Sample records for dynamic stabilization system

  1. Stability of dynamical systems

    Liao, Xiaoxin; Yu, P 0


    The main purpose of developing stability theory is to examine dynamic responses of a system to disturbances as the time approaches infinity. It has been and still is the object of intense investigations due to its intrinsic interest and its relevance to all practical systems in engineering, finance, natural science and social science. This monograph provides some state-of-the-art expositions of major advances in fundamental stability theories and methods for dynamic systems of ODE and DDE types and in limit cycle, normal form and Hopf bifurcation control of nonlinear dynamic systems.ʺ Presents

  2. Dynamical stability of Hamiltonian systems


    Dynamical stability has become the center of study on Hamiltonian system. In this article we intro-duce the recent development in some areas closely related to this topic, such as the KAM theory, Mather theory, Arnolddiffusion and non-singular collision of n-body problem.

  3. Stability in dynamical systems I

    Courant, E.D.; Ruth, R.D.; Weng, W.T.


    We have reviewed some of the basic techniques which can be used to analyze stability in nonlinear dynamical systems, particularly in circular particle accelerators. We have concentrated on one-dimensional systems in the examples in order to simply illustrate the general techniques. We began with a review of Hamiltonian dynamics and canonical transformations. We then reviewed linear equations with periodic coefficients using the basic techniques from accelerator theory. To handle nonlinear terms we developed a canonical perturbation theory. From this we calculated invariants and the amplitude dependence of the frequency. This led us to resonances. We studied the cubic resonance in detail by using a rotating coordinate system in phase space. We then considered a general isolated nonlinear resonance. In this case we calculated the width of the resonance and estimated the spacing of resonances in order to use the Chirikov criterion to restrict the validity of the analysis. Finally the resonance equation was reduced to the pendulum equation, and we examined the motion on a separatrix. This brought us to the beginnings of stochastic behavior in the neighborhood of the separatrix. It is this complex behavior in the neighborhood of the separatrix which causes the perturbation theory used here to diverge in many cases. In spite of this the methods developed here have been and are used quite successfully to study nonlinear effects in nearly integrable systems. When used with caution and in conjunction with numerical work they give tremendous insight into the nature of the phase space structure and the stability of nonlinear differential equations. 14 references.

  4. Stability Analysis of MEMS Gyroscope Dynamic Systems

    M. Naser-Moghadasi; S. A. Olamaei; F. Setoudeh


    In this paper, the existence of a common quadratic Lyapunov function for stability analysis of MEMS Gyroscope dynamic systems has been studied then a new method based on stochastic stability of MEMS Gyroscope system has been proposed.

  5. Geometry and stability of dynamical systems

    Punzi, Raffaele


    We reconsider both the global and local stability of solutions of continuously evolving dynamical systems from a geometric perspective. We clarify that an unambiguous definition of stability generally requires the choice of additional geometric structure that is not intrinsic to the dynamical system itself. While global Lyapunov stability is based on the choice of seminorms on the vector bundle of perturbations, we propose a definition of local stability based on the choice of a linear connection. We show how this definition reproduces known stability criteria for second order dynamical systems. In contrast to the general case, the special geometry of Lagrangian systems provides completely intrinsic notions of global and local stability. We demonstrate that these do not suffer from the limitations occurring in the analysis of the Maupertuis-Jacobi geodesics associated to natural Lagrangian systems.

  6. Biomechanics of Posterior Dynamic Stabilization Systems

    D. U. Erbulut


    Full Text Available Spinal rigid instrumentations have been used to fuse and stabilize spinal segments as a surgical treatment for various spinal disorders to date. This technology provides immediate stability after surgery until the natural fusion mass develops. At present, rigid fixation is the current gold standard in surgical treatment of chronic back pain spinal disorders. However, such systems have several drawbacks such as higher mechanical stress on the adjacent segment, leading to long-term degenerative changes and hypermobility that often necessitate additional fusion surgery. Dynamic stabilization systems have been suggested to address adjacent segment degeneration, which is considered to be a fusion-associated phenomenon. Dynamic stabilization systems are designed to preserve segmental stability, to keep the treated segment mobile, and to reduce or eliminate degenerative effects on adjacent segments. This paper aimed to describe the biomechanical aspect of dynamic stabilization systems as an alternative treatment to fusion for certain patients.

  7. Dynamic stability experiment of Maglev systems

    Cai, Y.; Mulcahy, T.M.; Chen, S.S. [and others


    This report summarizes the research performed on Maglev vehicle dynamic stability at Argonne National Laboratory during the past few years. It also documents magnetic-force data obtained from both measurements and calculations. Because dynamic instability is not acceptable for any commercial Maglev system, it is important to consider this phenomenon in the development of all Maglev systems. This report presents dynamic stability experiments on Maglev systems and compares their numerical simulation with predictions calculated by a nonlinear dynamic computer code. Instabilities of an electrodynamic system (EDS)-type vehicle model were obtained from both experimental observations and computer simulations for a five-degree-of-freedom Maglev vehicle moving on a guideway consisting of double L-shaped aluminum segments attached to a rotating wheel. The experimental and theoretical analyses developed in this study identify basic stability characteristics and future research needs of Maglev systems.

  8. Hybrid Dynamical Systems Modeling, Stability, and Robustness

    Goebel, Rafal; Teel, Andrew R


    Hybrid dynamical systems exhibit continuous and instantaneous changes, having features of continuous-time and discrete-time dynamical systems. Filled with a wealth of examples to illustrate concepts, this book presents a complete theory of robust asymptotic stability for hybrid dynamical systems that is applicable to the design of hybrid control algorithms--algorithms that feature logic, timers, or combinations of digital and analog components. With the tools of modern mathematical analysis, Hybrid Dynamical Systems unifies and generalizes earlier developments in continuous-time and discret

  9. Stability precision dynamic testing system on artillery

    Wang, Chunyan; Li, Bo


    Dynamic feature of Weapon equipments is one of important performance index for evaluating the performance of the whole weapon system. The construction of target range in our country in fire control dynamic testing is relatively backward; therefore, it has greatly influenced the evaluation on the fire control system. In order to solve this problem, it's urgent to develop a new testing instrument so as to adjust to the armament research process and promote weapon system working more efficiently and thereby meeting the needs of modernization in national defense. This paper proposes a new measure which is used to test the stability precision of the fire control system, and it is installed on the moving base. Using the method, we develop a testing system which can test the stability precision of the fire control system and achieve a high precision results after testing. The innovation of the system is we can receive the image not only by CCD, but our eyes. It also adopts digital image-forming and image processing technique for real-time measurement and storing of the target information; it simultaneously adopts the method adjusting the platform and the corresponding fixture mounted on a sample to measure the stable precision and the precision of corner of stabilizator. In this paper, we make a description on the construction of the system and the idea of the designing of the optical system. Finally, we introduce the actual application of the system and testing results.

  10. Dynamic Analysis of Power System Voltage Stability.

    Gebreselassie, Assefa

    This thesis investigates the effects of loads and voltage regulators on the dynamic voltage stability of power systems. The analysis focuses on the interactions of machine flux dynamics with loads and voltage control devices. The results are based on eigenvalue analysis of the linearized models and time simulation of the nonlinear models, using models from the Power System Toolbox, a Matlab -based package for the simulation and small signal analysis of nonlinear power systems. The voltage stability analysis results are developed using a single machine single load system with typical machine and network parameters and the NPCC 10-machine system. Dynamic models for generators, exciters and loads are used. The generator is modeled with a pair of poles and one damper circuit in both the d-axis and the q-axis. Saturation effects are included in the model. The IEEE Type DC1 DC commutator exciter model is used for all the exciters. Five different types of loads: constant impedance, constant current, constant power, a first order induction motor model (slip model) and a third order induction motor model (slip-flux model) are considered. The modes of instability and the stability limits of the different representation of loads are examined for two different operating modes of the exciters. The first, when all the exciters are on automatic control and the second when some exciters are on manual control. Modal participation factors are used to determine the characteristics of the critical modes. The characteristics of the unstable modes are verified by performing time simulation of the nonlinear models. Oscillatory and non-oscillatory instabilities are experienced by load buses when all the exciters are on automatic control and some exciters are on manual control respectively, for loads which are predominantly constant power and induction motors. It is concluded that the mode of instability does not depend on the type of loads but on the operating condition of the exciters

  11. Impulsive Stabilization of Uncertain Dynamical Systems and Chaos Control

    LIUBin; YAOJian; FANGJinqing; LIUXinzhi


    In this paper, a general impulsive control problem for uncertain dynamical systems is investigated.By utilizing the method of Lyapunov functions, a set of stability criteria for uncertain impulsive dynamical systems are established. These obtained results are then appliedto derive conditions under which an uncertain dynamical system can be robustly stabilized by an impulsive control law. Finally, we demonstrate our method by controlling the famous Lorenz system with uncertain perturbation.

  12. Power system dynamics stability and control

    Padiyar, K R


    Modern power systems tend to be very Complex not only due to increasing Demand for quality power, but also on Account of extensive interconnections and increasing dependence on control for optimum utilization for existing resources. A good Knowledge of system dynamics and control is Essential for secure operation of the system. This book is intended to serve the needs of the Student and practicing engineers. A Large number of illustrative examples are included to provide an insight into the application of the theory.


    GuoChonghui; TangHuanwen


    The dynamic input-output model is well known in economic theory and practice. In this paper, the asymptotic stability and balanced growth solutions of the dynamic input-output system are considered. Under some natural assumptions which do not require the technical coefficient matrix to be indecomposable,it has been proved that the dynamic input-output system is not asymptotically stable and the closed dynamic input-output model has a balanced growth solution.

  14. Solar Dynamic Power System Stability Analysis and Control

    Momoh, James A.; Wang, Yanchun


    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.

  15. Dynamic stability of repulsive-force maglev suspension systems

    Cai, Y.; Rote, D.M.; Mulcahy, T.M.; Wang, Z. [and others


    This report summarizes the research performed on maglev vehicle dynamic stability at Argonne National Laboratory during the past few years. It also documents both measured and calculated magnetic-force data. Because dynamic instability is not acceptable for any commercial maglev system, it is important to consider this phenomenon in the development of all maglev systems. This report presents dynamic stability experiments on maglev systems and compares the results with predictions calculated by a nonlinear-dynamics computer code. Instabilities of an electrodynamic-suspension system type vehicle model were obtained by experimental observation and computer simulation of a five-degree-of-freedom maglev vehicle moving on a guideway that consists of a pair of L-shaped aluminum conductors attached to a rotating wheel. The experimental and theoretical analyses developed in this study identify basic stability characteristics and future research needs of maglev systems.

  16. Handbook of electrical power system dynamics modeling, stability, and control

    Eremia, Mircea


    Complete guidance for understanding electrical power system dynamics and blackouts This handbook offers a comprehensive and up-to-date treatment of power system dynamics. Addressing the full range of topics, from the fundamentals to the latest technologies in modeling, stability, and control, Handbook of Electrical Power System Dynamics provides engineers with hands-on guidance for understanding the phenomena leading to blackouts so they can design the most appropriate solutions for a cost-effective and reliable operation. Focusing on system dynamics, the book details

  17. Dynamical stability of the Holographic System with Two Competing Orders

    Du, Yiqiang; Tian, Yu; Zhang, Hongbao


    We investigate the dynamical stability of the holographic system with two order parameters, which exhibits competition and coexistence of condensations. In the linear regime, we have developed the gauge dependent formalism to calculate the quasi-normal modes by gauge fixing, which turns out be considerably convenient. Furthermore, by giving different Gaussian wave packets as perturbations at the initial time, we numerically evolve the full nonlinear system until it arrives at the final equilibrium state. Our results show that the dynamical stability is consistent with the thermodynamical stability. Interestingly, the dynamical evolution, as well as the quasi-normal modes, shows that the relaxation time of this model is generically much longer than the simplest holographic system. We also find that the late time behavior can be well captured by the lowest lying quasi-normal modes except for the non-vanishing order towards the single ordered phase. To our knowledge, this exception is the first counter example t...

  18. Dynamic stabilization of regular linear systems

    Weiss, G; Curtain, RF

    We consider a general class of infinite-dimensional linear systems, called regular linear systems, for which convenient representations are known to exist both in time and in frequency domain, For this class of systems, we investigate the concepts of stabilizability and detectability, in particular,

  19. Dynamic stabilization of regular linear systems

    Weiss, G; Curtain, RF


    We consider a general class of infinite-dimensional linear systems, called regular linear systems, for which convenient representations are known to exist both in time and in frequency domain, For this class of systems, we investigate the concepts of stabilizability and detectability, in particular,

  20. Adaptive steady-state stabilization for nonlinear dynamical systems

    Braun, David J.


    By means of LaSalle’s invariance principle, we propose an adaptive controller with the aim of stabilizing an unstable steady state for a wide class of nonlinear dynamical systems. The control technique does not require analytical knowledge of the system dynamics and operates without any explicit knowledge of the desired steady-state position. The control input is achieved using only system states with no computer analysis of the dynamics. The proposed strategy is tested on Lorentz, van der Pol, and pendulum equations.

  1. Differentiable dynamical systems an introduction to structural stability and hyperbolicity

    Wen, Lan


    This is a graduate text in differentiable dynamical systems. It focuses on structural stability and hyperbolicity, a topic that is central to the field. Starting with the basic concepts of dynamical systems, analyzing the historic systems of the Smale horseshoe, Anosov toral automorphisms, and the solenoid attractor, the book develops the hyperbolic theory first for hyperbolic fixed points and then for general hyperbolic sets. The problems of stable manifolds, structural stability, and shadowing property are investigated, which lead to a highlight of the book, the \\Omega-stability theorem of Smale. While the content is rather standard, a key objective of the book is to present a thorough treatment for some tough material that has remained an obstacle to teaching and learning the subject matter. The treatment is straightforward and hence could be particularly suitable for self-study. Selected solutions are available electronically for instructors only. Please send email to for more informatio...


    孙继涛; 张银萍; 刘永清; 邓飞其


    Using the matrix measure and delay differential inequality, the sufficient conditions were obtained for exponential stability of interval dynamical system with multidelay. These conditions are an improvement and extension of the results achieved in earlier papers presented by LIAO, LIU, ZHANG, SUN, et al.

  3. Quasifission dynamics and stability of superheavy systems

    Sekizawa, Kazuyuki


    Recent experiments revealed intriguing similarities in the $^{64}$Ni+$^{207}$Pb, $^{132}$Xe+$^{208}$Pb, and $^{238}$U+$^{238}$U reactions at energies around the Coulomb barrier. The experimental data indicate that for all systems substantial energy dissipation takes place, in the first stage of the reaction, although the number of transferred nucleons is small. On the other hand, in the second stage, a large number of nucleons are transferred with small friction and small consumption of time. To understand the observed behavior, various reactions were analyzed based on the microscopic time-dependent Hartree-Fock (TDHF) theory. From a systematic analysis for $^{40,48}$Ca+$^{124}$Sn, $^{40}$Ca+$^{208}$Pb, $^{40}$Ar+$^{208}$Pb, $^{58}$Ni+$^{208}$Pb, $^{64}$Ni+$^{238}$U, $^{136}$Xe+ $^{198}$Pt, and $^{238}$U+$^{238}$U reactions, we find that TDHF reproduces well the measured trends. In addition, the Balian-V\\'en\\'eroni variational principle is applied to head-on collisions of $^{238}$U+$^{238}$U, and the variance...

  4. Exponential Stability of Stochastic Nonlinear Dynamical Price System with Delay

    Wenli Zhu


    Full Text Available Based on Lyapunov stability theory, Itô formula, stochastic analysis, and matrix theory, we study the exponential stability of the stochastic nonlinear dynamical price system. Using Taylor's theorem, the stochastic nonlinear system with delay is reduced to an n-dimensional semilinear stochastic differential equation with delay. Some sufficient conditions of exponential stability and corollaries for such price system are established by virtue of Lyapunov function. The time delay upper limit is solved by using our theoretical results when the system is exponentially stable. Our theoretical results show that if the classical price Rayleigh equation is exponentially stable, so is its perturbed system with delay provided that both the time delay and the intensity of perturbations are small enough. Two examples are presented to illustrate our results.

  5. Stabilization of computational procedures for constrained dynamical systems

    Park, K. C.; Chiou, J. C.


    A new stabilization method of treating constraints in multibody dynamical systems is presented. By tailoring a penalty form of the constraint equations, the method achieves stabilization without artificial damping and yields a companion matrix differential equation for the constraint forces; hence, the constraint forces are obtained by integrating the companion differential equation for the constraint forces in time. A principal feature of the method is that the errors committed in each constraint condition decay with its corresponding characteristic time scale associated with its constraint force. Numerical experiments indicate that the method yields a marked improvement over existing techniques.

  6. Dynamical stability of the holographic system with two competing orders

    Du, Yiqiang [School of Physics, University of Chinese Academy of Sciences,Beijing 100049 (China); Lan, Shan-Quan [Department of Physics, Beijing Normal University,Beijing 100875 (China); Tian, Yu [School of Physics, University of Chinese Academy of Sciences,Beijing 100049 (China); State Key Laboratory of Theoretical Physics,Institute of Theoretical Physics, Chinese Academy of Science,Beijing 100190 (China); Zhang, Hongbao [Department of Physics, Beijing Normal University,Beijing 100875 (China); Theoretische Natuurkunde, Vrije Universiteit Brussel and The International Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium)


    We investigate the dynamical stability of the holographic system with two order parameters, which exhibits competition and coexistence of condensations. In the linear regime, we have developed the gauge dependent formalism to calculate the quasi-normal modes by gauge fixing, which turns out be considerably convenient. Furthermore, by giving different Gaussian wave packets as perturbations at the initial time, we numerically evolve the full nonlinear system until it arrives at the final equilibrium state. Our results show that the dynamical stability is consistent with the thermodynamical stability. Interestingly, the dynamical evolution, as well as the quasi-normal modes, shows that the relaxation time of this model is generically much longer than the simplest holographic system. We also find that the late time behavior can be well captured by the lowest lying quasi-normal modes except for the non-vanishing order towards the single ordered phase. To our knowledge, this exception is the first counter example to the general belief that the late time behavior towards a final stable state can be captured by the lowest lying quasi-normal modes. In particular, a double relation is found for this exception in certain cases.

  7. Controllability, observability, realizability, and stability of dynamic linear systems

    John M. Davis


    Full Text Available We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time scales. The approach here is based on generalized Laplace transform methods (e.g. shifts and convolution from the recent work [13]. We study controllability in terms of the controllability Gramian and various rank conditions (including Kalman's in both the time invariant and time varying settings and compare the results. We explore observability in terms of both Gramian and rank conditions and establish related realizability results. We conclude by applying this systems theory to connect exponential and BIBO stability problems in this general setting. Numerous examples are included to show the utility of these results.

  8. Controllability, Observability, Reachability, and Stability of Dynamic Linear Systems

    Jackson, Billy J; Gravagne, Ian A; Marks, Robert J


    We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on generalized Laplace transform methods (e.g. shifts and convolution) from our recent work \\cite{DaGrJaMaRa}. We study controllability in terms of the controllability Gramian and various rank conditions (including Kalman's) in both the time invariant and time varying settings and compare the results. We also explore observability in terms of both Gramian and rank conditions as well as realizability results. We conclude by applying this systems theory to connect exponential and BIBO stability problems in this general setting. Numerous examples are included to show the utility of these results.

  9. Stability of power systems coupled with market dynamics

    Meng, Jianping

    This Ph.D. thesis presented here spans two relatively independent topics. The first part, Chapter 2 is self-contained, and is dedicated to studies of new algorithms for power system state estimation. The second part, encompassing the remaining chapters, is dedicated to stability analysis of power system coupled with market dynamics. The first part of this thesis presents improved Newton's methods employing efficient vectorized calculations of higher order derivatives in power system state estimation problems. The improved algorithms are proposed based on an exact Newton's method using the second order terms. By efficiently computing an exact gain matrix, combined with a special optimal multiplier method, the new algorithms show more reliable convergence compared with the existing methods of normal equations, orthogonal decomposition, and Hachtel's sparse tableau. Our methods are able to handle ill-conditioned problems, yet show minimal penalty in computational cost for well-conditioned cases. These claims are illustrated through the standard IEEE 118 and 300 bus test examples. The second part of the thesis focuses on stability analysis of market/power systems. The work presented is motivated by an emerging problem. As the frequency of market based dispatch updates increases, there will inevitably be interaction between the dynamics of markets determining the generator dispatch commands, and the physical response of generators and network interconnections, necessitating the development of stability analysis for such coupled systems. We begin with numeric tests using different market models, with detailed machine/exciter/turbine/governor dynamics, in the New England 39 bus test system. A progression of modeling refinements are introduced, including such non-ideal effects as time delays. Electricity market parameter identification algorithms are also studied based on real time data from the PJM electricity market. Finally our power market model is augmented by optimal

  10. Stability of molecular dynamics simulations of classical systems

    Toxværd, Søren


    The existence of a shadow Hamiltonian for discrete classical dynamics, obtained by an asymptotic expansion for a discrete symplectic algorithm, is employed to determine the limit of stability for molecular dynamics (MD) simulations with respect to the time-increment h of the discrete dynamics....... The investigation is based on the stability of the shadow energy, obtained by including the first term in the asymptotic expansion, and on the exact solution of discrete dynamics for a single harmonic mode. The exact solution of discrete dynamics for a harmonic potential with frequency ω gives a criterion...... an improved stability with a factor of , but the overhead of computer time is a factor of at least two. The conclusion is that the second-order “Verlet”-algorithm, most commonly used in MD, is superior. It gives the exact dynamics within the limit of the asymptotic expansion and this limit can be estimated...

  11. Dynamic simulation of universal spacer in Dynesys dynamic stabilization system for human vertebra

    Sung-Min KIM; In-Chul YANG; Seung-Yeol LEE; Sung-Youn CHO


    The aim of this study is to analyze the simulated behavior of universal spacer in Dynesys dynamic stabilization system inserted in human vertebra. Dynesys, so-called "Dynamic neutralization system for the spine", dynamic stabilization system is a new concept in the surgical treatment of lower back pain recently. Universal spacer used as flexible material is to stabilize the spine and the material property of universal spacer is polycarbonate urethane. Universal spacer may apply different kinematic behaviors at implanted level in vertebra. Spinal range of motion(SROM) of inter-vertebra with installed Dynesys dynamic stabilization system was studied using Adams+LifeMOD as simulation software package. The vertebra model was set up to closely resemble the in-vivo conditions. Inter-vertebra rotations were measured by post processor of Adams and compared with the intact values. SROMs of the flexion, extension, lateral bending, and axial rotation of human virtual models were measured, where three spinal fixation systems such as rigid system, Dynesys system, and fused system were installed. As a result, the value of SROM is decreased in flexion-extension and lateral bending when the spinal fixation system is implanted. The movement of Dynesys system is similar to that of intact model by allowing the movement of lumbar. This means that the Dynesys system is proved to be safe and effective in the treatment of unstable spinal condition.

  12. Stability Analysis for Hand-arm-forearm Dynamic System

    Florin Bausic


    Full Text Available In this paper we propose a model with four degrees of freedom for hand-arm-forearm dynamic system. Using experimental data from [9] by means of the Simulink program, is built block diagram to simulate the dynamic system motion and phase diagrams are drawn by using Matlab. From the interpretation of these diagrams result, for a set of parameters ( m, c, k, FO, ω , stable moves for the hand-arm-forearm dynamic system.

  13. Stability properties of nonlinear dynamical systems and evolutionary stable states

    Gleria, Iram, E-mail: [Instituto de Física, Universidade Federal de Alagoas, 57072-970 Maceió-AL (Brazil); Brenig, Leon [Faculté des Sciences, Université Libre de Bruxelles, 1050 Brussels (Belgium); Rocha Filho, Tarcísio M.; Figueiredo, Annibal [Instituto de Física and International Center for Condensed Matter Physics, Universidade de Brasília, 70919-970 Brasília-DF (Brazil)


    Highlights: • We address the problem of equilibrium stability in a general class of non-linear systems. • We link Evolutionary Stable States (ESS) to stable fixed points of square quasi-polynomial (QP) systems. • We show that an interior ES point may be related to stable interior fixed points of QP systems. - Abstract: In this paper we address the problem of stability in a general class of non-linear systems. We establish a link between the concepts of asymptotic stable interior fixed points of square Quasi-Polynomial systems and evolutionary stable states, a property of some payoff matrices arising from evolutionary games.

  14. Stability and Control of Large-Scale Dynamical Systems A Vector Dissipative Systems Approach

    Haddad, Wassim M


    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

  15. Impulsive and hybrid dynamical systems stability, dissipativity, and control

    Haddad, Wassim M; Nersesov, Sergey G


    This book develops a general analysis and synthesis framework for impulsive and hybrid dynamical systems. Such a framework is imperative for modern complex engineering systems that involve interacting continuous-time and discrete-time dynamics with multiple modes of operation that place stringent demands on controller design and require implementation of increasing complexity--whether advanced high-performance tactical fighter aircraft and space vehicles, variable-cycle gas turbine engines, or air and ground transportation systems. Impulsive and Hybrid Dynamical Systems goes beyond similar

  16. Dynamical output feedback stabilization for neutral systems with mixed delays

    Wei QIAN; Guo-jiang SHEN; You-xian SUN


    This paper is concerned with the issue of stabilization for the linear neutral systems with mixed delays.The attention is focused on the design of output feedback controllers which guarantee the asymptotical stability of the closed-loop systems.Based on the model transformation of neutral type,the Lyapunov-Krasovskii functional method is employed to establish the delay-dependent stability criterion.Then,through the controller parameterization and some matrix transformation techniques,the desired parameters are determined under the delay-dependent design condition in terms of linear matrix inequalities (LMIs),and the desired controller is explicitly formulated.A numerical example is given to illustrate the effectiveness of the proposed method.

  17. Robust adaptive dynamic programming and feedback stabilization of nonlinear systems.

    Jiang, Yu; Jiang, Zhong-Ping


    This paper studies the robust optimal control design for a class of uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (RADP). The objective is to fill up a gap in the past literature of adaptive dynamic programming (ADP) where dynamic uncertainties or unmodeled dynamics are not addressed. A key strategy is to integrate tools from modern nonlinear control theory, such as the robust redesign and the backstepping techniques as well as the nonlinear small-gain theorem, with the theory of ADP. The proposed RADP methodology can be viewed as an extension of ADP to uncertain nonlinear systems. Practical learning algorithms are developed in this paper, and have been applied to the controller design problems for a jet engine and a one-machine power system.

  18. A Robust Stability and Control Theory for Hybrid Dynamical Systems


    IEEE Transactions on Automatic Control , to...Dual Linear Differential Inclusions", IEEE Transactions on Automatic Control , Vol. 51, Issue 4, April 2006, pp. 661-666. D. Liberzon and J. Hespanha...34Stabilization of nonlinear systems with limited information feedback", IEEE Transactions on Automatic Control , vol. 50, no. 6, pp. 910-915,

  19. Distributed-Order Dynamic Systems Stability, Simulation, Applications and Perspectives

    Jiao, Zhuang; Podlubny, Igor


    Distributed-order differential equations, a generalization of fractional calculus, are of increasing importance in many fields of science and engineering from the behaviour of complex dielectric media to the modelling of nonlinear systems. This Brief will broaden the toolbox available to researchers interested in modeling, analysis, control and filtering. It contains contextual material outlining the progression from integer-order, through fractional-order to distributed-order systems. Stability issues are addressed with graphical and numerical results highlighting the fundamental differences between constant-, integer-, and distributed-order treatments. The power of the distributed-order model is demonstrated with work on the stability of noncommensurate-order linear time-invariant systems. Generic applications of the distributed-order operator follow: signal processing and viscoelastic damping of a mass–spring set up. A new general approach to discretization of distributed-order derivatives and integrals ...

