formulation of the problem are described as well as the physical mechanism that creates flutter in Darrieus turbines. Theoretical results are compared with measured experimental data from flutter tests of the Sandia 2 Meter turbine. Based on this comparison, the analysis appears to be an adequate design evaluation tool.
Stability Analysis of Some Nonlinear Anaerobic Digestion Models
Directory of Open Access Journals (Sweden)
Ivan Simeonov
2010-04-01
Full Text Available Abstract: The paper deals with local asymptotic stability analysis of some mass balance dynamic models (based on one and on two-stage reaction schemes of the anaerobic digestion (AD in CSTR. The equilibrium states for models based on one (with Monod, Contois and Haldane shapes for the specific growth rate and on two-stage (only with Monod shapes for both the specific growth rate of acidogenic and methanogenic bacterial populations reaction schemes have been determined solving sets of nonlinear algebraic equations using Maples. Their stability has been analyzed systematically, which provides insight and guidance for AD bioreactors design, operation and control.
Assessment of the Prony's method for BWR stability analysis
International Nuclear Information System (INIS)
Ortiz-Villafuerte, Javier; Castillo-Duran, Rogelio; Palacios-Hernandez, Javier C.
2011-01-01
Highlights: → This paper describes a method to determine the degree of stability of a BWR. → Performance comparison between Prony's and common AR techniques is presented. → Benchmark data and actual BWR transient data are used for comparison. → DR and f results are presented and discussed. → The Prony's method is shown to be a robust technique for BWR stability. - Abstract: It is known that Boiling Water Reactors are susceptible to present power oscillations in regions of high power and low coolant flow, in the power-flow operational map. It is possible to fall in one of such instability regions during reactor startup, since both power and coolant flow are being increased but not proportionally. One other possibility for falling into those areas is the occurrence of a trip of recirculation pumps. Stability monitoring in such cases can be difficult, because the amount or quality of power signal data required for calculation of the stability key parameters may not be enough to provide reliable results in an adequate time range. In this work, the Prony's Method is presented as one complementary alternative to determine the degree of stability of a BWR, through time series data. This analysis method can provide information about decay ratio and oscillation frequency from power signals obtained during transient events. However, so far not many applications in Boiling Water Reactors operation have been reported and supported to establish the scope of using such analysis for actual transient events. This work presents first a comparison of decay ratio and frequency oscillation results obtained by Prony's method and those results obtained by the participants of the Forsmark 1 and 2 Boiling Water Reactor Stability Benchmark using diverse techniques. Then, a comparison of decay ratio and frequency oscillation results is performed for four real BWR transient event data, using Prony's method and two other techniques based on an autoregressive modeling. The four
Construction of a Smooth Lyapunov Function for the Robust and Exact Second-Order Differentiator
Directory of Open Access Journals (Sweden)
Tonametl Sanchez
2016-01-01
Full Text Available Differentiators play an important role in (continuous feedback control systems. In particular, the robust and exact second-order differentiator has shown some very interesting properties and it has been used successfully in sliding mode control, in spite of the lack of a Lyapunov based procedure to design its gains. As contribution of this paper, we provide a constructive method to determine a differentiable Lyapunov function for such a differentiator. Moreover, the Lyapunov function is used to provide a procedure to design the differentiator’s parameters. Also, some sets of such parameters are provided. The determination of the positive definiteness of the Lyapunov function and negative definiteness of its derivative is converted to the problem of solving a system of inequalities linear in the parameters of the Lyapunov function candidate and also linear in the gains of the differentiator, but bilinear in both.
Time-delay effects and simplified control fields in quantum Lyapunov control
International Nuclear Information System (INIS)
Yi, X X; Wu, S L; Wu, Chunfeng; Feng, X L; Oh, C H
2011-01-01
Lyapunov-based quantum control has the advantage that it is free from the measurement-induced decoherence and it includes the instantaneous information of the system in the control. The Lyapunov control is often confronted with time delay in the control fields and difficulty in practical implementations of the control. In this paper, we study the effect of time delay on the Lyapunov control and explore the possibility of replacing the control field with a pulse train or a bang-bang signal. The efficiency of the Lyapunov control is also presented through examining the convergence time of the system. These results suggest that the Lyapunov control is robust against time delay, easy to realize and effective for high-dimensional quantum systems.
Analysis of rocket flight stability based on optical image measurement
Cui, Shuhua; Liu, Junhu; Shen, Si; Wang, Min; Liu, Jun
2018-02-01
Based on the abundant optical image measurement data from the optical measurement information, this paper puts forward the method of evaluating the rocket flight stability performance by using the measurement data of the characteristics of the carrier rocket in imaging. On the basis of the method of measuring the characteristics of the carrier rocket, the attitude parameters of the rocket body in the coordinate system are calculated by using the measurements data of multiple high-speed television sets, and then the parameters are transferred to the rocket body attack angle and it is assessed whether the rocket has a good flight stability flying with a small attack angle. The measurement method and the mathematical algorithm steps through the data processing test, where you can intuitively observe the rocket flight stability state, and also can visually identify the guidance system or failure analysis.
THE FINANCIAL STABILITY ANALYSIS THROUGH THE WORKING CAPITAL
Directory of Open Access Journals (Sweden)
LĂPĂDUŞI MIHAELA LOREDANA
2012-12-01
Full Text Available The main goal of any business is to maintain the financial stability not only on the short term but also on medium and long term, in other words to maintain a harmony between financial sources and financial needs, respectively the equality between the assets and liabilities from the balance sheet. On short term, maintaining the financial stability involves correlating the temporary resources with the temporary uses by using the necessary working capital, and on the long-term, the financial stability involves comparing the permanent resources with the permanent uses by working capital indicator. The determination of the financial state of the company at a certain moment represents the key moment in establishing and adopting the economic and financial decisions in the management of the company. Maintaining the financial stability of the company represents one of the main objectives of the financial analysis and management and it also provides the optimum development of the entire economic and financial activity of the company. The analysis of the working capital size is based on the financial statement data and information, and based on this analysis is considered the financial situation of the company, the financial equilibrium state at a certain moment. The purpose of this article is to highlight the fact that the maintenance of the financial stability on medium and long term is subordinated to the “working capital” indicator, its content and interpretation evolving in time and varying differently from one company to another. The results of this research may have broad applicability in the field of the companies’ activity and it materializes in the complex approach of the working capital regarded as a classic indicator, frequently used in the financial analysis and with profound significance in establishing the financial state in general and the equilibrium state in particular.
Dynamic stability and bifurcation analysis in fractional thermodynamics
Béda, Péter B.
2018-02-01
In mechanics, viscoelasticity was the first field of applications in studying geomaterials. Further possibilities arise in spatial non-locality. Non-local materials were already studied in the 1960s by several authors as a part of continuum mechanics and are still in focus of interest because of the rising importance of materials with internal micro- and nano-structure. When material instability gained more interest, non-local behavior appeared in a different aspect. The problem was concerned to numerical analysis, because then instability zones exhibited singular properties for local constitutive equations. In dynamic stability analysis, mathematical aspects of non-locality were studied by using the theory of dynamic systems. There the basic set of equations describing the behavior of continua was transformed to an abstract dynamic system consisting of differential operators acting on the perturbation field variables. Such functions should satisfy homogeneous boundary conditions and act as indicators of stability of a selected state of the body under consideration. Dynamic systems approach results in conditions for cases, when the differential operators have critical eigenvalues of zero real parts (dynamic stability or instability conditions). When the critical eigenvalues have non-trivial eigenspace, the way of loss of stability is classified as a typical (or generic) bifurcation. Our experiences show that material non-locality and the generic nature of bifurcation at instability are connected, and the basic functions of the non-trivial eigenspace can be used to determine internal length quantities of non-local mechanics. Fractional calculus is already successfully used in thermo-elasticity. In the paper, non-locality is introduced via fractional strain into the constitutive relations of various conventional types. Then, by defining dynamic systems, stability and bifurcation are studied for states of thermo-mechanical solids. Stability conditions and genericity
DEVELOPMENT OF METHODS FOR STABILITY ANALYSIS OF TOWER CRANES
Directory of Open Access Journals (Sweden)
Sinel'shchikov Aleksey Vladimirovich
2018-01-01
Full Text Available Tower cranes are one of the main tools for execution of reloading works during construction. Design of tower cranes is carried out in accordance with RD 22-166-86 “Construction of tower cranes. Rules of analysis”, according to which to ensure stability it is required not to exceed the overturning moment upper limit. The calculation of these moments is carried out with the use of empirical coefficients and quite time-consuming. Moreover, normative methodology only considers the static position of the crane and does not take into account the presence of dynamic transients due to crane functioning (lifting and swinging of the load, boom turning and the presence of the dynamic external load (e.g. from wind for different orientations of the crane. This paper proposes a method of determining the stability coefficient of the crane based on acting reaction forces at the support points - the points of contact of wheels with the crane rail track, which allows us, at the design stage, to investigate stability of tower crane under variable external loads and operating conditions. Subject: the safety of tower cranes operation with regard to compliance with regulatory requirements of ensuring their stability both at the design stage and at the operational stage. Research objectives: increasing the safety of operation of tower cranes on the basis of improving methodology of their design to ensure static and dynamic stability. Materials and methods: analysis and synthesis of the regulatory framework and modern research works on provision of safe operation of tower cranes, the method of numerical simulation. Results: we proposed the formula for analysis of stability of tower cranes using the resulting reaction forces at the supports of the crane at the point of contact of the wheel with the rail track.
Ideal MHD stability analysis of KSTAR target AT mode
International Nuclear Information System (INIS)
Yi, S.M.; Kim, J.H.; You, K.I.; Kim, J.Y.
2009-01-01
Full text: A main research objective of KSTAR (Korea Superconducting Tokamak Advanced Research) device is to demonstrate the steady-state operation capability of high-performance AT (Advanced Tokamak) mode. To meet this goal, it is critical for KSTAR to have a good MHD stability boundary, particularly against the high-beta ideal instabilities such as the external kink and the ballooning modes. To support this MHD stability KSTAR has been designed to have a strong plasma shape and a close interval between plasma and passive- plate wall. During the conceptual design phase of KSTAR, a preliminary study was performed to estimate the high beta MHD stability limit of KSTAR target AT mode using PEST and VACUUM codes and it was shown that the target AT mode can be stable up to β N ∼ 5 with a well-defined plasma pressure and current profiles. Recently, a new calculation has been performed to estimate the ideal stability limit in various KSTAR operating conditions using DCON code, and it has been observed that there is some difference between the new and old calculation results, particularly in the dependence of the maximum β N value on the toroidal mode number. Here, we thus present a more detailed analysis of the ideal MHD stability limit of KSTAR target AT mode using various codes, which include GATO as well as PEST and DCON, in the comparison of calculation results among the three codes. (author)
Fuzzy Logic Controller Stability Analysis Using a Satisfiability Modulo Theories Approach
Arnett, Timothy; Cook, Brandon; Clark, Matthew A.; Rattan, Kuldip
2017-01-01
While many widely accepted methods and techniques exist for validation and verification of traditional controllers, at this time no solutions have been accepted for Fuzzy Logic Controllers (FLCs). Due to the highly nonlinear nature of such systems, and the fact that developing a valid FLC does not require a mathematical model of the system, it is quite difficult to use conventional techniques to prove controller stability. Since safety-critical systems must be tested and verified to work as expected for all possible circumstances, the fact that FLC controllers cannot be tested to achieve such requirements poses limitations on the applications for such technology. Therefore, alternative methods for verification and validation of FLCs needs to be explored. In this study, a novel approach using formal verification methods to ensure the stability of a FLC is proposed. Main research challenges include specification of requirements for a complex system, conversion of a traditional FLC to a piecewise polynomial representation, and using a formal verification tool in a nonlinear solution space. Using the proposed architecture, the Fuzzy Logic Controller was found to always generate negative feedback, but inconclusive for Lyapunov stability.
Stability analysis of jointed rock slope by the block theory
International Nuclear Information System (INIS)
Yoshinaka, Ryunoshin; Yamabe, Tadashi; Fujita, Tomoo.
1990-01-01
The block theory to analyze three dimensional stability problems of discontinuous rock masses is applied to the actual discontinuous rock slope. Taking into consideration that the geometrical information about discontinuities generally increases according to progressive steps of rock investigation in field, the method adopted for analysis is divided into following two steps; 1) the statistical/probabilitical analysis using information from the primary investigation stage which mainly consists of that of natural rock outcrops, and 2) the deterministic analysis correspond to the secondary stage using exploration adits. (author)
Stability Analysis of Periodic Systems by Truncated Point Mappings
Guttalu, R. S.; Flashner, H.
1996-01-01
An approach is presented deriving analytical stability and bifurcation conditions for systems with periodically varying coefficients. The method is based on a point mapping(period to period mapping) representation of the system's dynamics. An algorithm is employed to obtain an analytical expression for the point mapping and its dependence on the system's parameters. The algorithm is devised to derive the coefficients of a multinominal expansion of the point mapping up to an arbitrary order in terms of the state variables and of the parameters. Analytical stability and bifurcation condition are then formulated and expressed as functional relations between the parameters. To demonstrate the application of the method, the parametric stability of Mathieu's equation and of a two-degree of freedom system are investigated. The results obtained by the proposed approach are compared to those obtained by perturbation analysis and by direct integration which we considered to the "exact solution". It is shown that, unlike perturbation analysis, the proposed method provides very accurate solution even for large valuesof the parameters. If an expansion of the point mapping in terms of a small parameter is performed the method is equivalent to perturbation analysis. Moreover, it is demonstrated that the method can be easily applied to multiple-degree-of-freedom systems using the same framework. This feature is an important advantage since most of the existing analysis methods apply mainly to single-degree-of-freedom systems and their extension to higher dimensions is difficult and computationally cumbersome.
Chen, Xiaofeng; Song, Qiankun; Li, Zhongshan; Zhao, Zhenjiang; Liu, Yurong
2018-07-01
This paper addresses the problem of stability for continuous-time and discrete-time quaternion-valued neural networks (QVNNs) with linear threshold neurons. Applying the semidiscretization technique to the continuous-time QVNNs, the discrete-time analogs are obtained, which preserve the dynamical characteristics of their continuous-time counterparts. Via the plural decomposition method of quaternion, homeomorphic mapping theorem, as well as Lyapunov theorem, some sufficient conditions on the existence, uniqueness, and global asymptotical stability of the equilibrium point are derived for the continuous-time QVNNs and their discrete-time analogs, respectively. Furthermore, a uniform sufficient condition on the existence, uniqueness, and global asymptotical stability of the equilibrium point is obtained for both continuous-time QVNNs and their discrete-time version. Finally, two numerical examples are provided to substantiate the effectiveness of the proposed results.
Preliminary hazards analysis of thermal scrap stabilization system. Revision 1
International Nuclear Information System (INIS)
Lewis, W.S.
1994-01-01
This preliminary analysis examined the HA-21I glovebox and its supporting systems for potential process hazards. Upon further analysis, the thermal stabilization system has been installed in gloveboxes HC-21A and HC-21C. The use of HC-21C and HC-21A simplified the initial safety analysis. In addition, these gloveboxes were cleaner and required less modification for operation than glovebox HA-21I. While this document refers to glovebox HA-21I for the hazards analysis performed, glovebox HC-21C is sufficiently similar that the following analysis is also valid for HC-21C. This hazards analysis document is being re-released as revision 1 to include the updated flowsheet document (Appendix C) and the updated design basis (Appendix D). The revised Process Flow Schematic has also been included (Appendix E). This Current revision incorporates the recommendations provided from the original hazards analysis as well. The System Design Description (SDD) has also been appended (Appendix H) to document the bases for Safety Classification of thermal stabilization equipment
Stability Analysis of Discontinuous Galerkin Approximations to the Elastodynamics Problem
Antonietti, Paola F.
2015-11-21
We consider semi-discrete discontinuous Galerkin approximations of both displacement and displacement-stress formulations of the elastodynamics problem. We prove the stability analysis in the natural energy norm and derive optimal a-priori error estimates. For the displacement-stress formulation, schemes preserving the total energy of the system are introduced and discussed. We verify our theoretical estimates on two and three dimensions test problems.
Stability Analysis of Discontinuous Galerkin Approximations to the Elastodynamics Problem
Antonietti, Paola F.; Ayuso de Dios, Blanca; Mazzieri, Ilario; Quarteroni, Alfio
2015-01-01
We consider semi-discrete discontinuous Galerkin approximations of both displacement and displacement-stress formulations of the elastodynamics problem. We prove the stability analysis in the natural energy norm and derive optimal a-priori error estimates. For the displacement-stress formulation, schemes preserving the total energy of the system are introduced and discussed. We verify our theoretical estimates on two and three dimensions test problems.
Tools for voltage stability analysis, including a probabilistic approach
Energy Technology Data Exchange (ETDEWEB)
Vieira Filho, X; Martins, N; Bianco, A; Pinto, H J.C.P. [Centro de Pesquisas de Energia Eletrica (CEPEL), Rio de Janeiro, RJ (Brazil); Pereira, M V.F. [Power System Research (PSR), Inc., Rio de Janeiro, RJ (Brazil); Gomes, P; Santos, M.G. dos [ELETROBRAS, Rio de Janeiro, RJ (Brazil)
1994-12-31
This paper reviews some voltage stability analysis tools that are being used or envisioned for expansion and operational planning studies in the Brazilian system, as well as, their applications. The paper also shows that deterministic tools can be linked together in a probabilistic framework, so as to provide complementary help to the analyst in choosing the most adequate operation strategies, or the best planning solutions for a given system. (author) 43 refs., 8 figs., 8 tabs.
International Nuclear Information System (INIS)
Norwood, Adrienne; Kalnay, Eugenia; Ide, Kayo; Yang, Shu-Chih; Wolfe, Christopher
2013-01-01
imitating the tropical El Niño–Southern Oscillation. The bred vectors are able to separate the fast and slow modes of growth through appropriate selection of the breeding perturbation size and rescaling interval. The Lyapunov vectors are able to successfully separate the fast ‘extratropical atmosphere’, but are unable to completely decouple the ‘tropical atmosphere’ from the ‘ocean’. This leads to ‘coupled’ Lyapunov vectors that are mainly useful in the (slow) ‘ocean’ system, but are still affected by changes in the (fast) ‘tropical’ system. The singular vectors are excellent in capturing the fast modes, but are unable to capture the slow modes of growth. The dissimilar behavior of the three types of vectors leads to a degradation in the similarities of the subspaces they inhabit and affects their relative ability of representing the coupled modes. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)
LAPUR5 BWR stability analysis in Kuosheng nuclear power plant
International Nuclear Information System (INIS)
Kunlung Wu; Chunkuan Shih; Wang, J.R.; Kao, L.S.
2005-01-01
Full text of publication follows: Unstable oscillation of a nuclear power reactor core is one of the main reasons that causes minor core damage. Stability analysis needs to be performed to predict the potential problem as early as possible and to prevent core instability events from happening. Nuclear Regulatory Commission (NRC) requests all BWR licensees to examine each core reload and to impose operating limitations, as appropriate, to ensure compliance with GDC 10 and 12. GDC 10 requires that the reactor core be designed with appropriate margin to assure that specified acceptable fuel design limits will not be exceeded during any condition of normal operation, including anticipated operational occurrences. GDC 12 requires assurance that power oscillations which can result in conditions exceeding specified acceptable fuel design limits are either not possible or can be reliably and readily detected and suppressed. Therefore, the core instability is directly related to the fuel design limits. The core and channel DR (decay ratio) calculation are commonly performed to determine system's stability when new fuel designs are introduced in the core. In order to establish the independent analysis technology for BWR licensees and verifications, the Institute of Nuclear Energy Research (INER) has obtained agreement from NRC and implemented the 'Methodology and Procedure for Calculation of Core and Channel Decay Ratios with LAPUR', which was developed by the IBERINCO in 2001. LAPUR5 uses a multi-nodal description of the neutron dynamics, together with a distributed parameter model of the core thermal hydrodynamics to produce a space-dependent representation of the dynamics of a BWR in the frequency domain for small perturbations around a steady state condition. From the output of LAPUR5, the following results are obtained: global core decay ratio, out-of phase core decay ratio, and channel decay ratio. They are key parameters in the determination of BWR core stability
Stability Analysis of a Reaction-Diffusion System Modeling Atherogenesis
Ibragimov, Akif
2010-01-01
This paper presents a linear, asymptotic stability analysis for a reaction-diffusionconvection system modeling atherogenesis, the initiation of atherosclerosis, as an inflammatory instability. Motivated by the disease paradigm articulated by Ross, atherogenesis is viewed as an inflammatory spiral with a positive feedback loop involving key cellular and chemical species interacting and reacting within the intimal layer of muscular arteries. The inflammatory spiral is initiated as an instability from a healthy state which is defined to be an equilibrium state devoid of certain key inflammatory markers. Disease initiation is studied through a linear, asymptotic stability analysis of a healthy equilibrium state. Various theorems are proved, giving conditions on system parameters guaranteeing stability of the health state, and a general framework is developed for constructing perturbations from a healthy state that exhibit blow-up, which are interpreted as corresponding to disease initiation. The analysis reveals key features that arterial geometry, antioxidant levels, and the source of inflammatory components (through coupled third-kind boundary conditions or through body sources) play in disease initiation. © 2010 Society for Industrial and Applied Mathematics.