  20. Controllability, observability, realizability, and stability of dynamic linear systems

    Davis, John M.; Gravagne, Ian A.; Jackson, Billy J.; Marks II, Robert J.


    We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time scales. The approach here is based on generalized Laplace transform methods (e.g. shifts and convolution) from the recent work [13]. We study controllability in terms of the controllability Gramian and various rank conditions (including Kalman's) in both the time invariant and time varying settings...

  1. Stability properties of a general class of nonlinear dynamical systems

    Gleria, I.M. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail:; Figueiredo, A. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail:; Rocha, T.M. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail:


    We establish sufficient conditions for the boundedness of the trajectories and the stability of the fixed points in a class of general nonlinear systems, the so-called quasi-polynomial vector fields, with the help of a natural embedding of such systems in a family of generalized Lotka-Volterra (LV) equations. A purely algebraic procedure is developed to determine such conditions. We apply our method to obtain new results for LV systems, by a reparametrization in time variable, and to study general nonlinear vector fields, originally far from the LV format. (author)

  2. Power system dynamics and stability with synchrophasor measurement and power system toolbox

    Sauer, Peter W; Chow, Joe H


    This new edition addresses the needs of dynamic modeling and simulation relevant to power system planning, design, and operation, including a systematic derivation of synchronous machine dynamic models together with speed and voltage control subsystems. Reduced-order modeling based on integral manifolds is used as a firm basis for understanding the derivations and limitations of lower-order dynamic models. Following these developments, a multi-machine model interconnected through the transmission network is formulated and simulated using numerical simulation methods. Energy function methods are discussed for direct evaluation of stability. Small-signal analysis is used for determining the electromechanical modes and mode-shapes, and for power system stabilizer design. Time-synchronized high-sampling-rate phasor measurement units (PMUs) to monitor power system disturbances ave been implemented throughout North America and many other countries. In this second edition, new chapters on synchrophasor measurement ...

  3. Criterion for stability of a special relativistically covariant dynamical system

    Horwitz, L. P.; Zucker, D.


    We study classically the problem of two relativistic particles with an invariant Duffing-like potential which reduces to the usual Duffing form in the nonrelativistic limit. We use a special relativistic generalization (RGEM) of the geometric method (GEM) developed for the analysis of nonrelativistic Hamiltonian systems to study the local stability of a relativistic Duffing oscillator. Poincaré plots of the simulated motion are consistent with the RGEM. We find a threshold for the external driving force required for chaotic behavior in the Minkowski spacetime.

  4. Dynamic compensator design for robust stability of linear uncertain systems

    Yedavalli, R. K.


    This paper presents a robust linear dynamic compensator design algorithm for linear uncertain systems whose parameters vary within given bounded sets. The algorithm explicitly incorporates the structure of the uncertainty into the design procedure and utilizes the elemental perturbation bounds developed recently. The special cases of linear state feedback and measurement feedback controllers are considered and the relative trade offs are discussed. The design algorithm is illustrated with the help of a simple example.

  5. Short term outcome of posterior dynamic stabilization system in degenerative lumbar diseases

    Mingyuan Yang


    Conclusion: Dynamic stabilization system treating lumbar degenerative disease showed clinical benefits with motion preservation of the operated segments, but does not have the significant advantage on motion preservation at adjacent segments, to avoid the degeneration of adjacent intervertebral disk.

  6. A review of dynamic stability of repulsive-force maglev suspension systems

    Cai, Y.; Rote, D.M.


    Vehicle dynamics and the need to satisfy ride quality requirements have long been recognized as crucial to the commercial success of passenger-carrying transportation systems. Design concepts for maglev systems are no exception. Early maglev investigators and designers were well aware of the importance of ride quality and took care to ensure that their designs would meet acceptable ride quality standards. In contrast, the dynamic stability of electrodynamic suspension (EDS) systems, which has obvious implications for system safety and cost as well as for ride quality, has not received nearly as much attention. Because of the well-known under-damped nature of EDS suspension systems and the observation of instabilities in laboratory-scale model systems, it is prudent to develop a better understanding of vehicle stability characteristics. The work reported in this was undertaken with the intention of summarizing information that has been accumulated worldwide and that is relevant to dynamic stability of repulsive-force maglev suspension systems, assimilating that information, and gaining an understanding of the factors that influence that stability. Included in the paper is a discussion and comparison of results acquired from some representative tests of large-scale vehicles on linear test tracks, together with analytical and laboratory-scale investigations of stability and dynamics of EDS systems. This paper will also summarize the R and D activities at Argonne National Laboratory (ANL) since 1991 to study the nature of the forces that are operative in an EDS system and the dynamic stability of such systems.

  7. On the Dynamical Stability of the Solar System

    Batygin, Konstantin


    A long-term numerical integration of the classical Newtonian approximation to the planetary orbital motions of the full Solar System (sun + 8 planets), spanning 20 Gyr, was performed. The results showed no severe instability arising over this time interval. Subsequently, utilizing a bifurcation method described by Jacques Laskar, two numerical experiments were performed with the goal of determining dynamically allowed evolutions for the Solar System in which the planetary orbits become unstable. The experiments yielded one evolution in which Mercury falls onto the Sun at ~1.261Gyr from now, and another in which Mercury and Venus collide in ~862Myr. In the latter solution, as a result of Mercury's unstable behavior, Mars was ejected from the Solar System at ~822Myr. We have performed a number of numerical tests that confirm these results, and indicate that they are not numerical artifacts. Using synthetic secular perturbation theory, we find that Mercury is destabilized via an entrance into a linear secular re...


    徐建国; 贾军国


    The dynamics, stability and control problem of a kind of infinite dimensional system are studied in the functional space with the method of modern mathematics. First,the dynamical control model of the distributed parameter system with multi-body flexible and multi-topological structure was established which has damping, gyroscopic parts and constrained damping. Secondly, the necessary and sufficient condition of controllability and observability, the stability theory and asymptotic property of the system were obtained.These results expand the theory of the field about the dynamics and control of the system with multi-body flexible structure, and have important engineering significance.

  9. Stability of dynamical systems on the role of monotonic and non-monotonic Lyapunov functions

    Michel, Anthony N; Liu, Derong


    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...

  10. Optimal placement of unified power flow controllers to improve dynamic voltage stability using power system variable based voltage stability indices.

    Albatsh, Fadi M; Ahmad, Shameem; Mekhilef, Saad; Mokhlis, Hazlie; Hassan, M A


    This study examines a new approach to selecting the locations of unified power flow controllers (UPFCs) in power system networks based on a dynamic analysis of voltage stability. Power system voltage stability indices (VSIs) including the line stability index (LQP), the voltage collapse proximity indicator (VCPI), and the line stability index (Lmn) are employed to identify the most suitable locations in the system for UPFCs. In this study, the locations of the UPFCs are identified by dynamically varying the loads across all of the load buses to represent actual power system conditions. Simulations were conducted in a power system computer-aided design (PSCAD) software using the IEEE 14-bus and 39- bus benchmark power system models. The simulation results demonstrate the effectiveness of the proposed method. When the UPFCs are placed in the locations obtained with the new approach, the voltage stability improves. A comparison of the steady-state VSIs resulting from the UPFCs placed in the locations obtained with the new approach and with particle swarm optimization (PSO) and differential evolution (DE), which are static methods, is presented. In all cases, the UPFC locations given by the proposed approach result in better voltage stability than those obtained with the other approaches.

  11. Optimal placement of unified power flow controllers to improve dynamic voltage stability using power system variable based voltage stability indices.

    Fadi M Albatsh

    Full Text Available This study examines a new approach to selecting the locations of unified power flow controllers (UPFCs in power system networks based on a dynamic analysis of voltage stability. Power system voltage stability indices (VSIs including the line stability index (LQP, the voltage collapse proximity indicator (VCPI, and the line stability index (Lmn are employed to identify the most suitable locations in the system for UPFCs. In this study, the locations of the UPFCs are identified by dynamically varying the loads across all of the load buses to represent actual power system conditions. Simulations were conducted in a power system computer-aided design (PSCAD software using the IEEE 14-bus and 39- bus benchmark power system models. The simulation results demonstrate the effectiveness of the proposed method. When the UPFCs are placed in the locations obtained with the new approach, the voltage stability improves. A comparison of the steady-state VSIs resulting from the UPFCs placed in the locations obtained with the new approach and with particle swarm optimization (PSO and differential evolution (DE, which are static methods, is presented. In all cases, the UPFC locations given by the proposed approach result in better voltage stability than those obtained with the other approaches.

  12. Optimal Placement of Unified Power Flow Controllers to Improve Dynamic Voltage Stability Using Power System Variable Based Voltage Stability Indices

    Albatsh, Fadi M.; Ahmad, Shameem; Mekhilef, Saad; Mokhlis, Hazlie; Hassan, M. A.


    This study examines a new approach to selecting the locations of unified power flow controllers (UPFCs) in power system networks based on a dynamic analysis of voltage stability. Power system voltage stability indices (VSIs) including the line stability index (LQP), the voltage collapse proximity indicator (VCPI), and the line stability index (Lmn) are employed to identify the most suitable locations in the system for UPFCs. In this study, the locations of the UPFCs are identified by dynamically varying the loads across all of the load buses to represent actual power system conditions. Simulations were conducted in a power system computer-aided design (PSCAD) software using the IEEE 14-bus and 39- bus benchmark power system models. The simulation results demonstrate the effectiveness of the proposed method. When the UPFCs are placed in the locations obtained with the new approach, the voltage stability improves. A comparison of the steady-state VSIs resulting from the UPFCs placed in the locations obtained with the new approach and with particle swarm optimization (PSO) and differential evolution (DE), which are static methods, is presented. In all cases, the UPFC locations given by the proposed approach result in better voltage stability than those obtained with the other approaches. PMID:25874560

  13. Adaptive Finite-Time Stabilization of High-Order Nonlinear Systems with Dynamic and Parametric Uncertainties

    Meng-Meng Jiang


    Full Text Available Under the weaker assumption on nonlinear functions, the adaptive finite-time stabilization of more general high-order nonlinear systems with dynamic and parametric uncertainties is solved in this paper. To solve this problem, finite-time input-to-state stability (FTISS is used to characterize the unmeasured dynamic uncertainty. By skillfully combining Lyapunov function, sign function, backstepping, and finite-time input-to-state stability approaches, an adaptive state feedback controller is designed to guarantee high-order nonlinear systems are globally finite-time stable.


    D. M. Malyutin


    Full Text Available It is now widely distributed systems stabilization based on gyroscopes with three-degree-freedom and based on gyroscopes with ball suspension. The accuracy and resource of operation of such systems requires an increase. The problem of improving the accuracy and increasing the service life of information – measuring systems of stabilization can be solved by using as a sensitive element of a dynamically tuned gyroscope. Today the issue of achieving the potential of the metrological characteristics of information-measuring systems stabilization on dynamically tuned gyroscope is not fully resolved. It requires the development of mathematical models, different from the known, detailed description of the perturbations acting on a device. In addition, it is necessary to develop structures amplifying-transforming paths of the contours stabilization of information-measuring systems of stabilization on dynamically tuned gyroscopes, assuring higher accuracy and noise immunity of the system, what is the purpose of the work. In using the Euler equations obtained a complete mathematical model of functioning system with three motion bases, in detail taking into account the disturbances acting on the device. Considered are the peculiarities of mathematical description of dynamically tuned gyroscope. Dominant frequencies of components noise is identified in the output signal of the gyroscope. The original scheme of the contours stabilization is presented, that help increase the accuracy of stabilization at low frequencies and of providing the absence of systematic drift of the gyrostabilizer from the action of the permanent disturbing moment along the axis of stabilization. The dynamic calculations show the possibility of providing error of stabilization on payload not more than 0,0042 degree. 

  15. Dynamic stability margin using a marker based system and Tekscan: a comparison of four gait conditions.

    Lugade, Vipul; Kaufman, Kenton


    Stability during gait is maintained through control of the center of mass (CoM) position and velocity in relation to the base of support (BoS). The dynamic stability margin, or the interaction of the extrapolated center of mass with the closest boundary of the BoS, can reveal possible control errors during gait. The purpose of this study was to investigate a marker based method for defining the BoS, and compare the dynamic stability margin throughout gait in comparison to a BoS defined from foot pressure sensors. The root mean squared difference between these two methodologies ranged from 0.9 cm to 3.5 cm, when walking under four conditions: plantigrade, equinus, everted, and inverted. As the stability margin approaches -35 cm prior to contralateral heel strike, there was approximately 90% agreement between the two systems at this time point. Underestimation of the marker based dynamic stability margin or overestimation of the pressure based dynamic stability margin was due to inaccuracies in defining the medial boundary of the BoS. Overall, care must be taken to ensure similar definitions of the BoS are utilized when comparing the dynamic stability margin between participants and gait conditions.

  16. Adaptive Stabilization for a Class of Dynamical Systems with Nonlinear Delayed State Perturbations


    The problem of adaptive stabilization for a class of systems with nonlinear delayed state perturbations is considered. The bound of the perturbations is assumed to be unknown, by using the adaptive control method, an adaptive controller is designed. Based on the Lyapunov- Karasovskii functional, it is shown that the dynamical system can be stabilized by the adaptive controller. The effectiveness of the proposed controller is demonstrated by some simulations.

  17. Combined analytical and numerical approaches in Dynamic Stability analyses of engineering systems

    Náprstek, Jiří


    Dynamic Stability is a widely studied area that has attracted many researchers from various disciplines. Although Dynamic Stability is usually associated with mechanics, theoretical physics or other natural and technical disciplines, it is also relevant to social, economic, and philosophical areas of our lives. Therefore, it is useful to occasionally highlight the general aspects of this amazing area, to present some relevant examples and to evaluate its position among the various branches of Rational Mechanics. From this perspective, the aim of this study is to present a brief review concerning the Dynamic Stability problem, its basic definitions and principles, important phenomena, research motivations and applications in engineering. The relationships with relevant systems that are prone to stability loss (encountered in other areas such as physics, other natural sciences and engineering) are also noted. The theoretical background, which is applicable to many disciplines, is presented. In this paper, the most frequently used Dynamic Stability analysis methods are presented in relation to individual dynamic systems that are widely discussed in various engineering branches. In particular, the Lyapunov function and exponent procedures, Routh-Hurwitz, Liénard, and other theorems are outlined together with demonstrations. The possibilities for analytical and numerical procedures are mentioned together with possible feedback from experimental research and testing. The strengths and shortcomings of these approaches are evaluated together with examples of their effective complementing of each other. The systems that are widely encountered in engineering are presented in the form of mathematical models. The analyses of their Dynamic Stability and post-critical behaviour are also presented. The stability limits, bifurcation points, quasi-periodic response processes and chaotic regimes are discussed. The limit cycle existence and stability are examined together with their

  18. Stability of Non-Neutral and Neutral Dynamic Switched Systems Subject to Internal Delays

    M. De la Sen


    Full Text Available This study deals with the quadratic stability and linear state-feedback and output-feedback stabilization of switched delayed linear dynamic systems with, in general, a finite number of non commensurate constant internal point delays. The results are obtained based on Lyapunov’s stability analysis via appropriate Krasovsky-Lyapunov’s functionals and the related stability study is performed to obtain both delay independent and delay dependent results. It is proved that the stabilizing switching rule is arbitrary if all the switched subsystems are quadratically stable and that it exists a (in general, non-unique stabilizing switching law when the system is polytopic, stable at some interior point of the polytope but with non-necessarily stable parameterizations at the vertices defining the subsystems.

  19. Walking in simulated Martian gravity: influence of the portable life support system's design on dynamic stability.

    Scott-Pandorf, Melissa M; O'Connor, Daniel P; Layne, Charles S; Josić, Kresimir; Kurz, Max J


    With human exploration of the moon and Mars on the horizon, research considerations for space suit redesign have surfaced. The portable life support system (PLSS) used in conjunction with the space suit during the Apollo missions may have influenced the dynamic balance of the gait pattern. This investigation explored potential issues with the PLSS design that may arise during the Mars exploration. A better understanding of how the location of the PLSS load influences the dynamic stability of the gait pattern may provide insight, such that space missions may have more productive missions with a smaller risk of injury and damaging equipment while falling. We explored the influence the PLSS load position had on the dynamic stability of the walking pattern. While walking, participants wore a device built to simulate possible PLSS load configurations. Floquet and Lyapunov analysis techniques were used to quantify the dynamic stability of the gait pattern. The dynamic stability of the gait pattern was influenced by the position of load. PLSS loads that are placed high and forward on the torso resulted in less dynamically stable walking patterns than loads placed evenly and low on the torso. Furthermore, the kinematic results demonstrated that all joints of the lower extremity may be important for adjusting to different load placements and maintaining dynamic stability. Space scientists and engineers may want to consider PLSS designs that distribute loads evenly and low, and space suit designs that will not limit the sagittal plane range of motion at the lower extremity joints.

  20. On the stability of nonautonomous binary dynamical systems of partial differential equations

    Salvatore Rionero


    Full Text Available Nonlinear nonautonomoua binary reaction-diffusion dynamical systems of partial differential equations (PDE are considered. Stability criteria - via a nonautonomous L²-energy - are obtained. Applications to nonautonomous Lotka-volterra systems of PDEs and to “preys” struggle for the life, are furnished.

  1. Stability of a time discrete perturbed dynamical system with delay

    Michael I. Gil'


    Full Text Available Let Cn be the set of n complex vectors endowed with a norm ‖⋅‖Cn. Let A,B be two complex n×n matrices and τ a positive integer. In the present paper we consider the nonlinear difference equation with delay of the type uk+1=Auk+Buk−τ+Fk(uk,uk−τ,      k=0,1,2,…, where Fk:Cn×Cn→Cn satisfies the condition ‖Fk(x,y‖Cn≤p‖x‖Cn+q‖y‖Cn,       k=0,1,2,…, where p and q are positive constants. In this paper, absolute stability conditions for this equation are established.


    ZHANG Shuang-de; HAO Hai


    An extended dynamic model for SARS epidemic was deduced on the basis of the K-M infection model with taking the density constraint of susceptible population and the cure and death rates of patients into consideration. It is shown that the infectionfree equilibrium is the global asymptotic stability under given conditions, and endemic equilibrium is not the asymptotic stability. It comes to the conclusion that the epidemic system is the permanent persistence existence under appropriate conditions.

  3. Total Stability Properties Based on Fixed Point Theory for a Class of Hybrid Dynamic Systems

    M. De la Sen


    Full Text Available Robust stability results for nominally linear hybrid systems are obtained from total stability theorems for purely continuous-time and discrete-time systems by using the powerful tool of fixed point theory. The class of hybrid systems dealt consists, in general, of coupled continuous-time and digital systems subject to state perturbations whose nominal (i.e., unperturbed parts are linear and, in general, time-varying. The obtained sufficient conditions on robust stability under a wide class of harmless perturbations are dependent on the values of the parameters defining the over-bounding functions of those perturbations. The weakness of the coupling dynamics in terms of norm among the analog and digital substates of the whole dynamic system guarantees the total stability provided that the corresponding uncoupled nominal subsystems are both exponentially stable. Fixed point stability theory is used for the proofs of stability. A generalization of that result is given for the case that sampling is not uniform. The boundedness of the state-trajectory solution at sampling instants guarantees the global boundedness of the solutions for all time. The existence of a fixed point for the sampled state-trajectory solution at sampling instants guarantees the existence of a fixed point of an extended auxiliary discrete system and the existence of a global asymptotic attractor of the solutions which is either a fixed point or a limit n globally stable asymptotic oscillation.

  4. Global Stability in Dynamical Systems with Multiple Feedback Mechanisms

    Andersen, Morten; Vinther, Frank; Ottesen, Johnny T.


    of the system. The proof relies on the contraction mapping theorem. Applications of this type of systems are numerous in biology, e.g., models of the hypothalamic-pituitary-adrenal axis and testosterone secretion. Some results important for modelling are: 1) Existence of an attractive trapping region...

  5. Dynamic Voltage Stability Studies using a Modified IEEE 30-Bus System

    Oluwafemi Emmanuel Oni


    Full Text Available Power System stability is an essential study in the planning and operation of an efficient, economic, reliable and secure electric power system because it encompasses all the facet of power systems operations, from planning, to conceptual design stages of the project as well as during the systems operating life span. This paper presents different scenario of power system stability studies on a modified IEEE 30-bus system which is subjected to different faults conditions. A scenario whereby the longest high voltage alternating current (HVAC line is replaced with a high voltage direct current (HVDC line was implemented. The results obtained show that the HVDC line enhances system stability more compared to the contemporary HVAC line. Dynamic analysis using RMS simulation tool was used on DigSILENT PowerFactory.

  6. Analytical stability analysis of periodic systems by Poincaré mappings with application to rotorcraft dynamics

    Henryk Flashner


    Full Text Available A point mapping analysis is employed to investigate the stability of periodic systems. The method is applied to simplified rotorcraft models. The proposed approach is based on a procedure to obtain an analytical expression for the period-to-period mapping description of system's dynamics, and its dependence on system's parameters. Analytical stability and bifurcation conditions are then determined and expressed as functional relations between important system parameters. The method is applied to investigate the parametric stability of flapping motion of a rotor and the ground resonance problem encountered in rotorcraft dynamics. It is shown that the proposed approach provides very accurate results when compared with direct numerical results which are assumed to be an “exact solution” for the purpose of this study. It is also demonstrated that the point mapping method yields more accurate results than the widely used classical perturbation analysis. The ability to perform analytical stability studies of systems with multiple degrees-of-freedom is an important feature of the proposed approach since most existing analysis methods are applicable to single degree-of-freedom systems. Stability analysis of higher dimensional systems, such as the ground resonance problems, by perturbation methods is not straightforward, and is usually very cumbersome.

  7. Global Stability in Dynamical Systems with Multiple Feedback Mechanisms

    Andersen, Morten; Vinther, Frank; Ottesen, Johnny T.


    . This is a bounded set with non-negative elements where solutions cannot escape. All solutions are shown to converge to a “minimal” trapping region. 2) At least one fixed point exists. 3) Sufficient criteria for a unique fixed point are formulated. One case where this is fulfilled is when the feedbacks are negative.......A class of n-dimensional ODEs with up to n feedbacks from the n’th variable is analysed. The feedbacks are represented by non-specific, bounded, non-negative C1 functions. The main result is the formulation and proof of an easily applicable criterion for existence of a globally stable fixed point...... of the system. The proof relies on the contraction mapping theorem. Applications of this type of systems are numerous in biology, e.g., models of the hypothalamic-pituitary-adrenal axis and testosterone secretion. Some results important for modelling are: 1) Existence of an attractive trapping region...

  8. Analyzing the dynamic stability of controlled electric power systems

    Nikolaeva, S.I.


    Techniques from the theory of optimal control are used to consider the possibilities for evaluating the effectiveness of emergency control of turbines at power plants of complex electric power systems. An algorithm is given for calculating the optimal control functions; it has been developed on the basis of the Pontryagin principle of the maximum and the method of quasi-linearization. Calculations for a particular four-machine circuit are used to evaluate the factors affecting the computational effectiveness of the algorithm.

  9. Arms Transfers: A System Dynamics Analysis Focusing on Regional Stability.


    protectionism ,the nature of this argument points to the often pervasive nature of global interdependence and the implications that arms sales have in...34 - Wilsonian ’League of Nations,’ - Protectionism , - ’Lend-Lease’, - World War IT, - Marshall Plan, - Containment, - NATO,SEATO,CENTO, - MAD...the very nature of the world system. Various cultures and nations have adopted methods for dealing with change ranging from isolationism and radical

  10. Diversity, Stability, Recursivity, and Rule Generation in Biological System Intra-inter Dynamics Approach

    Kaneko, K


    Basic problems for the construction of a scenario for the Life are discussed. To study the problems in terms of dynamical systems theory, a scheme of intra-inter dynamics is presented. It consists of internal dynamics of a unit, interaction among the units, and the dynamics to change the dynamics itself, for example by replication (and death) of units according to their internal states. Applying the dynamics to cell differentiation, isologous diversification theory is proposed. According to it, orbital instability leads to diversified cell behaviors first. At the next stage, several cell types are formed, first triggered by clustering of oscillations, and then as attracting states of internal dynamics stabilized by the cell-to-cell interaction. At the third stage, the differentiation is determined as a recursive state by cell division. At the last stage, hierarchical differentiation proceeds, with the emergence of stochastic rule for the differentiation to sub-groups, where regulation of the probability for t...

  11. Accuracy Enhanced Stability and Structure Preserving Model Reduction Technique for Dynamical Systems with Second Order Structure

    Tahavori, Maryamsadat; Shaker, Hamid Reza

    A method for model reduction of dynamical systems with the second order structure is proposed in this paper. The proposed technique preserves the second order structure of the system, and also preserves the stability of the original systems. The method uses the controllability and observability...... gramians within the time interval to build the appropriate Petrov-Galerkin projection for dynamical systems within the time interval of interest. The bound on approximation error is also derived. The numerical results are compared with the counterparts from other techniques. The results confirm...

  12. Linguistic dynamic systems based on computing with words and their stabilities

    MO Hong; WANG FeiYue


    Linguistic dynamic systems (LDS) are the systems based on computing with words (CW) instead of computing with numbers or symbols. In this paper, LDS are divided into two types: type-Ⅰ LDS being converted from conventional dynamical systems (CDS) by using extension principle and type-Ⅱ LDS by using fuzzy logic rules. For type-Ⅰ LDS, the method of endograph is provided to discuss the stabilities of type-Ⅰ LDS and two cases of stabilities of logistic mappings: one is the states being abstracted and the other is parameters also being abstracted. For type-Ⅱ LDS, the method of degree of match is used to discuss the dynamical behavior of arbitrary initial words under fuzzy rule.

  13. Stability and periodicity of solutions for delay dynamic systems on time scales

    Zhi-Qiang Zhu


    Full Text Available This article concerns the stability and periodicity of solutions to the delay dynamic system $$ x^{\\triangle}(t=A(t x(t + F(t, x(t, x(g(t+C(t $$ on a time scale. By the inequality technique for vectors, we obtain some stability criteria for the above system. Then, by using the Horn fixed point theorem, we present some conditions under which our system is asymptotically periodic and its periodic solution is unique. In particular, the periodic solution is positive under proper assumptions.

  14. Static and dynamic stability of the guidance force in a side-suspended HTS maglev system

    Zhou, Dajin; Cui, Chenyu; Zhao, Lifeng; Zhang, Yong; Wang, Xiqing; Zhao, Yong


    The static and dynamic stability of the guidance force in a side-suspended HTS-PMG (permanent magnetic guideway) system were studied theoretically and experimentally. It is found that there are two types of guidance force that exist in the HTS-PMG system, which are sensitive to the levitation gap and the arrangement of YBCO bulks around the central axis of the PMG. An optimized YBCO array was used to stabilize the system, which enabled a side-suspended HTS-PMG maglev vehicle to run stably at 102 km h-1 on a circular test track with 6.5 m in diameter.