Pressure potential and stability analysis in an acoustical noncontact transportation
Li, J.; Liu, C. J.; Zhang, W. J.
2017-01-01
Near field acoustic traveling wave is one of the most popular principles in noncontact manipulations and transportations. The stability behavior is a key factor in the industrial applications of acoustical noncontact transportation. We present here an in-depth analysis of the transportation stability of a planar object levitated in near field acoustic traveling waves. To more accurately describe the pressure distributions on the radiation surface, a 3D nonlinear traveling wave model is presented. A closed form solution is derived based on the pressure potential to quantitatively calculate the restoring forces and moments under small disturbances. The physical explanations of the effects of fluid inertia and the effects of non-uniform pressure distributions are provided in detail. It is found that a vibration rail with tapered cross section provides more stable transportation than a rail with rectangular cross section. The present study sheds light on the issue of quantitative evaluation of stability in acoustic traveling waves and proposes three main factors that influence the stability: (a) vibration shape, (b) pressure distribution and (c) restoring force/moment. It helps to provide a better understanding of the physics behind the near field acoustic transportation and provide useful design and optimization tools for industrial applications.
Stability Analysis of Receiver ISB for BDS/GPS
Zhang, H.; Hao, J. M.; Tian, Y. G.; Yu, H. L.; Zhou, Y. L.
2017-07-01
Stability analysis of receiver ISB (Inter-System Bias) is essential for understanding the feature of ISB as well as the ISB modeling and prediction. In order to analyze the long-term stability of ISB, the data from MGEX (Multi-GNSS Experiment) covering 3 weeks, which are from 2014, 2015 and 2016 respectively, are processed with the precise satellite clock and orbit products provided by Wuhan University and GeoForschungsZentrum (GFZ). Using the ISB calculated by BDS (BeiDou Navigation Satellite System)/GPS (Global Positioning System) combined PPP (Precise Point Positioning), the daily stability and weekly stability of ISB are investigated. The experimental results show that the diurnal variation of ISB is stable, and the average of daily standard deviation is about 0.5 ns. The weekly averages and standard deviations of ISB vary greatly in different years. The weekly averages of ISB are relevant to receiver types. There is a system bias between ISB calculated from the precise products provided by Wuhan University and GFZ. In addition, the system bias of the weekly average ISB of different stations is consistent with each other.
Dynamics, stability, and statistics on lattices and networks
International Nuclear Information System (INIS)
Livi, Roberto
2014-01-01
These lectures aim at surveying some dynamical models that have been widely explored in the recent scientific literature as case studies of complex dynamical evolution, emerging from the spatio-temporal organization of several coupled dynamical variables. The first message is that a suitable mathematical description of such models needs tools and concepts borrowed from the general theory of dynamical systems and from out-of-equilibrium statistical mechanics. The second message is that the overall scenario is definitely reacher than the standard problems in these fields. For instance, systems exhibiting complex unpredictable evolution do not necessarily exhibit deterministic chaotic behavior (i.e., Lyapunov chaos) as it happens for dynamical models made of a few degrees of freedom. In fact, a very large number of spatially organized dynamical variables may yield unpredictable evolution even in the absence of Lyapunov instability. Such a mechanism may emerge from the combination of spatial extension and nonlinearity. Moreover, spatial extension allows one to introduce naturally disorder, or heterogeneity of the interactions as important ingredients for complex evolution. It is worth to point out that the models discussed in these lectures share such features, despite they have been inspired by quite different physical and biological problems. Along these lectures we describe also some of the technical tools employed for the study of such models, e.g., Lyapunov stability analysis, unpredictability indicators for “stable chaos,” hydrodynamic description of transport in low spatial dimension, spectral decomposition of stochastic dynamics on directed networks, etc
Regularized semiclassical limits: Linear flows with infinite Lyapunov exponents
Athanassoulis, Agissilaos; Katsaounis, Theodoros; Kyza, Irene
2016-01-01
Semiclassical asymptotics for Schrödinger equations with non-smooth potentials give rise to ill-posed formal semiclassical limits. These problems have attracted a lot of attention in the last few years, as a proxy for the treatment of eigenvalue crossings, i.e. general systems. It has recently been shown that the semiclassical limit for conical singularities is in fact well-posed, as long as the Wigner measure (WM) stays away from singular saddle points. In this work we develop a family of refined semiclassical estimates, and use them to derive regularized transport equations for saddle points with infinite Lyapunov exponents, extending the aforementioned recent results. In the process we answer a related question posed by P.L. Lions and T. Paul in 1993. If we consider more singular potentials, our rigorous estimates break down. To investigate whether conical saddle points, such as -|x|, admit a regularized transport asymptotic approximation, we employ a numerical solver based on posteriori error control. Thus rigorous upper bounds for the asymptotic error in concrete problems are generated. In particular, specific phenomena which render invalid any regularized transport for -|x| are identified and quantified. In that sense our rigorous results are sharp. Finally, we use our findings to formulate a precise conjecture for the condition under which conical saddle points admit a regularized transport solution for the WM. © 2016 International Press.
Regularized semiclassical limits: Linear flows with infinite Lyapunov exponents
Athanassoulis, Agissilaos
2016-08-30
Semiclassical asymptotics for Schrödinger equations with non-smooth potentials give rise to ill-posed formal semiclassical limits. These problems have attracted a lot of attention in the last few years, as a proxy for the treatment of eigenvalue crossings, i.e. general systems. It has recently been shown that the semiclassical limit for conical singularities is in fact well-posed, as long as the Wigner measure (WM) stays away from singular saddle points. In this work we develop a family of refined semiclassical estimates, and use them to derive regularized transport equations for saddle points with infinite Lyapunov exponents, extending the aforementioned recent results. In the process we answer a related question posed by P.L. Lions and T. Paul in 1993. If we consider more singular potentials, our rigorous estimates break down. To investigate whether conical saddle points, such as -|x|, admit a regularized transport asymptotic approximation, we employ a numerical solver based on posteriori error control. Thus rigorous upper bounds for the asymptotic error in concrete problems are generated. In particular, specific phenomena which render invalid any regularized transport for -|x| are identified and quantified. In that sense our rigorous results are sharp. Finally, we use our findings to formulate a precise conjecture for the condition under which conical saddle points admit a regularized transport solution for the WM. © 2016 International Press.
Lyapunov spectra and conjugate-pairing rule for confined atomic fluids
DEFF Research Database (Denmark)
Bernadi, Stefano; Todd, B.D.; Hansen, Jesper Schmidt
2010-01-01
In this work we present nonequilibrium molecular dynamics simulation results for the Lyapunov spectra of atomic fluids confined in narrow channels of the order of a few atomic diameters. We show the effect that realistic walls have on the Lyapunov spectra. All the degrees of freedom of the confin...... evolved Lyapunov vectors projected into a reduced dimensional phase space. We finally observe that the phase-space compression due to the thermostat remains confined into the wall region and does not significantly affect the purely Newtonian fluid region....
Matter suppression of collective SN neutrino oscillations and stability analysis
International Nuclear Information System (INIS)
Saviano, N.; Chakraborty, S.; Mirizzi, A.
2014-01-01
We perform a detailed analysis of the supernova (SN) neutrino flavor evolution during the early time accretion phase (post-bounce time t pb ≤ 500 ms), characterizing the ν signal by recent SN hydrodynamics simulations. We find that collective oscillations induced the ν-ν interactions in the deepest SN regions are suppressed by trajectory-dependent 'multi-angle' effects associated with the dense ordinary matter. We confirm this result with a linearized stability analysis of the neutrino equations of motion in presence of realistic neutrino energy with angle distributions. (authors)
Stability analysis on natural circulation boiling water reactors
Energy Technology Data Exchange (ETDEWEB)
Metz, Peter
1999-05-01
The purpose of the study is a stability analysis of the simplified boiling water reactor concept. A fluid dynamics code, DYNOS, was developed and successfully validated against FRIGG and DESIRE data and a stability benchmark on the Ringhals 1 forced circulation BWR. Three simplified desings were considered in the analysis: The SWRIOOO by Siemens and the SBWR and ESBWR from the General Electric Co. For all three design operational characteristics, i.e. power versus flow rate maps, were calculated. The effects which different geometric and operational parameters, such as the riser height, inlet subcooling etc., have on the characteristics have been investigated. Dynamic simulations on the three simplified design revealed the geysering and the natural circulation oscillations modes only. They were, however, only encountered at pressure below 0.6 MPa. Stability maps for all tree simplified BWRs were calculated and plotted. The study concluded that a fast pressurisation of the reactor vessel is necessary to eliminate the possibility of geysering or natural circulation oscillations mode instability. (au) 26 tabs., 88 ills.
Stability analysis on natural circulation boiling water reactors
International Nuclear Information System (INIS)
Metz, Peter
1999-05-01
The purpose of the study is a stability analysis of the simplified boiling water reactor concept. A fluid dynamics code, DYNOS, was developed and successfully validated against FRIGG and DESIRE data and a stability benchmark on the Ringhals 1 forced circulation BWR. Three simplified desings were considered in the analysis: The SWRIOOO by Siemens and the SBWR and ESBWR from the General Electric Co. For all three design operational characteristics, i.e. power versus flow rate maps, were calculated. The effects which different geometric and operational parameters, such as the riser height, inlet subcooling etc., have on the characteristics have been investigated. Dynamic simulations on the three simplified design revealed the geysering and the natural circulation oscillations modes only. They were, however, only encountered at pressure below 0.6 MPa. Stability maps for all tree simplified BWRs were calculated and plotted. The study concluded that a fast pressurisation of the reactor vessel is necessary to eliminate the possibility of geysering or natural circulation oscillations mode instability. (au)
Finite element analysis of mechanical stability of coarsened nanoporous gold
International Nuclear Information System (INIS)
Cho, Hoon-Hwe; Chen-Wiegart, Yu-chen Karen; Dunand, David C.
2016-01-01
The mechanical stability of nanoporous gold (np-Au) at various stages of thermal coarsening is studied via finite element analysis under volumetric compression using np-Au architectures imaged via X-ray nano-tomography. As the np-Au is coarsened thermally over ligament sizes ranging from 185 to 465 nm, the pore volume fraction is determinant for the mechanical stability of the coarsened np-Au, unlike the curvature and surface orientation of the ligaments. The computed Young's modulus and yield strength of the structures are compared with the Gibson–Ashby model. The geometry of the structures determines the locations where stress concentrations occur at the onset of yielding.
Stability analysis of the Peregrine solution via squared eigenfunctions
Schober, C. M.; Strawn, M.
2017-10-01
A preliminary numerical investigation involving ensembles of perturbed initial data for the Peregrine soliton (the lowest order rational solution of the nonlinear Schrödinger equation) indicates that it is unstable [16]. In this paper we analytically investigate the linear stability of the Peregrine soliton, appealing to the fact that the Peregrine solution can be viewed as the singular limit of a single mode spatially periodic breathers (SPB). The "squared eigenfunction" connection between the Zakharov-Shabat (Z-S) system and the linearized NLS equation is employed in the stability analysis. Specifically, we determine the eigenfunctions of the Z-S system associated with the Peregrine soliton and construct a family of solutions of the associated linearized NLS (about the Peregrine) in terms of quadratic products of components of the eigenfunctions (i.e., the squared eigenfunction). We find there exist solutions of the linearization that grow exponentially in time, thus showing the Peregrine soliton is linearly unstable.
LOFT pump speed controller stability and accuracy analysis
International Nuclear Information System (INIS)
Good, R.R.
1978-01-01
Two system modifications to the primary coolant pumps motor generators control systems have recently been completed. The range of pump speed operation has been extended and the scoop tube positioner motor replaced. This has necessitated a re-analysis of PSMG stability throughout its range of operation. System accuracy requirements of less than 4 Hz differential pump speed when operating at less than 35 Hz and 8.5 Hz differential pump speed when operating at greater than 35 Hz can be guaranteed by specifying the gain of the system. The installation of the new scoop tube positioner motor will increase the PSMG system's bandwidth and stability. Low speed pump trips should be carefully evaluated if the pump's operational range is to extend to 10 Hz
Analysis of the hydrodynamic stability of natural circulation
International Nuclear Information System (INIS)
Olive, J.; Baby, J.P.
1980-01-01
A mathematical model (EOLE) for the analysis of the stability of boilers with natural circulation is discussed. The method employed consists in linearizing one-dimensional flow equations and in integrating them while employing the Laplace transformation. The properties of a two-phase fluid are schematized by a homogeneous model with slip. The computation results in the circulation loop transfer functions and its natural modes of oscillation (frequency and damping). A discussion follows which compares results obtained with this method to those of other existing models in the case of a straight pipe with forced circulation. Agreement proved to be satisfactory. The results are then given of a parametric study involving the stability of a PWR natural circulation steam generator. These results show that the model can satisfy, at least qualitatively, trends observed empirically or obtained with other more complex theoretical models. (author)
Modelling and finite-time stability analysis of psoriasis pathogenesis
Oza, Harshal B.; Pandey, Rakesh; Roper, Daniel; Al-Nuaimi, Yusur; Spurgeon, Sarah K.; Goodfellow, Marc
2017-08-01
A new systems model of psoriasis is presented and analysed from the perspective of control theory. Cytokines are treated as actuators to the plant model that govern the cell population under the reasonable assumption that cytokine dynamics are faster than the cell population dynamics. The analysis of various equilibria is undertaken based on singular perturbation theory. Finite-time stability and stabilisation have been studied in various engineering applications where the principal paradigm uses non-Lipschitz functions of the states. A comprehensive study of the finite-time stability properties of the proposed psoriasis dynamics is carried out. It is demonstrated that the dynamics are finite-time convergent to certain equilibrium points rather than asymptotically or exponentially convergent. This feature of finite-time convergence motivates the development of a modified version of the Michaelis-Menten function, frequently used in biology. This framework is used to model cytokines as fast finite-time actuators.
Stability Analysis of a Variant of the Prony Method
Directory of Open Access Journals (Sweden)
Rodney Jaramillo
2012-01-01
Full Text Available Prony type methods are used in many engineering applications to determine the exponential fit corresponding to a dataset. In this paper we study a variant of Prony's method that was used by Martín-Landrove et al., in a process of segmentation of T2-weighted MRI brain images. We show the equivalence between that method and the classical Prony method and study the stability of the computed solutions with respect to noise in the data set. In particular, we show that the relative error in the calculation of the exponential fit parameters is linear with respect to noise in the data. Our analysis is based on classical results from linear algebra, matrix computation theory, and the theory of stability for roots of polynomials.
Stability and boundary stabilization of 1-D hyperbolic systems
Bastin, Georges
2016-01-01
This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations. It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, allowing readers to understand the concepts in whichever setting is most familiar to them. With these examples, it also illustrates how control boundary conditions may be defined for the most commonly used control devices. The authors begin with the simple case of systems of two linear conservation laws and then consider the stability of systems under more general boundary conditions that may be differential, nonlinear, or switching. They then extend their discussion to the case of nonlinear conservation laws and demonstrate the use of Lyapunov functions in this type of analysis. Systems of balance laws are considered next, starting with the linear variety before they move on to more general cases of nonlinear ones. They go on to show how the problem of boundary...
Structural stability analysis considerations in fusion reactor plasma chamber design
International Nuclear Information System (INIS)
Delaney, M.J.; Cramer, B.A.
1978-01-01
This paper presents an approach to analyzing a toroidal plasma chamber for the prevention of both static and dynamic buckling. Results of stability analyses performed for the doublet shaped plasma chamber of the General Atomic 3.8 meter radius TNS ignition test reactor are presented. Load conditions are the static external atmospheric pressure load and the dynamic plasma disruption pulse load. Methods for analysis of plasma chamber structures are presented for both types of load. Analysis for static buckling is based on idealizing the plasma chamber into standard structural shapes and applying classical cylinder and circular torus buckling equations. Results are verified using the Buckling of Shells of Revolution (BOSOR4) finite difference computer code. Analysis for the dynamic loading is based on a pulse buckling analysis method for circular cylinders
Stability analysis of maize hybrids across north west of Pakistan
International Nuclear Information System (INIS)
Rahman, H.; Durreshawar; Ali, S.; Iftikhar, F.; Khalil, I.H.; Shah, S.M.A.; Ahmad, H.
2010-01-01
Stability analysis was carried out to study stability in performance and genotype x environment interactions for 18 maize hybrids across three locations of NWFP i.e., Agricultural University Peshawar (AUP), Agricultural Research Station (ARS), Baffa, (Mansehra) and Cereal Crops Research Institute (CCRI), Pirsabak (Nowshera), during 2006. Data were recorded on different morphological and yield parameters. Analysis of variance indicated significant differences among the three locations for all the traits studied. Hybrids showed significant differences for all parameters except anthesis silking interval (ASI) and ear height, which were non significant across the three locations. The hybrid x location interactions also revealed significant differences for days to 50% silking, days to 50% anthesis, ASI, grain moisture at harvest and grain yield per hectare while non significant differences were observed for plant height and ear height. Based on yield performance of hybrids across the three locations, Baffa ranked first as compared to the other two locations. Hybrid DK-1 x EV-9806 was the highest yielding across the three locations followed by hybrid AGB-108, while the lowest yield was observed for hybrid CSCY. Stability in performance was evident for hybrid CS-2Y2 with regard to days required for silking and anthesis. Stability in anthesis silking interval (ASI) was manifested for hybrid CS-222. Hybrid AGB-108 was comparatively stable for grain yield across the tested locations. Remaining hybrids seemed to be considerably influenced by Genotype x environment interactions encountered at the tested locations and location specific selection has to be made while selecting a maize hybrid for a particular location. (author)
Directory of Open Access Journals (Sweden)
Muhammad H. Al-Malack
2016-07-01
Full Text Available Fuel oil flyash (FFA produced in power and water desalination plants firing crude oils in the Kingdom of Saudi Arabia is being disposed in landfills, which increases the burden on the environment, therefore, FFA utilization must be encouraged. In the current research, the effect of adding FFA on the engineering properties of two indigenous soils, namely sand and marl, was investigated. FFA was added at concentrations of 5%, 10% and 15% to both soils with and without the addition of Portland cement. Mixtures of the stabilized soils were thoroughly evaluated using compaction, California Bearing Ratio (CBR, unconfined compressive strength (USC and durability tests. Results of these tests indicated that stabilized sand mixtures could not attain the ACI strength requirements. However, marl was found to satisfy the ACI strength requirement when only 5% of FFA was added together with 5% of cement. When the FFA was increased to 10% and 15%, the mixture’s strength was found to decrease to values below the ACI requirements. Results of the Toxicity Characteristics Leaching Procedure (TCLP, which was performed on samples that passed the ACI requirements, indicated that FFA must be cautiously used in soil stabilization.
Stability analysis of chalk sea cliffs using UAV photogrammetry
Barlow, John; Gilham, Jamie
2017-04-01
Cliff erosion and instability poses a significant hazard to communities and infrastructure located is coastal areas. We use point cloud and spectral data derived from close range digital photogrammetry to assess the stability of chalk sea cliffs located at Telscombe, UK. Data captured from an unmanned aerial vehicle (UAV) were used to generate dense point clouds for a 712 m section of cliff face which ranges from 20 to 49 m in height. Generated models fitted our ground control network within a standard error of 0.03 m. Structural features such as joints, bedding planes, and faults were manually mapped and are consistent with results from other studies that have been conducted using direct measurement in the field. Kinematic analysis of these data was used to identify the primary modes of failure at the site. Our results indicate that wedge failure is by far the most likely mode of slope instability. An analysis of sequential surveys taken from the summer of 2016 to the winter of 2017 indicate several large failures have occurred at the site. We establish the volume of failure through change detection between sequential data sets and use back analysis to determine the strength of shear surfaces for each failure. Our results show that data capture through UAV photogrammetry can provide useful information for slope stability analysis over long sections of cliff. The use of this technology offers significant benefits in equipment costs and field time over existing methods.
A more general model for the analysis of the rock slope stability
Indian Academy of Sciences (India)
slope stability analysis, the joint surfaces are assumed to be continuous along the potential ... of rock slope stability has many applications in the design of rock slopes, roofs and walls of .... cases the wedge failure analysis can be applied.
Heat conduction in one-dimensional chains and nonequilibrium Lyapunov spectrum
International Nuclear Information System (INIS)
Posch, H.A.; Hoover, W.G.
1998-01-01
We define and study the heat conductivity κ and the Lyapunov spectrum for a modified 'ding-a-ling' chain undergoing steady heat flow. Free and bound particles alternate along a chain. In the present work, we use a linear gravitational potential to bind all the even-numbered particles to their lattice sites. The chain is bounded by two stochastic heat reservoirs, one hot and one cold. The Fourier conductivity of the chain decreases smoothly to a finite large-system limit. Special treatment of satellite collisions with the stochastic boundaries is required to obtain Lyapunov spectra. The summed spectra are negative, and correspond to a relatively small contraction in phase space, with the formation of a multifractal strange attractor. The largest of the Lyapunov exponents for the ding-a-ling chain appears to converge to a limiting value with increasing chain length, so that the large-system Lyapunov spectrum has a finite limit. copyright 1998 The American Physical Society
Eleiwi, Fadi; Laleg-Kirati, Taous-Meriem
2015-01-01
This paper presents a nonlinear Lyapunov-based boundary control for the temperature difference of a membrane distillation boundary layers. The heat transfer mechanisms inside the process are modeled with a 2D advection-diffusion equation. The model
Dynamical behaviors determined by the Lyapunov function in competitive Lotka-Volterra systems
Tang, Ying; Yuan, Ruoshi; Ma, Yian
2013-01-01
Dynamical behaviors of the competitive Lotka-Volterra system even for 3 species are not fully understood. In this paper, we study this problem from the perspective of the Lyapunov function. We construct explicitly the Lyapunov function using three examples of the competitive Lotka-Volterra system for the whole state space: (1) the general 2-species case, (2) a 3-species model, and (3) the model of May-Leonard. The basins of attraction for these examples are demonstrated, including cases with bistability and cyclical behavior. The first two examples are the generalized gradient system, where the energy dissipation may not follow the gradient of the Lyapunov function. In addition, under a new type of stochastic interpretation, the Lyapunov function also leads to the Boltzmann-Gibbs distribution on the final steady state when multiplicative noise is added.
Hyperchaos of four state autonomous system with three positive Lyapunov exponents
International Nuclear Information System (INIS)
Ge Zhengming; Yang, C-H.
2009-01-01
This Letter gives the results of numerical simulations of Quantum Cellular Neural Network (Quantum-CNN) autonomous system with four state variables. Three positive Lyapunov exponents confirm hyperchaotic nature of its dynamics
Robust Stabilization of Discrete-Time Systems with Time-Varying Delay: An LMI Approach
Directory of Open Access Journals (Sweden)
Valter J. S. Leite
2008-01-01
Full Text Available Sufficient linear matrix inequality (LMI conditions to verify the robust stability and to design robust state feedback gains for the class of linear discrete-time systems with time-varying delay and polytopic uncertainties are presented. The conditions are obtained through parameter-dependent Lyapunov-Krasovskii functionals and use some extra variables, which yield less conservative LMI conditions. Both problems, robust stability analysis and robust synthesis, are formulated as convex problems where all system matrices can be affected by uncertainty. Some numerical examples are presented to illustrate the advantages of the proposed LMI conditions.
Robust H∞ Control for Singular Time-Delay Systems via Parameterized Lyapunov Functional Approach
Directory of Open Access Journals (Sweden)
Li-li Liu
2014-01-01
Full Text Available A new version of delay-dependent bounded real lemma for singular systems with state delay is established by parameterized Lyapunov-Krasovskii functional approach. In order to avoid generating nonconvex problem formulations in control design, a strategy that introduces slack matrices and decouples the system matrices from the Lyapunov-Krasovskii parameter matrices is used. Examples are provided to demonstrate that the results in this paper are less conservative than the existing corresponding ones in the literature.
Advanced methods for BWR transient and stability analysis
Energy Technology Data Exchange (ETDEWEB)
Schmidt, A; Wehle, F; Opel, S; Velten, R [AREVA, AREVA NP, Erlangen (Germany)
2008-07-01
The design of advanced Boiling Water Reactor (BWR) fuel assemblies and cores is governed by the basic requirement of safe, reliable and flexible reactor operation with optimal fuel utilization. AREVA NP's comprehensive steady state and transient BWR methodology allows the designer to respond quickly and effectively to customer needs. AREVA NP uses S-RELAP5/RAMONA as the appropriate methodology for the representation of the entire plant. The 3D neutron kinetics and thermal-hydraulics code has been developed for the prediction of system, fuel and core behavior and provides additional margins for normal operation and transients. Of major importance is the extensive validation of the methodology. The validation is based on measurements at AREVA NP's test facilities, and comparison of the predictions with a great wealth of measured data gathered from BWR plants during many years of operation. Three of the main fields of interest are stability analysis, operational transients and reactivity initiated accidents (RIAs). The introduced 3D methodology for operational transients shows significant margin regarding the operational limit of critical power ratio, which has been approved by the German licensing authority. Regarding BWR stability a large number of measurements at different plants under various conditions have been performed and successfully post-calculated with RAMONA. This is the basis of reliable pre-calculations of the locations of regional and core-wide stability boundaries. (authors)
Advanced methods for BWR transient and stability analysis
International Nuclear Information System (INIS)
Schmidt, A.; Wehle, F.; Opel, S.; Velten, R.
2008-01-01
The design of advanced Boiling Water Reactor (BWR) fuel assemblies and cores is governed by the basic requirement of safe, reliable and flexible reactor operation with optimal fuel utilization. AREVA NP's comprehensive steady state and transient BWR methodology allows the designer to respond quickly and effectively to customer needs. AREVA NP uses S-RELAP5/RAMONA as the appropriate methodology for the representation of the entire plant. The 3D neutron kinetics and thermal-hydraulics code has been developed for the prediction of system, fuel and core behavior and provides additional margins for normal operation and transients. Of major importance is the extensive validation of the methodology. The validation is based on measurements at AREVA NP's test facilities, and comparison of the predictions with a great wealth of measured data gathered from BWR plants during many years of operation. Three of the main fields of interest are stability analysis, operational transients and reactivity initiated accidents (RIAs). The introduced 3D methodology for operational transients shows significant margin regarding the operational limit of critical power ratio, which has been approved by the German licensing authority. Regarding BWR stability a large number of measurements at different plants under various conditions have been performed and successfully post-calculated with RAMONA. This is the basis of reliable pre-calculations of the locations of regional and core-wide stability boundaries. (authors)
Physical Analysis Work for Slope Stability at Shah Alam, Selangor
Ishak, M. F.; Zaini, M. S. I.
2018-04-01
Slope stability analysis is performed to assess the equilibrium conditions and the safe design of a human-made or natural slope to find the endangered areas. Investigation of potential failure and determination of the slope sensitivity with regard to safety, reliability and economics were parts of this study. Ground anchor is designed to support a structure in this study. Ground anchor were implemented at the Mechanically Stabilized Earth (MSE) wall along Anak Persiaran Jubli Perak to overcome the further cracking of pavement parking, concrete deck and building of the Apartments. A result from the laboratory testing of soil sample such as index test and shear strength test were applied to the Slope/W software with regard to the ground anchors that were implemented. The ground anchors were implemented to increase the value of the factor of safety (FOS) of the MSE Wall. The value of the factor of safety (FOS) before implementing the ground anchor was 0.800 and after the ground anchor was implemented the value increase to 1.555. The increase percentage of factor of safety by implementing on stability of slope was 94.38%.
Resistive MHD Stability Analysis in Near Real-time
Glasser, Alexander; Kolemen, Egemen
2017-10-01
We discuss the feasibility of a near real-time calculation of the tokamak Δ' matrix, which summarizes MHD stability to resistive modes, such as tearing and interchange modes. As the operational phase of ITER approaches, solutions for active feedback tokamak stability control are needed. It has been previously demonstrated that an ideal MHD stability analysis is achievable on a sub- O (1 s) timescale, as is required to control phenomena comparable with the MHD-evolution timescale of ITER. In the present work, we broaden this result to incorporate the effects of resistive MHD modes. Such modes satisfy ideal MHD equations in regions outside narrow resistive layers that form at singular surfaces. We demonstrate that the use of asymptotic expansions at the singular surfaces, as well as the application of state transition matrices, enable a fast, parallelized solution to the singular outer layer boundary value problem, and thereby rapidly compute Δ'. Sponsored by US DOE under DE-SC0015878 and DE-FC02-04ER54698.
Ionic liquid thermal stabilities: decomposition mechanisms and analysis tools.
Maton, Cedric; De Vos, Nils; Stevens, Christian V
2013-07-07
The increasing amount of papers published on ionic liquids generates an extensive quantity of data. The thermal stability data of divergent ionic liquids are collected in this paper with attention to the experimental set-up. The influence and importance of the latter parameters are broadly addressed. Both ramped temperature and isothermal thermogravimetric analysis are discussed, along with state-of-the-art methods, such as TGA-MS and pyrolysis-GC. The strengths and weaknesses of the different methodologies known to date demonstrate that analysis methods should be in line with the application. The combination of data from advanced analysis methods allows us to obtain in-depth information on the degradation processes. Aided with computational methods, the kinetics and thermodynamics of thermal degradation are revealed piece by piece. The better understanding of the behaviour of ionic liquids at high temperature allows selective and application driven design, as well as mathematical prediction for engineering purposes.
Analysis and Prediction of Micromilling Stability with Variable Tool Geometry
Directory of Open Access Journals (Sweden)
Ziyang Cao
2014-11-01
Full Text Available Micromilling can fabricate miniaturized components using micro-end mill at high rotational speeds. The analysis of machining stability in micromilling plays an important role in characterizing the cutting process, estimating the tool life, and optimizing the process. A numerical analysis and experimental method are presented to investigate the chatter stability in micro-end milling process with variable milling tool geometry. The schematic model of micromilling process is constructed and the calculation formula to predict cutting force and displacements is derived. This is followed by a detailed numerical analysis on micromilling forces between helical ball and square end mills through time domain and frequency domain method and the results are compared. Furthermore, a detailed time domain simulation for micro end milling with straight teeth and helical teeth end mill is conducted based on the machine-tool system frequency response function obtained through modal experiment. The forces and displacements are predicted and the simulation result between variable cutter geometry is deeply compared. The simulation results have important significance for the actual milling process.
Landslide stability analysis on basis of LIDAR data extraction
Hu, Hui; Fernandez-Steeger, Tomas M.; Dong, Mei; Azzam, Rafig
2010-05-01
Currently, existing contradictory between remediation and acquisition from natural resource induces a series of divergences. With regard to open pit mining, legal regulation requires human to fill back the open pit area with water or recreate new landscape by other materials; on the other hand, human can not help excavating the mining area due to the shortage of power resource. However, to engineering geologists, one coincident problem which takes place not only in filling but also in mining operation should be paid more attention to, i.e. the slope stability analysis within these areas. There are a number of construction activities during remediation or mining process which can directly or indirectly cause slope failure. Lives can be endangered since local failure either while or after remediation; for mining process, slope failure in a bench, which carries a main haul road or is adjacent to human activity area, would be significant catastrophe to the whole mining program. The stability of an individual bench or slope is controlled by several factors, which are geological condition, morphology, climate, excavation techniques and transportation approach. The task which takes the longest time is to collect the morphological data. Consequently, it is one of the most dangerous tasks due to the time consuming in mining field. LIDAR scanning for morphological data collecting can help to skip this obstacle since advantages of LIDAR techniques as follows: • Dynamic range available on the market: from 3 m to beyond 1 km, • Ruggedly designed for demanding field applications, • Compact, easily hand-carried and deployed by a single operator. In 2009, scanning campaigns for 2 open pit quarry have been carried out. The aim for these LIDAR detections is to construct a detailed 3D quarry model and analyze the bench stability to support the filling planning. The 3D quarry surface was built up by using PolyWorks 10.1 on basis of LIDAR data. LIDAR data refining takes an
Directory of Open Access Journals (Sweden)
Pornchai Bumroongsri
2012-04-01
Full Text Available In this paper, the model predictive control (MPC algorithm for linear parameter varying (LPV systems is proposed. The proposed algorithm consists of two steps. The first step is derived by using parameter-dependent Lyapunov function and the second step is derived by using the perturbation on control input strategy. In order to achieve good control performance, the bounds on the rate of variation of the parameters are taken into account in the controller synthesis. An overall algorithm is proved to guarantee robust stability. The controller design is illustrated with two case studies of continuous stirred-tank reactors. Comparisons with other MPC algorithms for LPV systems have been undertaken. The results show that the proposed algorithm can achieve better control performance.
An Effective Distributed Model for Power System Transient Stability Analysis
Directory of Open Access Journals (Sweden)
MUTHU, B. M.
2011-08-01
Full Text Available The modern power systems consist of many interconnected synchronous generators having different inertia constants, connected with large transmission network and ever increasing demand for power exchange. The size of the power system grows exponentially due to increase in power demand. The data required for various power system applications have been stored in different formats in a heterogeneous environment. The power system applications themselves have been developed and deployed in different platforms and language paradigms. Interoperability between power system applications becomes a major issue because of the heterogeneous nature. The main aim of the paper is to develop a generalized distributed model for carrying out power system stability analysis. The more flexible and loosely coupled JAX-RPC model has been developed for representing transient stability analysis in large interconnected power systems. The proposed model includes Pre-Fault, During-Fault, Post-Fault and Swing Curve services which are accessible to the remote power system clients when the system is subjected to large disturbances. A generalized XML based model for data representation has also been proposed for exchanging data in order to enhance the interoperability between legacy power system applications. The performance measure, Round Trip Time (RTT is estimated for different power systems using the proposed JAX-RPC model and compared with the results obtained using traditional client-server and Java RMI models.
Peach bottom cycle 2 stability analysis using RELAP5/PARCS
International Nuclear Information System (INIS)
Maggini, F.; D'Auria, F.; Miro, R.; Verdu, G.; Ginestar, D.
2003-01-01
Boiling channels and systems may oscillate owing to the behaviour of the liquid-steam mixture used for removing the thermal power. A thermal-hydraulic system may be unstable under particular operating conditions. Two kinds of power oscillation have been observed in BWR cores. One is an in-phase (core-wide) and the other is an out-of-phase (regional) oscillation. Since the above feature can make detection more difficult, the latter oscillation is potentially more severe. The problem is well known since the design of the first BWR system. However, to improve the safety systems of these reactors, it is necessary to be able to detect in a reliable way these oscillations from the neutronic signals. The purpose of this work is to characterize the unstable behaviour of a BWR. Within this study, it has been performed a number of perturbation analysis. The coupled codes RELAP5-Mod3.3/PARCS have used for the simulation of the transients. Validation has been performed against Peach Bottom-2 Low-Flow Stability Test PT3. Three dimensional time domain BWR stability analysis were performed on test point 3 for the core wide oscillation mode. In this transient dynamically complex events take place, i.e., neutron kinetics is coupled with thermal-hydraulics and an in-phase oscillation has been developed. The calculated results are compared against the available experimental data. (author)
Floquet stability analysis of viscoelastic flow over a cylinder
Richter, David
2011-06-01
A Floquet linear stability analysis has been performed on a viscoelastic cylinder wake. The FENE-P model is used to represent the non-Newtonian fluid, and the analysis is done using a modified version of an existing nonlinear code to compute the linearized initial value problem governing the growth of small perturbations in the wake. By measuring instability growth rates over a wide range of disturbance spanwise wavenumbers α, the effects of viscoelasticity were identified and compared directly to Newtonian results.At a Reynolds number of 300, two unstable bands exist over the range 0. ≤ α≤ 10 for Newtonian flow. For the low α band, associated with the "mode A" wake instability, a monotonic reduction in growth rates is found for increasing polymer extensibility L. For the high α band, associated with the "mode B" instability, first a rise, then a significant decrease to a stable state is found for the instability growth rates as L is increased from L= 10 to L= 30. The mechanism behind this stabilization of both mode A and mode B instabilities is due to the change of the base flow, rather than a direct effect of viscoelasticity on the perturbation. © 2011 Elsevier B.V.
Floquet stability analysis of viscoelastic flow over a cylinder
Richter, David; Shaqfeh, Eric S.G.; Iaccarino, Gianluca
2011-01-01
A Floquet linear stability analysis has been performed on a viscoelastic cylinder wake. The FENE-P model is used to represent the non-Newtonian fluid, and the analysis is done using a modified version of an existing nonlinear code to compute the linearized initial value problem governing the growth of small perturbations in the wake. By measuring instability growth rates over a wide range of disturbance spanwise wavenumbers α, the effects of viscoelasticity were identified and compared directly to Newtonian results.At a Reynolds number of 300, two unstable bands exist over the range 0. ≤ α≤ 10 for Newtonian flow. For the low α band, associated with the "mode A" wake instability, a monotonic reduction in growth rates is found for increasing polymer extensibility L. For the high α band, associated with the "mode B" instability, first a rise, then a significant decrease to a stable state is found for the instability growth rates as L is increased from L= 10 to L= 30. The mechanism behind this stabilization of both mode A and mode B instabilities is due to the change of the base flow, rather than a direct effect of viscoelasticity on the perturbation. © 2011 Elsevier B.V.
Stability Analysis for Rotating Stall Dynamics in Axial Flow Compressors
1999-01-01
modes determines collectively local stability of the compressor model. Explicit conditions are obtained for local stability of rotating stall which...critical modes determines the stability for rotating stall collectively . We point out that although in a special case our stability condition for...strict crossing assumption implies that the zero solution changes its stability as ~, crosses ~’c. For instance, odk (yc ) > 0 implies that the zero
Stability analysis of offshore wind farm and marine current farm
Shawon, Mohammad Hasanuzzaman
-trend for large electric energy production using offshore wind generators and marine current generators, respectively. Thus DFIG based offshore wind farm can be an economic solution to stabilize squirrel cage induction generator based marine current farm without installing any addition FACTS devices. This thesis first focuses on the stabilization of fixed speed IG based marine current farm using SDBR. Also stabilization of DFIG based variable speed wind farm utilizing SDBR is studied in this work. Finally a co-operative control strategy is proposed where DFIG is controlled in such a way that it can even provide necessary reactive power demand of induction generator, so that additional cost of FACTS devices can be avoided. In that way, the DFIGs of the offshore wind farm (OWF) will actively compensate the reactive power demand of adjacent IGs of the marine current farm (MCF) during grid fault. Detailed modeling and control scheme for the proposed system are demonstrated considering some realistic scenarios. The power system small signal stability analysis is also carried out by eigenvalue analysis for marine current generator topology, wind turbine generator topology and integrated topology. The relation between the modes and state variables are discussed in light of modal and sensitivity analyses. The results of theoretical analyses are verified by MATLAB/SIMULINK and laboratory standard power system simulator PSCAD/EMTDC.
Stability analysis of an uncooled segment of superconductor
Energy Technology Data Exchange (ETDEWEB)
Seol, S. Y. [Chonnam National University, Gwangju (Korea, Republic of)
2017-09-15
If the part of the HTS magnet is exposed to the outside of the cryogenic coolant due to the fluctuation of the height of the cooling liquid or the vapor generation, the uncooled part becomes very unstable. In this paper, the unstable equilibrium temperature distribution of the uncooled part of a superconductor is obtained, and the maximum temperature and energy are calculated as a function of the uncooled length. Similar to the superconductor stability problem, the current sharing model was applied to derive the theoretical formula and calculated by numerical integration. We also applied a jump model, which assumes that joule heat is generated in all of the uncooled segment, and compares it with the current sharing model results. As a result of the analysis, the stable equilibrium state and the critical uncooled length in the jump model are not shown in the current sharing model. The stability of the conductors to external disturbances was discussed based on the obtained temperature distribution, maximum temperature, and energy.
Analysis of the stability of events occurred in Laguna Verde
International Nuclear Information System (INIS)
Castillo D, R.; Ortiz V, J.; Calleros M, G.
2005-01-01
The new fuel designs for operation cycles more long have regions of uncertainty bigger that those of the old fuels, and therefore, they can have oscillations of power when an event is presented that causes that the reactor operates to high power and low flow of coolant. During the start up of the reactor there are continued procedures that avoid that oscillations are presented with that which makes sure the stable behavior of the reactor. However, when the reactor is operating to nominal conditions and they are shot or they are transferred to low speed the recirculation pumps, it cannot make sure that the reactor doesn't present oscillations of power when entering to the restricted operation regions. The methods of stability analysis commonly use signs of neutronic noise that require to be stationary, but after a transitory one where they commonly get lost the recirculation pumps the signs they don't have the required characteristics, for what they are used with certain level of uncertainty by the limited validity of the models. In this work the Prony method is used to determine the reactor stability, starting from signs of transitory and it is compared with autoregressive models. Four events are analyzed happened in the Laguna Verde power plant where the reactor was in the area of high power and low flow of coolant, giving satisfactory results. (Author)
Postural Stability Analysis with Inertial Measurement Units in Alzheimer's Disease
Directory of Open Access Journals (Sweden)
Miguel F. Gago
2014-01-01
Full Text Available Background: The cause of frequent falls in patients with Alzheimer's disease (AD is still not well understood. Nevertheless, balance control and sensory organization are known to be critical for moving safely and adapting to the environment. Methods: We evaluated postural stability in 20 AD patients (11 fallers and 9 nonfallers and 16 healthy controls with an inertial measurement unit (triaxial accelerometers and gyroscopes attached to the center of mass (COM in different balance conditions (Romberg on flat surface and frontward/backward-inclined surface, with or without visual suppression in a motor lab. Results: In AD patients, the group of fallers showed a different kinetic pattern of postural stability characterized by higher vulnerability to visual suppression, higher total/maximal displacement and a mediolateral/anteroposterior range of sway, and a consequent need for more corrections of COM pitch and roll angles. Conclusion: Further studies are needed to consolidate the normative values of the discriminatory kinetic variables with the potential of inclusion in a multifactorial analysis of the risk of falls. Nevertheless, these results highlight signs of impairment of central postural control in AD, which may require early therapeutic intervention.