  15. The Comprehensive Biomechanics and Load-Sharing of Semirigid PEEK and Semirigid Posterior Dynamic Stabilization Systems

    D. K. Sengupta


    Full Text Available Alternatives to conventional rigid fusion have been proposed for several conditions related to degenerative disc disease when nonoperative treatment has failed. Semirigid fixation, in the form of dynamic stabilization or PEEK rods, is expected to provide compression under loading as well as an intermediate level of stabilization. This study systematically examines both the load-sharing characteristics and kinematics of these two devices compared to the standard of internal rigid fixators. Load-sharing was studied by using digital pressure films inserted between an artificially machined disc and two loading fixtures. Rigid rods, PEEK rods, and the dynamic stabilization system were inserted posteriorly for stabilization. The kinematics were quantified on ten, human, cadaver lumbosacral spines (L3-S1 which were tested under a pure bending moment, in flexion-extension, lateral bending, and axial rotation. The magnitude of load transmission through the anterior column was significantly greater with the dynamic device compared to PEEK rods and rigid rods. The contact pressures were distributed more uniformly, throughout the disc with the dynamic stabilization devices, and had smaller maximum point-loading (pressures on any particular point within the disc. Kinematically, the motion was reduced by both semirigid devices similarly in all directions, with slight rigidity imparted by a lateral interbody device.

  16. Dynamical investigation and parameter stability region analysis of a flywheel energy storage system in charging mode

    Zhang, Wei-Ya; Li, Yong-Li; Chang, Xiao-Yong; Wang, Nan


    In this paper, the dynamic behavior analysis of the electromechanical coupling characteristics of a flywheel energy storage system (FESS) with a permanent magnet (PM) brushless direct-current (DC) motor (BLDCM) is studied. The Hopf bifurcation theory and nonlinear methods are used to investigate the generation process and mechanism of the coupled dynamic behavior for the average current controlled FESS in the charging mode. First, the universal nonlinear dynamic model of the FESS based on the BLDCM is derived. Then, for a 0.01 kWh/1.6 kW FESS platform in the Key Laboratory of the Smart Grid at Tianjin University, the phase trajectory of the FESS from a stable state towards chaos is presented using numerical and stroboscopic methods, and all dynamic behaviors of the system in this process are captured. The characteristics of the low-frequency oscillation and the mechanism of the Hopf bifurcation are investigated based on the Routh stability criterion and nonlinear dynamic theory. It is shown that the Hopf bifurcation is directly due to the loss of control over the inductor current, which is caused by the system control parameters exceeding certain ranges. This coupling nonlinear process of the FESS affects the stability of the motor running and the efficiency of energy transfer. In this paper, we investigate into the effects of control parameter change on the stability and the stability regions of these parameters based on the averaged-model approach. Furthermore, the effect of the quantization error in the digital control system is considered to modify the stability regions of the control parameters. Finally, these theoretical results are verified through platform experiments.

  17. Dynamical Stability of Imaged Planetary Systems in Formation: Application to HL Tau

    Tamayo, Daniel; Menou, Kristen; Rein, Hanno


    We present a general and simple framework for understanding the dynamical stability of planets embedded in a protoplanetary nebula over typical disk lifetimes, and provide estimates for the maximum allowable planetary masses. We collect these easily evaluated dynamical constraints into a workflow that can help guide the design and interpretation of new observational campaigns and numerical simulations of gap opening in such systems. We argue that the locations of resonances should be significantly shifted from integer period ratios in massive disks like HL Tau, and that theoretical uncertainties in the exact shift, together with observational errors, imply a large uncertainty in the dynamical state and stability in such disks. This renders our results largely insensitive to an improved determination of the gaps' orbital radii, and presents an important barrier to using systems like HL Tau as a proxy for the initial conditions following planet formation. An important observational avenue to breaking this degen...

  18. On the dynamical stability of the proposed planetary system orbiting NSVS 14256825

    Wittenmyer, Robert A; Marshall, Jonathan


    We present a detailed dynamical analysis of the orbital stability of the two circumbinary planets recently proposed to orbit the evolved eclipsing binary star system NSVS 14256825. As is the case for other recently proposed circumbinary planetary systems detected through the timing of mutual eclipses between the central binary stars, the proposed planets do not stand up to dynamical scrutiny. The proposed orbits for the two planets are extremely unstable on timescales of less than a thousand years, regardless of the mutual inclination between the planetary orbits. For the scenario where the planetary orbits are coplanar, a small region of moderate stability was observed, featuring orbits that were somewhat protected from destabilisation by the influence of mutual 2:1 mean-motion resonance between the orbits of the planets. Even in this stable region, however, the systems tested typically only survived on timescales of order 1 million years, far shorter than the age of the system. Our results suggest that, if ...

  19. Transmission stability and Raman-induced amplitude dynamics in multichannel soliton-based optical waveguide systems

    Peleg, Avner; Nguyen, Quan M.; Tran, Thinh P.


    We study transmission stability and dynamics of pulse amplitudes in N-channel soliton-based optical waveguide systems, taking into account second-order dispersion, Kerr nonlinearity, delayed Raman response, and frequency dependent linear gain-loss. We carry out numerical simulations with systems of N coupled nonlinear Schrödinger (NLS) equations and compare the results with the predictions of a simplified predator-prey model for Raman-induced amplitude dynamics. Coupled-NLS simulations for single-fiber transmission with 2 ≤ N ≤ 4 frequency channels show stable oscillatory dynamics of soliton amplitudes at short-to-intermediate distances, in excellent agreement with the predator-prey model's predictions. However, at larger distances, we observe transmission destabilization due to resonant formation of radiative sidebands, which is caused by Kerr nonlinearity. The presence of linear gain-loss in a single fiber leads to a limited increase in transmission stability. Significantly stronger enhancement of transmission stability is achieved in a nonlinear N-waveguide coupler due to efficient suppression of radiative sideband generation by the linear gain-loss. As a result, the distances along which stable Raman-induced dynamics of soliton amplitudes is observed are significantly larger in the waveguide coupler system compared with the single-fiber system.

  20. Dynamic angle stability of an industrial turbo generator connected in power system

    Grouni, S.; Hallak, M.; Aibeche, A.; Ramdani, A.; Bouallegue, K.


    This paper deals with the dynamic problem of oscillation and damping on an industrial turbo generator connected to infinite networks. A set of equations that governs the turbo generator connected to infinite bus are written in characteristic form. The power system stabilizer PSS applied in order to solve the problem of damping internal angle and operating power system synchronization. The PSS model described is inspired from Heffron-Philips model is applied on real parameters simulation under Matlab simulink. The results obtained from practical application are advantageous which variations of amplitude and time mitigation oscillations magnitude of electrical and mechanical output variables. This numerical experiment permits to gain more simplicity compared with several methods applied in a real operating prototyping systems. The PSS that is used will improve the dynamic stability.

  1. Stability of the Supply Chain Using System Dynamics Simulation and the Accumulated Deviations from Equilibrium

    Luis Rabelo


    Full Text Available We propose and demonstrate a new methodology to stabilize systems with complex dynamics like the supply chain. This method is based on the accumulated deviations from equilibrium (ADE. It is most beneficial for controlling system dynamic models characterized by multiple types of delays, many interacting variables, and feedback processes. We employ the classical version of particle swarm optimization as the optimization approach due to its performance in multidimensional space, stochastic properties, and global reach. We demonstrate the effectiveness of our method based on ADE using a manufacturing-supply-chain case study.

  2. Stability of conditionally invariant sets and controlled uncertain dynamic systems on time scales

    Lakshmikantham V.


    Full Text Available A basic feedback control problem is that of obtaining some desired stability property from a system which contains uncertainties due to unknown inputs into the system. Despite such imperfect knowledge in the selected mathematical model, we often seek to devise controllers that will steer the system in a certain required fashion. Various classes of controllers whose design is based on the method of Lyapunov are known for both discrete [4], [10], [15], and continuous [3–9], [11] models described by difference and differential equations, respectively. Recently, a theory for what is known as dynamic systems on time scales has been built which incorporates both continuous and discrete times, namely, time as an arbitrary closed sets of reals, and allows us to handle both systems simultaneously [1], [2], [12], [13]. This theory permits one to get some insight into and better understanding of the subtle differences between discrete and continuous systems. We shall, in this paper, utilize the framework of the theory of dynamic systems on time scales to investigate the stability properties of conditionally invariant sets which are then applied to discuss controlled systems with uncertain elements. For the notion of conditionally invariant set and its stability properties, see [14]. Our results offer a new approach to the problem in question.

  3. Periodic solutions of nonlinear dynamical systems numerical computation, stability, bifurcation and transition to chaos

    Reithmeier, Eduard


    Limit cycles or, more general, periodic solutions of nonlinear dynamical systems occur in many different fields of application. Although, there is extensive literature on periodic solutions, in particular on existence theorems, the connection to physical and technical applications needs to be improved. The bifurcation behavior of periodic solutions by means of parameter variations plays an important role in transition to chaos, so numerical algorithms are necessary to compute periodic solutions and investigate their stability on a numerical basis. From the technical point of view, dynamical systems with discontinuities are of special interest. The discontinuities may occur with respect to the variables describing the configuration space manifold or/and with respect to the variables of the vector-field of the dynamical system. The multiple shooting method is employed in computing limit cycles numerically, and is modified for systems with discontinuities. The theory is supported by numerous examples, mainly fro...

  4. Study on the Stability of Supply Chain System Under Perturbations of Dynamic Parameters

    YingjinLu; XiaowoTang; ZongfangZhou


    The stability of supply chain system is key to implement efficiently inventory policies and improve quality of service in the supply chain. If the supply chain system were unstable, the lead-time would be uncertain. As a result, directly affects the process of manufacture, and the service level. In this paper, we analyze the stability of the supply chain system under perturbations of dynamic parameters based on the Cobb-Douglas production function and study influences on supply chain performance. We prove that the supply chain system, with the increases of the re-production input funding, becomes unstable. Further, when the optimal combination of input parameter elements, the supply chain system becomes unstable.

  5. Global Stability and Dynamics of Strongly Nonlinear Systems Using Koopman Operator Theory


    calculus, applied mathematics, Director’s Research Initiative 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18...ARL-TR-7959 MAR 2017 US Army Research Laboratory Global Stability and Dynamics of Strongly Nonlinear Systems Using when it is no longer needed. Do not return it to the originator. ARL-TR-7959 ● MAR 2017 US Army Research Laboratory Global

  6. The Dynamic Impact of Large Wind Farms on Power System Stability

    Elkington, Katherine


    As the installed capacity of wind power increases across the world, its impact on power systems is becoming more important. To ensure the reliable operation of a power system which is significantly fed by wind power, the dynamics of the system must be understood. The purpose of this study is to analyse the dynamic impact of large-scale wind farms on the stability of a power grid, and to investigate the possibility of improving the stabilisation and damping of the grid by smart control strategies for wind turbines. When unconventional types of generators are used in a power system, the system behaves differently under abnormal dynamic events. For example, new types of generators such as doubly fed induction generators (DFIGs) cause different modes of oscillation in the system. In order to damp oscillations in the system, it is necessary to understand the equipment causing these oscillations, and the methods of optimally damping the oscillations. Large power oscillations can occur in a power system as a result of disturbances. Ordinarily these oscillations are slow and, in principle, it is possible to damp them with the help of wind power. This suggests the use of a power oscillation damping (POD) controller for a DFIG, similar to a power system stabiliser (PSS) for a synchronous generator. To demonstrate this concept, we design PODs for DFIGs in a wind farm. Voltage stability is another important aspect of the safe operation of a power system. It has been shown that the voltage stability of a power system is affected by induction generators and also DFIGs. The voltage stability must therefore also be analysed in order to guard against a power system collapse. In this study we develop models and control strategies for large wind farms comprising DFIGs, and study the impact of the wind farms on power systems. The design of multiple PODs in a wind farm is performed using linear matrix inequalities (LMIs), and the impact of the wind turbines is investigated through the

  7. Solutions Stability of Initial Boundary Problem, Modeling of Dynamics of Some Discrete Continuum Mechanical System

    D. A. Eliseev


    Full Text Available The solution stability of an initial boundary problem for a linear hybrid system of differential equations, which models the rotation of a rigid body with two elastic rods located in the same plane is studied in the paper. To an axis passing through the mass center of the rigid body perpendicularly to the rods location plane is applied the stabilizing moment proportional to the angle of the system rotation, derivative of the angle, integral of the angle. The external moment provides a feedback. A method of studying the behavior of solutions of the initial boundary problem is proposed. This method allows to exclude from the hybrid system of differential equations partial differential equations, which describe the dynamics of distributed elements of a mechanical system. It allows us to build one equation for an angle of the system rotation. Its characteristic equation defines the stability of solutions of all the system. In the space of feedback-coefficients the areas that provide the asymptotic stability of solutions of the initial boundary problem are built up.

  8. Data assimilation as a nonlinear dynamical systems problem: stability and convergence of the prediction-assimilation system.

    Carrassi, Alberto; Ghil, Michael; Trevisan, Anna; Uboldi, Francesco


    We study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system leads to the uniqueness of its sequentially estimated solutions and is required for the convergence of these solutions to the system's true, chaotic evolution. The key ideas of our approach are illustrated for a linearized Lorenz system. Stability of two nonlinear prediction-assimilation systems from dynamic meteorology is studied next via the complete spectrum of their Lyapunov exponents; these two systems are governed by a large set of ordinary and of partial differential equations, respectively. The degree of data-induced stabilization is crucial for the performance of such a system. This degree, in turn, depends on two key ingredients: (i) the observational network, either fixed or data-adaptive, and (ii) the assimilation method.

  9. Output feedback stabilization for stochastic nonlinear systems in observer canonical form with stable zero-dynamics

    潘子刚; 刘允刚; 施颂椒


    In this paper, we study the problem of output feedback stabilization for stochastic nonlinear systems. We consider a class of stochastic nonlinear systems in observer canonical form with stable zero-dynamics. We introduce a sequence of state transformations that transform the system into a lower triangular structure that is amenable for integrator backstepping design. Then we design the output-feedback controller and prove that the closed-loop system is bounded in probability. Furthermore, when the disturbance vector field vanishes at the origin, the closed-loop system is asymptotically stable in the large. With special care, the controller preserves the equilibrium of the nonlinear system. An example is included to illustrate the theoretical findings.

  10. Stabilization by deflation for sparse dynamical systems without loss of sparsity

    Cazzani, Antonio; Ruge, Peter


    Multiple-input, multiple-output models for coupled systems in structural dynamics including unbounded domains, like soil or fluid, are characterized by sparse system-matrices and unstable parts in the whole set of solutions due to spurious modes. Spectral shifting with deflation can stabilize these unstable parts; however the originally sparse system-matrices become fully populated when this procedure is applied. This paper presents a special consecutive treatment of the deflated system without losing the numerical advantages from sparsity. The procedure starts with an LU-decomposition of the sparse undeflated system and continues with restricting the solution space with respect to deflation using the same LU-decomposition. An example from soil-structure interaction shows the benefits of this consecutive treatment.

  11. Algorithm of dynamic stabilization system for a car 4x4 with a link rear axle

    M. M. Jileikin


    Full Text Available The slow development of active safety systems of the automobile all-wheel drive vehicles is the cause of lack of researches in the field of power distribution under the specific conditions of movement. The purpose of work is to develop methods to control a curvilinear motion of 4x4 cars with a link to the rear axle that provides the increase in directional and trajectory stability of the car. The paper analyses the known methods to increase wheeled vehicles movement stability. It also offers a method for power flow redistribution in the transmission of the car 4x4 with a link to the rear axle, providing the increase in directional and trajectory stability of the car.To study the performance and effectiveness of the proposed method a mathematical model of the moving car 4x4 with a link to the rear axle is developed. Simulation methods allowed us to establish the following:1. for car 4x4 with redistribution of torque between the driving axles in the range of 100:0 - 50:50 and with redistribution of torque between the wheels of the rear axle in the range of 0:100 the most effective are the stabilization algorithms used in combination “Lowing power consumption of the engine +Creation of stabilizing the moment due to the redistribution of torque on different wheels", providing the increase in directional and trajectory stability by 12...93%;2. for car 4x4 with redistribution of torque between the driving axles in the range 100:0 - 0:100 and with redistribution of torque between the wheels of the rear axle in the range of 0:100 the best option is a combination of algorithms "Lowing power consumption of the engine + Creation of stabilizing moment due to redistribution of torques on different wheels", providing the increase in directional and trajectory stability by 27...93%.A comparative analysis of algorithms efficiency of dynamic stabilization system operation for two-axle wheeled vehicles depending on the torque redistribution between the driving

  12. Voltage Stability Impact of Grid-Tied Photovoltaic Systems Utilizing Dynamic Reactive Power Control

    Omole, Adedamola

    Photovoltaic (PV) DGs can be optimized to provide reactive power support to the grid, although this feature is currently rarely utilized as most DG systems are designed to operate with unity power factor and supply real power only to the grid. In this work, the voltage stability of a power system embedded with PV DG is examined in the context of the high reactive power requirement after a voltage sag or fault. A real-time dynamic multi-function power controller that enables renewable source PV DGs to provide the reactive power support necessary to maintain the voltage stability of the microgrid, and consequently, the wider power system is proposed. The loadability limit necessary to maintain the voltage stability of an interconnected microgrid is determined by using bifurcation analysis to test for the singularity of the network Jacobian and load differential equations with and without the contribution of the DG. The maximum and minimum real and reactive power support permissible from the DG is obtained from the loadability limit and used as the limiting factors in controlling the real and reactive power contribution from the PV source. The designed controller regulates the voltage output based on instantaneous power theory at the point-of-common coupling (PCC) while the reactive power supply is controlled by means of the power factor and reactive current droop method. The control method is implemented in a modified IEEE 13-bus test feeder system using PSCADRTM power system analysis software and is applied to the model of a Tampa ElectricRTM PV installation at Lowry Park Zoo in Tampa, FL. This dissertation accomplishes the systematic analysis of the voltage impact of a PV DG-embedded power distribution system. The method employed in this work bases the contribution of the PV resource on the voltage stability margins of the microgrid rather than the commonly used loss-of-load probability (LOLP) and effective load-carrying capability (ELCC) measures. The results of

  13. Robust transmission stabilization and dynamic switching in broadband hybrid waveguide systems with nonlinear gain and loss

    Nguyen, Quan M.; Peleg, Avner; Tran, Thinh P.


    We develop a method for transmission stabilization and robust dynamic switching for colliding optical soliton sequences in broadband waveguide systems with nonlinear gain and loss. The method is based on employing hybrid waveguides, consisting of spans with linear gain and cubic loss, and spans with linear loss, cubic gain, and quintic loss. We show that the amplitude dynamics is described by a hybrid Lotka-Volterra (LV) model, and use the model to determine the physical parameter values required for enhanced transmission stabilization and switching. Numerical simulations with coupled nonlinear Schrödinger equations confirm the predictions of the LV model, and show complete suppression of radiative instability and pulse distortion. This enables stable transmission over distances larger by an order of magnitude compared with uniform waveguides with linear gain and cubic loss. Moreover, multiple on-off and off-on dynamic switching events are demonstrated over a wide range of soliton amplitudes, showing the superiority of hybrid waveguides compared with static switching in uniform waveguides.

  14. A Mechanism for Stabilization of Dynamics in Nonlinear Systems with Different Time Scales

    Lopez, Raquel M; Camacho, Erika T


    There are many natural, physical, and biological systems that exhibit multiple time scales. For example, the dynamics of a population of ticks can be described in continuous time during their individual life cycle yet discrete time is used to describe the generation of offspring. These characteristics cause the population levels to be reset periodically. A similar phenomenon can be observed in a sociological college drinking model in which the population is reset by the incoming class each year, as described in the 2006 work of Camacho et al. With the latter as our motivation we analytically and numerically investigate the mechanism by which solutions in certain systems with this resetting conditions stabilize. We further utilize the sociological college drinking model as an analogue to analyze certain one-dimensional and two-dimensional nonlinear systems, as we attempt to generalize our results to higher dimensions.

  15. Dynamic neutronic and stability analysis of a burst mode, single cavity gas core reactor Brayton cycle space power system

    Dugan, Edward T.; Kutikkad, Kiratadas

    The conceptual, burst-mode gaseous-core reactor (GCR) space nuclear power system presently subjected to reactor-dynamics and system stability studies operates on a closed Brayton cycle, via disk MHD generator for energy conversion. While the gaseous fuel density power coefficient of reactivity is found to be capable of rapidly stabilizing the GCR system, the power of this feedback renders standard external reactivity insertions inadequate for significant power-level changes during normal operation.

  16. Diagonal recurrent neural network based adaptive control of nonlinear dynamical systems using lyapunov stability criterion.

    Kumar, Rajesh; Srivastava, Smriti; Gupta, J R P


    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.

  17. Comparison of the Dynesys Dynamic Stabilization System and Posterior Lumbar Interbody Fusion for Lumbar Degenerative Disease.

    Yang Zhang

    Full Text Available There have been few studies comparing the clinical and radiographic outcomes between the Dynesys dynamic stabilization system and posterior lumbar interbody fusion (PLIF. The objective of this study is to compare the clinical and radiographic outcomes of Dynesys and PLIF for lumbar degenerative disease.Of 96 patients with lumbar degenerative disease included in this retrospectively analysis, 46 were treated with the Dynesys system and 50 underwent PLIF from July 2008 to March 2011. Clinical and radiographic outcomes were evaluated. We also evaluated the occurrence of radiographic and symptomatic adjacent segment degeneration (ASD.The mean follow-up time in the Dynesys group was 53.6 ± 5.3 months, while that in the PLIF group was 55.2 ± 6.8 months. At the final follow-up, the Oswestry disability index and visual analogue scale score were significantly improved in both groups. The range of motion (ROM of stabilized segments in Dynesys group decreased from 7.1 ± 2.2° to 4.9 ± 2.2° (P < 0.05, while that of in PLIF group decreased from 7.3 ± 2.3° to 0° (P < 0.05. The ROM of the upper segments increased significantly in both groups at the final follow-up, the ROM was higher in the PLIF group. There were significantly more radiographic ASDs in the PLIF group than in the Dynesys group. The incidence of complications was comparable between groups.Both Dynesys and PLIF can improve the clinical outcomes for lumbar degenerative disease. Compared to PLIF, Dynesys stabilization partially preserves the ROM of the stabilized segments, limits hypermobility in the upper adjacent segment, and may prevent the occurrence of ASD.

  18. Power system dynamic stability by SSSC-based supplementary damping controller using Imperialist Competitive Algorithm

    Eskandar Gholipour


    Full Text Available Power-system dynamic stability improvement by a static synchronous series compensator (SSSC based damping controller is thoroughly investigated in this paper. In order to design the optimal parameters of the controller, Imperialist Competitive Algorithm (ICA is employed to search for the optimal controller parameters. Both local and remote signals are considered in the present study and the performance of the proposed controllers with variations in the signal transmission delays has been investigated. The performances of the proposed controllers are evaluated under different disturbances for both single-machine-infinite-bus and multi-machine power systems. Finally, the results of ICA method are compared with the results of Genetic Algorithm (GA.

  19. Molecular Dynamics Study of the Foam Stability of a Mixed Surfactant System with and without Calcium Ions

    Yang, Xiaozhen; Yang, Wenhong; Institute of Chemistry, CAS Team


    Foam stability performance of a mixture surfactant system with and without calcium ions, including linear alkylbenzene sulfonate (LAS) and sodium dodecyl sulfate (SDS), has been studied by molecular dynamics. Microscopic interaction analysis reveals that the fraction of free calcium ions, Xf , in film system indicates the extent of the foam stabilities when Xf is in different calcium ion zones. In the system without ions, we found the variable of the surfactant tail mass out of water film, W , is indicator of foam stability. Performance of the mixture system predicted here was supported by experiments.

  20. Orbital stability analysis and chaotic dynamics of exoplanets in multi-stellar systems

    Satyal, Suman

    The advancement in detection technology has substantially increased the discovery rate of exoplanets in the last two decades. The confirmation of thousands of exoplanets orbiting the solar type stars has raised new astrophysical challenges, including the studies of orbital dynamics and long-term stability of such planets. Continuous orbital stability of the planet in stellar habitable zone is considered vital for life to develop. Hence, these studies furthers one self-evident aim of mankind to find an answer to the century old question: Are we alone?. This dissertation investigates the planetary orbits in single and binary star systems. Within binaries, a planet could orbit either one or both stars as S-type or P-type, respectively. I have considered S-type planets in two binaries, gamma Cephei and HD 196885, and compute their orbits by using various numerical techniques to assess their periodic, quasi-periodic or chaotic nature. The Hill stability (HS) function, which measures the orbital perturbation induced by the nearby companion, is calculated for each system and then its efficacy as a new chaos indicator is tested against Maximum Lyapunov Exponents (MLE) and Mean Exponential Growth factor of Nearby Orbits (MEGNO). The dynamics of HD 196885 AB is further explored with an emphasis on the planet's higher orbital inclination relative to the binary plane. I have quantitatively mapped out the chaotic and quasi-periodic regions of the system's phase space, which indicates a likely regime of the planet's inclination. In, addition, the resonant angle is inspected to determine whether alternation between libration and circulation occurs as a consequence of Kozai oscillations, a probable mechanism that can drive the planetary orbit to a large inclination. The studies of planetary system in GJ 832 shows potential of hosting multiple planets in close orbits. The phase space of GJ 832c (inner planet) and the Earth-mass test planet(s) are analyzed for periodic

  1. Basin stability in delayed dynamics

    Leng, Siyang; Lin, Wei; Kurths, Jürgen


    Basin stability (BS) is a universal concept for complex systems studies, which focuses on the volume of the basin of attraction instead of the traditional linearization-based approach. It has a lot of applications in real-world systems especially in dynamical systems with a phenomenon of multi-stability, which is even more ubiquitous in delayed dynamics such as the firing neurons, the climatological processes, and the power grids. Due to the infinite dimensional property of the space for the initial values, how to properly define the basin’s volume for delayed dynamics remains a fundamental problem. We propose here a technique which projects the infinite dimensional initial state space to a finite-dimensional Euclidean space by expanding the initial function along with different orthogonal or nonorthogonal basis. A generalized concept of basin’s volume in delayed dynamics and a highly practicable calculating algorithm with a cross-validation procedure are provided to numerically estimate the basin of attraction in delayed dynamics. We show potential applicabilities of this approach by applying it to study several representative systems of biological or/and physical significance, including the delayed Hopfield neuronal model with multistability and delayed complex networks with synchronization dynamics.

  2. Molecular Dynamics Study of Stability and Diffusion of Graphene-Based Drug Delivery Systems

    Xiunan Wang


    Full Text Available Graphene, a two-dimensional nanomaterial with unique biomedical properties, has attracted great attention due to its potential applications in graphene-based drug delivery systems (DDS. In this work graphene sheets with various sizes and graphene oxide functionalized with polyethylene glycol (GO-PEG are utilized as nanocarriers to load anticancer drug molecules including CE6, DOX, MTX, and SN38. We carried out molecular dynamics calculations to explore the energetic stabilities and diffusion behaviors of the complex systems with focuses on the effects of the sizes and functionalization of graphene sheets as well as the number and types of drug molecules. Our study shows that the binding of graphene-drug complex is favorable when the drug molecules and finite graphene sheets become comparable in sizes. The boundaries of finite sized graphene sheets restrict the movement of drug molecules. The double-side loading often slows down the diffusion of drug molecules compared with the single-side loading. The drug molecules bind more strongly with GO-PEG than with pristine graphene sheets, demonstrating the advantages of functionalization in improving the stability and biocompatibility of graphene-based DDS.