International Nuclear Information System (INIS)
Aruquipa Coloma, Wilmer
2017-01-01
Nuclear reactors are susceptible to instability, causing oscillations in reactor power in specific working regions characterized by determined values of power and coolant mass flow. During reactor startup, there is a greater probability that these regions of instability will be present; another reason may be due to transient processes in some reactor parameters. The analysis of the temporal evolution of the power reveals a stable or unstable process after the disturbance in a light water reactor of type BWR (Boiling Water Reactor). In this work, the instability problem was approached in two ways. The first form is based on the ARMA (Autoregressive Moving Average models) model. This model was used to calculate the Decay Ratio (DR) and natural frequency (NF) of the oscillations, parameters that indicate if the one power signal is stable or not. In this sense, the DRARMA code was developed. In the second form, the problems of instability were analyzed using the classical concepts of non-linear systems, such as Lyapunov exponents, phase space and attractors. The Lyapunov exponents quantify the exponential divergence of the trajectories initially close to the phase space and estimate the amount of chaos in a system; the phase space and the attractors describe the dynamic behavior of the system. The main aim of the instability phenomena studies in nuclear reactors is to try to identify points or regions of operation that can lead to power oscillations conditions. The two approaches were applied to two sets of signals. The first set comes from signals of instability events of the commercial Forsmark reactors 1 and 2 and were used to validate the DRARMA code. The second set was obtained from the simulation of transient events of the Peach Bottom reactor; for the simulation, the PARCS and RELAP5 codes were used for the neutronic/thermal hydraulic coupling calculation. For all analyzes made in this work, the Matlab software was used due to its ease of programming and
Slope Stability Analysis of Waste Dump in Sandstone Open Pit Osielec
Adamczyk, Justyna; Cała, Marek; Flisiak, Jerzy; Kolano, Malwina; Kowalski, Michał
2013-03-01
This paper presents the slope stability analysis for the current as well as projected (final) geometry of waste dump Sandstone Open Pit "Osielec". For the stability analysis six sections were selected. Then, the final geometry of the waste dump was designed and the stability analysis was conducted. On the basis of the analysis results the opportunities to improve the stability of the object were identified. The next issue addressed in the paper was to determine the proportion of the mixture containing mining and processing wastes, for which the waste dump remains stable. Stability calculations were carried out using Janbu method, which belongs to the limit equilibrium methods.
Models and Stability Analysis of Boiling Water Reactors
International Nuclear Information System (INIS)
Dorning, John
2002-01-01
We have studied the nuclear-coupled thermal-hydraulic stability of boiling water reactors (BWRs) using a model that includes: space-time modal neutron kinetics based on spatial w-modes; single- and two-phase flow in parallel boiling channels; fuel rod heat conduction dynamics; and a simple model of the recirculation loop. The BR model is represented by a set of time-dependent nonlinear ordinary differential equations, and is studied as a dynamical system using the modern bifurcation theory and nonlinear dynamical systems analysis. We first determine the stability boundary (SB) - or Hopf bifurcation set- in the most relevant parameter plane, the inlet-subcooling-number/external-pressure-drop plane, for a fixed control rod induced external reactivity equal to the 100% rod line value; then we transform the SB to the practical power-flow map used by BWR operating engineers and regulatory agencies. Using this SB, we show that the normal operating point at 100% power is very stable, that stability of points on the 100% rod line decreases as the flow rate is reduced, and that operating points in the low-flow/high-power region are least stable. We also determine the SB that results when the modal kinetics is replaced by simple point reactor kinetics, and we thereby show that the first harmonic mode does not have a significant effect on the SB. However, we later show that it nevertheless has a significant effect on stability because it affects the basin of attraction of stable operating points. Using numerical simulations we show that, in the important low-flow/high-power region, the Hopf bifurcation that occurs as the SB is crossed is subcritical; hence, growing oscillations can result following small finite perturbations of stable steady-states on the 100% rod line at points in the low-flow/high-power region. Numerical simulations are also performed to calculate the decay ratios (DRs) and frequencies of oscillations for various points on the 100% rod line. It is
Models and Stability Analysis of Boiling Water Reactors
Energy Technology Data Exchange (ETDEWEB)
John Dorning
2002-04-15
We have studied the nuclear-coupled thermal-hydraulic stability of boiling water reactors (BWRs) using a model that includes: space-time modal neutron kinetics based on spatial w-modes; single- and two-phase flow in parallel boiling channels; fuel rod heat conduction dynamics; and a simple model of the recirculation loop. The BR model is represented by a set of time-dependent nonlinear ordinary differential equations, and is studied as a dynamical system using the modern bifurcation theory and nonlinear dynamical systems analysis. We first determine the stability boundary (SB) - or Hopf bifurcation set- in the most relevant parameter plane, the inlet-subcooling-number/external-pressure-drop plane, for a fixed control rod induced external reactivity equal to the 100% rod line value; then we transform the SB to the practical power-flow map used by BWR operating engineers and regulatory agencies. Using this SB, we show that the normal operating point at 100% power is very stable, that stability of points on the 100% rod line decreases as the flow rate is reduced, and that operating points in the low-flow/high-power region are least stable. We also determine the SB that results when the modal kinetics is replaced by simple point reactor kinetics, and we thereby show that the first harmonic mode does not have a significant effect on the SB. However, we later show that it nevertheless has a significant effect on stability because it affects the basin of attraction of stable operating points. Using numerical simulations we show that, in the important low-flow/high-power region, the Hopf bifurcation that occurs as the SB is crossed is subcritical; hence, growing oscillations can result following small finite perturbations of stable steady-states on the 100% rod line at points in the low-flow/high-power region. Numerical simulations are also performed to calculate the decay ratios (DRs) and frequencies of oscillations for various points on the 100% rod line. It is
Exponential stability of uncertain stochastic neural networks with mixed time-delays
International Nuclear Information System (INIS)
Wang Zidong; Lauria, Stanislao; Fang Jian'an; Liu Xiaohui
2007-01-01
This paper is concerned with the global exponential stability analysis problem for a class of stochastic neural networks with mixed time-delays and parameter uncertainties. The mixed delays comprise discrete and distributed time-delays, the parameter uncertainties are norm-bounded, and the neural networks are subjected to stochastic disturbances described in terms of a Brownian motion. The purpose of the stability analysis problem is to derive easy-to-test criteria under which the delayed stochastic neural network is globally, robustly, exponentially stable in the mean square for all admissible parameter uncertainties. By resorting to the Lyapunov-Krasovskii stability theory and the stochastic analysis tools, sufficient stability conditions are established by using an efficient linear matrix inequality (LMI) approach. The proposed criteria can be checked readily by using recently developed numerical packages, where no tuning of parameters is required. An example is provided to demonstrate the usefulness of the proposed criteria
Stability analysis for an age-dependent vaccination model
International Nuclear Information System (INIS)
El-Doma, M.
1993-05-01
The stability of an SIR epidemic model with vaccination is investigated. We determine the steady states and examine their stability. Furthermore, a critical vaccination coverage that will eventually eradicate the disease is determined. (author). 9 refs
Modeling and Stability Analysis of Wedge Clutch System
Directory of Open Access Journals (Sweden)
Jian Yao
2014-01-01
Full Text Available A wedge clutch with unique features of self-reinforcement and small actuation force was designed. Its self-reinforcement feature, associated with different factors such as the wedge angle and friction coefficient, brings different dynamics and unstable problem with improper parameters. To analyze this system, a complete mathematical model of the actuation system is built, which includes the DC motor, the wedge mechanism, and the actuated clutch pack. By considering several nonlinear factors, such as the slip-stick friction and the contact or not of the clutch plates, the system is piecewise linear. Through the stability analysis of the linearized system in clutch slipping phase, the stable condition of the designed parameters is obtained as α>arctan(μc. The mathematical model of the actuation system is validated by prototype testing. And with the validated model, the system dynamics in both stable and unstable conditions is investigated and discussed in engineering side.
Dynamic Stability Analysis Using High-Order Interpolation
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Juarez-Toledo C.
2012-10-01
Full Text Available A non-linear model with robust precision for transient stability analysis in multimachine power systems is proposed. The proposed formulation uses the interpolation of Lagrange and Newton's Divided Difference. The High-Order Interpolation technique developed can be used for evaluation of the critical conditions of the dynamic system.The technique is applied to a 5-area 45-machine model of the Mexican interconnected system. As a particular case, this paper shows the application of the High-Order procedure for identifying the slow-frequency mode for a critical contingency. Numerical examples illustrate the method and demonstrate the ability of the High-Order technique to isolate and extract temporal modal behavior.
Stability analysis of a pressure-solution surface
Gal, Doron; Nur, Amos; Aharonov, Einat
We present a linear stability analysis of a dissolution surface subjected to non-hydrostatic stress. A sinusoidal perturbation is imposed on an initially flat solid/fluid interface, and the consequent changes in elastic strain energy and surface energy are calculated. Our results demonstrate that if the far-field lateral stresses are either greater, or much smaller than the fluid pressure, the perturbed configuration has a lower strain energy than the initial one. For wavelengths greater than a critical wavelength this energy decrease may be large enough to offset the increased surface energy. Under these conditions, the perturbation grows unstably. If these conditions are not met, the surface becomes flat. The growth rate and wavelength of the maximally unstable mode depend on the mechanism of matter transport. We conclude that the instability discussed in this paper may account for the formation of stylolites and other pressure-solution phenomena, such as roughening of grain contacts.
Robust stability analysis of adaptation algorithms for single perceptron.
Hui, S; Zak, S H
1991-01-01
The problem of robust stability and convergence of learning parameters of adaptation algorithms in a noisy environment for the single preceptron is addressed. The case in which the same input pattern is presented in the adaptation cycle is analyzed. The algorithm proposed is of the Widrow-Hoff type. It is concluded that this algorithm is robust. However, the weight vectors do not necessarily converge in the presence of measurement noise. A modified version of this algorithm in which the reduction factors are allowed to vary with time is proposed, and it is shown that this algorithm is robust and that the weight vectors converge in the presence of bounded noise. Only deterministic-type arguments are used in the analysis. An ultimate bound on the error in terms of a convex combination of the initial error and the bound on the noise is obtained.
Directory of Open Access Journals (Sweden)
Pablo César Rodríguez Gómez
2017-05-01
Full Text Available Context: Because feedback systems are very common and widely used, studies of the structural characteristics under which chaotic behavior is generated have been developed. These can be separated into a nonlinear system and a linear system at least of the third order. Methods such as the descriptive function have been used for analysis. Method: A feedback system is proposed comprising a linear system, a nonlinear system and a delay block, in order to assess his behavior using Lyapunov exponents. It is evaluated with three different linear systems, different delay values and different values for parameters of nonlinear characteristic, aiming to reach chaotic behavior. Results: One hundred experiments were carried out for each of the three linear systems, by changing the value of some parameters, assessing their influence on the dynamics of the system. Contour plots that relate these parameters to the Largest Lyapunov exponent were obtained and analyzed. Conclusions: In spite non-linearity is a condition for the existence of chaos, this does not imply that any nonlinear characteristic generates a chaotic system, it is reflected by the contour plots showing the transitions between chaotic and no chaotic behavior of the feedback system. Language: English
An alternative bifurcation analysis of the Rose-Hindmarsh model
International Nuclear Information System (INIS)
Nikolov, Svetoslav
2005-01-01
The paper presents an alternative study of the bifurcation behavior of the Rose-Hindmarsh model using Lyapunov-Andronov's theory. This is done on the basis of the obtained analytical formula expressing the first Lyapunov's value (this is not Lyapunov exponent) at the boundary of stability. From the obtained results the following new conclusions are made: Transition to chaos and the occurrence of chaotic oscillations in the Rose-Hindmarsh system take place under hard stability loss
A new method for tear film stability analysis using videokeratography.
Goto, Tomoko; Zheng, Xiaodong; Klyce, Stephen D; Kataoka, Hisashi; Uno, Toshihiko; Karon, Mike; Tatematsu, Yoshiyuki; Bessyo, Takeo; Tsubota, Kazuo; Ohashi, Yuichi
2003-05-01
To report a new tear film stability analysis system using videokeratography. Observational case series. New videokeratography software for TMS-2N (topographic modeling system; TOMEY Corporation, Nagoya, Japan) was developed that can automatically capture consecutive corneal surface images every second for 10 seconds. Forty-eight adult volunteers (80 eyes) were recruited for this study, and all subjects were examined with the new system. Corneal topographs were analyzed for tear breakup time (TMS-BUT) and the ratio of breakup area to entire color-code area (TMS-BUA) was calculated. Routine methods for tear film breakup time evaluation using slit-lamp microscope and fluorescence staining (SLE-BUT) were performed for comparison purposes. Regressive correlations of TMS-BUT or TMS-BUA with SLE-BUT were analyzed. Based on SLE results, subjects were separated into two groups with normal and short BUT, respectively. TMS-BUT and TMS-BUA were compared with SLE-BUT data with regard to the sensitivity and specificity of evaluation of dry eye symptoms. Topographic modeling system-tear breakup time (TMS-BUT) had a positive correlation with SLE-BUT (R = 0.7219, P TMS-BUA showed a negative correlation (R = 0.6317, P TMS-BUT, 9 (81.82%) of which were associated with dry eye symptoms. The sensitivities of TMS-BUT and TMS-BUA were 97.5% and 95%, respectively, significantly higher than that of SLE-BUT (75%), with P =.008 and 0.01, respectively. Topographic modeling system-BUT and TMS-BUA displayed a similar rate of specificity in comparison with SLE-BUT. This new videokeratography system is a noninvasive and objective method with increased sensitivity for tear film stability analysis.
Directory of Open Access Journals (Sweden)
Yingwei Li
2013-01-01
Full Text Available The global exponential stability issues are considered for almost periodic solution of the neural networks with mixed time-varying delays and discontinuous neuron activations. Some sufficient conditions for the existence, uniqueness, and global exponential stability of almost periodic solution are achieved in terms of certain linear matrix inequalities (LMIs, by applying differential inclusions theory, matrix inequality analysis technique, and generalized Lyapunov functional approach. In addition, the existence and asymptotically almost periodic behavior of the solution of the neural networks are also investigated under the framework of the solution in the sense of Filippov. Two simulation examples are given to illustrate the validity of the theoretical results.
Eleiwi, Fadi
2016-09-19
This paper presents a nonlinear observer-based Lyapunov control for a membrane distillation (MD) process. The control considers the inlet temperatures of the feed and the permeate solutions as inputs, transforming it to boundary control process, and seeks to maintain the temperature difference along the membrane boundaries around a sufficient level to promote water production. MD process is modeled with advection diffusion equation model in two dimensions, where the diffusion and convection heat transfer mechanisms are best described. Model analysis, effective order reduction and parameters physical interpretation, are provided. Moreover, a nonlinear observer has been designed to provide the control with estimates of the temperature evolution at each time instant. In addition, physical constraints are imposed on the control to have an acceptable range of feasible inputs, and consequently, better energy consumption. Numerical simulations for the complete process with real membrane parameter values are provided, in addition to detailed explanations for the role of the controller and the observer. (C) 2016 Elsevier Ltd. All rights reserved.
Designing Hyperchaotic Cat Maps With Any Desired Number of Positive Lyapunov Exponents.
Hua, Zhongyun; Yi, Shuang; Zhou, Yicong; Li, Chengqing; Wu, Yue
2018-02-01
Generating chaotic maps with expected dynamics of users is a challenging topic. Utilizing the inherent relation between the Lyapunov exponents (LEs) of the Cat map and its associated Cat matrix, this paper proposes a simple but efficient method to construct an -dimensional ( -D) hyperchaotic Cat map (HCM) with any desired number of positive LEs. The method first generates two basic -D Cat matrices iteratively and then constructs the final -D Cat matrix by performing similarity transformation on one basic -D Cat matrix by the other. Given any number of positive LEs, it can generate an -D HCM with desired hyperchaotic complexity. Two illustrative examples of -D HCMs were constructed to show the effectiveness of the proposed method, and to verify the inherent relation between the LEs and Cat matrix. Theoretical analysis proves that the parameter space of the generated HCM is very large. Performance evaluations show that, compared with existing methods, the proposed method can construct -D HCMs with lower computation complexity and their outputs demonstrate strong randomness and complex ergodicity.
A perturbation method to the tent map based on Lyapunov exponent and its application
Cao, Lv-Chen; Luo, Yu-Ling; Qiu, Sen-Hui; Liu, Jun-Xiu
2015-10-01
Perturbation imposed on a chaos system is an effective way to maintain its chaotic features. A novel parameter perturbation method for the tent map based on the Lyapunov exponent is proposed in this paper. The pseudo-random sequence generated by the tent map is sent to another chaos function — the Chebyshev map for the post processing. If the output value of the Chebyshev map falls into a certain range, it will be sent back to replace the parameter of the tent map. As a result, the parameter of the tent map keeps changing dynamically. The statistical analysis and experimental results prove that the disturbed tent map has a highly random distribution and achieves good cryptographic properties of a pseudo-random sequence. As a result, it weakens the phenomenon of strong correlation caused by the finite precision and effectively compensates for the digital chaos system dynamics degradation. Project supported by the Guangxi Provincial Natural Science Foundation, China (Grant No. 2014GXNSFBA118271), the Research Project of Guangxi University, China (Grant No. ZD2014022), the Fund from Guangxi Provincial Key Laboratory of Multi-source Information Mining & Security, China (Grant No. MIMS14-04), the Fund from the Guangxi Provincial Key Laboratory of Wireless Wideband Communication & Signal Processing, China (Grant No. GXKL0614205), the Education Development Foundation and the Doctoral Research Foundation of Guangxi Normal University, the State Scholarship Fund of China Scholarship Council (Grant No. [2014]3012), and the Innovation Project of Guangxi Graduate Education, China (Grant No. YCSZ2015102).
International Nuclear Information System (INIS)
Feng Yi-Fu; Zhang Qing-Ling; Feng De-Zhi
2012-01-01
The global stability problem of Takagi—Sugeno (T—S) fuzzy Hopfield neural networks (FHNNs) with time delays is investigated. Novel LMI-based stability criteria are obtained by using Lyapunov functional theory to guarantee the asymptotic stability of the FHNNs with less conservatism. Firstly, using both Finsler's lemma and an improved homogeneous matrix polynomial technique, and applying an affine parameter-dependent Lyapunov—Krasovskii functional, we obtain the convergent LMI-based stability criteria. Algebraic properties of the fuzzy membership functions in the unit simplex are considered in the process of stability analysis via the homogeneous matrix polynomials technique. Secondly, to further reduce the conservatism, a new right-hand-side slack variables introducing technique is also proposed in terms of LMIs, which is suitable to the homogeneous matrix polynomials setting. Finally, two illustrative examples are given to show the efficiency of the proposed approaches
[Analysis of the stability and adaptability of near infrared spectra qualitative analysis model].
Cao, Wu; Li, Wei-jun; Wang, Ping; Zhang, Li-ping
2014-06-01
The stability and adaptability of model of near infrared spectra qualitative analysis were studied. Method of separate modeling can significantly improve the stability and adaptability of model; but its ability of improving adaptability of model is limited. Method of joint modeling can not only improve the adaptability of the model, but also the stability of model, at the same time, compared to separate modeling, the method can shorten the modeling time, reduce the modeling workload; extend the term of validity of model, and improve the modeling efficiency. The experiment of model adaptability shows that, the correct recognition rate of separate modeling method is relatively low, which can not meet the requirements of application, and joint modeling method can reach the correct recognition rate of 90%, and significantly enhances the recognition effect. The experiment of model stability shows that, the identification results of model by joint modeling are better than the model by separate modeling, and has good application value.
On Stabilization of Nonautonomous Nonlinear Systems
International Nuclear Information System (INIS)
Bogdanov, A. Yu.
2008-01-01
The procedures to obtain the sufficient conditions of asymptotic stability for nonlinear nonstationary continuous-time systems are discussed. We consider different types of the following general controlled system: x = X(t,x,u) = F(t,x)+B(t,x)u, x(t 0 ) = x 0 . (*) The basis of investigation is limiting equations, limiting Lyapunov functions, etc. The improved concept of observability of the pair of functional matrices is presented. By these results the problem of synthesis of asymptotically stable control nonlinear nonautonomous systems (with linear parts) involving the quadratic time-dependent Lyapunov functions is solved as well as stabilizing a given unstable system with nonlinear control law.
Rusconi, C. C.; Pöchhacker, V.; Cirac, J. I.; Romero-Isart, O.
2017-10-01
We theoretically study the levitation of a single magnetic domain nanosphere in an external static magnetic field. We show that, apart from the stability provided by the mechanical rotation of the nanomagnet (as in the classical Levitron), the quantum spin origin of its magnetization provides two additional mechanisms to stably levitate the system. Despite the Earnshaw theorem, such stable phases are present even in the absence of mechanical rotation. For large magnetic fields, the Larmor precession of the quantum magnetic moment stabilizes the system in full analogy with magnetic trapping of a neutral atom. For low magnetic fields, the magnetic anisotropy stabilizes the system via the Einstein-de Haas effect. These results are obtained with a linear stability analysis of a single magnetic domain rigid nanosphere with uniaxial anisotropy in a Ioffe-Pritchard magnetic field.
The brief time-reversibility of the local Lyapunov exponents for a small chaotic Hamiltonian system
International Nuclear Information System (INIS)
Waldner, Franz; Hoover, William G.; Hoover, Carol G.
2014-01-01
Highlights: •We consider the local Lyapunov spectrum for a four-dimensional Hamilton system. •Its stable periodic motion can be reversed for long times. •In the chaotic motion, time reversal occurs only for a short time. •Perturbations will change this short unstable case into a different stable case. •These observations might relate chaos to the Second Law of Thermodynamics. - Abstract: We consider the local (instantaneous) Lyapunov spectrum for a four-dimensional Hamiltonian system. Its stable periodic motion can be reversed for long times. Its unstable chaotic motion, with two symmetric pairs of exponents, cannot. In the latter case reversal occurs for more than a thousand fourth-order Runge–Kutta time steps, followed by a transition to a new set of paired Lyapunov exponents, unrelated to those seen in the forward time direction. The relation of the observed chaotic dynamics to the Second Law of Thermodynamics is discussed
Critical behavior of the Lyapunov exponent in type-III intermittency
Energy Technology Data Exchange (ETDEWEB)
Alvarez-Llamoza, O. [Departamento de Fisica, FACYT, Universidad de Carabobo, Valencia (Venezuela); Centro de Fisica Fundamental, Grupo de Caos y Sistemas Complejos, Universidad de Los Andes, Merida 5251, Merida (Venezuela)], E-mail: llamoza@ula.ve; Cosenza, M.G. [Centro de Fisica Fundamental, Grupo de Caos y Sistemas Complejos, Universidad de Los Andes, Merida 5251, Merida (Venezuela); Ponce, G.A. [Departamento de Fisica, Universidad Nacional Autonoma de Honduras (Honduras); Departamento de Ciencias Naturales, Universidad Pedagogica Nacional Francisco Morazan, Tegucigalpa (Honduras)
2008-04-15
The critical behavior of the Lyapunov exponent near the transition to robust chaos via type-III intermittency is determined for a family of one-dimensional singular maps. Critical boundaries separating the region of robust chaos from the region where stable fixed points exist are calculated on the parameter space of the system. A critical exponent {beta} expressing the scaling of the Lyapunov exponent is calculated along the critical curve corresponding to the type-III intermittent transition to chaos. It is found that {beta} varies on the interval 0 {<=} {beta} < 1/2 as a function of the order of the singularity of the map. This contrasts with earlier predictions for the scaling behavior of the Lyapunov exponent in type-III intermittency. The variation of the critical exponent {beta} implies a continuous change in the nature of the transition to chaos via type-III intermittency, from a second-order, continuous transition to a first-order, discontinuous transition.
Yu, Jue; Zhuang, Jian; Yu, Dehong
2015-01-01
This paper concerns a state feedback integral control using a Lyapunov function approach for a rotary direct drive servo valve (RDDV) while considering parameter uncertainties. Modeling of this RDDV servovalve reveals that its mechanical performance is deeply influenced by friction torques and flow torques; however, these torques are uncertain and mutable due to the nature of fluid flow. To eliminate load resistance and to achieve satisfactory position responses, this paper develops a state feedback control that integrates an integral action and a Lyapunov function. The integral action is introduced to address the nonzero steady-state error; in particular, the Lyapunov function is employed to improve control robustness by adjusting the varying parameters within their value ranges. This new controller also has the advantages of simple structure and ease of implementation. Simulation and experimental results demonstrate that the proposed controller can achieve higher control accuracy and stronger robustness. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
Behaviour of Lyapunov exponents near crisis points in the dissipative standard map
Pompe, B.; Leven, R. W.
1988-11-01
We numerically study the behaviour of the largest Lyapunov characteristic exponent λ1 in dependence on a control parameter in the 2D standard map with dissipation. In order to investigate the system's motion in parameter intervals slightly above crisis points we introduce "partial" Lyapunov exponents which characterize the average exponential divergence of nearby orbits on a semi-attractor at a boundary crisis and on distinct parts of a "large" chaotic attractor near an interior crisis. In the former case we find no significant difference between λ1 in the pre-crisis regime and the partial Lyapunov exponent describing transient chaotic motions slightly above the crisis. For the latter case we give a quantitative description of the drastic increase of λ1. Moreover, a formula which connects the critical exponent of a chaotic transient above a boundary crisis with a pointwise dimension is derived.
Stability and failure analysis of steering tie-rod
Jiang, GongFeng; Zhang, YiLiang; Xu, XueDong; Ding, DaWei
2008-11-01
A new car in operation of only 8,000 km, because of malfunction, resulting in lost control and rammed into the edge of the road, and then the basic vehicle scrapped. According to the investigation of the site, it was found that the tie-rod of the car had been broken. For the subjective analysis of the accident and identifying the true causes of rupture of the tierod, a series of studies, from the angle of theory to experiment on the bended broken tie-rod, were conducted. The mechanical model was established; the stability of the defective tie-rod was simulated based on ANSYS software. Meanwhile, the process of the accident was simulated considering the effect of destabilization of different vehicle speed and direction of the impact. Simultaneously, macro graphic test, chemical composition analysis, microstructure analysis and SEM analysis of the fracture were implemented. The results showed that: 1) the toughness of the tie-rod is at a normal level, but there is some previous flaws. One quarter of the fracture surface has been cracked before the accident. However, there is no relationship between the flaw and this incident. The direct cause is the dynamic instability leading to the large deformation of impact loading. 2) The declining safety factor of the tie-rod greatly due to the previous flaws; the result of numerical simulation shows that previous flaw is the vital factor of structure instability, on the basis of the comparison of critical loads of the accident tie-rod and normal. The critical load can decrease by 51.3% when the initial defect increases 19.54% on the cross-sectional area, which meets the Theory of Koiter.
Frequency prediction by linear stability analysis around mean flow
Bengana, Yacine; Tuckerman, Laurette
2017-11-01
The frequency of certain limit cycles resulting from a Hopf bifurcation, such as the von Karman vortex street, can be predicted by linear stability analysis around their mean flows. Barkley (2006) has shown this to yield an eigenvalue whose real part is zero and whose imaginary part matches the nonlinear frequency. This property was named RZIF by Turton et al. (2015); moreover they found that the traveling waves (TW) of thermosolutal convection have the RZIF property. They explained this as a consequence of the fact that the temporal Fourier spectrum is dominated by the mean flow and first harmonic. We could therefore consider that only the first mode is important in the saturation of the mean flow as presented in the Self-Consistent Model (SCM) of Mantic-Lugo et al. (2014). We have implemented a full Newton's method to solve the SCM for thermosolutal convection. We show that while the RZIF property is satisfied far from the threshold, the SCM model reproduces the exact frequency only very close to the threshold. Thus, the nonlinear interaction of only the first mode with itself is insufficiently accurate to estimate the mean flow. Our next step will be to take into account higher harmonics and to apply this analysis to the standing waves, for which RZIF does not hold.
Linear Stability Analysis of an Acoustically Vaporized Droplet
Siddiqui, Junaid; Qamar, Adnan; Samtaney, Ravi
2015-11-01
Acoustic droplet vaporization (ADV) is a phase transition phenomena of a superheat liquid (Dodecafluoropentane, C5F12) droplet to a gaseous bubble, instigated by a high-intensity acoustic pulse. This approach was first studied in imaging applications, and applicable in several therapeutic areas such as gas embolotherapy, thrombus dissolution, and drug delivery. High-speed imaging and theoretical modeling of ADV has elucidated several physical aspects, ranging from bubble nucleation to its subsequent growth. Surface instabilities are known to exist and considered responsible for evolving bubble shapes (non-spherical growth, bubble splitting and bubble droplet encapsulation). We present a linear stability analysis of the dynamically evolving interfaces of an acoustically vaporized micro-droplet (liquid A) in an infinite pool of a second liquid (liquid B). We propose a thermal ADV model for the base state. The linear analysis utilizes spherical harmonics (Ynm, of degree m and order n) and under various physical assumptions results in a time-dependent ODE of the perturbed interface amplitudes (one at the vapor/liquid A interface and the other at the liquid A/liquid B interface). The perturbation amplitudes are found to grow exponentially and do not depend on m. Supported by KAUST Baseline Research Funds.
Lai, Ying-Cheng; Harrison, Mary Ann F; Frei, Mark G; Osorio, Ivan
2004-09-01
Lyapunov exponents are a set of fundamental dynamical invariants characterizing a system's sensitive dependence on initial conditions. For more than a decade, it has been claimed that the exponents computed from electroencephalogram (EEG) or electrocorticogram (ECoG) signals can be used for prediction of epileptic seizures minutes or even tens of minutes in advance. The purpose of this paper is to examine the predictive power of Lyapunov exponents. Three approaches are employed. (1) We present qualitative arguments suggesting that the Lyapunov exponents generally are not useful for seizure prediction. (2) We construct a two-dimensional, nonstationary chaotic map with a parameter slowly varying in a range containing a crisis, and test whether this critical event can be predicted by monitoring the evolution of finite-time Lyapunov exponents. This can thus be regarded as a "control test" for the claimed predictive power of the exponents for seizure. We find that two major obstacles arise in this application: statistical fluctuations of the Lyapunov exponents due to finite time computation and noise from the time series. We show that increasing the amount of data in a moving window will not improve the exponents' detective power for characteristic system changes, and that the presence of small noise can ruin completely the predictive power of the exponents. (3) We report negative results obtained from ECoG signals recorded from patients with epilepsy. All these indicate firmly that, the use of Lyapunov exponents for seizure prediction is practically impossible as the brain dynamical system generating the ECoG signals is more complicated than low-dimensional chaotic systems, and is noisy. Copyright 2004 American Institute of Physics
Order-2 Stability Analysis of Particle Swarm Optimization.
Liu, Qunfeng
2015-01-01
Several stability analyses and stable regions of particle swarm optimization (PSO) have been proposed before. The assumption of stagnation and different definitions of stability are adopted in these analyses. In this paper, the order-2 stability of PSO is analyzed based on a weak stagnation assumption. A new definition of stability is proposed and an order-2 stable region is obtained. Several existing stable analyses for canonical PSO are compared, especially their definitions of stability and the corresponding stable regions. It is shown that the classical stagnation assumption is too strict and not necessary. Moreover, among all these definitions of stability, it is shown that our definition requires the weakest conditions, and additional conditions bring no benefit. Finally, numerical experiments are reported to show that the obtained stable region is meaningful. A new parameter combination of PSO is also shown to be good, even better than some known best parameter combinations.
Analysis on soil compressibility changes of samples stabilized with lime
Directory of Open Access Journals (Sweden)
Elena-Andreea CALARASU
2016-12-01
Full Text Available In order to manage and control the stability of buildings located on difficult foundation soils, several techniques of soil stabilization were developed and applied worldwide. Taking into account the major significance of soil compressibility on construction durability and safety, the soil stabilization with a binder like lime is considered one of the most used and traditional methods. The present paper aims to assess the effect of lime content on soil geotechnical parameters, especially on compressibility ones, based on laboratory experimental tests, for several soil categories in admixture with different lime dosages. The results of this study indicate a significant improvement of stabilized soil parameters, such as compressibility and plasticity, in comparison with natural samples. The effect of lime stabilization is related to an increase of soil structure stability by increasing the bearing capacity.
Stability analysis of distributed order fractional chen system.
Aminikhah, H; Refahi Sheikhani, A; Rezazadeh, H
2013-01-01
We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain. Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractional Chen system is discussed. In addition, we have found that chaos exists in the double fractional order Chen system. Numerical solutions are used to verify the analytical results.
Stability Analysis of Distributed Order Fractional Chen System
Aminikhah, H.; Refahi Sheikhani, A.; Rezazadeh, H.
2013-01-01
We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain. Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractional Chen system is discussed. In addition, we have found that chaos exists in the double fractional order Chen system. Numerical solutions are used to verify the analytical results. PMID:24489508
Large-signal stability analysis of PWM converters
Energy Technology Data Exchange (ETDEWEB)
Huynh, P.T. [Philips Labs., Briarcliff Manor, NY (United States); Cho, B.H. [Seoul National Univ. (Korea, Republic of). Dept. of Electrical Engineering
1995-12-31
Investigation of the effects of existing nonlinearities on the stability of PWM converters is performed. The bilinear structure, the duty cycle saturation, and the opamp saturation are the principal nonlinearities in PWM converters. These nonlinearities are incorporated in the large-signal analytical models of PWM converters, and the basic input-output stability theory is applied to analyze their stability. Design and optimization of the small-signal loop gains to counteract the undesirable nonlinear effects are also discussed.
Modulational estimate for the maximal Lyapunov exponent in Fermi-Pasta-Ulam chains
Dauxois, Thierry; Ruffo, Stefano; Torcini, Alessandro
1997-12-01
In the framework of the Fermi-Pasta-Ulam (FPU) model, we show a simple method to give an accurate analytical estimation of the maximal Lyapunov exponent at high energy density. The method is based on the computation of the mean value of the modulational instability growth rates associated to unstable modes. Moreover, we show that the strong stochasticity threshold found in the β-FPU system is closely related to a transition in tangent space, the Lyapunov eigenvector being more localized in space at high energy.
An Isomorphism between Lyapunov Exponents and Shannon's Channel Capacity
Energy Technology Data Exchange (ETDEWEB)
Friedland, Gerald [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Metere, Alfredo [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2017-06-07
We demonstrate that discrete Lyapunov exponents are isomorphic to numeric overflows of the capacity of an arbitrary noiseless and memoryless channel in a Shannon communication model with feedback. The isomorphism allows the understanding of Lyapunov exponents in terms of Information Theory, rather than the traditional definitions in chaos theory. The result also implies alternative approaches to the calculation of related quantities, such as the Kolmogorov Sinai entropy which has been linked to thermodynamic entropy. This work provides a bridge between fundamental physics and information theory. It suggests, among other things, that machine learning and other information theory methods can be employed at the core of physics simulations.
New prediction of chaotic time series based on local Lyapunov exponent
International Nuclear Information System (INIS)
Zhang Yong
2013-01-01
A new method of predicting chaotic time series is presented based on a local Lyapunov exponent, by quantitatively measuring the exponential rate of separation or attraction of two infinitely close trajectories in state space. After reconstructing state space from one-dimensional chaotic time series, neighboring multiple-state vectors of the predicting point are selected to deduce the prediction formula by using the definition of the local Lyapunov exponent. Numerical simulations are carried out to test its effectiveness and verify its higher precision over two older methods. The effects of the number of referential state vectors and added noise on forecasting accuracy are also studied numerically. (general)
On the relation between Lyapunov exponents and exponential decay of correlations
International Nuclear Information System (INIS)
Slipantschuk, Julia; Bandtlow, Oscar F; Just, Wolfram
2013-01-01
Chaotic dynamics with sensitive dependence on initial conditions may result in exponential decay of correlation functions. We show that for one-dimensional interval maps the corresponding quantities, that is, Lyapunov exponents and exponential decay rates, are related. More specifically, for piecewise linear expanding Markov maps observed via piecewise analytic functions, we show that the decay rate is bounded above by twice the Lyapunov exponent, that is, we establish lower bounds for the subleading eigenvalue of the corresponding Perron–Frobenius operator. In addition, we comment on similar relations for general piecewise smooth expanding maps. (paper)
Analysis of stability for stochastic delay integro-differential equations.
Zhang, Yu; Li, Longsuo
2018-01-01
In this paper, we concern stability of numerical methods applied to stochastic delay integro-differential equations. For linear stochastic delay integro-differential equations, it is shown that the mean-square stability is derived by the split-step backward Euler method without any restriction on step-size, while the Euler-Maruyama method could reproduce the mean-square stability under a step-size constraint. We also confirm the mean-square stability of the split-step backward Euler method for nonlinear stochastic delay integro-differential equations. The numerical experiments further verify the theoretical results.
Analysis of Physical Education Students’ Emotional Stability and Reactibility
Directory of Open Access Journals (Sweden)
Radka Peřinová
2015-03-01
Full Text Available Analysis of Physical Education Students’ Emotional Stability and Reactibility This paper will aim to show the possible association between emotional stability and reaction time variability of Physical Education students. It can be stated that our study confirmed our suppositions which were based on works that have focused on similar topics. Our research sample showed the expected characteristics: primarily lower neuroticism values and higher extraversion when compared to the non-sporting population. Emotional stability which was reflected in the neuroticism dimension in EPQ-R (Eysenck Personality Questionnaire was shown to be connected with variability of the reaction time in the test of reactability to selected visual stimulus, disregarding the reaction rate. The effect of extraversion is partly reflected by the tendency of the sanguine temperament type to react in a balanced manner (i.e. with low reaction time variability during the reactability test. Due to the relatively low number of other temperament types in our sample, it is not possible to draw any conclusions in this regard. Analýza emocionální stability a reaktibility studentů tělesné výchovy Tento příspěvek poukazuje na možnou asociaci mezi emocionální stabilitou a časovou variabilitou dob reakcí u studentů tělesné výchovy. Lze konstatovat, že studie potvrdila naše předpoklady vycházející z odborných prací na obdobná témata. Výzkumný soubor vykazoval předpokládané charakteristiky, především nižších hodnot neuroticismu a vyšší extroverze oproti nesportující populaci. Emocionální stabilita vyjádřená pomocí dimenze neuroticismu (v EPQ-R se ukázala v asociaci s časovou variabilitou dob reakcí v testu reaktibility na výběrový zrakový podnět bez ohledu na rychlost reakce. Vliv extroverze do jisté míry odráží naznačená tendence sangvinického typu temperamentu reagovat vyrovnaně (tedy s nízkou časovou variabilitou dob
Stabilization of Parametric Roll Resonance with Active U-Tanks via Lyapunov Control Design
DEFF Research Database (Denmark)
Holden, Christian; Galeazzi, Roberto; Fossen, Thor Inge
2009-01-01
Parametric ship roll resonance is a phenomenon where a ship can rapidly develop high roll motion while sailing in longitudinal waves. This effect can be described mathematically by periodic changes of the parameters of the equations of motion, which lead to a bifurcation. In this paper, the control...
Palatella, Luigi; Trevisan, Anna; Rambaldi, Sandro
2013-08-01
Valuable information for estimating the traffic flow is obtained with current GPS technology by monitoring position and velocity of vehicles. In this paper, we present a proof of concept study that shows how the traffic state can be estimated using only partial and noisy data by assimilating them in a dynamical model. Our approach is based on a data assimilation algorithm, developed by the authors for chaotic geophysical models, designed to be equivalent but computationally much less demanding than the traditional extended Kalman filter. Here we show that the algorithm is even more efficient if the system is not chaotic and demonstrate by numerical experiments that an accurate reconstruction of the complete traffic state can be obtained at a very low computational cost by monitoring only a small percentage of vehicles.
Precessing rotating flows with additional shear: stability analysis.
Salhi, A; Cambon, C
2009-03-01
We consider unbounded precessing rotating flows in which vertical or horizontal shear is induced by the interaction between the solid-body rotation (with angular velocity Omega(0)) and the additional "precessing" Coriolis force (with angular velocity -epsilonOmega(0)), normal to it. A "weak" shear flow, with rate 2epsilon of the same order of the Poincaré "small" ratio epsilon , is needed for balancing the gyroscopic torque, so that the whole flow satisfies Euler's equations in the precessing frame (the so-called admissibility conditions). The base flow case with vertical shear (its cross-gradient direction is aligned with the main angular velocity) corresponds to Mahalov's [Phys. Fluids A 5, 891 (1993)] precessing infinite cylinder base flow (ignoring boundary conditions), while the base flow case with horizontal shear (its cross-gradient direction is normal to both main and precessing angular velocities) corresponds to the unbounded precessing rotating shear flow considered by Kerswell [Geophys. Astrophys. Fluid Dyn. 72, 107 (1993)]. We show that both these base flows satisfy the admissibility conditions and can support disturbances in terms of advected Fourier modes. Because the admissibility conditions cannot select one case with respect to the other, a more physical derivation is sought: Both flows are deduced from Poincaré's [Bull. Astron. 27, 321 (1910)] basic state of a precessing spheroidal container, in the limit of small epsilon . A Rapid distortion theory (RDT) type of stability analysis is then performed for the previously mentioned disturbances, for both base flows. The stability analysis of the Kerswell base flow, using Floquet's theory, is recovered, and its counterpart for the Mahalov base flow is presented. Typical growth rates are found to be the same for both flows at very small epsilon , but significant differences are obtained regarding growth rates and widths of instability bands, if larger epsilon values, up to 0.2, are considered. Finally
In situ vitrification: application analysis for stabilization of transuranic waste
International Nuclear Information System (INIS)
Oma, K.H.; Farnsworth, R.K.; Rusin, J.M.