  3. Thermal stability assessment of antibiotics in moderate temperature and subcriticalwater using a pressurized dynamic flow-through system

    Svahn, Ola; Björklund, Erland


    Thermal degradation of antibiotics has been studied for decades in a broad range of disciplines including food production, agriculture and analytical chemistry. Yet, there is a lack of thermal stability data for many antibiotics. Here we systematically investigated the thermal stability of ten commonly prescribed antibiotics applying a laborsaving automated inhouse pressurized dynamic flow-through system. The design of the system allowed a fast access to a large number of data at medium to su...

  4. The Dynamic Stabilizing Innersole System (DSIS): the management of hyperpronation in children.

    Jay, R M; Schoenhaus, H D; Seymour, C; Gamble, S


    In a study of 50 children, the Dynamic Stabilizing Innersole System (DSIS) was found to decrease the mean resting calcaneal stance position (RCSP) by an average of 6 degrees. A comparison between the neutral calcaneal stance position and the RCSP with the DSIS showed no statistically significant difference between the means for the right or left foot, indicating that the DSIS is capable of returning severe flat foot deformities to their neutral calcaneal stance position. The RCSP with and without the DSIS differed significantly, indicating that the DSIS provides a considerable and statistically significant amount of correction in the RCSP in our study population. Furthermore, the results of linear regression showed that the DSIS appears to be sensitive to the severity of the deformity, preventing overcorrection of less severe flatfoot deformities and providing a long awaited alternative to traditional pediatric corrective flatfoot devices.

  5. Clinical experiences of dynamic stabilizers: Dynesys and Dynesys top loading system for lumbar spine degenerative disease.

    Hsieh, Cheng-Ta; Chang, Chih-Ju; Su, I-Chang; Lin, Li-Ying


    Dynesys (Dynamic Neutralization System) was designed to overcome the shortcomings of fusion. The Dynesys top loading (DTL) system is a new alternative Dynesys system that can be applied via a minimally invasive procedure. This study aimed to ascertain whether DTL is a suitable device for motion preservation and prevention of instability, and to compare the clinical and radiological outcomes between DTL and Dynesys. In this study, 12 patients were treated with Dynesys and 21 patients were treated with DTL. Back and leg pain were evaluated using the visual analog scale. The Oswestry Disability Index was used to evaluate the patients' function. Range of motion (ROM) at the operative level and for the whole lumbar spine was measured pre- and postoperatively. The length of wound, blood loss, length of hospital stay, and operation duration were also compared. All patients were followed up for 12-76 months. Scores on the visual analog scale and Oswestry Disability Index were significantly improved postoperatively. The median ROM of the whole spine and index level ROM in all patients showed 12.5% and 79.6% loss, respectively. The DTL group exhibited significantly better results in terms of blood loss, wound length, and operation duration, in addition to early ambulation. In conclusion, Dynesys and DTL are semirigid fixation systems that can significantly improve clinical symptoms and signs. Our results suggested that DTL was better than Dynesys as a result of it being a minimally invasive procedure. However, further study with large sample sizes and longer follow-up durations is required to validate the effects of these dynamic stabilizers.

  6. Students' Understanding of Equilibrium and Stability: The Case of Dynamic Systems

    Canu, Michaël; de Hosson, Cécile; Duque, Mauricio


    Engineering students in control courses have been observed to lack an understanding of equilibrium and stability, both of which are crucial concepts in this discipline. The introduction of these concepts is generally based on the study of classical examples from Newtonian mechanics supplemented with a control system. Equilibrium and stability are…

  7. Dynamic stability requirements during gait and standing exergames on the wii fit® system in the elderly

    Duclos Cyril


    Full Text Available Abstract Background In rehabilitation, training intensity is usually adapted to optimize the trained system to attain better performance (overload principle. However, in balance rehabilitation, the level of intensity required during training exercises to optimize improvement in balance has rarely been studied, probably due to the difficulty in quantifying the stability level during these exercises. The goal of the present study was to test whether the stabilizing/destabilizing forces model could be used to analyze how stability is challenged during several exergames, that are more and more used in balance rehabilitation, and a dynamic functional task, such as gait. Methods Seven healthy older adults were evaluated with three-dimensional motion analysis during gait at natural and fast speed, and during three balance exergames (50/50 Challenge, Ski Slalom and Soccer. Mean and extreme values for stabilizing force, destabilizing force and the ratio of the two forces (stability index were computed from kinematic and kinetic data to determine the mean and least level of dynamic, postural and overall balance stability, respectively. Results Mean postural stability was lower (lower mean destabilizing force during the 50/50 Challenge game than during all the other tasks, but peak postural instability moments were less challenging during this game than during any of the other tasks, as shown by the minimum destabilizing force values. Dynamic stability was progressively more challenged (higher mean and maximum stabilizing force from the 50/50 Challenge to the Soccer and Slalom games, to the natural gait speed task and to the fast gait speed task, increasing the overall stability difficulty (mean and minimum stability index in the same manner. Conclusions The stabilizing/destabilizing forces model can be used to rate the level of balance requirements during different tasks such as gait or exergames. The results of our study showed that postural stability

  8. Generalized and Stability Rational Functions for Dynamic Systems of Reactor Kinetics

    Ahmed E. Aboanber


    Full Text Available The base of reactor kinetics dynamic systems is a set of coupled stiff ordinary differential equations known as the point reactor kinetics equations. These equations which express the time dependence of the neutron density and the decay of the delayed neutron precursors within a reactor are first order nonlinear and essentially describe the change in neutron density within the reactor due to a change in reactivity. Outstanding the particular structure of the point kinetic matrix, a semianalytical inversion is performed and generalized for each elementary step resulting eventually in substantial time saving. Also, the factorization techniques based on using temporarily the complex plane with the analytical inversion is applied. The theory is of general validity and involves no approximations. In addition, the stability of rational function approximations is discussed and applied to the solution of the point kinetics equations of nuclear reactor with different types of reactivity. From the results of various benchmark tests with different types of reactivity insertions, the developed generalized Padé approximation (GPA method shows high accuracy, high efficiency, and stable character of the solution.

  9. Asymptotic Stability of Caputo Type Fractional Neutral Dynamical Systems with Multiple Discrete Delays

    Hai Zhang


    Full Text Available We discuss the delay-independent asymptotic stability of Caputo type fractional-order neutral differential systems with multiple discrete delays. Based on the algebraic approach and matrix theory, the sufficient conditions are derived to ensure the asymptotic stability for all time-delay parameters. By applying the stability criteria, one can avoid solving the roots of transcendental equations. The results obtained are computationally flexible and convenient. Moreover, an example is provided to illustrate the effectiveness and applicability of the proposed theoretical results.

  10. Stabilizing fixed points of time-delay systems close to the Hopf bifurcation using a dynamic delayed feedback control method

    Rezaie, B; Motlagh, M R Jahed; Analoui, M [Iran University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of); Khorsandi, S [Amirkabir University of Technology, Hafez St., Tehran (Iran, Islamic Republic of)], E-mail:


    This paper deals with the problem of Hopf bifurcation control for a class of nonlinear time-delay systems. A dynamic delayed feedback control method is utilized for stabilizing unstable fixed points near Hopf bifurcation. Using a linear stability analysis, we show that under certain conditions of the control parameters, and without changing the operating point of the system, the onset of Hopf bifurcation is delayed. Meanwhile, by applying the center manifold theorem and the normal form theory, we obtain formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions of the closed loop system. Numerical simulations are given to justify the validity of the analytical results for the system controlled by the proposed method.

  11. Global Stability of Polytopic Linear Time-Varying Dynamic Systems under Time-Varying Point Delays and Impulsive Controls

    M. de la Sen


    Full Text Available This paper investigates the stability properties of a class of dynamic linear systems possessing several linear time-invariant parameterizations (or configurations which conform a linear time-varying polytopic dynamic system with a finite number of time-varying time-differentiable point delays. The parameterizations may be timevarying and with bounded discontinuities and they can be subject to mixed regular plus impulsive controls within a sequence of time instants of zero measure. The polytopic parameterization for the dynamics associated with each delay is specific, so that (q+1 polytopic parameterizations are considered for a system with q delays being also subject to delay-free dynamics. The considered general dynamic system includes, as particular cases, a wide class of switched linear systems whose individual parameterizations are timeinvariant which are governed by a switching rule. However, the dynamic system under consideration is viewed as much more general since it is time-varying with timevarying delays and the bounded discontinuous changes of active parameterizations are generated by impulsive controls in the dynamics and, at the same time, there is not a prescribed set of candidate potential parameterizations.

  12. A Short History of Posterior Dynamic Stabilization

    Cengiz Gomleksiz


    Full Text Available Interspinous spacers were developed to treat local deformities such as degenerative spondylolisthesis. To treat patients with chronic instability, posterior pedicle fixation and rod-based dynamic stabilization systems were developed as alternatives to fusion surgeries. Dynamic stabilization is the future of spinal surgery, and in the near future, we will be able to see the development of new devices and surgical techniques to stabilize the spine. It is important to follow the development of these technologies and to gain experience using them. In this paper, we review the literature and discuss the dynamic systems, both past and present, used in the market to treat lumbar degeneration.

  13. Stabilization strategies for unstable dynamics.

    Devjani J Saha

    Full Text Available BACKGROUND: When humans are faced with an unstable task, two different stabilization mechanisms are possible: a high-stiffness strategy, based on the inherent elastic properties of muscles/tools/manipulated objects, or a low-stiffness strategy, based on an explicit positional feedback mechanism. Specific constraints related to the dynamics of the task and/or the neuromuscular system often force people to adopt one of these two strategies. METHODOLOGY/FINDINGS: This experiment was designed such that subjects could achieve stability using either strategy, with a marked difference in terms of effort and control requirements between the two strategies. The task was to balance a virtual mass in an unstable environment via two elastic linkages that connected the mass to each hand. The dynamics of the mass under the influence of the unstable force field and the forces applied through the linkages were simulated using a bimanual, planar robot. The two linkages were non-linear, with a stiffness that increased with the amount of stretch. The mass could be stabilized by stretching the linkages to achieve a stiffness that was greater than the instability coefficient of the unstable field (high-stiffness, or by balancing the mass with sequences of small force impulses (low-stiffness. The results showed that 62% of the subjects quickly adopted the high-stiffness strategy, with stiffness ellipses that were aligned along the direction of instability. The remaining subjects applied the low-stiffness strategy, with no clear preference for the orientation of the stiffness ellipse. CONCLUSIONS: The choice of a strategy was based on the bimanual coordination of the hands: high-stiffness subjects achieved stability quickly by separating the hands to stretch the linkages, while the low-stiffness subjects kept the hands close together and took longer to achieve stability but with lower effort. We suggest that the existence of multiple solutions leads to different types

  14. Sufficient LMI conditions and Lyapunov redesign for the robust stability of a class of feedback linearized dynamical systems.

    Azizi, Sajad


    The robust stability of a class of feedback linearizable minimum-phase nonlinear system, having parametric uncertainties, is investigated in this study. The system in new coordinates is represented to an equivalent formulation after the attempt of feedback linearization. Due to the parametric uncertainties the approximately linearized system entails a norm bounded input nonlinearity such that the equilibrium point condition in error dynamics can not be satisfied. Accordingly, to guarantee the regional asymptotic stability a control synthesis problem is proposed by means of sufficient Linear Matrix Inequalities (LMIs) together with an amended nonlinear control term, derived from the Lyapunov redesign method, which tackles zero steady-state error condition. The numerical examples of a general aviation aircraft's longitudinal dynamics and inverted pendulum are simulated to show the proficiency of the proposed control technique. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.


    王永英; 王铁英


    In this paper, some sufficient conditions for the stability of system dx/dt =A(t)x +f(t,x) are given which are based on the assumption of that the eigenvalues of the leading principal submatrix of order r and its complementary submatrix of order m in A(t) all have negative real parts.

  16. Computer program system for dynamic simulation and stability analysis of passive and actively controlled spacecraft. Volume 1. Theory

    Bodley, C. S.; Devers, D. A.; Park, C. A.


    A theoretical development and associated digital computer program system is presented. The dynamic system (spacecraft) is modeled as an assembly of rigid and/or flexible bodies not necessarily in a topological tree configuration. The computer program system may be used to investigate total system dynamic characteristics including interaction effects between rigid and/or flexible bodies, control systems, and a wide range of environmental loadings. Additionally, the program system may be used for design of attitude control systems and for evaluation of total dynamic system performance including time domain response and frequency domain stability analyses. Volume 1 presents the theoretical developments including a description of the physical system, the equations of dynamic equilibrium, discussion of kinematics and system topology, a complete treatment of momentum wheel coupling, and a discussion of gravity gradient and environmental effects. Volume 2, is a program users' guide and includes a description of the overall digital program code, individual subroutines and a description of required program input and generated program output. Volume 3 presents the results of selected demonstration problems that illustrate all program system capabilities.

  17. Reliable grading robust stabilization for uncertain time-varying systems via dynamic compensator


    A new general model for uncertain time-varying parameters and a new measure sensor failure model are presented, and the problems of both grading robust stabilization and reliable grading robust stabilization for such systems are studied. By the Lyapunov stability theory and matrix algebra method, some sufficient criteria for the above two control problems are established in quasi-linear matrix inequalities (Q-LMIS) forms. In view of linear matrix inequality (LMI) approach, a solving procedure for the Q-LMIS problem is proposed. The solvability of the Q-LMIS problem can be improved obviously by adding some LMI constraints to the Q-LMIS. Based on the two Q-LMIS criteria, a grading robust stable control strategy, namely, the controller with different energy is acted on the system with different uncertain parameter range, is presented. The numerical simulating results show that the grading robust stable control strategy for the robust stabilization of uncertain systems has important theoretical and practical significance.

  18. Trojan resonant dynamics, stability, and chaotic diffusion, for parameters relevant to exoplanetary systems

    Páez, Rocío Isabel; Efthymiopoulos, Christos


    The possibility that giant extrasolar planets could have small Trojan co-orbital companions has been examined in the literature from both viewpoints of the origin and dynamical stability of such a configuration. Here we aim to investigate the dynamics of hypothetical small Trojan exoplanets in domains of secondary resonances embedded within the tadpole domain of motion. To this end, we consider the limit of a massless Trojan companion of a giant planet. Without other planets, this is a case of the elliptic restricted three body problem (ERTBP). The presence of additional planets (hereafter referred to as the restricted multi-planet problem, RMPP) induces new direct and indirect secular effects on the dynamics of the Trojan body. The paper contains a theoretical and a numerical part. In the theoretical part, we develop a Hamiltonian formalism in action-angle variables, which allows us to treat in a unified way resonant dynamics and secular effects on the Trojan body in both the ERTBP or the RMPP. In both cases, our formalism leads to a decomposition of the Hamiltonian in two parts, . , called the basic model, describes resonant dynamics in the short-period (epicyclic) and synodic (libration) degrees of freedom, while contains only terms depending trigonometrically on slow (secular) angles. is formally identical in the ERTBP and the RMPP, apart from a re-definition of some angular variables. An important physical consequence of this analysis is that the slow chaotic diffusion along resonances proceeds in both the ERTBP and the RMPP by a qualitatively similar dynamical mechanism. We found that this is best approximated by the paradigm of `modulational diffusion'. In the paper's numerical part, we then focus on the ERTBP in order to make a detailed numerical demonstration of the chaotic diffusion process along resonances. Using color stability maps, we first provide a survey of the resonant web for characteristic mass parameter values of the primary, in which the

  19. The Nonlinear Stability Prediction and FEM Modeling of High-Speed Spindle System with Joints Dynamic Characteristics

    Bo Wang


    Full Text Available When predicting the nonlinear stability of high-speed spindle system, it is necessary to create an accurate model that reflects the dynamic characteristics of the whole system, including the spindle-bearing joint and spindle-holder-tool joints. In this paper, the distribution spring model of spindle-holder-tool joints was built with the consideration of its dynamic characteristics; the five-DOF dynamic model of the angle contact ball bearing was also established to study the influence of speed and preload on the spindle-bearing joint, both of which were used in the general whole complete spindle system FEM model. The rationality of the model was verified by comparison with the FRF of traditional rigid model and experiments. At last, the influences of speed and cutting force on the nonlinear stability were analyzed by amplitude spectrum, bifurcation, and Poincaré mapping. The results provided a theoretical basis and an evaluating criterion for nonlinear stability prediction and product surface quality improvement.

  20. A novel optimization method of transient stability emergency control based on practical dynamic security region (PDSR) of power systems

    YU; Yixin; LIU; Hui; ZENG; Yuan


    This paper proposes a novel optimization method of transient stability emergency control based on a new concept of the so-called extended practical dynamic security region (EPDSR) defined in this paper and four experiential laws about the EPDSRs found from a number of studies in real power systems. In this method, the effect of a control action is represented by the displacement of EPDSR's critical hyper-plane boundary in the direction of its outer normal vector. If an unstable contingency occurs, appropriate emergency control actions are triggered so that the enlarged EPDSR can cover the current operating point. Based on these ideas, a mathematics model of emergency control strategy is developed for minimizing its total cost and guaranteeing power system transient stability. The simulation results on the 10-generator, 39-bus New-England Test System as well as other real power systems have shown the validity of this method.

  1. Dynesys dynamic stabilization system for the lumbar degenerative disease: a preliminary report from China

    LI Hai-peng; LI Fang; GUAN Kai; ZHAO Guang-ming; SHAN Jian-lin; SUN Tian-sheng


    Background Dynesys dynamic stabilization system was first implanted in patients in 1994,and introduced to China in 2007.Therefore,it was a new technique for Chinese orthopedics and hence necessary to collect clinical data about Dynesys in China.The objective of this study was to report the preliminary results of Dynesys for the lumbar degenerative disease in China.Methods Twenty-seven patients were treated with the Dynesys between July 2007 and January 2009.The diagnosis included degenerative spondylolisthesis (12 cases),degenerative spinal stenosis (nine cases),and lumbar intervertebral disc herniation (six cases).Back pain and leg pain were evaluated using 100-mm visual analog scales (VAS).The Oswestry Disability Index (ODI) was used to evaluate the patients' function.The intervertebral disc height and range of motion at the operative level were taken on radiographs.Results All the patients were followed-up,with an average of (22.40±4.23) months (range 15-32 months).VAS of back pain and leg pain were improved significantly (P <0.05) at follow-up.The ODI scores were reduced from (62.58±12.01)%preoperatively to (15.01±5.71)% at follow-up (P <0.05).The preoperative mean height of the intervertebral disc was (11.21±1.58) mm (range 8.5-13.8 mm) and mean was (10.10±1.78) mm (range 7.0-13.4 mm) at follow-up (P <0.05).The mean range of motion of the implanted segment was (6.00±1.79)° (range 2.5-9.3°) preoperatively and (5.47±1.27)°(range 2.9-7.8°) at follow-up (P=0.11).Conclusions The preliminary results of Dynesys for the lumbar degenerative disease in China are similar to the published results of other countries.It can significantly improve the clinic symptoms and preserved motion at the level of implantation.However,the long-term follow-up data need to be collected.

  2. Application of stabilization techniques in the dynamic analysis of multibody systems

    Hajžman M.


    Full Text Available This paper is intended to the discussion of possible methods for the solution of the motion equations of constrained multibody systems. They can be formulated in the form of differential-algebraic equations and their numerical solution brings the problems of constraint violation and numerical stability. Therefore special methods were proposed to handle these problems. Various approaches for the numerical solution of equations are briefly reviewed and the application of the Baumgarte’s stabilization method on testing examples is shown. The paper was motivated by the effort to find the suitable solution methods for the equations of motion in the form of differentialalgebraic equations using the MATLAB standard computational system.

  3. Dynamical stability of quasi-periodic response solutions in planar conservative systems

    Hanssmann, H.|info:eu-repo/dai/nl/107757435; Simo, Carles


    We study non-autonomous planar Hamiltonian or reversible vector fields that vanish at the origin. The time-dependence is quasi-periodic with strongly non-resonant frequencies. First we give a simple criterion in terms of the averaged system for the trivial solution to be dynamically stable. Then we

  4. Dynamical stability of quasi-periodic response solutions in planar conservative systems

    Hanssmann, H.; Simo, Carles


    We study non-autonomous planar Hamiltonian or reversible vector fields that vanish at the origin. The time-dependence is quasi-periodic with strongly non-resonant frequencies. First we give a simple criterion in terms of the averaged system for the trivial solution to be dynamically stable. Then we

  5. Super Earths and Dynamical Stability of Planetary Systems: First Parallel GPU Simulations Using GENGA

    Elser, S; Stadel, J G


    We report on the stability of hypothetical Super-Earths in the habitable zone of known multi-planetary systems. Most of them have not yet been studied in detail concerning the existence of additional low-mass planets. The new N-body code GENGA developed at the UZH allows us to perform numerous N-body simulations in parallel on GPUs. With this numerical tool, we can study the stability of orbits of hypothetical planets in the semi-major axis and eccentricity parameter space in high resolution. Massless test particle simulations give good predictions on the extension of the stable region and show that HIP 14180 and HD 37124 do not provide stable orbits in the habitable zone. Based on these simulations, we carry out simulations of 10 Earth mass planets in several systems (HD 11964, HD 47186, HD 147018, HD 163607, HD 168443, HD 187123, HD 190360, HD 217107 and HIP 57274). They provide more exact information about orbits at the location of mean motion resonances and at the edges of the stability zones. Beside the ...

  6. Unified stabilizing controller synthesis approach for discrete-time intelligent systems with time delays by dynamic output feedback

    LIU MeiQin


    A novel model, termed the standard neural network model (SNNM), is advanced to describe some delayed (or non-delayed) discrete-time intelligent systems composed of neural networks and Takagi and Sugeno (T-S) fuzzy models. The SNNM is composed of a discrete-time linear dynamic system and a bounded static nonlinear operator. Based on the global asymptotic stability analysis of the SNNMs, linear and nonlinear dynamic output feedback controllers are designed for the SNNMs to stabilize the closed-loop systems, respectively. The control design equations are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms to determine the control signals. Most neural-network-based (or fuzzy) discrete-time intelligent systems with time delays or without time delays can be transformed into the SNNMs for controller synthesis in a unified way. Three application examples show that the SNNMs not only make controller synthesis of neural-network-based (or fuzzy) discrete-time intelligent systems much easier, but also provide a new approach to the synthesis of the controllers for the other type of nonlinear systems.

  7. Stability of Switched Feedback Time-Varying Dynamic Systems Based on the Properties of the Gap Metric for Operators

    M. De la Sen


    Full Text Available The stabilization of dynamic switched control systems is focused on and based on an operator-based formulation. It is assumed that the controlled object and the controller are described by sequences of closed operator pairs (L,C on a Hilbert space H of the input and output spaces and it is related to the existence of the inverse of the resulting input-output operator being admissible and bounded. The technical mechanism addressed to get the results is the appropriate use of the fact that closed operators being sufficiently close to bounded operators, in terms of the gap metric, are also bounded. That philosophy is followed for the operators describing the input-output relations in switched feedback control systems so as to guarantee the closed-loop stabilization.

  8. Unifying dynamical and structural stability of equilibria

    Arnoldi, Jean-François; Haegeman, Bart


    We exhibit a fundamental relationship between measures of dynamical and structural stability of linear dynamical systems-e.g. linearized models in the vicinity of equilibria. We show that dynamical stability, quantified via the response to external perturbations (i.e. perturbation of dynamical variables), coincides with the minimal internal perturbation (i.e. perturbations of interactions between variables) able to render the system unstable. First, by reformulating a result of control theory, we explain that harmonic external perturbations reflect the spectral sensitivity of the Jacobian matrix at the equilibrium, with respect to constant changes of its coefficients. However, for this equivalence to hold, imaginary changes of the Jacobian's coefficients have to be allowed. The connection with dynamical stability is thus lost for real dynamical systems. We show that this issue can be avoided, thus recovering the fundamental link between dynamical and structural stability, by considering stochastic noise as external and internal perturbations. More precisely, we demonstrate that a linear system's response to white-noise perturbations directly reflects the intensity of internal white-noise disturbance that it can accommodate before becoming stochastically unstable.

  9. for hybrid dynamical systems

    Wassim M. Haddad


    Full Text Available In this paper we develop a unified dynamical systems framework for a general class of systems possessing left-continuous flows; that is, left-continuous dynamical systems. These systems are shown to generalize virtually all existing notions of dynamical systems and include hybrid, impulsive, and switching dynamical systems as special cases. Furthermore, we generalize dissipativity, passivity, and nonexpansivity theory to left-continuous dynamical systems. Specifically, the classical concepts of system storage functions and supply rates are extended to left-continuous dynamical systems providing a generalized hybrid system energy interpretation in terms of stored energy, dissipated energy over the continuous-time dynamics, and dissipated energy over the resetting events. Finally, the generalized dissipativity notions are used to develop general stability criteria for feedback interconnections of left-continuous dynamical systems. These results generalize the positivity and small gain theorems to the case of left-continuous, hybrid, and impulsive dynamical systems.


    郭崇慧; 唐焕文


    The dynamic input-output model is well known in economic theory and practice.In this paper,the asymptotic stability and balanced growth solutions of the dynamic input-output system are considered.Under some natural assumptions which do not require the technical coefficient matrix to be indecomposable,it has been proved that the dynamic input-output system is not asymptotically stable and the closed dynamic input-output model has a balanced growth solution.

  11. The Dynamics of Stability

    Hedegaard, Troels Fage

    politiske aktører der greb disse muligheder. Disse historiske faktorer, der hjalp med at skabe opbakning til velfærdsstaten, er dog blevet svækket med tiden, mens støtten til modellen forbliver stabil. Denne umiddelbare modsætning er denne afhandlings omdrejningspunkt. Derfor vender jeg I denne afhandling...... trække på policy feedback teori, som den primære teoretiske ramme, og ud fra dette beskrive og teste sociale mekanismer der kan forklare den vedvarende opbakning til velfærdsmodellen. Disse social mekanismer eksisterer ikke kun i de nordiske lande, men skulle være mere udbredt her, og kan dermed hjælpe...

  12. Stability and comparative analysis of AOT/water/isooctane reverse micelle system using dynamic light scattering and molecular dynamics.

    Vasquez, V R; Williams, B C; Graeve, O A


    We use molecular dynamics (MD) and dynamic light scattering (DLS) measurements to analyze the size of reverse micellar structures in the AOT-water-isooctane system at different water-to-surfactant ratios at ambient temperature and pressure. We find good qualitative agreement for the size and morphology behavior of the reverse micelle structures between molecular dynamics calculations and DLS measurements; however, the average values for the reverse micelle size distributions are systematically larger for the DLS measurements. The latter tends to capture the average hydrodynamic size of the structures based on self-diffusion rather than the average physical size as measured in MD simulations, explaining the systematic deviations observed. The combination of MD with DLS allows a better interpretation of the experimental results, in particular for conditions where the structures are nonspherical, commonly observed at lower water-to-surfactant ratios. We also present and analyze the effect of zirconyl chloride on the micellar size distributions in this system. These type of salts are common for reverse micellar synthesis processes. We find that zirconyl chloride affects significantly the size distributions.

  13. Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks.

    Hu, Cheng; Yu, Juan; Chen, Zhanheng; Jiang, Haijun; Huang, Tingwen


    In this paper, the fixed-time stability of dynamical systems and the fixed-time synchronization of coupled discontinuous neural networks are investigated under the framework of Filippov solution. Firstly, by means of reduction to absurdity, a theorem of fixed-time stability is established and a high-precision estimation of the settling-time is given. It is shown by theoretic proof that the estimation bound of the settling time given in this paper is less conservative and more accurate compared with the classical results. Besides, as an important application, the fixed-time synchronization of coupled neural networks with discontinuous activation functions is proposed. By designing a discontinuous control law and using the theory of differential inclusions, some new criteria are derived to ensure the fixed-time synchronization of the addressed coupled networks. Finally, two numerical examples are provided to show the effectiveness and validity of the theoretical results. Copyright © 2017 Elsevier Ltd. All rights reserved.

  14. Dynamic stability of the Solar System: Statistically inconclusive results from ensemble integrations

    Zeebe, Richard E


    Due to the chaotic nature of the Solar System, the question of its long-term stability can only be answered in a statistical sense, for instance, based on numerical ensemble integrations of nearby orbits. Destabilization of the inner planets, leading to close encounters and/or collisions can be initiated through a large increase in Mercury's eccentricity, with a currently assumed likelihood of ~1%. However, little is known at present about the robustness of this number. Here I report ensemble integrations of the full equations of motion of the eight planets and Pluto over 5 Gyr, including contributions from general relativity. The results show that different numerical algorithms lead to statistically different results for the evolution of Mercury's eccentricity (eM). For instance, starting at present initial conditions (eM ~= 0.21), Mercury's maximum eccentricity achieved over 5 Gyr is on average significantly higher in symplectic ensemble integrations using heliocentricthan Jacobi coordinates and stricter er...

  15. The condition for dynamic stability

    Hof, AL; Gazendam, MGJ; Sinke, WE

    The well-known condition for standing stability in static situations is that the vertical projection of the centre of mass (CoM) should be within the base of support (BoS). On the basis of a simple inverted pendulum model, an extension of this rule is proposed for dynamical situations: the position

  16. The condition for dynamic stability

    Hof, AL; Gazendam, MGJ; Sinke, WE


    The well-known condition for standing stability in static situations is that the vertical projection of the centre of mass (CoM) should be within the base of support (BoS). On the basis of a simple inverted pendulum model, an extension of this rule is proposed for dynamical situations: the position

  17. Dynamics of Edge Dislocations in a Low-Stability FCC-System Irradiated by High-Energy Particles

    Starostenkov, M. D.; Potekaev, A. I.; Markidonov, A. V.; Kulagina, V. V.; Grinkevich, L. S.


    Using the method of molecular dynamics, the behavior of plastic deformation and defect structure selforganization are investigated in a low-stability condensed FCC-system irradiated with high-energy particles. An analysis of the dynamics of a single edge dislocation and elementary dislocation ensembles, subjected to the action of a post-cascade shock wave, demonstrates that as a result of this action the dislocations are displaced towards the wave source. As this goes on, the roles of both collective effects and external influences on the ensembles of complex interacting defects increase. In particular, the investigation performed in this work demonstrates that the post-cascade shock waves can give rise to migration of not only single edge dislocation but also elementary dislocation ensembles. It is demonstrated that the changes in the dislocation structure of the irradiated material result from the unloading waves following the post-cascade waves, rather than from the latter waves themselves.

  18. Dynamic Stability Parameters


    resonance. A system of resolvers, filters, and damped digital voltmeters is used to separate the torque signal into in- phase and out-of-phase...lavion A 8 Hz environ). 2.3.4 - Instrumentation embarquge - 1’Aq~.ipoent habitual des maquettes do vol libro destin6 A Is reconnaissance des mouvements s...initialisation de lacquisition), la diterminetion do Ia date du largage (initialisation du vol libro ), Ia datation du passage au droit des bases

  19. Dynamic Stability Parameters


    reduction, and presentation system for the rotary balance setup is composed of a 12-channel scanner /voltmeter, a minicomputer, and a plotter. This...Fuchs, " Dynamische Derivativa von Flugkbrpern (Phase I), Auswertung der Wind- kanalmessungen und Vergleich mit theoretischen Ergebnissen", January 1979...who helped to complete this lecture and lecture 12 in due time. II 18-10 REFERENCES 1. L. Stiklorus, "Das dynamische Verhalten von Flugkdrpern, Teil 1

  20. Spent nuclear fuel system dynamic stability under normal conditions of transportation

    Jiang, Hao; Wang, Jy-An John, E-mail:


    Highlights: • A conformational potential effect of fuel assembly contact interaction induced transient shock. • Complex vibration modes and vibration load intensity were observed from fuel assembly system. • The project was able to link the periodic transient shock to spent fuel fatigue strength reduction. - Abstract: In a horizontal layout of a spent nuclear fuel (SNF) assembly under normal conditions of transportation (NCT), the fuel assembly’s skeleton formed by guide tubes and spacer grids is the primary load bearing structure for carrying and transferring the vibration loads within an SNF assembly. Therefore, the integrity of guide tubes and spacer grids will dictate the vibration amplitude/intensity of the fuel assembly during transport, and must be considered when designing multipurpose purpose canister (MPC) for safe SNF transport. This paper investigates the SNF assembly deformation dynamics during normal vibration mode, as well as the transient shock mode inside the cask during NCT. Dynamic analyses were performed in the frequency domain to study frequency characteristic of the fuel assembly system and in the time domain to simulate the transient dynamic response of the fuel assembly. To further evaluate the intensity of contact interaction induced by the local contacts’ impact loading at the spacer grid, detailed models of the actual spring and dimples of the spacer grids were created. The impacts between the fuel rod and springs and dimples were simulated with a 20 g transient shock load. The associated contact interaction intensities, in terms of reaction forces, were estimated from the finite element analyses (FEA) results. The bending moment estimated from the resultant stress on the clad under 20 g transient shock can be used to define the loading in cyclic integrated reversible-bending fatigue tester (CIRFT) vibration testing for the equivalent condition. To estimate the damage potential of the transient shock to the SNF vibration

  1. Constraint Stabilization and One-Step Correction Method for Dynamical Systems

    SHANG Mei; CHEN Xiang-wei; MEI Feng-xiang


    A computational method of constraint stabilization and correction is introduced.The method is based on the Baumgart's one-step method.Constraint conditions are addressed to stabilize and correct the solution.Two examples are given to illustrate the results of the method.

  2. A nonlinear variable structure stabilizer for power system stability

    Cao, Y.; Jiang, L.; Cheng, S.; Chen, D. (Huazhong Univ. of Science and Technology, Wuhan (China). Dept. of Electrical Power Engineering); Malik, O.P.; Hope, G.S. (Univ. of Calgary, Alberta (Canada). Dept. of Electrical and Computer Engineering)


    A nonlinear variable structure stabilizer is proposed in this paper. Design of this stabilizer involves the nonlinear transformation technique, the variable structure control technique and the linear system theory. Performance of the proposed nonlinear variable structure controller in a single machine connected to an infinite bus power and a multi-machine system with multi-mode oscillations is simulated. The responses of the system with the proposed stabilizer are compared with those obtained with some other kinds of stabilizers when the system is subjected to a variety of disturbances. Simulation results show that the nonlinear variable structure stabilizer gives satisfactory dynamic performance and good robustness.

  3. Dynamical Stability of Earth-Like Planetary Orbits in Binary Systems

    David, E M; Fatuzzo, M; Adams, F C; David, Eva-Marie; Quintana, Elisa V.; Fatuzzo, Marco; Adams, Fred C.


    This paper explores the stability of an Earth-like planet orbiting a solar mass star in the presence of an outer-lying intermediate mass companion. The overall goal is to estimate the fraction of binary systems that allow Earth-like planets to remain stable over long time scales. We numerically determine the planet's ejection time $\\tauej$ over a range of companion masses ($M_C$ = 0.001 -- 0.5 $M_\\odot$), orbital eccentricities $\\epsilon$, and semi-major axes $a$. This suite of $\\sim40,000$ numerical experiments suggests that the most important variables are the companion's mass $M_C$ and periastron distance $\\rmin$ = $a(1-\\epsilon)$ to the primary star. At fixed $M_C$, the ejection time is a steeply increasing function of $\\rmin$ over the range of parameter space considered here (although the ejection time has a distribution of values for a given $\\rmin$). Most of the integration times are limited to 10 Myr, but a small set of integrations extend to 500 Myr. For each companion mass, we find fitting formulae ...




    The authors investigate the existence and the global stability of periodic solution for dynamical systems with periodic interconnections, inputs and self-inhibitions. The model is very general, the conditions are quite weak and the results obtained are universal.


    Zeebe, Richard E., E-mail: [School of Ocean and Earth Science and Technology, University of Hawaii at Manoa, 1000 Pope Road, MSB 629, Honolulu, HI 96822 (United States)


    Due to the chaotic nature of the solar system, the question of its long-term stability can only be answered in a statistical sense, for instance, based on numerical ensemble integrations of nearby orbits. Destabilization of the inner planets, leading to close encounters and/or collisions can be initiated through a large increase in Mercury's eccentricity, with a currently assumed likelihood of ∼1%. However, little is known at present about the robustness of this number. Here I report ensemble integrations of the full equations of motion of the eight planets and Pluto over 5 Gyr, including contributions from general relativity. The results show that different numerical algorithms lead to statistically different results for the evolution of Mercury's eccentricity (e{sub M}). For instance, starting at present initial conditions (e{sub M}≃0.21), Mercury's maximum eccentricity achieved over 5 Gyr is, on average, significantly higher in symplectic ensemble integrations using heliocentric rather than Jacobi coordinates and stricter error control. In contrast, starting at a possible future configuration (e{sub M}≃0.53), Mercury's maximum eccentricity achieved over the subsequent 500 Myr is, on average, significantly lower using heliocentric rather than Jacobi coordinates. For example, the probability for e{sub M} to increase beyond 0.53 over 500 Myr is >90% (Jacobi) versus only 40%-55% (heliocentric). This poses a dilemma because the physical evolution of the real system—and its probabilistic behavior—cannot depend on the coordinate system or the numerical algorithm chosen to describe it. Some tests of the numerical algorithms suggest that symplectic integrators using heliocentric coordinates underestimate the odds for destabilization of Mercury's orbit at high initial e{sub M}.

  6. Dynamic model of wind energy conversion systems with variable speed synchronous generator and full-size power converter for large-scale power system stability studies

    Sanchez, J.A.; Herrero, N.; Wilhelmi, J.R. [Department of Civil Engineering: Hydraulics and Energy, ETSICCP, Universidad Politecnica de Madrid, Ciudad Universitaria, s/n. 28040 Madrid (Spain); Veganzones, C.; Martinez, S.; Blazquez, F. [Department of Electrical Engineering, ETSII, Universidad Politecnica de Madrid, C/Jose Gutierrez Abascal, 2. 28006 Madrid (Spain)


    This paper presents a dynamic model for variable speed wind energy conversion systems, equipped with a variable pitch wind turbine, a synchronous electrical generator, and a full power converter, specially developed for its use in power system stability studies involving large networks, with a high number of buses and a high level of wind generation penetration. The validity of the necessary simplifications has been contrasted against a detailed model that allows a thorough insight into the mechanical and electrical behavior of the system, and its interaction with the grid. The developed dynamic model has been implemented in a widely used power system dynamics simulation software, PSS/E, and its performance has been tested in a well-documented test power network. (author)

  7. Vehicle lateral dynamics stabilization using active suspension

    Drobný V.


    Full Text Available The paper deals with the investigation of active nonlinear suspension control in order to stabilize the lateral vehicle motion in similar way as systems like ESP do. The lateral stabilization of vehicle based on braking forces can be alternatively provided by the different setting of suspension forces. The basis of this control is the nonlinear property of the tyres. The vehicle has at least four wheels and it gives one or more redundant vertical forces that can be used for the different distribution of vertical suspension forces in such a way that resulting lateral and/or longitudinal forces create the required correction moment for lateral dynamic vehicle stabilization.

  8. Treating dynamical stability as an observable: a 5:2 MMR configuration for the extrasolar system HD 181433

    Campanella, Giammarco


    The three-planet extrasolar system of HD 181433 has been detected with HARPS. The best-fit solution, announced by the discovery team, describes a highly unstable, self-disrupting configuration. In fact, a narrow observational window, only partially covering the longest orbital period, can lead to solutions representing unrealistic scenarios. Taking into account the dynamical stability as an additional observable while interpreting the RV data, we can analyse the phase space in a neighbourhood of the statistically best-fit and derive dynamically stable configurations that reproduce the observed RV signal. Our Newtonian stable best-fit model is capable of surviving for at least 250 Myrs. The two giant companions are found to be locked in the 5:2 MMR as Jupiter and Saturn in the Solar System. This mechanism does not allow close encounters even in case of highly eccentric orbits. Moreover, planets c and d are located in regions spanned by many other strong low-order MMRs. We study the dynamics of some plausible s...

  9. Long term stability of power systems

    Kundur, P.; Gao, B. [Powertech Labs. Inc., Surrey, BC (Canada)


    Power system long term stability is still a developing subject. In this paper we provide our perspectives and experiences related to long term stability. The paper begins with the description of the nature of the long term stability problem, followed by the discussion of issues related to the modeling and solution techniques of tools for long term stability analysis. Cases studies are presented to illustrate the voltage stability aspect and plant dynamics aspect of long term stability. (author) 20 refs., 11 figs.

  10. Collaborative Research: Robust Climate Projections and Stochastic Stability of Dynamical Systems

    Ghil, Michael; McWilliams, James; Neelin, J. David; Zaliapin, Ilya; Chekroun, Mickael; Kondrashov, Dmitri; Simonnet, Eric


    The project was completed along the lines of the original proposal, with additional elements arising as new results were obtained. The originally proposed three thrusts were expanded to include an additional, fourth one. (i) The e ffects of stochastic perturbations on climate models have been examined at the fundamental level by using the theory of deterministic and random dynamical systems, in both nite and in nite dimensions. (ii) The theoretical results have been implemented first on a delay-diff erential equation (DDE) model of the El-Nino/Southern-Oscillation (ENSO) phenomenon. (iii) More detailed, physical aspects of model robustness have been considered, as proposed, within the stripped-down ICTP-AGCM (formerly SPEEDY) climate model. This aspect of the research has been complemented by both observational and intermediate-model aspects of mid-latitude and tropical climate. (iv) An additional thrust of the research relied on new and unexpected results of (i) and involved reduced-modeling strategies and associated prediction aspects have been tested within the team's empirical model reduction (EMR) framework. Finally, more detailed, physical aspects have been considered within the stripped-down SPEEDY climate model. The results of each of these four complementary e fforts are presented in the next four sections, organized by topic and by the team members concentrating on the topic under discussion.

  11. Improvement of the dynamic behavior of large-scale power systems by using robust power system stabilizers based on fuzzy logic

    M. Ramírez


    Full Text Available In this paper, the effect of fuzzy logic-based robust power system stabilizers on the improvement of the dynamics of a large-scale power system is investigated. The study is particularly focused on the Mexican Interconnected System and on adding damping to two critical inter-area system oscillation modes: the north-south mode and the western-peninsular mode. The fuzzy power system stabilizers (FPSSs applied here are based on a significantly reduced rule base, small number of tuning parameters, and simple control algorithm and architecture, which makes their design and implementation easier and suitable for practical applications. Non-linear time-domain simulations for a set of test cases and results from Prony Analysis verify the robustness of the designed FPSSs, as compared to conventional PSSs.

  12. On the Marginal Stability of Glassy Systems

    Yan, Le; Baity-Jesi, Marco; Müller, Markus; Wyart, Matthieu


    In various glassy systems that are out of equilibrium, like spin glasses and granular packings, the dynamics appears to be critical: avalanches involving almost the whole system could happen. A recent conceptual breakthrough argues that such glassy systems sample the ensemble of marginal stable states, which inevitably results into critical dynamics. However, it is unclear how the marginal stability is dynamically guaranteed. We investigate this marginal stability assumption by studying specifically the critical athermal dynamics of the Sherrington-Kirkpatrick model. We discuss how a pseudo-gap in the density distribution of local fields characterizing the marginal stability arises dynamically.

  13. Stabilizing Randomly Switched Systems

    Chatterjee, Debasish


    This article is concerned with stability analysis and stabilization of randomly switched systems under a class of switching signals. The switching signal is modeled as a jump stochastic (not necessarily Markovian) process independent of the system state; it selects, at each instant of time, the active subsystem from a family of systems. Sufficient conditions for stochastic stability (almost sure, in the mean, and in probability) of the switched system are established when the subsystems do not possess control inputs, and not every subsystem is required to be stable. These conditions are employed to design stabilizing feedback controllers when the subsystems are affine in control. The analysis is carried out with the aid of multiple Lyapunov-like functions, and the analysis results together with universal formulae for feedback stabilization of nonlinear systems constitute our primary tools for control design

  14. Dynamical systems

    Sternberg, Shlomo


    Celebrated mathematician Shlomo Sternberg, a pioneer in the field of dynamical systems, created this modern one-semester introduction to the subject for his classes at Harvard University. Its wide-ranging treatment covers one-dimensional dynamics, differential equations, random walks, iterated function systems, symbolic dynamics, and Markov chains. Supplementary materials offer a variety of online components, including PowerPoint lecture slides for professors and MATLAB exercises.""Even though there are many dynamical systems books on the market, this book is bound to become a classic. The the

  15. Feedback stabilization of controlled dynamical systems in honor of Laurent Praly


    This book is a tribute to Professor Laurent Praly and follows on from a workshop celebrating the occasion of his 60th birthday. It presents new and unified visions of the numerous problems that Laurent Praly has worked on in his prolific career: adaptive control, output feedback and observers, stability and stabilization. His main contributions are the central topic of this book. The book collects contributions written by prominent international experts in the control community, addressing a rich variety of topics: emerging ideas, advanced applications, and theoretical concepts. Organized in three sections, the first section covers the field of adaptive control, where Laurent Praly started his career. The second section focuses on stabilization and output feedback, which is also the topic of the second half of his career. Lastly, the third section presents the emerging research that will form Laurent Praly’s scientific legacy.

  16. Aging of dynamically stabilized microtubules

    Ebbinghaus, M


    The microtubule network, an important part of the cytoskeleton, is constantly remodeled by alternating phases of growth and shrinkage of individual filaments. Plus-end tracking proteins (+TIPs) interact with the microtubule and in many cases alter its dynamics. While it is established that the prototypal CLIP-170 enhances microtubule stability by increasing rescues, the plus-end tracking mechanism is still under debate. We present a model for microtubule dynamics in which a rescue factor is dynamically added to the filament while growing. As a consequence, the filament shows aging behavior which should be experimentally accessible and thus allow one to exclude some hypothesized models of the inclusion of rescue factors at the microtubule plus end. Additionally, we show the strong influence of the cell geometry on the quantitative results.


    Wang Yong; Zeng Jing; Cao Dengqing


    The lateral stability for railway vehicle dynamic system with uncertain parameters and nonlinear uncertain force vector is studied by using the Lyapunov stability theory. A robust stability condition for the considered system is derived, and the obtained stability bounds are not necessarily symmetric with respect to the origin in the parameter space. The lateral stability analysis for a railway bogie model is analyzed by using the proposed approach. The symmetric and asymmetric results are both given and the influence of the adjustable parameter ( on the stability bounds is also discussed. With the help of the proposed method, the robust stability analysis can provide a reference for the design of the railway vehicle systems.

  18. Stability and dynamics of magnetocapillary interactions

    Chinomona, Rujeko; Mitchell, William H; Yao, Yao; Spagnolie, Saverio E


    Recent experiments have shown that floating ferromagnetic beads, under the influence of an oscillating background magnetic field, can move along a liquid-air interface in a sustained periodic locomotion [Lumay et al., Soft Matter, 2013, 9, 2420]. Dynamic activity arises from a periodically induced dipole-dipole repulsion between the beads acting in concert with capillary attraction. We investigate analytically and numerically the stability and dynamics of this magnetocapillary swimming, and explore other related topics including the steady and periodic equilibrium configurations of two and three beads. The swimming speed and system stability depend on a dimensionless measure of the relative repulsive and attractive forces which we term the magnetocapillary number. An oscillatory magnetic field may stabilize an otherwise unstable collinear configuration, and striking behaviors are observed in fast transitions to and from locomotory states, offering insight into the behavior and self-assembly of interface-bound...

  19. Jacobi stability analysis of Rikitake system

    Gupta, M. K.; Yadav, C. K.


    We study the Rikitake system through the method of differential geometry, i.e. Kosambi-Cartan-Chern (KCC) theory for Jacobi stability analysis. For applying KCC theory we reformulate the Rikitake system as two second-order nonlinear differential equations. The five KCC invariants are obtained which express the intrinsic properties of nonlinear dynamical system. The deviation curvature tensor and its eigenvalues are obtained which determine the stability of the system. Jacobi stability of the equilibrium points is studied and obtain the conditions for stability. We study the dynamics of Rikitake system which shows the chaotic behaviour near the equilibrium points.

  20. Lipid digestion of protein stabilized emulsions investigated in a dynamic in vitro gastro-intestinal model system

    Helbig, A.; Silletti, E.; Aken, G.A. van; Oosterveld, A.; Minekus, M.; Hamer, R.J.; Gruppen, H.


    This study investigated the effect of gastric passage of protein stabilized emulsions, i.e., whey protein isolate (WPI) and lysozyme, under dynamic in vitro conditions on both the gastric and intestinal lipolysis. Emulsions were prepared at neutral pH to enable an opposite surface charge. Experiment

  1. Lipid Digestion of Protein Stabilized Emulsions Investigated in a Dynamic In Vitro Gastro-Intestinal Model System

    Helbig, A.; Silletti, E.; Aken, van G.A.; Oosterveld, A.; Minekus, M.; Hamer, R.J.; Gruppen, H.


    This study investigated the effect of gastric passage of protein stabilized emulsions, i.e., whey protein isolate (WPI) and lysozyme, under dynamic in vitro conditions on both the gastric and intestinal lipolysis. Emulsions were prepared at neutral pH to enable an opposite surface charge. Experiment

  2. Clinical evaluation of a lumbar interspinous dynamic stabilization device (the Wallis system) with a 13-year mean follow-up.

    Sénégas, Jacques; Vital, Jean-Marc; Pointillart, Vincent; Mangione, Paolo


    The authors determined current health status of patients who had been included in a long-term survivorship analysis of a lumbar dynamic stabilizer. Among 133 living patients, 107 (average age at surgery, 44.2 +/- 9.9 years) completed health questionnaires. All patients had initially been scheduled for decompression and fusion for canal stenosis, herniated disc, or both. In 20 patients, the implant was removed, and fusion was performed. The other 87 still had the dynamic stabilizer. Satisfaction, Oswestry disability index, visual analog scales for back and leg pain, short-form (SF-36) quality-of-life physical composite score, physical function, and social function were significantly better (p stabilization device. SF-36 scores of the fused subgroup were no worse than those reported elsewhere in patients who had primary pedicle-screw enhanced lumbar fusion. This anatomy-sparing device provided a good 13-year clinical outcome and obviated arthrodesis in 80% of patients.


    At-Tasneem Mohd Amin


    Full Text Available Hybrid systems are dynamic systems that arise out of the interaction of continuous state dynamics and discrete state dynamics. Switched systems, which are a type of hybrid system, have been given much attention by control systems research over the past decade. Problems with the controllability, observability, converseability and stabilizability of switched systems have always been discussed. In this paper, the trend in research regarding the stability of switched systems will be investigated. Then the variety of methods that have been discovered by researchers for stabilizing switched linear systems with arbitrary switching will be discussed in detail.

  4. System dynamics with interaction discontinuity

    Luo, Albert C J


    This book describes system dynamics with discontinuity caused by system interactions and presents the theory of flow singularity and switchability at the boundary in discontinuous dynamical systems. Based on such a theory, the authors address dynamics and motion mechanism of engineering discontinuous systems due to interaction. Stability and bifurcations of fixed points in nonlinear discrete dynamical systems are presented, and mapping dynamics are developed for analytical predictions of periodic motions in engineering discontinuous dynamical systems. Ultimately, the book provides an alternative way to discuss the periodic and chaotic behaviors in discontinuous dynamical systems.

  5. Topological stabilization for synchronized dynamics on networks

    Cencetti, Giulia; Bagnoli, Franco; Battistelli, Giorgio; Chisci, Luigi; Di Patti, Francesca; Fanelli, Duccio


    A general scheme is proposed and tested to control the symmetry breaking instability of a homogeneous solution of a spatially extended multispecies model, defined on a network. The inherent discreteness of the space makes it possible to act on the topology of the inter-nodes contacts to achieve the desired degree of stabilization, without altering the dynamical parameters of the model. Both symmetric and asymmetric couplings are considered. In this latter setting the web of contacts is assumed to be balanced, for the homogeneous equilibrium to exist. The performance of the proposed method are assessed, assuming the Complex Ginzburg-Landau equation as a reference model. In this case, the implemented control allows one to stabilize the synchronous limit cycle, hence time-dependent, uniform solution. A system of coupled real Ginzburg-Landau equations is also investigated to obtain the topological stabilization of a homogeneous and constant fixed point.

  6. Molecular Dynamics Study of Stability of Solid Solutions and Amorphous Phase in the Cu-Al System

    YANG Bin; LAI Wen-Sheng


    The relative stability of fcc and bcc solid solutions and amorphous phase with different compositions in the Cu-Al system is studied by molecular dynamics simulations with n-body potentials.For Cu1-xAlx alloys,the calculations show that the fcc solid solution has the lowest energies in the composition region with x<0.32 or x>0.72,while the bcc solid solution has the lowest energies in the central composition range,in agreement with the ball-milling experiments that a single bcc solid solution with 0.30<x< 0.70 is obtained.The evolution of structures in solid solutions and amorphous phase is studied by the coordination number (CN) and bond-length analysis so as to unveil the underlying physics.It is found that the energy sequence among three phases is determined by the competition in energy change originating from the bond length and CNs (or the number of bonds).

  7. Stability studies of Solar Optical Telescope dynamics

    Gullapalli, Sarma N.; Pal, Parimal K.; Ruthven, Gregory P.


    The Solar Optical Telescope (SOT) is designed to operate as an attached payload mounted on the Instrument Pointing System (IPS) in the cargo bay of the Shuttle Orbiter. Pointing and control of SOT is accomplished by an active Articulated Primary Mirror (APM), an active Tertiary Mirror (TM), an elaborate set of optical sensors, electromechanical actuators and programmable controllers. The structural interactions of this complex control system are significant factors in the stability of the SOT. The preliminary stability study results of the SOT dynamical system are presented. Structural transfer functions obtained from the NASTRAN model of the structure were used. These studies apply to a single degree of freedom (elevation). Fully integrated model studies will be conducted in the future.