1982-09-01
The in situ vitrification process builds upon the electric melter technology previously developed for high-level waste immobilization. In situ vitrification converts buried wastes and contaminated soil to an extremely durable glass and crystalline waste form by melting the materials, in place, using joule heating. Once the waste materials have been solidified, the high integrity waste form should not cause future ground subsidence. Environmental transport of the waste due to water or wind erosion, and plant or animal intrusion, is minimized. Environmental studies are currently being conducted to determine whether additional stabilization is required for certain in-ground transuranic waste sites. An applications analysis has been performed to identify several in situ vitrification process limitations which may exist at transuranic waste sites. Based on the process limit analysis, in situ vitrification is well suited for solidification of most in-ground transuranic wastes. The process is best suited for liquid disposal sites. A site-specific performance analysis, based on safety, health, environmental, and economic assessments, will be required to determine for which sites in situ vitrification is an acceptable disposal technique. Process economics of in situ vitrification compare favorably with other in-situ solidification processes and are an order of magnitude less than the costs for exhumation and disposal in a repository. Leachability of the vitrified product compares closely with that of Pyrex glass and is significantly better than granite, marble, or bottle glass. Total release to the environment from a vitrified waste site is estimated to be less than 10 -5 parts per year. 32 figures, 30 tables
Directory of Open Access Journals (Sweden)
G. Kondrat'ev
1999-10-01
Full Text Available In this article some ideas of Hamilton mechanics and differential-algebraic Geometry are used to exact definition of the potential function (Bellman-Lyapunov function in the optimal stabilization problem of smooth finite-dimensional systems.
ON THE BOUNDEDNESS AND THE STABILITY OF SOLUTION TO THIRD ORDER NON-LINEAR DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
In this paper we investigate the global asymptotic stability,boundedness as well as the ultimate boundedness of solutions to a general third order nonlinear differential equation,using complete Lyapunov function.
Stability analysis of a boundary layer over a hump using parabolized stability equations
Energy Technology Data Exchange (ETDEWEB)
Gao, B; Park, D H; Park, S O, E-mail: sopark@kaist.ac.kr [Division of Aerospace Engineering, Korea Advanced Institute of Science and Technology, Gusong-dong, Yusong-gu, Daejeon 305-701 (Korea, Republic of)
2011-10-15
Parabolized stability equations (PSEs) were used to investigate the stability of boundary layer flows over a small hump. The applicability of PSEs to flows with a small separation bubble was examined by comparing the result with DNS data. It was found that PSEs can efficiently track the disturbance waves with an acceptable accuracy in spite of a small separation bubble. A typical evolution scenario of Tollmien-Schlichting (TS) wave is presented. The adverse pressure gradient and the flow separation due to the hump have a strong effect on the amplification of the disturbances. The effect of hump width and height is also examined. When the width of the hump is reduced, the amplification factor is increased. The height of the hump is found to obviously influence the stability only when it is greater than the critical layer thickness.
Stability analysis of a boundary layer over a hump using parabolized stability equations
International Nuclear Information System (INIS)
Gao, B; Park, D H; Park, S O
2011-01-01
Parabolized stability equations (PSEs) were used to investigate the stability of boundary layer flows over a small hump. The applicability of PSEs to flows with a small separation bubble was examined by comparing the result with DNS data. It was found that PSEs can efficiently track the disturbance waves with an acceptable accuracy in spite of a small separation bubble. A typical evolution scenario of Tollmien-Schlichting (TS) wave is presented. The adverse pressure gradient and the flow separation due to the hump have a strong effect on the amplification of the disturbances. The effect of hump width and height is also examined. When the width of the hump is reduced, the amplification factor is increased. The height of the hump is found to obviously influence the stability only when it is greater than the critical layer thickness.
Analysis of the gyroscopic stabilization of a system of rigid bodies
DEFF Research Database (Denmark)
Kliem, Wolfhard; Seyranian, Alexander P.
1997-01-01
We study the gyroscopic stability of a three-body system. A new method of finding stability regions, based on mechanism and criteria for gyroscopic stabilization, is presented. Of particular interest in this connection is the theory of interaction of eigenvalues. This leads to a complete 3......-dimensional analysis, which shows the regions of stability, divergence, and flutter of a simple model of a rotating spaceship....
Analysis of the CAREM reactor's primary loop stability
International Nuclear Information System (INIS)
Mazzi, R.
1990-01-01
The results obtained to determine the stability conditions of the CAREM reactor's primary loop, using techniques based on the frequential response to the system, are presented. The stability margins were evaluated employing different alternatives; all of them predict a behaviour acceptable to the nominal working conditions. (Author) [es
Harmonics and voltage stability analysis in power systems including ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
two parameters affecting power quality – harmonics and voltage stability. ... is necessary to pay attention to energy system stability in the planning, management, and ... where k ∈ {m, m + 1,... ,n} and n is total number of the buses in the system.
Stability analysis of a class of fractional delay differential equations
Indian Academy of Sciences (India)
Abstract. In this paper we analyse stability of nonlinear fractional order delay differential equa- tions of the form Dα y(t) = af (y(t − τ )) − by(t), where Dα is a Caputo fractional derivative of order 0 < α ≤ 1. We describe stability regions using critical curves. To explain the proposed theory, we discuss fractional order logistic ...
Stability analysis of a class of fractional delay differential equations
Indian Academy of Sciences (India)
In this paper we analyse stability of nonlinear fractional order delay differential equations of the form D y ( t ) = a f ( y ( t − ) ) − by ( t ) , where D is a Caputo fractional derivative of order 0 < ≤ 1. We describe stability regions using critical curves. To explain the proposed theory, we discuss fractional order logistic ...
Systematic analysis of stability patterns in plant primary metabolism.
Directory of Open Access Journals (Sweden)
Dorothee Girbig
Full Text Available Metabolic networks are characterized by complex interactions and regulatory mechanisms between many individual components. These interactions determine whether a steady state is stable to perturbations. Structural kinetic modeling (SKM is a framework to analyze the stability of metabolic steady states that allows the study of the system Jacobian without requiring detailed knowledge about individual rate equations. Stability criteria can be derived by generating a large number of structural kinetic models (SK-models with randomly sampled parameter sets and evaluating the resulting Jacobian matrices. Until now, SKM experiments applied univariate tests to detect the network components with the largest influence on stability. In this work, we present an extended SKM approach relying on supervised machine learning to detect patterns of enzyme-metabolite interactions that act together in an orchestrated manner to ensure stability. We demonstrate its application on a detailed SK-model of the Calvin-Benson cycle and connected pathways. The identified stability patterns are highly complex reflecting that changes in dynamic properties depend on concerted interactions between several network components. In total, we find more patterns that reliably ensure stability than patterns ensuring instability. This shows that the design of this system is strongly targeted towards maintaining stability. We also investigate the effect of allosteric regulators revealing that the tendency to stability is significantly increased by including experimentally determined regulatory mechanisms that have not yet been integrated into existing kinetic models.
International Nuclear Information System (INIS)
Vittal, V.
2000-01-01
The electric utility industry is undergoing unprecedented changes in its structure worldwide. With the advent of an open market environment and competition in the industry, and restructuring of the industry into separate generation, transmission, and distribution entities, new issues in power system operation and planning are inevitable. One of the major consequences of this new electric utility environment is the greater emphasis on reliability and secure operation of the power system. This paper examines the impact of restructuring on power system dynamic analysis. It specifically addresses issues related to transient stability analysis and small-signal stability analysis. Four major topics to examine the effect on the nature of studies conducted are considered. These topics are (1) system adequacy and security, (2) system modeling data requirements, (3) system protection and control, and (4) system restoration. The consequences and impact of each of these topics on the nature of the studies conducted are examined and discussed. The emphasis on greater reliability has led to a clearer enunciation of standards, measurements, and guides in some countries. These requirements will result in: (1) more measurements on existing systems, (2) rigorous analysis of transient stability and small-signal stability to determine operating limits and plan systems, (3) greater emphasis on studies to verify coordination and proper performance of protection and controls, and (4) development of a detailed plan for system restoration in the case of wide-spread outages
Improving Power System Stability Using Transfer Function: A Comparative Analysis
Directory of Open Access Journals (Sweden)
G. Shahgholian
2017-10-01
Full Text Available In this paper, a small-signal dynamic model of a single-machine infinite-bus (SMIB power system that includes IEEE type-ST1 excitation system and PSS based on transfer fu¬n¬c¬¬tion structure is presented. The changes in the operating co¬n¬dition of a power system on dynamic performance have been exa¬m¬ined. The dynamic performance of the closed-loop system is ana¬lyzed base on its eigenvalues. The effectiveness of the par¬a¬m¬e¬t¬ers changes on dynamic stability is verified by simulation res¬u¬l¬ts. Three types of PSS have been considered for analysis: (a the derivative PSS, (b the lead-lag PSS or conventional PSS, and (c the proportional-integral-derivative PSS. The objective fu¬nc¬t¬i¬o¬n is formulated to increase the dam¬¬ping ratio of the electromechanical mode eigenvalues. Simu¬la¬tion results show that the PID-PSS performs better for less ov¬e¬r¬shoot and less settling time comp¬ared with the CPSS and DPSS un¬der different load ope¬ration and the significant system pa¬r¬am¬eter variation conditions.
Stability analysis of an implicitly defined labor market model
Mendes, Diana A.; Mendes, Vivaldo M.
2008-06-01
Until very recently, the pervasive existence of models exhibiting well-defined backward dynamics but ill-defined forward dynamics in economics and finance has apparently posed no serious obstacles to the analysis of their dynamics and stability, despite the problems that may arise from possible erroneous conclusions regarding theoretical considerations and policy prescriptions from such models. A large number of papers have dealt with this problem in the past by assuming the existence of symmetry between forward and backward dynamics, even in the case when the map cannot be invertible either forward or backwards. However, this procedure has been seriously questioned over the last few years in a series of papers dealing with implicit difference equations and inverse limit spaces. This paper explores the search and matching labor market model developed by Bhattacharya and Bunzel [J. Bhattacharya, H. Bunzel, Chaotic Planning Solution in the Textbook Model of Equilibrium Labor Market Search and Matching, Mimeo, Iowa State University, 2002; J. Bhattacharya, H. Bunzel, Economics Bulletin 5 (19) (2003) 1-10], with the following objectives in mind: (i) to show that chaotic dynamics may still be present in the model for acceptable parameter values, (ii) to clarify some open questions related with the admissible dynamics in the forward looking setting, by providing a rigorous proof of the existence of cyclic and chaotic dynamics through the application of tools from symbolic dynamics and inverse limit theory.
Slope stability analysis using limit equilibrium method in nonlinear criterion.
Lin, Hang; Zhong, Wenwen; Xiong, Wei; Tang, Wenyu
2014-01-01
In slope stability analysis, the limit equilibrium method is usually used to calculate the safety factor of slope based on Mohr-Coulomb criterion. However, Mohr-Coulomb criterion is restricted to the description of rock mass. To overcome its shortcomings, this paper combined Hoek-Brown criterion and limit equilibrium method and proposed an equation for calculating the safety factor of slope with limit equilibrium method in Hoek-Brown criterion through equivalent cohesive strength and the friction angle. Moreover, this paper investigates the impact of Hoek-Brown parameters on the safety factor of slope, which reveals that there is linear relation between equivalent cohesive strength and weakening factor D. However, there are nonlinear relations between equivalent cohesive strength and Geological Strength Index (GSI), the uniaxial compressive strength of intact rock σ ci , and the parameter of intact rock m i . There is nonlinear relation between the friction angle and all Hoek-Brown parameters. With the increase of D, the safety factor of slope F decreases linearly; with the increase of GSI, F increases nonlinearly; when σ ci is relatively small, the relation between F and σ ci is nonlinear, but when σ ci is relatively large, the relation is linear; with the increase of m i , F decreases first and then increases.
Stability Analysis of Reactive Multiphase Slug Flows in Microchannels
Directory of Open Access Journals (Sweden)
Alejandro A. Munera Parra
2014-05-01
Full Text Available Conducting multiphase reactions in micro-reactors is a promising strategy for intensifying chemical and biochemical processes. A major unresolved challenge is to exploit the considerable benefits offered by micro-scale operation for industrial scale throughputs by numbering-up whilst retaining the underlying advantageous flow characteristics of the single channel system in multiple parallel channels. Fabrication and installation tolerances in the individual micro-channels result in different pressure losses and, thus, a fluid maldistribution. In this work, an additional source of maldistribution, namely the flow multiplicities, which can arise in a multiphase reactive or extractive flow in otherwise identical micro-channels, was investigated. A detailed experimental and theoretical analysis of the flow stability with and without reaction for both gas-liquid and liquid-liquid slug flow has been developed. The model has been validated using the extraction of acetic acid from n-heptane with the ionic liquid 1-Ethyl-3-methylimidazolium ethyl sulfate. The results clearly demonstrate that the coupling between flow structure, the extent of reaction/extraction and pressure drop can result in multiple operating states, thus, necessitating an active measurement and control concept to ensure uniform behavior and optimal performance.
Stability analysis of lower dimensional gravastars in noncommutative geometry
Energy Technology Data Exchange (ETDEWEB)
Banerjee, Ayan [Jadavpur University, Department of Mathematics, Kolkata (India); Hansraj, Sudan [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Durban (South Africa)
2016-11-15
The Banados et al. (Phys. Rev. Lett 69:1849, 1992), black hole solution is revamped from the Einstein field equations in (2 + 1)-dimensional anti-de Sitter spacetime, in a context of noncommutative geometry (Phys. Rev. D 87:084014, 2013). In this article, we explore the exact gravastar solutions in three-dimensional anti-de Sitter space given in the same geometry. As a first step we derive BTZ solution assuming the source of energy density as point-like structures in favor of smeared objects, where the particle mass M, is diffused throughout a region of linear size √(α) and is described by a Gaussian function of finite width rather than a Dirac delta function. We matched our interior solution to an exterior BTZ spacetime at a junction interface situated outside the event horizon. Furthermore, a stability analysis is carried out for the specific case when χ < 0.214 under radial perturbations about the static equilibrium solutions. To give theoretical support we are also trying to explore their physical properties and characteristics. (orig.)
Crack stability analysis of low alloy steel primary coolant pipe
Energy Technology Data Exchange (ETDEWEB)
Tanaka, T.; Kameyama, M. [Kansai Electric Power Company, Osaka (Japan); Urabe, Y. [Mitsubishi Heavy Industries, Ltd., Takasago (Japan)] [and others
1997-04-01
At present, cast duplex stainless steel has been used for the primary coolant piping of PWRs in Japan and joints of dissimilar material have been applied for welding to reactor vessels and steam generators. For the primary coolant piping of the next APWR plants, application of low alloy steel that results in designing main loops with the same material is being studied. It means that there is no need to weld low alloy steel with stainless steel and that makes it possible to reduce the welding length. Attenuation of Ultra Sonic Wave Intensity is lower for low alloy steel than for stainless steel and they have advantageous inspection characteristics. In addition to that, the thermal expansion rate is smaller for low alloy steel than for stainless steel. In consideration of the above features of low alloy steel, the overall reliability of primary coolant piping is expected to be improved. Therefore, for the evaluation of crack stability of low alloy steel piping to be applied for primary loops, elastic-plastic future mechanics analysis was performed by means of a three-dimensioned FEM. The evaluation results for the low alloy steel pipings show that cracks will not grow into unstable fractures under maximum design load conditions, even when such a circumferential crack is assumed to be 6 times the size of the wall thickness.
Preliminary Analysis of Slope Stability in Kuok and Surrounding Areas
Directory of Open Access Journals (Sweden)
Dewandra Bagus Eka Putra
2016-12-01
Full Text Available The level of slope influenced by the condition of the rocks beneath the surface. On high level of slopes, amount of surface runoff and water transport energy is also enlarged. This caused by greater gravity, in line with the surface tilt from the horizontal plane. In other words, topsoil eroded more and more. When the slope becomes twice as steep, then the amount of erosion per unit area be 2.0 - 2.5 times more. Kuok and surrounding area is the road access between the West Sumatra and Riau which plays an important role economies of both provinces. The purpose of this study is to map the locations that have fairly steep slopes and potential mode of landslides. Based on SRTM data obtained, the roads in Kuok area has a minimum elevation of + 33 m and a maximum + 217.329 m. Rugged road conditions with slope ranging from 24.08 ° to 44.68 ° causing this area having frequent landslides. The result of slope stability analysis in a slope near the Water Power Plant Koto Panjang, indicated that mode of active failure is toppling failure or rock fall and the potential zone of failure is in the center part of the slope.
High beta and second stability region transport and stability analysis: Technical progress report
International Nuclear Information System (INIS)
Hughes, M.H.; Phillips, M.W.
1995-03-01
This report summarizes MHD equilibrium and stability studies carried out at Northrop Grumman's Advanced Technology and Development Center during the 12 month period starting March 1, 1994. Progress is reported in both ideal and resistive MHD modeling of TFTR plasmas. The development of codes to calculate the significant effects of highly anisotropic pressure distributions is discussed along with results from this model
High beta and second stability region transport and stability analysis. Technical progress report
International Nuclear Information System (INIS)
Hughes, M.H.; Phillips, M.W.
1994-09-01
This report summarizes MHD equilibrium and stability studies carried out at Grumman's Corporate Research Center during the 6 month period starting March 1, 1994. Progress is reported in both ideal and resistive MHD modeling of TFTR plasmas. The development of codes to calculate the significant effects of highly anisotropic pressure distributions is discussed along with initial results from this model
Dadashzadeh, N.; Duzgun, H. S. B.; Yesiloglu-Gultekin, N.
2017-08-01
While advanced numerical techniques in slope stability analysis are successfully used in deterministic studies, they have so far found limited use in probabilistic analyses due to their high computation cost. The first-order reliability method (FORM) is one of the most efficient probabilistic techniques to perform probabilistic stability analysis by considering the associated uncertainties in the analysis parameters. However, it is not possible to directly use FORM in numerical slope stability evaluations as it requires definition of a limit state performance function. In this study, an integrated methodology for probabilistic numerical modeling of rock slope stability is proposed. The methodology is based on response surface method, where FORM is used to develop an explicit performance function from the results of numerical simulations. The implementation of the proposed methodology is performed by considering a large potential rock wedge in Sumela Monastery, Turkey. The accuracy of the developed performance function to truly represent the limit state surface is evaluated by monitoring the slope behavior. The calculated probability of failure is compared with Monte Carlo simulation (MCS) method. The proposed methodology is found to be 72% more efficient than MCS, while the accuracy is decreased with an error of 24%.
Hydrodynamic Stability Analysis of Particle-Laden Solid Rocket Motors
Elliott, T. S.; Majdalani, J.
2014-11-01
Fluid-wall interactions within solid rocket motors can result in parietal vortex shedding giving rise to hydrodynamic instabilities, or unsteady waves, that translate into pressure oscillations. The oscillations can result in vibrations observed by the rocket, rocket subsystems, or payload, which can lead to changes in flight characteristics, design failure, or other undesirable effects. For many years particles have been embedded in solid rocket propellants with the understanding that their presence increases specific impulse and suppresses fluctuations in the flowfield. This study utilizes a two dimensional framework to understand and quantify the aforementioned two-phase flowfield inside a motor case with a cylindrical grain perforation. This is accomplished through the use of linearized Navier-Stokes equations with the Stokes drag equation and application of the biglobal ansatz. Obtaining the biglobal equations for analysis requires quantification of the mean flowfield within the solid rocket motor. To that end, the extended Taylor-Culick form will be utilized to represent the gaseous phase of the mean flowfield while the self-similar form will be employed for the particle phase. Advancing the mean flowfield by quantifying the particle mass concentration with a semi-analytical solution the finalized mean flowfield is combined with the biglobal equations resulting in a system of eight partial differential equations. This system is solved using an eigensolver within the framework yielding the entire spectrum of eigenvalues, frequency and growth rate components, at once. This work will detail the parametric analysis performed to demonstrate the stabilizing and destabilizing effects of particles within solid rocket combustion.
Hydrodynamic Stability Analysis of Particle-Laden Solid Rocket Motors
International Nuclear Information System (INIS)
Elliott, T S; Majdalani, J
2014-01-01
Fluid-wall interactions within solid rocket motors can result in parietal vortex shedding giving rise to hydrodynamic instabilities, or unsteady waves, that translate into pressure oscillations. The oscillations can result in vibrations observed by the rocket, rocket subsystems, or payload, which can lead to changes in flight characteristics, design failure, or other undesirable effects. For many years particles have been embedded in solid rocket propellants with the understanding that their presence increases specific impulse and suppresses fluctuations in the flowfield. This study utilizes a two dimensional framework to understand and quantify the aforementioned two-phase flowfield inside a motor case with a cylindrical grain perforation. This is accomplished through the use of linearized Navier-Stokes equations with the Stokes drag equation and application of the biglobal ansatz. Obtaining the biglobal equations for analysis requires quantification of the mean flowfield within the solid rocket motor. To that end, the extended Taylor-Culick form will be utilized to represent the gaseous phase of the mean flowfield while the self-similar form will be employed for the particle phase. Advancing the mean flowfield by quantifying the particle mass concentration with a semi-analytical solution the finalized mean flowfield is combined with the biglobal equations resulting in a system of eight partial differential equations. This system is solved using an eigensolver within the framework yielding the entire spectrum of eigenvalues, frequency and growth rate components, at once. This work will detail the parametric analysis performed to demonstrate the stabilizing and destabilizing effects of particles within solid rocket combustion
Some stability and boundedness criteria for a class of Volterra integro-differential systems
Directory of Open Access Journals (Sweden)
Jito Vanualailai
2002-01-01
Full Text Available Using Lyapunov and Lyapunov-like functionals, we study the stability and boundedness of the solutions of a system of Volterra integrodifferential equations. Our results, also extending some of the more well-known criteria, give new sufficient conditions for stability of the zero solution of the nonperturbed system, and prove that the same conditions for the perturbed system yield boundedness when the perturbation is $L^2$.
TRANSMISSION LINE-WIRE DANCING (GALLOPING – LYAPUNOV INSTABILITY
Directory of Open Access Journals (Sweden)
V. I. Vanko
2014-01-01
Full Text Available This article describes aerodynamic losses of damping, or aerodynamic instability, which we observe in experiments and in engineering practice. As applied to industrial high-voltage lines this phenomenon is usually called galloping (dancing of phase line wires. This phenolmenon can be explained by Lyapunov’s instability of equilibrium state of wires profile (cross-section. In addition to known condition of Grauert-den-Hartog’s instability there was obtained practical condition of instability, which depends only on stationary aerodynamic profile’s factor – dimensionless coefficient of head resistance and lift coefficient, and also on their derivative with respect to the angle of attack.There was suggested an effective numerical-analytical method of investigation of stability for equilibrium of profile’s state in flow, which was developed at the department “Applied mathematics” of Bauman MSTU. This method allows to determine the stationary aerodynamics characteristics of profile by numerical simulation of profile flow under different angles of attack by vortex element method and later on the application of analytical conditions of stability and Lyapunov’s instability of equilibrium positions. The obtained results during the investigation of rhombic and square profiles stability, as well as general profile of iced wire, and their comparisons with the known experiments’ results in aerodynamic tubes indicate the precision of developed methods and algorithms. The usage of mesh-free Lagrange method of vortex elements and software for their realization allows to solve also dual problems of aerohydroelasticity and to carry out direct numerical simulation of profile movement in flow. In this article the investigations’ results of different authors in this field were taken into account.
International Nuclear Information System (INIS)
Zheng Youqi; Wu Hongchun; Cao Liangzhi
2013-01-01
This paper describes the stability analysis for the coarse mesh finite difference (CMFD) acceleration used in the wavelet expansion method. The nonlinear CMFD acceleration scheme is transformed by linearization and the Fourier ansatz is introduced into the linearized formulae. The spectral radius is defined as the stability criterion, which is the least upper bound (LUB) of the largest eigenvalue of Fourier analysis matrix. The stability analysis considers the effect of mesh size (spectral length), coarse mesh division and scattering ratio. The results show that for the wavelet expansion method, the CMFD acceleration is conditionally stable. The small size of fine mesh brings stability and fast convergent. With the increase of the mesh size, the stability becomes worse. The scattering ratio does not impact the stability obviously. It makes the CMFD acceleration highly efficient in the strong scattering case. The results of Fourier analysis are verified by the numerical tests based on a homogeneous slab problem.
Lyapunov based control of hybrid energy storage system in electric vehicles
DEFF Research Database (Denmark)
El Fadil, H.; Giri, F.; Guerrero, Josep M.
2012-01-01
This paper deals with a Lyapunov based control principle in a hybrid energy storage system for electric vehicle. The storage system consists on fuel cell (FC) as a main power source and a supercapacitor (SC) as an auxiliary power source. The power stage of energy conversion consists on a boost...
A new interpretation of zero Lyapunov exponents in BKL time for Mixmaster cosmology
International Nuclear Information System (INIS)
Wu Xin
2010-01-01
A global relationship between cosmological time and Belinskii-Khalatnikov-Lifshitz (BKL) time during the entire evolution of the Mixmaster Bianchi IX universe is used to explain why all the Lyapunov exponents are zero at the BKL time. The actual reason is that the domain of the cosmological time is finite as the BKL time runs from minus infinity to infinity.
Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data
Pathak, Jaideep; Lu, Zhixin; Hunt, Brian R.; Girvan, Michelle; Ott, Edward
2017-12-01
We use recent advances in the machine learning area known as "reservoir computing" to formulate a method for model-free estimation from data of the Lyapunov exponents of a chaotic process. The technique uses a limited time series of measurements as input to a high-dimensional dynamical system called a "reservoir." After the reservoir's response to the data is recorded, linear regression is used to learn a large set of parameters, called the "output weights." The learned output weights are then used to form a modified autonomous reservoir designed to be capable of producing an arbitrarily long time series whose ergodic properties approximate those of the input signal. When successful, we say that the autonomous reservoir reproduces the attractor's "climate." Since the reservoir equations and output weights are known, we can compute the derivatives needed to determine the Lyapunov exponents of the autonomous reservoir, which we then use as estimates of the Lyapunov exponents for the original input generating system. We illustrate the effectiveness of our technique with two examples, the Lorenz system and the Kuramoto-Sivashinsky (KS) equation. In the case of the KS equation, we note that the high dimensional nature of the system and the large number of Lyapunov exponents yield a challenging test of our method, which we find the method successfully passes.
Adiabatic invariants and asymptotic behavior of Lyapunov exponents of the Schrodinger equation
International Nuclear Information System (INIS)
Delyon, F.; Foulon, P.
1986-01-01
We give an upper bound for the high-energy behavior of the Lyapunov exponent of the one-dimensional Schrodinger equation. We relate this behavior to the diffrentiability properties of the potential. As an application, this result provides an upper bound for the asymptotic length of the gaps of the Schrodinger equation
Predicting Traffic Flow in Local Area Networks by the Largest Lyapunov Exponent
Directory of Open Access Journals (Sweden)
Yan Liu
2016-01-01
Full Text Available The dynamics of network traffic are complex and nonlinear, and chaotic behaviors and their prediction, which play an important role in local area networks (LANs, are studied in detail, using the largest Lyapunov exponent. With the introduction of phase space reconstruction based on the time sequence, the high-dimensional traffic is projected onto the low dimension reconstructed phase space, and a reduced dynamic system is obtained from the dynamic system viewpoint. Then, a numerical method for computing the largest Lyapunov exponent of the low-dimensional dynamic system is presented. Further, the longest predictable time, which is related to chaotic behaviors in the system, is studied using the largest Lyapunov exponent, and the Wolf method is used to predict the evolution of the traffic in a local area network by both Dot and Interval predictions, and a reliable result is obtained by the presented method. As the conclusion, the results show that the largest Lyapunov exponent can be used to describe the sensitivity of the trajectory in the reconstructed phase space to the initial values. Moreover, Dot Prediction can effectively predict the flow burst. The numerical simulation also shows that the presented method is feasible and efficient for predicting the complex dynamic behaviors in LAN traffic, especially for congestion and attack in networks, which are the main two complex phenomena behaving as chaos in networks.
Lyapunov-Based Control Scheme for Single-Phase Grid-Connected PV Central Inverters
Meza, C.; Biel, D.; Jeltsema, D.; Scherpen, J. M. A.
A Lyapunov-based control scheme for single-phase single-stage grid-connected photovoltaic central inverters is presented. Besides rendering the closed-loop system globally stable, the designed controller is able to deal with the system uncertainty that depends on the solar irradiance. A laboratory
Analysis and design of singular Markovian jump systems
Wang, Guoliang; Yan, Xinggang
2014-01-01
This monograph is an up-to-date presentation of the analysis and design of singular Markovian jump systems (SMJSs) in which the transition rate matrix of the underlying systems is generally uncertain, partially unknown and designed. The problems addressed include stability, stabilization, H∞ control and filtering, observer design, and adaptive control. applications of Markov process are investigated by using Lyapunov theory, linear matrix inequalities (LMIs), S-procedure and the stochastic Barbalat's Lemma, among other techniques.Features of the book include:·???????? study of the stability pr
Analysis of stability parameters in relation to precipitation associated ...
Indian Academy of Sciences (India)
erty and crops; human and animal fatalities, and also aviation hazards. ... Keywords. Atmospheric instability; stability indices; Richardson number; vertical wind shear; energy-helicity index; ... ing the genesis and development of severe weather.
Analysis of stability parameters in relation to precipitation associated
Indian Academy of Sciences (India)
Atmospheric instability; stability indices; Richardson number; vertical wind ... is used to compute some important dynamic/thermodynamic parameters and are ... (i*) well indicate the occurrence of thunderstorms about 2 hours in advance.
Stability Analysis of Spacecraft Motion in the Vicinity of Asteroids
National Aeronautics and Space Administration — The objective of my proposal is to determine the stability of a spacecraft when in the vicinity of an asteroid. Orbiting an asteroid is a difficult task. The unique...
analysis and correlation of stability parameters in malting barley
African Journals Online (AJOL)
Administrator
food, feed, medicinal purposes and malt of alcoholic beverages. Stability parameters are ... and animal food, health benefits and malting and brewing in many ..... targeted for environmental conditions which are ... Market Update. Available at ...
Stability analysis of non-axisymmetric three-dimensional finite ...
Indian Academy of Sciences (India)
The present work explores the use of mass-lumping in stability ... further considers orthotropic flexible support which makes the stiffness matrix a ... symmetric rotor on rigid, isotropic and orthotropic bearing is stable in absence of a destabilizing.
Mavkov, B.; Witrant, E.; Prieur, C.; Maljaars, E.; Felici, F.; Sauter, O.; the TCV-Team
2018-05-01
In this paper, model-based closed-loop algorithms are derived for distributed control of the inverse of the safety factor profile and the plasma pressure parameter β of the TCV tokamak. The simultaneous control of the two plasma quantities is performed by combining two different control methods. The control design of the plasma safety factor is based on an infinite-dimensional setting using Lyapunov analysis for partial differential equations, while the control of the plasma pressure parameter is designed using control techniques for single-input and single-output systems. The performance and robustness of the proposed controller is analyzed in simulations using the fast plasma transport simulator RAPTOR. The control is then implemented and tested in experiments in TCV L-mode discharges using the RAPTOR model predicted estimates for the q-profile. The distributed control in TCV is performed using one co-current and one counter-current electron cyclotron heating actuation.
Stabilization of exact nonlinear Timoshenko beams in space by boundary feedback
Do, K. D.
2018-05-01
Boundary feedback controllers are designed to stabilize Timoshenko beams with large translational and rotational motions in space under external disturbances. The exact nonlinear partial differential equations governing motion of the beams are derived and used in the control design. The designed controllers guarantee globally practically asymptotically (and locally practically exponentially) stability of the beam motions at the reference state. The control design, well-posedness and stability analysis are based on various relationships between the earth-fixed and body-fixed coordinates, Sobolev embeddings, and a Lyapunov-type theorem developed to study well-posedness and stability for a class of evolution systems in Hilbert space. Simulation results are included to illustrate the effectiveness of the proposed control design.
Population Stabilization in India: A Sub-State level Analysis
Purohit C, Dr Brijesh
2007-01-01
The study aims at analyzing economic and policy factors impinging upon population stabilization measures at the district (sub-state level) in India. It reflects upon popularly debated notions, namely, that development is the best contraceptive or whether contraceptive is the best development. In order to reflect upon this notion, we hypothesize that the factors determining the success of population stabilization measures are likely to be different across rich and poor states. It is more likel...
On the pth moment stability of the binary airfoil induced by bounded noise
International Nuclear Information System (INIS)
Wu, Jiancheng; Li, Xuan; Liu, Xianbin
2017-01-01
Highlights: • We obtain finite pth moment Lyapunov exponent for binary airfoil subject to a bounded noise. • Based on perturbation approach and Green's functions method, second differential eigenvalue equation governing moment Lyapunov exponent is established. • The types of singular points are investigated. • The eigenvalue problem is solved analytically and numerically. • The effects of noise and system parameters on the moment Lyapunov exponent and the stochastic stability of the system are discussed. - Abstract: In the paper, the stochastic stability of the binary airfoil subject to the effect of a bounded noise is studied through the determination of moment Lyapunov exponents. The noise excitation here is often used to model a realistic model of noise in many engineering application. The partial differential eigenvalue problem governing the moment Lyapunov exponent is established. Via the Feller boundary classification, the types of singular points are discussed here, and for the system discussed, the singular points only exist in end points. The fundamental methods used are the perturbation approach and the Green's functions method. With these methods, the second-order expansions of the moment Lyapunov exponents are obtained, which are shown to be in good agreement with those obtained using Monte Carlo simulation. The effects of noise and system parameters on the moment Lyapunov exponent and the stochastic stability of the binary airfoil system are discussed.
Directory of Open Access Journals (Sweden)
Jianguo Ren
2014-01-01
Full Text Available A new computer virus propagation model with delay and incomplete antivirus ability is formulated and its global dynamics is analyzed. The existence and stability of the equilibria are investigated by resorting to the threshold value R0. By analysis, it is found that the model may undergo a Hopf bifurcation induced by the delay. Correspondingly, the critical value of the Hopf bifurcation is obtained. Using Lyapunov functional approach, it is proved that, under suitable conditions, the unique virus-free equilibrium is globally asymptotically stable if R01. Numerical examples are presented to illustrate possible behavioral scenarios of the mode.
Directory of Open Access Journals (Sweden)
Yongkun Li
2009-01-01
Full Text Available Based on the theory of calculus on time scales, the homeomorphism theory, Lyapunov functional method, and some analysis techniques, sufficient conditions are obtained for the existence, uniqueness, and global exponential stability of the equilibrium point of Cohen-Grossberg bidirectional associative memory (BAM neural networks with distributed delays and impulses on time scales. This is the first time applying the time-scale calculus theory to unify the discrete-time and continuous-time Cohen-Grossberg BAM neural network with impulses under the same framework.
Stability analysis of multi-group deterministic and stochastic epidemic models with vaccination rate
International Nuclear Information System (INIS)
Wang Zhi-Gang; Gao Rui-Mei; Fan Xiao-Ming; Han Qi-Xing
2014-01-01
We discuss in this paper a deterministic multi-group MSIR epidemic model with a vaccination rate, the basic reproduction number ℛ 0 , a key parameter in epidemiology, is a threshold which determines the persistence or extinction of the disease. By using Lyapunov function techniques, we show if ℛ 0 is greater than 1 and the deterministic model obeys some conditions, then the disease will prevail, the infective persists and the endemic state is asymptotically stable in a feasible region. If ℛ 0 is less than or equal to 1, then the infective disappear so the disease dies out. In addition, stochastic noises around the endemic equilibrium will be added to the deterministic MSIR model in order that the deterministic model is extended to a system of stochastic ordinary differential equations. In the stochastic version, we carry out a detailed analysis on the asymptotic behavior of the stochastic model. In addition, regarding the value of ℛ 0 , when the stochastic system obeys some conditions and ℛ 0 is greater than 1, we deduce the stochastic system is stochastically asymptotically stable. Finally, the deterministic and stochastic model dynamics are illustrated through computer simulations. (general)
Stability analysis of high temperature superconducting coil in liquid hydrogen
International Nuclear Information System (INIS)
Nakayama, T.; Yagai, T.; Tsuda, M.; Hamajima, T.
2007-01-01
Recently, it is expected that hydrogen plays an important role in energy source including electric power in near future. Liquid hydrogen has high potential for cooling down superconducting coil wound with high temperature superconductors (HTS), such as BSCCO, YBCO. In this paper, we study stabilities of the coils wound with BSCCO tapes, which are immersed in the liquid hydrogen, and compare stability results with those cooled by liquid helium. We treat a minimum propagation zone (MPZ) theory to evaluate the coil stability considering boiling heat flux of the liquid hydrogen, and specific heat, heat conduction and resistivity of HTS materials as a function of temperature. It is found that the coil cooled by the liquid hydrogen has higher stability margin than that cooled by the liquid helium. We compare the stability margins of both coils wound with Bi-2223/Ag tape and Bi-2212/Ag tape in liquid hydrogen. As a result, it is found that the stability of Bi-2212 coil is equivalent to that of Bi-2223 coil in low and high magnetic field, while the maximum current of Bi-2212 coil exceeds a little bit that of Bi-2223 coil in both magnetic fields
Kinematic Analysis of a Posterior-stabilized Knee Prosthesis
Zhao, Zhi-Xin; Wen, Liang; Qu, Tie-Bing; Hou, Li-Li; Xiang, Dong; Bin, Jia
2015-01-01
Background: The goal of total knee arthroplasty (TKA) is to restore knee kinematics. Knee prosthesis design plays a very important role in successful restoration. Here, kinematics models of normal and prosthetic knees were created and validated using previously published data. Methods: Computed tomography and magnetic resonance imaging scans of a healthy, anticorrosive female cadaver were used to establish a model of the entire lower limbs, including the femur, tibia, patella, fibula, distal femur cartilage, and medial and lateral menisci, as well as the anterior cruciate, posterior cruciate, medial collateral, and lateral collateral ligaments. The data from the three-dimensional models of the normal knee joint and a posterior-stabilized (PS) knee prosthesis were imported into finite element analysis software to create the final kinematic model of the TKA prosthesis, which was then validated by comparison with a previous study. The displacement of the medial/lateral femur and the internal rotation angle of the tibia were analyzed during 0–135° flexion. Results: Both the output data trends and the measured values derived from the normal knee's kinematics model were very close to the results reported in a previous in vivo study, suggesting that this model can be used for further analyses. The PS knee prosthesis underwent an abnormal forward displacement compared with the normal knee and has insufficient, or insufficiently aggressive, “rollback” compared with the lateral femur of the normal knee. In addition, a certain degree of reverse rotation occurs during flexion of the PS knee prosthesis. Conclusions: There were still several differences between the kinematics of the PS knee prosthesis and a normal knee, suggesting room for improving the design of the PS knee prosthesis. The abnormal kinematics during early flexion shows that the design of the articular surface played a vital role in improving the kinematics of the PS knee prosthesis. PMID:25591565
Kinematic analysis of a posterior-stabilized knee prosthesis.
Zhao, Zhi-Xin; Wen, Liang; Qu, Tie-Bing; Hou, Li-Li; Xiang, Dong; Bin, Jia
2015-01-20
The goal of total knee arthroplasty (TKA) is to restore knee kinematics. Knee prosthesis design plays a very important role in successful restoration. Here, kinematics models of normal and prosthetic knees were created and validated using previously published data. Computed tomography and magnetic resonance imaging scans of a healthy, anticorrosive female cadaver were used to establish a model of the entire lower limbs, including the femur, tibia, patella, fibula, distal femur cartilage, and medial and lateral menisci, as well as the anterior cruciate, posterior cruciate, medial collateral, and lateral collateral ligaments. The data from the three-dimensional models of the normal knee joint and a posterior-stabilized (PS) knee prosthesis were imported into finite element analysis software to create the final kinematic model of the TKA prosthesis, which was then validated by comparison with a previous study. The displacement of the medial/lateral femur and the internal rotation angle of the tibia were analyzed during 0-135° flexion. Both the output data trends and the measured values derived from the normal knee's kinematics model were very close to the results reported in a previous in vivo study, suggesting that this model can be used for further analyses. The PS knee prosthesis underwent an abnormal forward displacement compared with the normal knee and has insufficient, or insufficiently aggressive, "rollback" compared with the lateral femur of the normal knee. In addition, a certain degree of reverse rotation occurs during flexion of the PS knee prosthesis. There were still several differences between the kinematics of the PS knee prosthesis and a normal knee, suggesting room for improving the design of the PS knee prosthesis. The abnormal kinematics during early flexion shows that the design of the articular surface played a vital role in improving the kinematics of the PS knee prosthesis.
Kinematic Analysis of a Posterior-stabilized Knee Prosthesis
Directory of Open Access Journals (Sweden)
Zhi-Xin Zhao
2015-01-01
Full Text Available Background: The goal of total knee arthroplasty (TKA is to restore knee kinematics. Knee prosthesis design plays a very important role in successful restoration. Here, kinematics models of normal and prosthetic knees were created and validated using previously published data. Methods: Computed tomography and magnetic resonance imaging scans of a healthy, anticorrosive female cadaver were used to establish a model of the entire lower limbs, including the femur, tibia, patella, fibula, distal femur cartilage, and medial and lateral menisci, as well as the anterior cruciate, posterior cruciate, medial collateral, and lateral collateral ligaments. The data from the three-dimensional models of the normal knee joint and a posterior-stabilized (PS knee prosthesis were imported into finite element analysis software to create the final kinematic model of the TKA prosthesis, which was then validated by comparison with a previous study. The displacement of the medial/lateral femur and the internal rotation angle of the tibia were analyzed during 0-135° flexion. Results: Both the output data trends and the measured values derived from the normal knee′s kinematics model were very close to the results reported in a previous in vivo study, suggesting that this model can be used for further analyses. The PS knee prosthesis underwent an abnormal forward displacement compared with the normal knee and has insufficient, or insufficiently aggressive, "rollback" compared with the lateral femur of the normal knee. In addition, a certain degree of reverse rotation occurs during flexion of the PS knee prosthesis. Conclusions: There were still several differences between the kinematics of the PS knee prosthesis and a normal knee, suggesting room for improving the design of the PS knee prosthesis. The abnormal kinematics during early flexion shows that the design of the articular surface played a vital role in improving the kinematics of the PS knee prosthesis.