  8. System Dynamics

    Morecroft, John

    System dynamics is an approach for thinking about and simulating situations and organisations of all kinds and sizes by visualising how the elements fit together, interact and change over time. This chapter, written by John Morecroft, describes modern system dynamics which retains the fundamentals developed in the 1950s by Jay W. Forrester of the MIT Sloan School of Management. It looks at feedback loops and time delays that affect system behaviour in a non-linear way, and illustrates how dynamic behaviour depends upon feedback loop structures. It also recognises improvements as part of the ongoing process of managing a situation in order to achieve goals. Significantly it recognises the importance of context, and practitioner skills. Feedback systems thinking views problems and solutions as being intertwined. The main concepts and tools: feedback structure and behaviour, causal loop diagrams, dynamics, are practically illustrated in a wide variety of contexts from a hot water shower through to a symphony orchestra and the practical application of the approach is described through several real examples of its use for strategic planning and evaluation.

  9. Is it possible to preserve lumbar lordosis after hybrid stabilization? Preliminary results of a novel rigid-dynamic stabilization system in degenerative lumbar pathologies.

    Formica, Matteo; Cavagnaro, Luca; Basso, Marco; Zanirato, Andrea; Felli, Lamberto; Formica, Carlo


    To evaluate the results of a novel rigid-dynamic stabilization technique in lumbar degenerative segment diseases (DSD), expressly pointing out the preservation of postoperative lumbar lordosis (LL). Forty-one patients with one level lumbar DSD and initial disc degeneration at the adjacent level were treated. Circumferential lumbar arthrodesis and posterior hybrid instrumentation were performed to preserve an initial disc degeneration above the segment that has to be fused. Clinical and spino-pelvic parameters were evaluated pre- and postoperatively. At 2-year follow-up, a significant improvement of clinical outcomes was reported. No statistically significant difference was noted between postoperative and 2-year follow-up in LL and in disc/vertebral body height ratio at the upper adjacent fusion level. When properly selected, this technique leads to good results. A proper LL should be achieved after any hybrid stabilization to preserve the segment above the fusion.

  10. Dynamical systems

    Birkhoff, George D


    His research in dynamics constitutes the middle period of Birkhoff's scientific career, that of maturity and greatest power. -Yearbook of the American Philosophical Society The author's great book€¦is well known to all, and the diverse active modern developments in mathematics which have been inspired by this volume bear the most eloquent testimony to its quality and influence. -Zentralblatt MATH In 1927, G. D. Birkhoff wrote a remarkable treatise on the theory of dynamical systems that would inspire many later mathematicians to do great work. To a large extent, Birkhoff was writing about his o

  11. Dynamic Logics of Dynamical Systems

    Platzer, André


    We survey dynamic logics for specifying and verifying properties of dynamical systems, including hybrid systems, distributed hybrid systems, and stochastic hybrid systems. A dynamic logic is a first-order modal logic with a pair of parametrized modal operators for each dynamical system to express necessary or possible properties of their transition behavior. Due to their full basis of first-order modal logic operators, dynamic logics can express a rich variety of system properties, including safety, controllability, reactivity, liveness, and quantified parametrized properties, even about relations between multiple dynamical systems. In this survey, we focus on some of the representatives of the family of differential dynamic logics, which share the ability to express properties of dynamical systems having continuous dynamics described by various forms of differential equations. We explain the dynamical system models, dynamic logics of dynamical systems, their semantics, their axiomatizations, and proof calcul...

  12. Local Dynamic Stability Associated with Load Carrying

    Jian Liu


    Conclusion: Current study confirmed the sensitivity of local dynamic stability measure in load carrying situation. It was concluded that load carrying tasks were associated with declined local dynamic stability, which may result in increased risk of fall accident. This finding has implications in preventing fall accidents associated with occupational load carrying.

  13. Trait diversity promotes stability of community dynamics

    Zhang, Lai; Thygesen, Uffe Høgsbro; Knudsen, Kim;


    The theoretical exploration of how diversity influences stability has traditionally been approached by species-centric methods. Here we offer an alternative approach to the diversity–stability problem by examining the stability and dynamics of size and trait distributions of individuals. The anal...

  14. Dynamical Stability of Slip-stacking Particles

    Eldred, Jeffrey


    We study the stability of particles in slip-stacking configuration, used to nearly double proton beam intensity at Fermilab. We introduce universal area factors to calculate the available phase space area for any set of beam parameters without individual simulation. We find perturbative solutions for stable particle trajectories. We establish Booster beam quality requirements to achieve 97\\% slip-stacking efficiency. We show that slip-stacking dynamics directly correspond to the driven pendulum and to the system of two standing-wave traps moving with respect to each other.

  15. Dynamical stability of slip-stacking particles

    Eldred, Jeffrey; Zwaska, Robert


    We study the stability of particles in slip-stacking configuration, used to nearly double proton beam intensity at Fermilab. We introduce universal area factors to calculate the available phase space area for any set of beam parameters without individual simulation. We find perturbative solutions for stable particle trajectories. We establish Booster beam quality requirements to achieve 97% slip-stacking efficiency. We show that slip-stacking dynamics directly correspond to the driven pendulum and to the system of two standing-wave traps moving with respect to each other.

  16. Dynamical Stability of Slip-stacking Particles

    Eldred, Jeffrey [Fermilab; Zwaska, Robert [Fermilab


    We study the stability of particles in slip-stacking configuration, used to nearly double proton beam intensity at Fermilab. We introduce universal area factors to calculate the available phase space area for any set of beam parameters without individual simulation. We find perturbative solutions for stable particle trajectories. We establish Booster beam quality requirements to achieve 97% slip-stacking efficiency. We show that slip-stacking dynamics directly correspond to the driven pendulum and to the system of two standing-wave traps moving with respect to each other.

  17. Stability Problems for Chua System with One Linear Control

    Camelia Pop Arieşanu


    Full Text Available A Hamilton-Poisson realization and some stability problems for a dynamical system arisen from Chua system are presented. The stability and dynamics of a linearized smooth version of the Chua system are analyzed using the Hamilton-Poisson formalism. This geometrical approach allows to deduce the nonlinear stabilization near different equilibria.

  18. Stability and Restoration phenomena in Competitive Systems

    Uechi, Lisa


    A conservation law and stability, recovering phenomena and characteristic patterns of a nonlinear dynamical system have been studied and applied to biological and ecological systems. In our previous study, we proposed a system of symmetric 2n-dimensional conserved nonlinear differential equations with external perturbations. In this paper, competitive systems described by 2-dimensional nonlinear dynamical (ND) model with external perturbations are applied to population cycles and recovering phenomena of systems from microbes to mammals. The famous 10-year cycle of population density of Canadian lynx and snowshoe hare is numerically analyzed. We find that a nonlinear dynamical system with a conservation law is stable and generates a characteristic rhythm (cycle) of population density, which we call the {\\it standard rhythm} of a nonlinear dynamical system. The stability and restoration phenomena are strongly related to a conservation law and balance of a system. The {\\it standard rhythm} of population density ...

  19. Dynamic Stabilization in The Double-Well Duffing Oscillator

    Kim, S Y; Kim, Sang-Yoon; Kim, Youngtae


    Bifurcations associated with stability of the saddle fixed point of the Poincaré map, arising from the unstable equilibrium point of the potential, are investigated in a forced Duffing oscillator with a double-well potential. One interesting behavior is the dynamic stabilization of the saddle fixed point. When the driving amplitude is increased through a threshold value, the saddle fixed point becomes stabilized via a pitchfork bifurcation. We note that this dynamic stabilization is similar to that of the inverted pendulum with a vertically oscillating suspension point. After the dynamic stabilization, the double-well Duffing oscillator behaves as the single-well Duffing oscillator, because the effect of the central potential barrier on the dynamics of the system becomes negligible.

  20. Dynamical systems in classical mechanics

    Kozlov, V V


    This book shows that the phenomenon of integrability is related not only to Hamiltonian systems, but also to a wider variety of systems having invariant measures that often arise in nonholonomic mechanics. Each paper presents unique ideas and original approaches to various mathematical problems related to integrability, stability, and chaos in classical dynamics. Topics include… the inverse Lyapunov theorem on stability of equilibria geometrical aspects of Hamiltonian mechanics from a hydrodynamic perspective current unsolved problems in the dynamical systems approach to classical mechanics

  1. Crack stability in a representative piping system under combined inertial and seismic/dynamic displacement-controlled stresses. Subtask 1.3 final report

    Scott, P.; Olson, R.; Wilkowski, O.G.; Marschall, C.; Schmidt, R.


    This report presents the results from Subtask 1.3 of the International Piping Integrity Research Group (IPIRG) program. The objective of Subtask 1.3 is to develop data to assess analysis methodologies for characterizing the fracture behavior of circumferentially cracked pipe in a representative piping system under combined inertial and displacement-controlled stresses. A unique experimental facility was designed and constructed. The piping system evaluated is an expansion loop with over 30 meters of 16-inch diameter Schedule 100 pipe. The experimental facility is equipped with special hardware to ensure system boundary conditions could be appropriately modeled. The test matrix involved one uncracked and five cracked dynamic pipe-system experiments. The uncracked experiment was conducted to evaluate piping system damping and natural frequency characteristics. The cracked-pipe experiments evaluated the fracture behavior, pipe system response, and stability characteristics of five different materials. All cracked-pipe experiments were conducted at PWR conditions. Material characterization efforts provided tensile and fracture toughness properties of the different pipe materials at various strain rates and temperatures. Results from all pipe-system experiments and material characterization efforts are presented. Results of fracture mechanics analyses, dynamic finite element stress analyses, and stability analyses are presented and compared with experimental results.

  2. Stabilization of structure-preserving power networks with market dynamics

    Stegink, Tjerk W; van der Schaft, Arjan J


    This paper studies the problem of maximizing the social welfare while stabilizing both the physical power network as well as the market dynamics. For the physical power grid a third-order structure-preserving model is considered involving both frequency and voltage dynamics. By applying the primal-dual gradient method to the social welfare problem, a distributed dynamic pricing algorithm in port-Hamiltonian form is obtained. After interconnection with the physical system a closed-loop port-Hamiltonian system of differential-algebraic equations is obtained, whose properties are exploited to prove local asymptotic stability of the optimal points.

  3. Reliability Analysis of Dynamic Stability in Waves

    Søborg, Anders Veldt


    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...

  4. Qualitative stability of nonlinear networked systems

    Angulo, Marco Tulio; Slotine, Jean-Jacques


    In many large systems, such as those encountered in biology or economics, the dynamics are nonlinear and are only known very coarsely. It is often the case, however, that the signs (excitation or inhibition) of individual interactions are known. This paper extends to nonlinear systems the classical criteria of linear sign stability introduced in the 70's, yielding simple sufficient conditions to determine stability using only the sign patterns of the interactions.

  5. The Nature of Stability in Replicating Systems

    Addy Pross


    Full Text Available We review the concept of dynamic kinetic stability, a type of stability associated specifically with replicating entities, and show how it differs from the well-known and established (static kinetic and thermodynamic stabilities associated with regular chemical systems. In the process we demonstrate how the concept can help bridge the conceptual chasm that continues to separate the physical and biological sciences by relating the nature of stability in the animate and inanimate worlds, and by providing additional insights into the physicochemical nature of abiogenesis.

  6. Multistability in dynamical systems

    Mendes, R V


    In neuroscience, optics and condensed matter there is ample physical evidence for multistable dynamical systems, that is, systems with a large number of attractors. The known mathematical mechanisms that lead to multiple attractors are homoclinic tangencies and stabilization, by small perturbations or by coupling, of systems possessing a large number of unstable invariant sets. A short review of the existent results is presented, as well as two new results concerning the existence of a large number of stable periodic orbits in a perturbed marginally stable dissipative map and an infinite number of such orbits in two coupled quadratic maps working on the Feigenbaum accumulation point.

  7. Dynamics of human categorization in a collaborative tagging system: How social processes of semantic stabilization shape individual sensemaking.

    Ley, Tobias; Seitlinger, Paul


    We study how categories form and develop over time in a sensemaking task by groups of students employing a collaborative tagging system. In line with distributed cognition theories, we look at both the tags students use and their strength of representation in memory. We hypothesize that categories get more differentiated over time as students learn, and that semantic stabilization on the group level (i.e. the convergence in the use of tags) mediates this relationship. Results of a field experiment that tested the impact of topic study duration on the specificity of tags confirms these hypotheses, although it was not study duration that produced this effect, but rather the effectiveness of the collaborative taxonomy the groups built. In the groups with higher levels of semantic stabilization, we found use of more specific tags and better representation in memory. We discuss these findings with regard to the important role of the information value of tags that would drive both the convergence on the group level as well as a shift to more specific levels of categorization. We also discuss the implication for cognitive science research by highlighting the importance of collaboratively built artefacts in the process of how knowledge is acquired, and implications for educational applications of collaborative tagging environments.


    张立翔; 黄文虎


    Nonlinearly dynamic stability of flexible liquid-conveying pipe in fluid structure interaction was analyzed by using modal disassembling technique. The effects of Poisson,Junction and Friction couplings in the wave-flowing-vibration system on the pipe dynamic stability were included in the analytical model constituted by four nonlinear differential equations. An analyzing example of cantilevered pipe was done to illustrate the dynamic stability characteristics of the pipe in the full coupling mechanisms, and the phase curves related to the first four modal motions were drawn. The results show that the dynamic stable characteristics of the pipe are very complicated in the complete coupling mechanisms, and the kinds of the singularity points corresponding to the various modal motions are different.

  9. Generalized Extreme Value distribution parameters as dynamical indicators of Stability

    Faranda, Davide; Turchetti, Giorgio; Vaienti, Sandro


    We introduce a new dynamical indicator of stability based on the Extreme Value statistics showing that it provides an insight on the local stability properties of dynamical systems. The indicator perform faster than other based on the iteration of the tangent map since it requires only the evolution of the original systems and, in the chaotic regions, gives further information about the information dimension of the attractor. A numerical validation of the method is presented through the analysis of the motions in a Standard map.

  10. Dynamic stability enhancement of power system based on a typical unified power flow controllers using imperialist competitive algorithm

    M.R. Banaei


    Full Text Available This paper presents dynamic model of power system installed with a novel UPFC that consist of two shunt converters and a series capacitor. In this configuration, a series capacitor is used between two shunt converters to inject desired series voltage. As a result, it is possible to control the active and reactive power flow. The main advantage of the proposed UPFC in comparison with the conventional configuration is injection of a series voltage waveform with a very low total harmonic distortion (THD. In addition, a linearized Phillips–Heffron model is obtained and a supplementary controller for the modeling of proposed UPFC to damp low frequency oscillations with considering four alternative damping controllers is recommended. The problem of robustly novel UPFC based damping controller is formulated as an optimization problem according to the time domain-based objective function, which are solved using particle swarm optimization (PSO and Imperialist Competitive Algorithm (ICA techniques.

  11. Nonlinear physical systems spectral analysis, stability and bifurcations

    Kirillov, Oleg N


    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

  12. Modeling, Dynamics, Bifurcation Behavior and Stability Analysis of a DC-DC Boost Converter in Photovoltaic Systems

    Zhioua, M.; El Aroudi, A.; Belghith, S.; Bosque-Moncusí, J. M.; Giral, R.; Al Hosani, K.; Al-Numay, M.

    A study of a DC-DC boost converter fed by a photovoltaic (PV) generator and supplying a constant voltage load is presented. The input port of the converter is controlled using fixed frequency pulse width modulation (PWM) based on the loss-free resistor (LFR) concept whose parameter is selected with the aim to force the PV generator to work at its maximum power point. Under this control strategy, it is shown that the system can exhibit complex nonlinear behaviors for certain ranges of parameter values. First, using the nonlinear models of the converter and the PV source, the dynamics of the system are explored in terms of some of its parameters such as the proportional gain of the controller and the output DC bus voltage. To present a comprehensive approach to the overall system behavior under parameter changes, a series of bifurcation diagrams are computed from the circuit-level switched model and from a simplified model both implemented in PSIM© software showing a remarkable agreement. These diagrams show that the first instability that takes place in the system period-1 orbit when a primary parameter is varied is a smooth period-doubling bifurcation and that the nonlinearity of the PV generator is irrelevant for predicting this phenomenon. Different bifurcation scenarios can take place for the resulting period-2 subharmonic regime depending on a secondary bifurcation parameter. The boundary between the desired period-1 orbit and subharmonic oscillation resulting from period-doubling in the parameter space is obtained by calculating the eigenvalues of the monodromy matrix of the simplified model. The results from this model have been validated with time-domain numerical simulation using the circuit-level switched model and also experimentally from a laboratory prototype. This study can help in selecting the parameter values of the circuit in order to delimit the region of period-1 operation of the converter which is of practical interest in PV systems.

  13. Structural Stability of Planar Bimodal Linear Systems

    Josep Ferrer


    Full Text Available Structural stability ensures that the qualitative behavior of a system is preserved under small perturbations. We study it for planar bimodal linear dynamical systems, that is, systems consisting of two linear dynamics acting on each side of a given hyperplane and assuming continuity along the separating hyperplane. We describe which one of these systems is structurally stable when (real spiral does not appear and when it does we give necessary and sufficient conditions concerning finite periodic orbits and saddle connections. In particular, we study the finite periodic orbits and the homoclinic orbits in the saddle/spiral case.

  14. Minimum 5-year follow-up study on the effects of the Wallis dynamic stabilization system in the treatment of lumbar degenerative disease

    Chen Zheng; Peng Baogan; Li Duanming; Pang Xiaodong; Yang Hong


    Background Short-term outcomes of the Wallis system in the treatment of lumbar degenerative disease (LDD) have been shown to be effective,whereas there is a paucity of studies on the mid-long-term effects of the treatment of the Wallis system.This study was to evaluate the mid-long-term effects of the Wallis dynamic stabilization system in the treatment of LDD.Methods A total of 26 patients who received the treatment of the Wallis system between February 2008 and January 2009 were included in the study,with 14 patients (Group 1) with L4/5 disc herniation and 12 patients (Group 2) with L5/S1 disc herniation and L4/5 intervertebral disc degeneration (IDD).Visual analog scale (VAS) and Oswestry Disability Index (ODI) were used to evaluate the clinical outcomes and lumbar x-rays and MRI were obtained to observe imaging changes before and after operation.Results The mean follow-up period was (63.50±2.12) months.The mean ODI and VAS scores decreased obviously three months and five years after operation (P <0.05).In Groups 1 and 2,L4/5 Cobb angle and range of motion (ROM) decreased and L4/5 posterior disc height increased at the last follow-up (P <0.05).There were no statistically significant changes in L4/5 anterior disc height and L3/4 University of California at Los Angeles grading before and after operation.There was no statistically significant change in Pfirrmann grading system of L4/5 IDD in Group 2 before and after operation.Adjacent segment degeneration at the last follow-up was found in two patients (2/26,7.69%) and Modic changes in L4/5 endplates were detected in one patient (1/26,3.85%).Conclusions The mid-long-term effects of the Wallis system in the treatment of LDD were satisfied.The Wallis system,as a dynamic stabilization system,which can preserve some ROM of the fixed segment,sustain the lumbar stabilization,and prevent adjacent segment disease and fixed segment degeneration,is an effective instrument to treat LDD.

  15. On stability of randomly switched nonlinear systems

    Chatterjee, Debasish


    This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic process which is independent of the state of the system, and between two consecutive switching instants the dynamics are deterministic. Our results provide sufficient conditions for almost sure global asymptotic stability using Lyapunov-based methods when individual subsystems are stable and a certain ``slow switching'' condition holds. This slow switching condition takes the form of an asymptotic upper bound on the probability mass function of the number of switches that occur between the initial and current time instants. This condition is shown to hold for switching signals coming from the states of finite-dimensional continuous-time Markov chains; our results therefore hold for Markov jump systems in particular. For systems with control inputs we provide explicit control s...

  16. Survey of European and Major ISC Facilities for Supporting Mars and Sample Return Mission Aerothermodynamics and Tests Required for Thermal Protection System and Dynamic Stability

    Mathilde Bugel


    Full Text Available In the frame of future sample return missions to Mars, asteroids, and comets, investigated by the European Space Agency, a review of the actual aerodynamics and aerothermodynamics capabilities in Europe for Mars entry of large vehicles and high-speed Earth reentry of sample return capsule has been undertaken. Additionally, capabilities in Canada and Australia for the assessment of dynamic stability, as well as major facilities for hypersonic flows available in ISC, have been included. This paper provides an overview of European current capabilities for aerothermodynamics and testing of thermal protection systems. This assessment has allowed the identification of the needs in new facilities or upgrade of existing ground tests for covering experimentally Mars entries and Earth high-speed reentries as far as aerodynamics, aerothermodynamics, and thermal protection system testing are concerned.

  17. Robust adaptive output stabilization using dynamic normalizing signal

    Haixia SU; Xuejun XIE; Haikuan LIU


    For a class of nonlinear systems with dynamic uncertainties,robust adaptive stabilization problem is considered in this paper.Firstly,by introducing an observer,an augmented system is obtained.Based on the system,we construct an exp-ISpS Lyapunov function for the unmodeled dynamics,prove that the unmodeled dynamics is exp-ISpS,and then obtain a dynamic normalizing signal to counteract the dynamic disturbances.By the backstepping technique,an adaptive controller is given,it is proved that all the signals in the adaptive control system are globally uniformly ultimately bounded,and the output can be regulated to the origin with any prescribed accuracy.A simulation example further demonstrates the efficiency of the control scheme.

  18. Stability Analysis and Design for Nonlinear Singular Systems

    Yang, Chunyu; Zhou, Linna


    Singular systems which are also referred to as descriptor systems, semi-state systems, differential- algebraic systems or generalized state-space systems have attracted much attention because of their extensive applications in the Leontief dynamic model, electrical and mechanical models, etc. This monograph presented up-to-date research developments and references on stability analysis and design of nonlinear singular systems. It investigated the problems of practical stability, strongly absolute stability, input-state stability and observer design for nonlinear singular systems and the problems of absolute stability and multi-objective control for nonlinear singularly perturbed systems by using Lyapunov stability theory, comparison principle, S-procedure and linear matrix inequality (LMI), etc. Practical stability, being quite different from stability in the sense of Lyapunov, is a significant performance specification from an engineering point of view. The basic concepts and results on practical stability f...

  19. Practical stability of nonlinear systems

    Lakshmikantham, Vangipuram; Martynyuk, Anatolii Andreevich


    This is the first book that deals with practical stability and its development. It presents a systematic study of the theory of practical stability in terms of two different measures and arbitrary sets and demonstrates the manifestations of general Lyapunov's method by showing how this effective technique can be adapted to investigate various apparently diverse nonlinear problems including control systems and multivalued differential equations.

  20. Plutonium stabilization and packaging system



    This document describes the functional design of the Plutonium Stabilization and Packaging System (Pu SPS). The objective of this system is to stabilize and package plutonium metals and oxides of greater than 50% wt, as well as other selected isotopes, in accordance with the requirements of the DOE standard for safe storage of these materials for 50 years. This system will support completion of stabilization and packaging campaigns of the inventory at a number of affected sites before the year 2002. The package will be standard for all sites and will provide a minimum of two uncontaminated, organics free confinement barriers for the packaged material.


    Zhiqiang LI; Yupeng QIAO; Hongsheng QI; Daizhan CHENG


    This paper investigates the stability of (switched) polynomial systems. Using semi-tensor product of matrices, the paper develops two tools for testing the stability of a (switched) polynomial system. One is to convert a product of multi-variable polynomials into a canonical form, and the other is an easily verifiable sufficient condition to justify whether a multi-variable polynomial is positive definite. Using these two tools, the authors construct a polynomial function as a candidate Lyapunov function and via testing its derivative the authors provide some sufficient conditions for the global stability of polynomial systems.

  2. Approximate reduction of dynamical systems

    Tabuada, Paulo; Julius, Agung; Pappas, George J


    The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with mechanical systems with symmetry--which, unfortunately, limits the type of systems to which it can be applied. The goal of this paper is to consider a more general form of reduction, termed approximate reduction, in order to extend the class of systems that can be reduced. Using notions related to incremental stability, we give conditions on when a dynamical system can be projected to a lower dimensional space while providing hard bounds on the induced errors, i.e., when it is behaviorally similar to a dynamical system on a lower dimensional space. These concepts are illustrated on a series of examples.

  3. Exponential stability of dynamic equations on time scales

    Raffoul Youssef N


    Full Text Available We investigate the exponential stability of the zero solution to a system of dynamic equations on time scales. We do this by defining appropriate Lyapunov-type functions and then formulate certain inequalities on these functions. Several examples are given.

  4. Multiple-node basin stability in complex dynamical networks

    Mitra, Chiranjit; Choudhary, Anshul; Sinha, Sudeshna; Kurths, Jürgen; Donner, Reik V.


    Dynamical entities interacting with each other on complex networks often exhibit multistability. The stability of a desired steady regime (e.g., a synchronized state) to large perturbations is critical in the operation of many real-world networked dynamical systems such as ecosystems, power grids, the human brain, etc. This necessitates the development of appropriate quantifiers of stability of multiple stable states of such systems. Motivated by the concept of basin stability (BS) [P. J. Menck et al., Nat. Phys. 9, 89 (2013), 10.1038/nphys2516], we propose here the general framework of multiple-node basin stability for gauging the global stability and robustness of networked dynamical systems in response to nonlocal perturbations simultaneously affecting multiple nodes of a system. The framework of multiple-node BS provides an estimate of the critical number of nodes that, when simultaneously perturbed, significantly reduce the capacity of the system to return to the desired stable state. Further, this methodology can be applied to estimate the minimum number of nodes of the network to be controlled or safeguarded from external perturbations to ensure proper operation of the system. Multiple-node BS can also be utilized for probing the influence of spatially localized perturbations or targeted attacks to specific parts of a network. We demonstrate the potential of multiple-node BS in assessing the stability of the synchronized state in a deterministic scale-free network of Rössler oscillators and a conceptual model of the power grid of the United Kingdom with second-order Kuramoto-type nodal dynamics.

  5. Linear Stability Analysis of Dynamical Quadratic Gravity

    Ayzenberg, Dimitry; Yunes, Nicolas


    We perform a linear stability analysis of dynamical, quadratic gravity in the high-frequency, geometric optics approximation. This analysis is based on a study of gravitational and scalar modes propagating on spherically-symmetric and axially-symmetric, vacuum solutions of the theory. We find dispersion relations that do no lead to exponential growth of the propagating modes, suggesting the theory is linearly stable on these backgrounds. The modes are found to propagate at subluminal and superluminal speeds, depending on the propagating modes' direction relative to the background geometry, just as in dynamical Chern-Simons gravity.

  6. The research analysis and application of stability of ventilation system

    卢国斌; 陈长华; 葛少成


    The stability of ventilation system includes stabilities of branch, network and main fan. The ventilation system is a dynamic process. The parameters in the ventilation system vary with time. In the paper, a group of mathematical models of quantitative analysis are set up, and the mathematical models are suitable to any ventilation system.

  7. Dynamical system synchronization

    Luo, Albert C J


    Dynamical System Synchronization (DSS) meticulously presents for the first time the theory of dynamical systems synchronization based on the local singularity theory of discontinuous dynamical systems. The book details the sufficient and necessary conditions for dynamical systems synchronizations, through extensive mathematical expression. Techniques for engineering implementation of DSS are clearly presented compared with the existing techniques.  This book also:  Presents novel concepts and methods for dynamical system synchronization Extends beyond the Lyapunov theory for dynamical system synchronization Introduces companion and synchronization of discrete dynamical systems Includes local singularity theory for discontinuous dynamical systems Covers the invariant domains of synchronization Features more than 75 illustrations Dynamical System Synchronization is an ideal book for those interested in better understanding new concepts and methodology for dynamical system synchronization, local singularity...

  8. Role of reflex dynamics in spinal stability: intrinsic muscle stiffness alone is insufficient for stability.

    Moorhouse, Kevin M; Granata, Kevin P


    Spinal stability is related to both the intrinsic stiffness of active muscle as well as neuromuscular reflex response. However, existing analyses of spinal stability ignore the role of the reflex response, focusing solely on the intrinsic muscle stiffness associated with voluntary activation patterns in the torso musculature. The goal of this study was to empirically characterize the role of reflex components of spinal stability during voluntary trunk extension exertions. Pseudorandom position perturbations of the torso and associated driving forces were recorded in 11 healthy adults. Nonlinear systems-identification analyses of the measured data provided an estimate of total systems dynamics that explained 81% of the movement variability. Proportional intrinsic response was less than zero in more than 60% of the trials, e.g. mean value of P(INT) during the 20% maximum voluntary exertion trunk extension exertions -415+/-354N/m. The negative value indicated that the intrinsic muscle stiffness was not sufficient to stabilize the spine without reflex response. Reflexes accounted for 42% of the total stabilizing trunk stiffness. Both intrinsic and reflex components of stiffness increased significantly with trunk extension effort. Results reveal that reflex dynamics are a necessary component in the stabilizing control of spinal stability.

  9. Evolutionary stability in Lotka-Volterra systems.

    Cressman, Ross; Garay, József


    The Lotka-Volterra model of population ecology, which assumes all individuals in each species behave identically, is combined with the behavioral evolution model of evolutionary game theory. In the resultant monomorphic situation, conditions for the stability of the resident Lotka-Volterra system, when perturbed by a mutant phenotype in each species, are analysed. We develop an evolutionary ecology stability concept, called a monomorphic evolutionarily stable ecological equilibrium, which contains as a special case the original definition by Maynard Smith of an evolutionarily stable strategy for a single species. Heuristically, the concept asserts that the resident ecological system must be stable as well as the phenotypic evolution on the "stationary density surface". The conditions are also shown to be central to analyse stability issues in the polymorphic model that allows arbitrarily many phenotypes in each species, especially when the number of species is small. The mathematical techniques are from the theory of dynamical systems, including linearization, centre manifolds and Molchanov's Theorem.

  10. 离散动态系统的稳定性判据%The Criteria for Stability of Discrete Dynamic Systems

    龙瑞仙; 李海燕


    对离散动态系统x(k+1)=A()x(k),x(0)=x0的渐近稳定性进行了讨论,利用特殊矩阵方法和技巧,对区间矩阵的最大模阵M的元素进行探讨,获得了新的简单实用的判据,并用数值例子说明了结果的有效性和优越性.%The asymptotic stability of discrete dynamic system x(k+1)=A()x(k),x(0)=x0 is discussed.The special matrix analysis method and technique are used to investigate the properties of the maximal module matrix M′s elements of interval matrix.Several new algebra criterian of stability are obtained,and then some examples to illustrate the effectiveness and superiority of the results are given.

  11. Adaptive Dynamic Programming for Control Algorithms and Stability

    Zhang, Huaguang; Luo, Yanhong; Wang, Ding


    There are many methods of stable controller design for nonlinear systems. In seeking to go beyond the minimum requirement of stability, Adaptive Dynamic Programming for Control approaches the challenging topic of optimal control for nonlinear systems using the tools of  adaptive dynamic programming (ADP). The range of systems treated is extensive; affine, switched, singularly perturbed and time-delay nonlinear systems are discussed as are the uses of neural networks and techniques of value and policy iteration. The text features three main aspects of ADP in which the methods proposed for stabilization and for tracking and games benefit from the incorporation of optimal control methods: • infinite-horizon control for which the difficulty of solving partial differential Hamilton–Jacobi–Bellman equations directly is overcome, and  proof provided that the iterative value function updating sequence converges to the infimum of all the value functions obtained by admissible control law sequences; • finite-...

  12. Dynesys 动态固定系统与腰椎相邻节段退变的研究进展%Research progress of Dynesys dynamic stabilization system and lumbar adjacent segment degeneration

    张阳; 李放


      In recent years, the lumbar non-fusion technique remains a hot research topic in spine surgery, and the Dynesys dynamic stabilization system is one of the most widely applied non-fusion techniques clinically. The system is designed to stabilize the operated segments and meanwhile preserve some mobility, so as to prevent the stress concentration of adjacent segments and relieve adjacent segment degeneration. Many clinical studies show that the Dynesys system could have satisfied clinical results, but at present there are still some controversies about the role of the Dynesys dynamic stabilization system in reducing adjacent segment degeneration. The biomechanical and clinical research about the role of the Dynesys system in preventing adjacent segment degeneration is reviewed in this article, to provide clinical evidence.

  13. Stability of Evolving Multiagent Systems.

    De Wilde, P; Briscoe, G


    A multiagent system is a distributed system where the agents or nodes perform complex functions that cannot be written down in analytic form. Multiagent systems are highly connected, and the information they contain is mostly stored in the connections. When agents update their state, they take into account the state of the other agents, and they have access to those states via the connections. There is also external user-generated input into the multiagent system. As so much information is stored in the connections, agents are often memory less. This memory-less property, together with the randomness of the external input, has allowed us to model multiagent systems using Markov chains. In this paper, we look at multiagent systems that evolve, i.e., the number of agents varies according to the fitness of the individual agents. We extend our Markov chain model and define stability. This is the start of a methodology to control multiagent systems. We then build upon this to construct an entropy-based definition for the degree of instability (entropy of the limit probabilities), which we used to perform a stability analysis. We then investigated the stability of evolving agent populations through simulation and show that the results are consistent with the original definition of stability in nonevolving multiagent systems, proposed by Chli and De Wilde. This paper forms the theoretical basis for the construction of digital business ecosystems, and applications have been reported elsewhere.

  14. Stability analysis of spacecraft power systems

    Halpin, S. M.; Grigsby, L. L.; Sheble, G. B.; Nelms, R. M.


    The problems in applying standard electric utility models, analyses, and algorithms to the study of the stability of spacecraft power conditioning and distribution systems are discussed. Both single-phase and three-phase systems are considered. Of particular concern are the load and generator models that are used in terrestrial power system studies, as well as the standard assumptions of load and topological balance that lead to the use of the positive sequence network. The standard assumptions regarding relative speeds of subsystem dynamic responses that are made in the classical transient stability algorithm, which forms the backbone of utility-based studies, are examined. The applicability of these assumptions to a spacecraft power system stability study is discussed in detail. In addition to the classical indirect method, the applicability of Liapunov's direct methods to the stability determination of spacecraft power systems is discussed. It is pointed out that while the proposed method uses a solution process similar to the classical algorithm, the models used for the sources, loads, and networks are, in general, more accurate. Some preliminary results are given for a linear-graph, state-variable-based modeling approach to the study of the stability of space-based power distribution networks.

  15. Longitudinal dynamic stability of a shuttle vehicle.

    Vinh, N. X.; Laitone, E. V.


    Analytical study of the longitudinal dynamic stability of a nonrolling, lifting vehicle gliding at hypersonic speeds. The analysis applies to shuttle vehicles designed for operating up to the rim of a planetary atmosphere. A general nondimensional time transformation is introduced to derive a unified second-order linear differential equation for the angle of attack, valid for all types of reentry of a general type of vehicle. The stability of motion is discussed for two fundamental regimes of flight that are based on widely different assumptions. For near ballistic entry along a straight line trajectory, the equation reduces to a confluent hypergeometric equation, the solution of which can be expressed in terms of Whittaker's function. Using a theorem in the theory of stability of differential equations, criteria for damped oscillations are derived. It is shown that the aerodynamic criteria for stability are the same as for the case of ballistic entry. In addition, for each vehicle configuration, and specified planetary atmosphere, there exists an altitude range where the angle of attack frequency is nearly equal to the orbital frequency causing instability in pitch. This resonance instability is due to the ellipticity of the orbit. Criteria for eccentricity instability are derived.

  16. Reliability Analysis of Dynamic Stability in Waves

    Søborg, Anders Veldt


    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......-4 per ship year such brute force Monte-Carlo simulations are not always feasible due to the required computational resources. Previous studies of dynamic stability of ships in waves typically focused on the capsizing event. In this study the objective is to establish a procedure that can identify...... the distribution of the exceedance probability may be established by an estimation of the out-crossing rate of the "safe set" defined by the utility function. This out-crossing rate will be established using the so-called Madsen's Formula. A bi-product of this analysis is a set of short wave time series...

  17. 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




    A class of Beddington-DeAngelis' type predator-prey dynamic system with prey and predator both having linear density restriction is considered. By using the qualitative methods of ODE, the existence and uniqueness of positive equilibrium and its global asymptotic stability are analyzed. The direct criterions for local stability of positive equilibrium and existence of limit cycle are also established when inference parameter of predator is small.

  19. Quadratic stabilization of switched nonlinear systems

    DONG YaLi; FAN JiaoJiao; MEI ShengWei


    In this paper, the problem of quadratic stabilization of multi-input multi-output switched nonlinear systems under an arbitrary switching law is investigated. When switched nonlinear systems have uniform normal form and the zero dynamics of uniform normal form is asymptotically stable under an arbitrary switching law, state feedbacks are designed and a common quadratic Lyapunov function of all the closed-loop subsystems is constructed to realize quadratic stabilizability of the class of switched nonlinear systems under an arbitrary switching law. The results of this paper are also applied to switched linear systems.

  20. Classical and quantum stability of higher-derivative dynamics

    Kaparulin, D S; Sharapov, A A


    We observe that a wide class of higher-derivative systems admits a bounded integral of motion that ensures the classical stability of dynamics, while the canonical energy is unbounded. We use the concept of a Lagrange anchor to demonstrate that the bounded integral of motion is connected with the time-translation invariance. A procedure is suggested for switching on interactions in free higher-derivative systems without breaking their stability. We also demonstrate the quantization technique that keeps the higher-derivative dynamics stable at quantum level. The general construction is illustrated by the examples of the Pais-Uhlenbeck oscillator, higher-derivative scalar field model, and the Podolsky electrodynamics. For all these models, the positive integrals of motion are explicitly constructed and the interactions are included such that keep the system stable.

  1. Beam stability & nonlinear dynamics. Formal report

    Parsa, Z. [ed.


    his Report includes copies of transparencies and notes from the presentations made at the Symposium on Beam Stability and Nonlinear Dynamics, December 3-5, 1996 at the Institute for Theoretical Physics, University of California, Santa Barbara California, that was made available by the authors. Editing, reduction and changes to the authors contributions were made only to fulfill the printing and publication requirements. We would like to take this opportunity and thank the speakers for their informative presentations and for providing copies of their transparencies and notes for inclusion in this Report.

  2. Stability theory for dynamic equations on time scales

    Martynyuk, Anatoly A


    This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations. The second is based on the generalization of the direct Lyapunovs method for equations on time scales, using scalar, vector and matrix-valued auxiliary functions. The third approach is the application of auxiliary functions (scalar, vector, or matrix-valued ones) in combination with differential dynamic inequalities. This is an alternative comparison method, developed for time continuous and time discrete systems. In recent decades, automatic control theory in the study of air- and spacecraft dynamics and in other areas of modern applied mathematics has encountered problems in the analysis of the behavior of solutions of time continuous-discrete linear and/or nonlinear equations of perturbed motion. In the book “Men of Ma...

  3. Dynamic and galvanic stability of stretchable supercapacitors.

    Li, Xin; Gu, Taoli; Wei, Bingqing


    Stretchable electronics are emerging as a new technological advancement, since they can be reversibly stretched while maintaining functionality. To power stretchable electronics, rechargeable and stretchable energy storage devices become a necessity. Here, we demonstrate a facile and scalable fabrication of full stretchable supercapacitor, using buckled single-walled carbon nanotube macrofilms as the electrodes, an electrospun membrane of elastomeric polyurethane as the separator, and an organic electrolyte. We examine the electrochemical performance of the fully stretchable supercapacitors under dynamic stretching/releasing modes in different stretching strain rates, which reveal the true performance of the stretchable cells, compared to the conventional method of testing the cells under a statically stretched state. In addition, the self-discharge of the supercapacitor and the electrochemical behavior under bending mode are also examined. The stretchable supercapacitors show excellent cyclic stability under electrochemical charge/discharge during in situ dynamic stretching/releasing.

  4. Morocco; Financial System Stability Assessment

    International Monetary Fund


    The Financial System Stability Assessment of Morocco reviews the reform program that is aimed at establishing a modern, market-oriented financial system that optimizes the mobilization of savings and the allocation of financial resources. It reviews the modernization of the banking sector and the development of competition within the sector, development of financial markets, and removal of constraints on financial system activity. It also provides reports on the Observance of Standards and Co...

  5. Maximum Allowable Dynamic Load of Mobile Manipulators with Stability Consideration

    Heidary H. R.


    Full Text Available High payload to mass ratio is one of the advantages of mobile robot manipulators. In this paper, a general formula for finding the maximum allowable dynamic load (MADL of wheeled mobile robot is presented. Mobile manipulators operating in field environments will be required to manipulate large loads, and to perform such tasks on uneven terrain, which may cause the system to reach dangerous tip-over instability. Therefore, the method is expanded for finding the MADL of mobile manipulators with stability consideration. Moment-Height Stability (MHS criterion is used as an index for the system stability. Full dynamic model of wheeled mobile base and mounted manipulator is considered with respect to the dynamic of non-holonomic constraint. Then, a method for determination of the maximum allowable loads is described, subject to actuator constraints and by imposing the stability limitation as a new constraint. The actuator torque constraint is applied by using a speed-torque characteristics curve of a typical DC motor. In order to verify the effectiveness of the presented algorithm, several simulation studies considering a two-link planar manipulator, mounted on a mobile base are presented and the results are discussed.

  6. Stabilization and synchronization of networked mechanical systems

    Nair, Sujit S.

    The main theme of this thesis is coordination and stabilization of a network of mechanical systems or rigid bodies to achieve synchronized behaviour. The idea is to use controls derived from potentials to couple the systems such that the closed-loop system is also a mechanical system with a Lagrangian structure. This permits the closed-loop Hamiltonian to be used as a Lyapunov function for stability analysis. It is a big challenge to develop a provable, systematic methodology to control and coordinate a network of systems to perform a given task. The control law should be robust enough to handle environment uncertainties, avoid obstacles and collisions and keep the system formation going. The fact that these systems may even have unstable dynamics makes the problem even more interesting and exciting both from a theoretical and applied point of view. This work investigates the coordination problem when each individual system has its own (maybe unstable) dynamics; this distinguishes this work from many other recent works on coordination control where the individual system dynamics are assumed to be single/double integrators. We build coordination techniques for three kinds of systems. The first one consists of underactuated Lagrangian systems with Abelian symmetry groups lacking gyroscopic forces. Asymptotic stabilization is proved for two cases, one which yields convergence to synchronized motion restricted to a constant momentum surface and one in which the system converges asymptotically to a relative equilibrium. Next we consider rigid body systems where the configuration space of each individual body is the non Abelian Lie group SO(3) or SE(3). In the SO(3) case, the asymptotically stabilized solution corresponds to each rigid body rotating about its unstable middle axis and all the bodies synchronized and pointing in a particular direction in inertial space. In the SE(3) case, the asymptotically stabilized solution corresponds to each rigid body rotating about

  7. W-Stability of Multistable Nonlinear Discrete-Time Systems

    Zhishuai Ding


    Full Text Available Motivated by the importance and application of discrete dynamical systems, this paper presents a new Lyapunov characterization which is an extension of conventional Lyapunov characterization for multistable discrete-time nonlinear systems. Based on a new type stability notion of W-stability introduced by D. Efimov, the estimates of solution and the Lyapunov stability theorem and converse theorem are proposed for multi-stable discrete-time nonlinear systems.

  8. Facet joint changes after application of lumbar nonfusion dynamic stabilization.

    Lee, Soo Eon; Jahng, Tae-Ahn; Kim, Hyun Jib


    OBJECTIVE The long-term effects on adjacent-segment pathology after nonfusion dynamic stabilization is unclear, and, in particular, changes at the adjacent facet joints have not been reported in a clinical study. This study aims to compare changes in the adjacent facet joints after lumbar spinal surgery. METHODS Patients who underwent monosegmental surgery at L4-5 with nonfusion dynamic stabilization using the Dynesys system (Dynesys group) or transforaminal lumbar interbody fusion with pedicle screw fixation (fusion group) were retrospectively compared. Facet joint degeneration was evaluated at each segment using the CT grading system. RESULTS The Dynesys group included 15 patients, while the fusion group included 22 patients. The preoperative facet joint degeneration CT grades were not different between the 2 groups. Compared with the preoperative CT grades, 1 side of the facet joints at L3-4 and L4-5 had significantly more degeneration in the Dynesys group. In the fusion group, significant facet joint degeneration developed on both sides at L2-3, L3-4, and L5-S1. The subjective back and leg pain scores were not different between the 2 groups during follow-up, but functional outcome based on the Oswestry Disability Index improved less in the fusion group than in the Dynesys group. CONCLUSIONS Nonfusion dynamic stabilization using the Dynesys system had a greater preventative effect on facet joint degeneration in comparison with that obtained using fusion surgery. The Dynesys system, however, resulted in facet joint degeneration at the instrumented segments and above. An improved physiological nonfusion dynamic stabilization system for lumbar spinal surgery should be developed.

  9. Asymptotic Stability and Balanced Growth Solution of the Singular Dynamic Input-Output System*

    ChonghuiGuo; HuanwenTang


    The dynamic input-output system is well known in economic theory and practice. In this paper the asymptotic stability and balanced growth solution of the dynamic input-output system are considered. Under three natural assumptions, we obtain four theorems about asymptotic stability and balanced growth solution of the dynamic input-output system and bring together in a unified manner some contributions scattered in the literature.




    Full Text Available To analyze the stability of a linear system of differential equations  ẋ = Ax we can study the location of the roots of the characteristic polynomial pA(t associated with the matrix A. We present various criteria - algebraic and geometric - that help us to determine where the roots are located without calculating them directly.

  11. Dynamic stability of passive dynamic walking on an irregular surface.

    Su, Jimmy Li-Shin; Dingwell, Jonathan B


    Falls that occur during walking are a significant health problem. One of the greatest impediments to solve this problem is that there is no single obviously "correct" way to quantify walking stability. While many people use variability as a proxy for stability, measures of variability do not quantify how the locomotor system responds to perturbations. The purpose of this study was to determine how changes in walking surface variability affect changes in both locomotor variability and stability. We modified an irreducibly simple model of walking to apply random perturbations that simulated walking over an irregular surface. Because the model's global basin of attraction remained fixed, increasing the amplitude of the applied perturbations directly increased the risk of falling in the model. We generated ten simulations of 300 consecutive strides of walking at each of six perturbation amplitudes ranging from zero (i.e., a smooth continuous surface) up to the maximum level the model could tolerate without falling over. Orbital stability defines how a system responds to small (i.e., "local") perturbations from one cycle to the next and was quantified by calculating the maximum Floquet multipliers for the model. Local stability defines how a system responds to similar perturbations in real time and was quantified by calculating short-term and long-term local exponential rates of divergence for the model. As perturbation amplitudes increased, no changes were seen in orbital stability (r(2)=2.43%; p=0.280) or long-term local instability (r(2)=1.0%; p=0.441). These measures essentially reflected the fact that the model never actually "fell" during any of our simulations. Conversely, the variability of the walker's kinematics increased exponentially (r(2)>or=99.6%; pwalking stability are related to each other and to risk of falling.

  12. Nonnegative and Compartmental Dynamical Systems

    Haddad, Wassim M; Hui, Qing


    This comprehensive book provides the first unified framework for stability and dissipativity analysis and control design for nonnegative and compartmental dynamical systems, which play a key role in a wide range of fields, including engineering, thermal sciences, biology, ecology, economics, genetics, chemistry, medicine, and sociology. Using the highest standards of exposition and rigor, the authors explain these systems and advance the state of the art in their analysis and active control design. Nonnegative and Compartmental Dynamical Systems presents the most complete treatment available o


    Peter BIGOŠ


    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.

  14. Stability analysis of nonlinear systems

    Lakshmikantham, Vangipuram; Martynyuk, Anatoly A


    The book investigates stability theory in terms of two different measure, exhibiting the advantage of employing families of Lyapunov functions and treats the theory of a variety of inequalities, clearly bringing out the underlying theme. It also demonstrates manifestations of the general Lyapunov method, showing how this technique can be adapted to various apparently diverse nonlinear problems. Furthermore it discusses the application of theoretical results to several different models chosen from real world phenomena, furnishing data that is particularly relevant for practitioners. Stability Analysis of Nonlinear Systems is an invaluable single-sourse reference for industrial and applied mathematicians, statisticians, engineers, researchers in the applied sciences, and graduate students studying differential equations.

  15. Preservation of stability and synchronization in nonlinear systems

    Fernandez-Anaya, G. [Departamento de Fisica y Matematicas, Universidad Iberoamericana, Prol. Paseo de la Reforma 880, Lomas de Santa Fe, Mexico, D.F. 01210 (Mexico)], E-mail:; Flores-Godoy, J.J. [Departamento de Fisica y Matematicas, Universidad Iberoamericana, Prol. Paseo de la Reforma 880, Lomas de Santa Fe, Mexico, D.F. 01210 (Mexico)], E-mail:; Femat, R. [Division de Matematicas Aplicadas y Sistemas Computacionales, IPICyT, Camino a la Presa San Jose 2055, Col. Lomas 4a. seccion, San Luis Potosi, San Luis Potosi 78216 (Mexico)], E-mail:; Alvarez-Ramirez, J.J. [Ingenieria de Procesos e Hidraulica, Universidad Autonoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Mexico, D.F. 09340 (Mexico)], E-mail:


    Preservation of stability in the presence of structural and/or parametric changes is an important issue in the study of dynamical systems. A specific case is the synchronization of chaos in complex networks where synchronization should be preserved in spite of changes in the network parameters and connectivity. In this work, a methodology to establish conditions for preservation of stability in a class of dynamical system is given in terms of Lyapunov methods. The idea is to construct a group of dynamical transformations under which stability is retained along certain manifolds. Some synchronization examples illustrate the results.

  16. First-principles studies of phase stability and the structural and dynamical properties of hydrogen-metal systems. Final report

    Chou, M.Y.


    First-principles calculations were carried for the hydrogen-yttrium system using the pseudopotential method within the local density functional approximation (LDA). We have studied the nature of hydrogen pairing in the solid solution phase ({alpha}-YH{sub x}.) and identified the connection with electronic structure. The vibrational spectra, diffusion barrier, and migration path were also investigated. We have also studied the binding characteristics for different interstitial sites and the (420)-plane ordering of octahedral hydrogen in {beta}YH{sub 2+x} within the lattice gas model. Temperature-composition phase diagram was calculated by cluster variational method with the multibody interactions extracted from total energies of related ordered structures. Moreover, the discovery of Peierls distortions in YH{sub 3} explained the unusual hydrogen displacements found in neutron diffraction and the possibility of an excitonic insulating ground state was speculated. Several new improvements in the calculational techniques also been developed: Separable nonlocal pseudopotentials, scheme to calculate the full phonon spectrum, and distance dependent tight-binding parameters. The Ru(0001)-H system was also studied.

  17. Dynamic stability and phase resetting during biped gait

    Nomura, Taishin; Kawa, Kazuyoshi; Suzuki, Yasuyuki; Nakanishi, Masao; Yamasaki, Taiga


    Dynamic stability during periodic biped gait in humans and in a humanoid robot is considered. Here gait systems of human neuromusculoskeletal system and a humanoid are simply modeled while keeping their mechanical properties plausible. We prescribe periodic gait trajectories in terms of joint angles of the models as a function of time. The equations of motion of the models are then constrained by one of the prescribed gait trajectories to obtain types of periodically forced nonlinear dynamical systems. Simulated gait of the models may or may not fall down during gait, since the constraints are made only for joint angles of limbs but not for the motion of the body trunk. The equations of motion can exhibit a limit cycle solution (or an oscillatory solution that can be considered as a limit cycle practically) for each selected gait trajectory, if an initial condition is set appropriately. We analyze the stability of the limit cycle in terms of Poincaré maps and the basin of attraction of the limit cycle in order to examine how the stability depends on the prescribed trajectory. Moreover, the phase resetting of gait rhythm in response to external force perturbation is modeled. Since we always prescribe a gait trajectory in this study, reacting gait trajectories during the phase resetting are also prescribed. We show that an optimally prescribed reacting gait trajectory with an appropriate amount of the phase resetting can increase the gait stability. Neural mechanisms for generation and modulation of the gait trajectories are discussed.

  18. A Point Dynamic Model for Stability Analysis of the PGSFR

    Ha, Pham Nhu Viet; Choi, Sun Rock; Lee, Min Jae; Kang, Chang Moo; Kim, Sang Ji [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)


    To ensure the enhanced safety criteria for an advanced reactor system, the PGSFR design is highly based on the inherent safety mechanisms, i.e., passive responses to abnormal and emergency conditions, and thereby minimizes the need for active or engineered safety systems. In this regard, various inherent reactivity feedbacks in the PGSFR including thermal expansion of the sodium coolant, fuel temperature change, thermal bowing of the fuel, thermal expansion of the core and structure, and thermal expansion of the control rod drive line should be carefully evaluated in the design process. Of primary importance is to clarify the influence of the inherent reactivity feedbacks on the reactor dynamics and stability against small reactivity disturbances under power operating conditions. The reactor response to such small reactivity disturbances is determined by the interaction of the various reactivity coefficients, magnitude of the initial reactivity insertion, and nature of the heat removal system. It was shown that the stability property of the PGSFR is the same for all the three considered forcing functions. Furthermore, the PGSFR was found to be inherently stable thanks to the inherent negative reactivity coefficients and its stability is even more enhanced with fuel burnup in the equilibrium cycle. Especially, the conditions under which the PGSFR can become unstable in the presence of one or more positive reactivity coefficients were revealed. As a result, this study can provide designers useful information about the reactor dynamics along with the impacts of positive reactivity coefficients for further improvements of the reactor stability under power operating conditions.

  19. Survivability of Deterministic Dynamical Systems

    Hellmann, Frank; Schultz, Paul; Grabow, Carsten; Heitzig, Jobst; Kurths, Jürgen


    The notion of a part of phase space containing desired (or allowed) states of a dynamical system is important in a wide range of complex systems research. It has been called the safe operating space, the viability kernel or the sunny region. In this paper we define the notion of survivability: Given a random initial condition, what is the likelihood that the transient behaviour of a deterministic system does not leave a region of desirable states. We demonstrate the utility of this novel stability measure by considering models from climate science, neuronal networks and power grids. We also show that a semi-analytic lower bound for the survivability of linear systems allows a numerically very efficient survivability analysis in realistic models of power grids. Our numerical and semi-analytic work underlines that the type of stability measured by survivability is not captured by common asymptotic stability measures.