Dynamic remedial action scheme using online transient stability analysis
Shrestha, Arun
Economic pressure and environmental factors have forced the modern power systems to operate closer to their stability limits. However, maintaining transient stability is a fundamental requirement for the operation of interconnected power systems. In North America, power systems are planned and operated to withstand the loss of any single or multiple elements without violating North American Electric Reliability Corporation (NERC) system performance criteria. For a contingency resulting in the loss of multiple elements (Category C), emergency transient stability controls may be necessary to stabilize the power system. Emergency control is designed to sense abnormal conditions and subsequently take pre-determined remedial actions to prevent instability. Commonly known as either Remedial Action Schemes (RAS) or as Special/System Protection Schemes (SPS), these emergency control approaches have been extensively adopted by utilities. RAS are designed to address specific problems, e.g. to increase power transfer, to provide reactive support, to address generator instability, to limit thermal overloads, etc. Possible remedial actions include generator tripping, load shedding, capacitor and reactor switching, static VAR control, etc. Among various RAS types, generation shedding is the most effective and widely used emergency control means for maintaining system stability. In this dissertation, an optimal power flow (OPF)-based generation-shedding RAS is proposed. This scheme uses online transient stability calculation and generator cost function to determine appropriate remedial actions. For transient stability calculation, SIngle Machine Equivalent (SIME) technique is used, which reduces the multimachine power system model to a One-Machine Infinite Bus (OMIB) equivalent and identifies critical machines. Unlike conventional RAS, which are designed using offline simulations, online stability calculations make the proposed RAS dynamic and adapting to any power system
Stability analysis for tidal inlets of Thuan An and Tu Hien using Escoffier diagram
Lam, N.T.; Verhagen, H.J.; Van der Wegen, M.
2004-01-01
Stability analysis of tidal inlets is very important in providing knowledge on the behaviour of tidal inlet and lagoon systems. The analysis results can help to plan and manage the system effectively as well as to provide information for stability design of the inlets. This paper presents a method
Rohmer, Jeremy; Verdel, Thierry
2017-04-01
Uncertainty analysis is an unavoidable task of stability analysis of any geotechnical systems. Such analysis usually relies on the safety factor SF (if SF is below some specified threshold), the failure is possible). The objective of the stability analysis is then to estimate the failure probability P for SF to be below the specified threshold. When dealing with uncertainties, two facets should be considered as outlined by several authors in the domain of geotechnics, namely "aleatoric uncertainty" (also named "randomness" or "intrinsic variability") and "epistemic uncertainty" (i.e. when facing "vague, incomplete or imprecise information" such as limited databases and observations or "imperfect" modelling). The benefits of separating both facets of uncertainty can be seen from a risk management perspective because: - Aleatoric uncertainty, being a property of the system under study, cannot be reduced. However, practical actions can be taken to circumvent the potentially dangerous effects of such variability; - Epistemic uncertainty, being due to the incomplete/imprecise nature of available information, can be reduced by e.g., increasing the number of tests (lab or in site survey), improving the measurement methods or evaluating calculation procedure with model tests, confronting more information sources (expert opinions, data from literature, etc.). Uncertainty treatment in stability analysis usually restricts to the probabilistic framework to represent both facets of uncertainty. Yet, in the domain of geo-hazard assessments (like landslides, mine pillar collapse, rockfalls, etc.), the validity of this approach can be debatable. In the present communication, we propose to review the major criticisms available in the literature against the systematic use of probability in situations of high degree of uncertainty. On this basis, the feasibility of using a more flexible uncertainty representation tool is then investigated, namely Possibility distributions (e
Simon, Anne-Laure; Lugade, Vipul; Bernhardt, Kathie; Larson, A Noelle; Kaufman, Kenton
2017-06-01
Daily living activities are dynamic, requiring spinal motion through space. Current assessment of spinal deformities is based on static measurements from full-spine standing radiographs. Tools to assess dynamic stability during gait might be useful to enhance the standard evaluation. The aim of this study was to evaluate gait dynamic imbalance in patients with spinal deformity using the dynamic stability margin (DSM). Twelve normal subjects and 17 patients with spinal deformity were prospectively recruited. A kinematic 3D gait analysis was performed for the control group (CG) and the spinal deformity group (SDG). The DSM (distance between the extrapolated center of mass and the base of support) and time-distance parameters were calculated for the right and left side during gait. The relationship between DSM and step length was assessed using three variables: gait stability, symmetry, and consistency. Variables' accuracy was validated by a discriminant analysis. Patients with spinal deformity exhibited gait instability according to the DSM (0.25m versus 0.31m) with decreased velocity (1.1ms -1 versus 1.3ms -1 ) and decreased step length (0.32m versus 0.38m). According to the discriminant analysis, gait stability was the more accurate variable (area under the curve AUC=0.98) followed by gait symmetry and consistency. However, gait consistency showed 100% of specificity, sensitivity, and accuracy of precision. The DSM showed that patients with spinal malalignment exhibit decreased gait stability, symmetry, and consistency besides gait time-distance parameter changes. Additional work is required to determine how to apply the DSM for preoperative and postoperative spinal deformity management. Copyright © 2017. Published by Elsevier B.V.
International Nuclear Information System (INIS)
Suhwan, JI; Shirahama, H.; Koshizuka, S.; Oka, Y.
2001-01-01
The purpose of this study is to evaluate the thermal-hydraulic and the thermal-nuclear coupled stabilities of a supercritical pressure light water-cooled reactor. A stability analysis code at supercritical pressure is developed. Using this code, stabilities of full and partial-power reactor operating at supercritical pressure are investigated by the frequency-domain analysis. Two types of SCRs are analyzed; a supercritical light water reactor (SCLWR) and a supercritical water-cooled fast reactor (SCFR). The same stability criteria as Boiling Water Reactor are applied. The thermal-hydraulic stability of SCLWR and SCFR satisfies the criteria with a reasonable orifice loss coefficient. The decay ratio of the thermal-nuclear coupled stability in SCFR is almost zero because of a small coolant density coefficient of the fast reactor. The evaluated decay ratio of the thermal-nuclear coupled stability is 3,41 ∼ 10 -V at 100% power in SCFR and 0,028 at 100% power in SCLWR. The sensitivity is investigated. It is found that the thermal-hydraulic stability is sensitive to the mass flow rate strongly and the thermal-nuclear coupled stability to the coolant density coefficient. The bottom power peak distribution makes the thermal-nuclear stability worse and the thermal-nuclear stability better. (author)
Dynamic and Static Combination Analysis Method of Slope Stability Analysis during Earthquake
Liang Lu; Zongjian Wang; Xiaoyuan Huang; Bin Zheng; Katsuhiko Arai
2014-01-01
The results of laboratory model tests for simulating the slope failure due to vibration, including unreinforced slope and the slope reinforced by using geotextile, show that the slope failure occurs when a cumulative plastic displacement exceeds a certain critical value. To overcome the defects of conventional stability analysis, which evaluates the slope characteristics only by its strength parameters, a numerical procedure considering the stiffness and deformation of materials and geosynthe...
Analysis of feeding function and jaw stability in bedridden elderly.
Tamura, Fumiyo; Mizukami, Miki; Ayano, Rika; Mukai, Yoshiharu
2002-01-01
The purpose of this study was to analyze the relationship between jaw stability and the feeding function of 53 bedridden elderly dysphagic patients. Investigations included a questionnaire on daily life activities and meals, oral examinations, functional tests for feeding ability, and assessments of feeding function during the meal. The results of intraoral examination of this patient population for jaw stability revealed that 34.0% of individuals had posterior support for occlusion regardless of whether they had natural teeth or dentures. Thus, the number classified as having mandibular stability (ST) was 18 and that with no mandibular stability (NST) was 35. In a Repetitive Saliva Swallowing Test (RSST), 83.3% of the NST group and 40.0% of the ST group were unable to swallow more than 3 times within 30 seconds. In a water swallowing test, 91.4% of the NST of group was unable to swallow 15 mL of water by a single swallow, while 40.0% of ST group was capable. The results suggest that jaw stabilization by occlusion with the posterior teeth or dental prosthetics is important to feeding function, particularly swallowing.
Strength Analysis of Coconut Fiber Stabilized Earth for Farm Structures
Enokela, O. S.; P. O, Alada
2012-07-01
Investigation of the strength characteristic of soil from alluvial deposit of River Benue in makurdi stabilized with coconut fiber as a stabilizer was carried as local building material for farm structure. Processed coconut fibers were mixed with the soil at four different mix ratios of 1% fiber, 2% fiber, 3% fiber and 4% fiber by percentage weight with 0% fiber as control. Compaction test and compressive strength were carried out on the various stabilizing ratio. From the compaction test, the correlation between the maximum dry density and optimum moisture content is a second order polynomial with a coefficient of 63% obtained at1.91kg/m3and 20.0% respectively while the compressive strength test shows an optimum failure load of 8.62N/mm2 at 2%fibre:100% soil mix ratio at 2.16 maximum dry density.
Analytic robust stability analysis of SVD orbit feedback
Pfingstner, Jürgen
2012-01-01
Orbit feedback controllers are indispensable for the operation of modern particle accelerators. Many such controllers are based on the decoupling of the inputs and outputs of the system to be controlled with the help of the singular value decomposition (SVD controller). It is crucial to verify the stability of SVD controllers, also in the presence of mismatches between the used accelerator model and the real machine (robust stability problem). In this paper, analytical criteria for guaranteed stability margins of SVD orbit feedback systems for three different types of model mismatches are presented: scaling errors of actuators and BPMs (beam position monitors) and additive errors of the orbit response matrix. For the derivation of these criteria, techniques from robust control theory have been used, e.g the small gain theorem. The obtained criteria can be easily applied directly to other SVD orbit feedback systems. As an example, the criteria were applied to the orbit feedback system of the Compact Linear ...
Stability analysis of the Euler discretization for SIR epidemic model
International Nuclear Information System (INIS)
Suryanto, Agus
2014-01-01
In this paper we consider a discrete SIR epidemic model obtained by the Euler method. For that discrete model, existence of disease free equilibrium and endemic equilibrium is established. Sufficient conditions on the local asymptotical stability of both disease free equilibrium and endemic equilibrium are also derived. It is found that the local asymptotical stability of the existing equilibrium is achieved only for a small time step size h. If h is further increased and passes the critical value, then both equilibriums will lose their stability. Our numerical simulations show that a complex dynamical behavior such as bifurcation or chaos phenomenon will appear for relatively large h. Both analytical and numerical results show that the discrete SIR model has a richer dynamical behavior than its continuous counterpart
Stochastic stability and bifurcation in a macroeconomic model
International Nuclear Information System (INIS)
Li Wei; Xu Wei; Zhao Junfeng; Jin Yanfei
2007-01-01
On the basis of the work of Goodwin and Puu, a new business cycle model subject to a stochastically parametric excitation is derived in this paper. At first, we reduce the model to a one-dimensional diffusion process by applying the stochastic averaging method of quasi-nonintegrable Hamiltonian system. Secondly, we utilize the methods of Lyapunov exponent and boundary classification associated with diffusion process respectively to analyze the stochastic stability of the trivial solution of system. The numerical results obtained illustrate that the trivial solution of system must be globally stable if it is locally stable in the state space. Thirdly, we explore the stochastic Hopf bifurcation of the business cycle model according to the qualitative changes in stationary probability density of system response. It is concluded that the stochastic Hopf bifurcation occurs at two critical parametric values. Finally, some explanations are given in a simply way on the potential applications of stochastic stability and bifurcation analysis
Stability of large scale interconnected dynamical systems
International Nuclear Information System (INIS)
Akpan, E.P.
1993-07-01
Large scale systems modelled by a system of ordinary differential equations are considered and necessary and sufficient conditions are obtained for the uniform asymptotic connective stability of the systems using the method of cone-valued Lyapunov functions. It is shown that this model significantly improves the existing models. (author). 9 refs
International Nuclear Information System (INIS)
Bettencourt, João H; López, Cristóbal; Hernández-García, Emilio
2013-01-01
In this paper, we use the finite-size Lyapunov exponent (FSLE) to characterize Lagrangian coherent structures in three-dimensional (3D) turbulent flows. Lagrangian coherent structures act as the organizers of transport in fluid flows and are crucial to understand their stirring and mixing properties. Generalized maxima (ridges) of the FSLE fields are used to locate these coherent structures. 3D FSLE fields are calculated in two phenomenologically distinct turbulent flows: a wall-bounded flow (channel flow) and a regional oceanic flow obtained by the numerical solution of the primitive equations where two-dimensional (2D) turbulence dominates. In the channel flow, autocorrelations of the FSLE field show that the structure is substantially different from the near wall to the mid-channel region and relates well to the more widely studied Eulerian coherent structure of the turbulent channel flow. The ridges of the FSLE field have complex shapes due to the 3D character of the turbulent fluctuations. In the oceanic flow, strong horizontal stirring is present and the flow regime is similar to that of 2D turbulence where the domain is populated by coherent eddies that interact strongly. This in turn results in the presence of high FSLE lines throughout the domain leading to strong non-local mixing. The ridges of the FSLE field are quasi-vertical surfaces, indicating that the horizontal dynamics dominates the flow. Indeed, due to rotation and stratification, vertical motions in the ocean are much less intense than horizontal ones. This suppression is absent in the channel flow, as the 3D character of the FSLE ridges shows. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)
Stability analysis and trend study of a balloon tethered in a wind, with experimental comparisons
Redd, L. T.; Bland, S. R.; Bennett, R. M.
1973-01-01
A stability analysis and trend study for a balloon tethered in a steady wind are presented. The linearized, stability-derivative type analysis includes balloon aerodynamics, buoyancy, mass (including apparent mass), and static forces resulting from the tether cable. The analysis has been applied to a balloon 7.64 m in length, and the results are compared with those from tow tests of this balloon. This comparison shows that the analysis gives reasonable predictions for the damping, frequencies, modes of motion, and stability boundaries exhibited by the balloon. A trend study for the 7.64-m balloon was made to illustrate how the stability boundaries are affected by changes in individual stability parameters. The trends indicated in this study may also be applicable to many other tethered-balloon systems.
International Nuclear Information System (INIS)
Gordin, V.A.
1998-01-01
First integral of the systems of nonlinear equations governing the behaviour of atmospheric, oceanic and MHD plasma models are determined. The Lyapunov stability conditions for the solutions under small initial disturbances are analyzed. (author)
Harmonics and voltage stability analysis in power systems including
Indian Academy of Sciences (India)
In this study, non-sinusoidal quantities and voltage stability, both known as power quality criteria, are examined together in detail. The widespread use of power electronics elements cause the existence of signiﬁcant non-sinusoidal quantities in the system. These non-sinusoidal quantities can create serious harmonic ...
A reliable method for the stability analysis of structures ...
African Journals Online (AJOL)
The detection of structural configurations with singular tangent stiffness matrix is essential because they can be unstable. The secondary paths, especially in unstable buckling, can play the most important role in the loss of stability and collapse of the structure. A new method for reliable detection and accurate computation of ...
Stability analysis of switched linear systems defined by graphs
Athanasopoulos, N.; Lazar, M.
2014-01-01
We present necessary and sufficient conditions for global exponential stability for switched discrete-time linear systems, under arbitrary switching, which is constrained within a set of admissible transitions. The class of systems studied includes the family of systems under arbitrary switching,
Experimental analysis of aerodynamic stability of stress-ribbon footbridges
Czech Academy of Sciences Publication Activity Database
Pirner, Miroš; Fischer, Ondřej
1999-01-01
Roč. 2, č. 2 (1999), s. 95-104 ISSN 1226-6116 Institutional support: RVO:68378297 Keywords : footbridges * aerodynamic stability * bending-torsional vibrations * wind-excited vibrations * wind-tunnel in civil engineering Subject RIV: JM - Building Engineering http://koreascience.or.kr/article/ArticleFullRecord.jsp?cn=KJKHCF_1999_v2n2_95&ordernum=5
Dynamical behavior and Jacobi stability analysis of wound strings
Lake, Matthew J.; Harko, Tiberiu
2016-06-01
We numerically solve the equations of motion (EOM) for two models of circular cosmic string loops with windings in a simply connected internal space. Since the windings cannot be topologically stabilized, stability must be achieved (if at all) dynamically. As toy models for realistic compactifications, we consider windings on a small section of mathbb {R}^2, which is valid as an approximation to any simply connected internal manifold if the winding radius is sufficiently small, and windings on an S^2 of constant radius mathcal {R}. We then use Kosambi-Cartan-Chern (KCC) theory to analyze the Jacobi stability of the string equations and determine bounds on the physical parameters that ensure dynamical stability of the windings. We find that, for the same initial conditions, the curvature and topology of the internal space have nontrivial effects on the microscopic behavior of the string in the higher dimensions, but that the macroscopic behavior is remarkably insensitive to the details of the motion in the compact space. This suggests that higher-dimensional signatures may be extremely difficult to detect in the effective (3+1)-dimensional dynamics of strings compactified on an internal space, even if configurations with nontrivial windings persist over long time periods.
Dynamics, stability analysis and quantization of β-Fermi–Pasta ...
Indian Academy of Sciences (India)
We study the well-known one-dimensional problem of particles with nonlinear interaction. The -Fermi–Pasta–Ulam model is the special case of quadratic and quartic interaction potential among nearest neighbours. We enumerate and classify the simple periodic orbits for this system and find the stability zones, ...
Stability and dynamic analysis of a service robot
Bouten, J.T.; Alvarez Aguirre, A.; Derks, R.J.S.; Nijmeijer, H.
2011-01-01
A Remote Operated SErvice robot (ROSE) is built to assist elderly people in health care. The use of technology to assist the elderly and disabled is desirable to ease the burden on the decreasing working population in the Netherlands and all over Europe. In this report the stability of the ROSE
Surface stability analysis of dikes subject to overtopping and infiltration
Karim, U. F.A.; Tran, Q.T.; Meij, R.
2015-01-01
The key contribution of this paper is the coupling of hydraulic loading conditions due to wave overtopping with slope stability of the surface layer of earthen flood protection embankments. Overtopping wave conditions impact overtopping discharges and infiltration time, and thereby the infiltration
Stability analysis of multipoint tool equipped with metal cutting ceramics
Maksarov, V. V.; Khalimonenko, A. D.; Matrenichev, K. G.
2017-10-01
The article highlights the issues of determining the stability of the cutting process by a multipoint cutting tool equipped with cutting ceramics. There were some recommendations offered on the choice of parameters of replaceable cutting ceramic plates for milling based of the conducted researches. Ceramic plates for milling are proposed to be selected on the basis of value of their electrical volume resistivity.
Intact stability analysis of dead ship conditions using FORM
DEFF Research Database (Denmark)
Choi, Ju Hyuck; Jensen, Jørgen Juncher; Kristensen, Hans Otto Holmegaard
2017-01-01
The IMO Weather Criterion has proven to be the governing stability criteria regarding minimum GM for e.g. small ferries and large passenger ships. The formulation of the Weather Criterion is based on some empirical relations derived many years ago for vessels not necessarily representative for cu...
Post Earthquack Slope Stability Analysis of Rubble Mound Breakwater
Amin Moradi; Amir Mahmoudzadeh; Yahya Rahim Safavi
2017-01-01
Rubble mound breakwaters are structures built mainly of quarried rock. Generally armourstone or artificial concrete armour units are used for the outer armour layer,which should protect the structure againist wave attack. Armour stones and concrete armoure unites in this outer layer are usually placed with care to obtain effective interlocking and consequently better stability .
Dynamical behavior and Jacobi stability analysis of wound strings
Energy Technology Data Exchange (ETDEWEB)
Lake, Matthew J. [Naresuan University, The Institute for Fundamental Study, ' ' The Tah Poe Academia Institute' ' , Phitsanulok (Thailand); Thailand Center of Excellence in Physics, Ministry of Education, Bangkok (Thailand); Harko, Tiberiu [Babes-Bolyai University, Department of Physics, Cluj-Napoca (Romania); University College London, Department of Mathematics, London (United Kingdom)
2016-06-15
We numerically solve the equations of motion (EOM) for two models of circular cosmic string loops with windings in a simply connected internal space. Since the windings cannot be topologically stabilized, stability must be achieved (if at all) dynamically. As toy models for realistic compactifications, we consider windings on a small section of R{sup 2}, which is valid as an approximation to any simply connected internal manifold if the winding radius is sufficiently small, and windings on an S{sup 2} of constant radius R. We then use Kosambi-Cartan-Chern (KCC) theory to analyze the Jacobi stability of the string equations and determine bounds on the physical parameters that ensure dynamical stability of the windings. We find that, for the same initial conditions, the curvature and topology of the internal space have nontrivial effects on the microscopic behavior of the string in the higher dimensions, but that the macroscopic behavior is remarkably insensitive to the details of the motion in the compact space. This suggests that higher-dimensional signatures may be extremely difficult to detect in the effective (3+1)-dimensional dynamics of strings compactified on an internal space, even if configurations with nontrivial windings persist over long time periods. (orig.)
Stability analysis of direct current control in current source rectifier
DEFF Research Database (Denmark)
Lu, Dapeng; Wang, Xiongfei; Blaabjerg, Frede
2017-01-01
Current source rectifier with high switching frequency has a great potential for improving the power efficiency and power density in ac-dc power conversion. This paper analyzes the stability of direct current control based on the time delay effect. Small signal model including dynamic behaviors...