  20. Dynesys dynamic stabilization-related facet arthrodesis.

    Fay, Li-Yu; Chang, Peng-Yuan; Wu, Jau-Ching; Huang, Wen-Cheng; Wang, Chun-Hao; Tsai, Tzu-Yun; Tu, Tsung-Hsi; Chang, Hsuan-Kan; Wu, Ching-Lan; Cheng, Henrich


    OBJECTIVE Dynamic stabilization devices are designed to stabilize the spine while preserving some motion. However, there have been reports demonstrating limited motion at the instrumented level of the lumbar spine after Dynesys dynamic stabilization (DDS). The causes of this limited motion and its actual effects on outcomes after DDS remain elusive. In this study, the authors investigate the incidence of unintended facet arthrodesis after DDS and clinical outcomes. METHODS This retrospective study included 80 consecutive patients with 1- or 2-level lumbar spinal stenosis who underwent laminectomy and DDS. All medical records, radiological data, and clinical evaluations were analyzed. Imaging studies included pre- and postoperative radiographs, MR images, and CT scans. Clinical outcomes were measured by a visual analog scale (VAS) for back and leg pain, the Oswestry Disability Index (ODI), and Japanese Orthopaedic Association (JOA) scores. Furthermore, all patients had undergone postoperative CT for the detection of unintended arthrodesis of the facets at the indexed level, and range of motion was measured on standing dynamic radiographs. RESULTS A total of 70 patients (87.5%) with a mean age of 64.0 years completed the minimum 24-month postoperative follow-up (mean duration 29.9 months). Unintended facet arthrodesis at the DDS instrumented level was demonstrated by CT in 38 (54.3%) of the 70 patients. The mean age of patients who had facet arthrodesis was 9.8 years greater than that of the patients who did not (68.3 vs 58.5 years, p = 0.009). There were no significant differences in clinical outcomes, including VAS back and leg pain, ODI, and JOA scores between patients with and without the unintended facet arthrodesis. Furthermore, those patients older than 60 years were more likely to have unintended facet arthrodesis (OR 12.42) and immobile spinal segments (OR 2.96) after DDS. Regardless of whether unintended facet arthrodesis was present or not, clinical

  1. Dynamic Interactive Learning Systems

    Sabry, Khaled; Barker, Jeff


    This paper reviews and discusses the notions of interactivity and dynamicity of learning systems in relation to information technologies and design principles that can contribute to interactive and dynamic learning. It explores the concept of dynamic interactive learning systems based on the emerging generation of information as part of a…

  2. Sufficient Conditions for Dynamical Output Feedback Stabilization Via the Circle Criterion


    This paper suggests sufficient conditions for asymptotically stable dynamical output feedback controller design based on the circle criterion. It is shown that a dynamic output feedback stabilization problem with impending problems of finite escape time, previously attacked by observer-based design, can be successfully solved using circle criterion design. Stability of the closed-loop system is global and robust to parameter uncertainty.

  3. Development of a transfer function method for dynamic stability measurement

    Johnson, W.


    Flutter testing method based on transfer function measurements is developed. The error statistics of several dynamic stability measurement methods are reviewed. It is shown that the transfer function measurement controls the error level by averaging the data and correlating the input and output. The method also gives a direct estimate of the error in the response measurement. An algorithm is developed for obtaining the natural frequency and damping ratio of low damped modes of the system, using integrals of the transfer function in the vicinity of a resonant peak. Guidelines are given for selecting the parameters in the transfer function measurement. Finally, the dynamic stability measurement technique is applied to data from a wind tunnel test of a proprotor and wing model.

  4. Dynamic Stability of Euler Beams under Axial Unsteady Wind Force

    You-Qin Huang


    Full Text Available Dynamic instability of beams in complex structures caused by unsteady wind load has occurred more frequently. However, studies on the parametric resonance of beams are generally limited to harmonic loads, while arbitrary dynamic load is rarely involved. The critical frequency equation for simply supported Euler beams with uniform section under arbitrary axial dynamic forces is firstly derived in this paper based on the Mathieu-Hill equation. Dynamic instability regions with high precision are then calculated by a presented eigenvalue method. Further, the dynamically unstable state of beams under the wind force with any mean or fluctuating component is determined by load normalization, and the wind-induced parametric resonant response is computed by the Runge-Kutta approach. Finally, a measured wind load time-history is input into the dynamic system to indicate that the proposed methods are effective. This study presents a new method to determine the wind-induced dynamic stability of Euler beams. The beam would become dynamically unstable provided that the parametric point, denoting the relation between load properties and structural frequency, is located in the instability region, no matter whether the wind load component is large or not.

  5. Active Stabilization of Aeromechanical Systems


    feedback, the resulting two-mode proportonal control law further extended the stable range of operation of the compresor . Stall flow coefficient control of surge and stall in gas turbine engines. The use of small amplitude waves predicted by theory as stall precursors were tested with...stabilization system for rotating stall which was tested on both a single-stage and a three-stage axial compressor, increasing the stable operating range

  6. Dynamic stabilization for degenerative spondylolisthesis and lumbar spinal instability.

    Ohtonari, Tatsuya; Nishihara, Nobuharu; Suwa, Katsuyasu; Ota, Taisei; Koyama, Tsunemaro


    Lumbar interbody fusion is a widely accepted surgical procedure for patients with lumbar degenerative spondylolisthesis and lumbar spinal instability in the active age group. However, in elderly patients, it is often questionable whether it is truly necessary to construct rigid fixation for a short period of time. In recent years, we have been occasionally performing posterior dynamic stabilization in elderly patients with such lumbar disorders. Posterior dynamic stabilization was performed in 12 patients (6 women, 70.9 ± 5.6 years old at the time of operation) with lumbar degenerative spondylolisthesis in whom % slip was less than 20% or instability associated with lumbar disc herniation between March 2011 and March 2013. Movement occurs through the connector linked to the pedicle screw. In practice, 9 pairs of D connector system where the rod moves in the perpendicular direction alone and 8 pairs of Dynamic connector system where the connector linked to the pedicle screw rotates in the sagittal direction were installed. The observation period was 77-479 days, and the mean recovery rate of lumbar Japanese Orthopedic Association (JOA) score was 65.6 ± 20.8%. There was progression of slippage due to slight loosening in a case with lumbar degenerative spondylolisthesis, but this did not lead to exacerbation of the symptoms. Although follow-up was short, there were no symptomatic adjacent vertebral and disc disorders during this period. Posterior dynamic stabilization may diminish the development of adjacent vertebral or disc disorders due to lumbar interbody fusion, especially in elderly patients, and it may be a useful procedure that facilitates decompression and ensures a certain degree of spinal stabilization.

  7. Dynamical Systems Conference

    Gils, S; Hoveijn, I; Takens, F; Nonlinear Dynamical Systems and Chaos


    Symmetries in dynamical systems, "KAM theory and other perturbation theories", "Infinite dimensional systems", "Time series analysis" and "Numerical continuation and bifurcation analysis" were the main topics of the December 1995 Dynamical Systems Conference held in Groningen in honour of Johann Bernoulli. They now form the core of this work which seeks to present the state of the art in various branches of the theory of dynamical systems. A number of articles have a survey character whereas others deal with recent results in current research. It contains interesting material for all members of the dynamical systems community, ranging from geometric and analytic aspects from a mathematical point of view to applications in various sciences.

  8. Nonlinear dynamics non-integrable systems and chaotic dynamics

    Borisov, Alexander


    This monograph reviews advanced topics in the area of nonlinear dynamics. Starting with theory of integrable systems – including methods to find and verify integrability – the remainder of the book is devoted to non-integrable systems with an emphasis on dynamical chaos. Topics include structural stability, mechanisms of emergence of irreversible behaviour in deterministic systems as well as chaotisation occurring in dissipative systems.

  9. Stability and Stabilization of Block-cascading Switched Linear Systems

    Ya-Hong Zhu; Dai-Zhan Cheng


    The main purpose of this paper is to investigate the problem of quadratic stability and stabilization in switched linear systems using reducible Lie algebra. First, we investigate the structure of all real invariant subspaces for a given linear system. The result is then used to provide a comparable cascading form for switching models. Using the commoncascading form, a common quadratic Lyapunov function is (QLFs) is explored by finding common QLFs of diagonal blocks.In addition, a cascading Quaker Lemma is proved. Combining it with stability results, the problem of feedback stabilization for a class of switched linear systems is solved.

  10. Investigation on shock waves stability in relativistic gas dynamics

    Alexander Blokhin


    Full Text Available This paper is devoted to investigation of the linearized mixed problem of shock waves stability in relativistic gas dynamics. The problem of symmetrization of relativistic gas dynamics equations is also discussed.

  11. On the Dynamic Stability of a Missile

    K.C. Sharma


    Full Text Available The P-method given by Parks and Pritchard has been used to discuss the stability behaviour of a missile in free flight. General stability criteria for aerodynamic stabilisation have been obtained for slowly varying coefficients. The effect of pressure gradient on the stability of a coasting rocket has been explicitly examined. It is observed that the positive Magnus moment parameter ensures stability whereas a negative moment parameter would enhance the requirements of a larger stability margin.

  12. Dynamic flight stability of hovering insects

    Mao Sun; Jikang Wang; Yan Xiong


    The equations of motion of an insect with flapping wings are derived and then simplified to that of a flying body using the "rigid body" assumption. On the basis of the simplified equations of motion, the longitudinal dynamic flight stability of four insects (hoverfly, cranefly, dronefly and hawkmoth) in hovering flight is studied (the mass of the insects ranging from 11 to 1,648 mg and wingbeat frequency from 26 to 157Hz). The method of computational fluid dynamics is used to compute the aerodynamic derivatives and the techniques of eigenvalue and eigenvector analysis are used to solve the equations of motion. The validity of the "rigid body" assumption is tested and how differencesin size and wing kinematics influence the applicability of the "rigid body" assumption is investigated. The primary findings are: (1) For insects considered in the present study and those with relatively high wingbeat frequency (hover-fly, drone fly and bumblebee), the "rigid body" assumptionis reasonable, and for those with relatively low wingbeatfrequency (cranefly and howkmoth), the applicability of the"rigid body" assumption is questionable. (2) The same three natural modes of motion as those reported recently for a bumblebee are identified, i.e., one unstable oscillatory mode,one stable fast subsidence mode and one stable slow subsidence mode. (3) Approximate analytical expressions of the eigenvalues, which give physical insight into the genesis of the natural modes of motion, are derived. The expressions identify the speed derivative Mu (pitching moment produced by unit horizontal speed) as the primary source of the unstable oscillatory mode and the stable fast subsidence mode and Zw (vertical force produced by unit vertical speed) as the primary source of the stable slow subsidence mode.

  13. Stability properties of autonomous homogeneous polynomial differential systems

    Samardzija, Nikola

    A geometrical approach is used to derive a generalized characteristic value problem for dynamic systems described by homogeneous polynomials. It is shown that a nonlinear homogeneous polynomial system possesses eigenvectors and eigenvalues, quantities normally associated with a linear system. These quantities are then employed in studying stability properties. The necessary and sufficient conditions for all forms of stabilities characteristic of a two-dimensional system are provided. This result, together with the classical theorem of Frommer, completes a stability analysis for a two-dimensional homogeneous polynomial system.

  14. An improved robust stability and robust stabilization method for linear discrete-time uncertain systems

    Xianming ZHANG; Min WU; Jinhua SHE; Dongsheng HAN


    This paper addresses the problems of the robust stability and robust stabilization of a discrete-time system with polytopic uncertainties.A new and simple method is presented to directly decouple the Lyapunov matrix and the system dynamic matrix.Combining this method with the parameter-dependent Lyapunov function approach yields new criteria that include some existing ones as special cases.A numerical example illustrates the improvement over the existing ones.

  15. Bisimulation of Dynamical Systems

    Schaft, Arjan van der


    A general notion of bisimulation is studied for dynamical systems. An algebraic characterization of bisimulation together with an algorithm for computing the maximal bisimulation relation is derived using geometric control theory. Bisimulation of dynamical systems is shown to be a concept which

  16. Non-Linear Dynamics and Stability of Circular Cylindrical Shells Containing Flowing Fluid. Part i: Stability



    The study presented is an investigation of the non-linear dynamics and stability of simply supported, circular cylindrical shells containing inviscid incompressible fluid flow. Non-linearities due to large-amplitude shell motion are considered by using the non-linear Donnell's shallow shell theory, with account taken of the effect of viscous structural damping. Linear potential flow theory is applied to describe the fluid-structure interaction. The system is discretiszd by Galerkin's method, and is investigated by using a model involving seven degrees of freedom, allowing for travelling wave response of the shell and shell axisymmetric contraction. Two different boundary conditions are applied to the fluid flow beyond the shell, corresponding to: (i) infinite baffles (rigid extensions of the shell), and (ii) connection with a flexible wall of infinite extent in the longitudinal direction, permitting solution by separation of variables; they give two different kinds of dynamical behaviour of the system, as a consequence of the fact that axisymmetric contraction, responsible for the softening non-linear dynamical behaviour of shells, is not allowed if the fluid flow beyond the shell is constrained by rigid baffles. Results show that the system loses stability by divergence.

  17. Heisenberg Picture Approach to the Stability of Quantum Markov Systems

    Pan, Yu; Amini, Hadis; Miao, Zibo; Gough, John; Ugrinovskii, Valery; James, Matthew R.


    Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this...

  18. Slope stability hazard management systems


    Weather-related geo-hazards are a major concern for both natural slopes and man-made slopes and embankments.Government agencies and private companies are increasingly required to ensure that there is adequate protection of sloping surfaces in order that interaction with the climate does not produce instability. Superior theoretical formulations and computer tools are now available to address engineering design issues related to the near ground surface soil-atmospheric interactions. An example is given in this paper that illustrates the consequences of not paying adequate attention to the hazards of slope stability prior to the construction of a highway in South America. On the other hand, examples are given from Hong Kong and Mainland China where significant benefits are derived from putting in place a hazard slope stability management system. Some results from a hazard management slope stability study related to the railway system in Canada are also reported. The study took advantage of recent research on unsaturated soil behaviour and applied this information to real-time modelling of climatic conditions. The quantification of the water balance at the ground surface, and subsequent infiltration, is used as the primary tool for hazard level assessment. The suggested hazard model can be applied at either specific high risk locations or in a more general, broad-based manner over large areas. A more thorough understanding of unsaturated soil behaviour as it applies to near ground surface soils,along with the numerical computational power of the computer has made it possible for new approaches to be used in slope hazard management engineering.

  19. Dynamic stability of spine using stability-based optimization and muscle spindle reflex.

    Zeinali-Davarani, Shahrokh; Hemami, Hooshang; Barin, Kamran; Shirazi-Adl, Aboulfazl; Parnianpour, Mohamad


    A computational method for simulation of 3-D movement of the trunk under the control of 48 anatomically oriented muscle actions was developed. Neural excitation of muscles was set based on inverse dynamics approach along with the stability-based optimization. The effect of muscle spindle reflex response on the trunk movement stability was evaluated upon the application of a perturbation moment. The method was used to simulate the trunk movement from the upright standing to 60 degrees of flexion. Incorporation of the stability condition as an additional constraint in the optimization resulted in an increase in antagonistic activities demonstrating that the antagonistic co-activation acts to increase the trunk stability in response to self-induced postural internal perturbation. In presence of a 30 Nm flexion perturbation moment, muscle spindles decreased the induced deviation of the position and velocity profiles from the desired ones. The stability-generated co-activation decreased the reflexive response of muscle spindles to the perturbation demonstrating that the rise in muscle co-activation can ameliorate the corruption of afferent neural sensory system at the expense of higher loading of the spine.

  20. Stability of multiplanet systems in binaries

    Marzari, F.; Gallina, G.


    eccentricity of the binary orbit, below which stable two planet systems cannot exist. Conclusions: The superposition of different resonances between two or more planets and the binary companion may prevent the existence of stable dynamical configurations in binaries. As a consequence, care must be devoted when applying the Holman and Wiegert criterion and the Hill stability against mutual close encounters for a multiplanet system in binaries.

  1. Advanced dynamics of mechanical systems

    Cheli, Federico


    This book introduces a general approach for schematization of mechanical systems with rigid and deformable bodies. It proposes a systems approach to reproduce the interaction of the mechanical system with different force fields such as those due to the action of fluids or contact forces between bodies, i.e., with forces dependent on the system states, introducing the concepts of the stability of motion. In the first part of the text mechanical systems with one or more degrees of freedom with large motion and subsequently perturbed in the neighborhood of the steady state position are analyzed. Both discrete and continuous systems (modal approach, finite elements) are analyzed. The second part is devoted to the study of mechanical systems subject to force fields, the rotor dynamics, techniques of experimental identification of the parameters, and random excitations. The book will be especially valuable for students of engineering courses in Mechanical Systems, Aerospace, Automation, and Energy but will also b...

  2. Predator interference and stability of predator-prey dynamics.

    Přibylová, Lenka; Berec, Luděk


    Predator interference, that is, a decline in the per predator consumption rate as predator density increases, is generally thought to promote predator-prey stability. Indeed, this has been demonstrated in many theoretical studies on predator-prey dynamics. In virtually all of these studies, the stabilization role is demonstrated as a weakening of the paradox of enrichment. With predator interference, stable limit cycles that appear as a result of environmental enrichment occur for higher values of the environmental carrying capacity of prey, and even a complete absence of the limit cycles can happen. Here we study predator-prey dynamics using the Rosenzweig-MacArthur-like model in which the Holling type II functional response has been replaced by a predator-dependent family which generalizes many of the commonly used descriptions of predator interference. By means of a bifurcation analysis we show that sufficiently strong predator interference may bring about another stabilizing mechanism. In particular, hysteresis combined with (dis)appearance of stable limit cycles imply abrupt increases in both the prey and predator densities and enhanced persistence and resilience of the predator-prey system. We encourage refitting the previously collected data on predator consumption rates as well as for conducting further predation experiments to see what functional response from the explored family is the most appropriate.

  3. Vibrations and stability of complex beam systems

    Stojanović, Vladimir


     This book reports on solved problems concerning vibrations and stability of complex beam systems. The complexity of a system is considered from two points of view: the complexity originating from the nature of the structure, in the case of two or more elastically connected beams; and the complexity derived from the dynamic behavior of the system, in the case of a damaged single beam, resulting from the harm done to its simple structure. Furthermore, the book describes the analytical derivation of equations of two or more elastically connected beams, using four different theories (Euler, Rayleigh, Timoshenko and Reddy-Bickford). It also reports on a new, improved p-version of the finite element method for geometrically nonlinear vibrations. The new method provides more accurate approximations of solutions, while also allowing us to analyze geometrically nonlinear vibrations. The book describes the appearance of longitudinal vibrations of damaged clamped-clamped beams as a result of discontinuity (damage). It...

  4. Application of small-signal modeling and measurement techniques to the stability analysis of an integrated switching-mode power system. [onboard Dynamics Explorer Satellite

    Wong, R. C.; Owen, H. A., Jr.; Wilson, T. G.; Rodriguez, G. E.


    Small-signal modeling techniques are used in a system stability analysis of a breadboard version of a complete functional electrical power system. The system consists of a regulated switching dc-to-dc converter, a solar-cell-array simulator, a solar-array EMI filter, battery chargers and linear shunt regulators. Loss mechanisms in the converter power stage, including switching-time effects in the semiconductor elements, are incorporated into the modeling procedure to provide an accurate representation of the system without requiring frequency-domain measurements to determine the damping factor. The small-signal system model is validated by the use of special measurement techniques which are adapted to the poor signal-to-noise ratio encountered in switching-mode systems. The complete electrical power system with the solar-array EMI filter is shown to be stable over the intended range of operation.

  5. Application of small-signal modeling and measurement techniques to the stability analysis of an integrated switching-mode power system. [onboard Dynamics Explorer Satellite

    Wong, R. C.; Owen, H. A., Jr.; Wilson, T. G.; Rodriguez, G. E.


    Small-signal modeling techniques are used in a system stability analysis of a breadboard version of a complete functional electrical power system. The system consists of a regulated switching dc-to-dc converter, a solar-cell-array simulator, a solar-array EMI filter, battery chargers and linear shunt regulators. Loss mechanisms in the converter power stage, including switching-time effects in the semiconductor elements, are incorporated into the modeling procedure to provide an accurate representation of the system without requiring frequency-domain measurements to determine the damping factor. The small-signal system model is validated by the use of special measurement techniques which are adapted to the poor signal-to-noise ratio encountered in switching-mode systems. The complete electrical power system with the solar-array EMI filter is shown to be stable over the intended range of operation.

  6. Dynamical systems revisited : Hybrid systems with Zeno executions

    ZHANG, JUN; Johansson, Karl Henrik; Lygeros, John; Sastry, Shankar


    Results from classical dynamical systems are generalized to hybrid dynamical systems. The concept of omega limit set is introduced for hybrid systems and is used to prove new results on invariant sets and stability, where Zeno and non-Zeno hybrid systems can be treated within the same framework. As an example, LaSalle's Invariance Principle is extended to hybrid systems. Zeno hybrid systems are discussed in detail. The omega limit set of a Zeno execution is characterized for classes of hybrid...

  7. Stability of Cascaded Fuzzy Systems and Observers

    Lendek, Z.; Babuska, R.; De Schutter, B.


    A large class of nonlinear systems can be well approximated by Takagi-Sugeno (TS) fuzzy models with linear or affine consequents. It is well known that the stability of these consequent models does not ensure the stability of the overall fuzzy system. Therefore, several stability conditions have bee

  8. Stability of Fractional Order Switching Systems

    HosseinNia, S Hassan; Vinagre, Blas M


    This paper addresses the stabilization issue for fractional order switching systems. Common Lyapunov method is generalized for fractional order systems and frequency domain stability equivalent to this method is proposed to prove the quadratic stability. Some examples are given to show the applicability and effectiveness of the proposed theory.

  9. Shadowing in dynamical systems

    Pilyugin, Sergei Yu


    This book is an introduction to the theory of shadowing of approximate trajectories in dynamical systems by exact ones. This is the first book completely devoted to the theory of shadowing. It shows the importance of shadowing theory for both the qualitative theory of dynamical systems and the theory of numerical methods. Shadowing Methods allow us to estimate differences between exact and approximate solutions on infinite time intervals and to understand the influence of error terms. The book is intended for specialists in dynamical systems, for researchers and graduate students in the theory of numerical methods.

  10. Fractional Dynamical Systems

    Edelman, Mark


    In this paper the author presents the results of the preliminary investigation of fractional dynamical systems based on the results of numerical simulations of fractional maps. Fractional maps are equivalent to fractional differential equations describing systems experiencing periodic kicks. Their properties depend on the value of two parameters: the non-linearity parameter, which arises from the corresponding regular dynamical systems; and the memory parameter which is the order of the fractional derivative in the corresponding non-linear fractional differential equations. The examples of the fractional Standard and Logistic maps demonstrate that phase space of non-linear fractional dynamical systems may contain periodic sinks, attracting slow diverging trajectories, attracting accelerator mode trajectories, chaotic attractors, and cascade of bifurcations type trajectories whose properties are different from properties of attractors in regular dynamical systems. The author argues that discovered properties s...

  11. Dynamic Modeling, Testing, and Stability Analysis of an Ornithoptic Blimp

    John Dietl; Thomas Herrmann; Gregory Reich; Ephrahim Garcia


    In order to study omithopter flight and to improve a dynamic model of flapping propulsion,a series of tests are conducted on a flapping-wing blimp.The blimp is designed and constructed from mylar plastic and balsa wood as a test platform for aerodynamics and flight dynamics.The blimp,2.3 meters long and 420 gram mass,is propelled by its flapping wings.Due to buoyancy the wings have no lift requirement so that the distinction between lift and propulsion can be analyzed in a flight platform at low flight speeds.The blimp is tested using a Vicon motion tracking system and various initial conditions are tested including accelerating flight from standstill,decelerating from an initial speed higher than its steady state,and from its steady-state speed but disturbed in pitch angle.Test results are used to estimate parameters in a coupled quasi-steady aerodynamics/Newtonian flight dynamics model.This model is then analyzed using Floquet theory to determine local dynamic modes and stability.It is concluded that the dynamic model adequately describes the vehicle's nonlinear behavior near the steady-state velocity and that the vehicle's linearized modes are akin to those of a fixed-wing aircraft.

  12. Design for robust stabilization of nonlinear systems with uncertain parameters

    赖旭芝; 文静; 吴敏


    Based on Lyapunov stability theory, a design method for the robust stabilization problem of a class of nonlinear systems with uncertain parameters is presented. The design procedure is divided into two steps: the first is to design controllers for the nominal system and make the system asymptotically stabilize at the expected equilibrium point; the second is to construct closed-loop nominal system based on the first step, then design robust controller to make the error of state between the original system and the nominal system converge to zero, thereby a dynamic controller with the constructed closed-loop nominal system served as interior dynamic is obtained. A numerical simulation verifies the correctness of the design method.

  13. Invitation to dynamical systems

    Scheinerman, Edward R


    This text is designed for those who wish to study mathematics beyond linear algebra but are unready for abstract material. Rather than a theorem-proof-corollary exposition, it stresses geometry, intuition, and dynamical systems. 1996 edition.

  14. Dynamic performance management system


    An integrated, efficient and effective performance management system, "dynamic performance management system", is presented, which covers the entire performance management process including measures design, analysis, and dynamic update. The analysis of performance measures using causal loop diagrams, qualitative inference and analytic network process is mainly discussed. A real world case study is carried out throughout the paper to explain how the framework works. A software tool for DPMS, Performance Analyzer, is also introduced.


    周承倜; 王列东


    Hamilton Principle was uaed to derive the general governing equations of nonlinear dynamic stability for laminated cylindrical shells in which, factors of nonlinear large deflection, transverse shear and longitudinal inertia force were concluded. Equations were solved by variational method. Analysis reveals that under the action of dynamic load,laminated cylindrical shells will fall into a state of parametric resonance and enter into the dynamic unstable region that causes dynamic instability of shells. Laminated shells of three typical composites were computed: i.e. T300/5 208 graphite epoxy E-glass epoxy, and ARALL shells. Results show that all factors will induce important influence for dynamic stability of laminated shells. So, in research of dynamic stability for laminated shells, to consider these factors is important.

  16. Stochastic stabilization analysis of networked control systems

    Ma Changlin; Fang Huajing


    Considering the stochastic delay problems existing in networked control systems, a new control mode is proposed for networked control systems whose delay is longer than a sampling period. Under the control mode, the mathematical model of such a system is established. A stochastic stabilization condition for the system is given. The maximum delay can be derived from the stabilization condition.

  17. Dynamic Stability Analysis Using High-Order Interpolation

    Juarez-Toledo C.


    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.

  18. The stability and dynamic behaviour of fluid-loaded structures

    Suliman, Ridhwaan


    Full Text Available ECCOMAS Young Investigators Conference 6th GACM Colloquium, July 20–23, 2015, Aachen, Germany The stability and dynamic behaviour of fluid-loaded structures R. Suliman, N. Peake Abstract. The deformation of slender elastic structures due...

  19. Asymptotic stability and stabilizability of nonlinear systems with delay.

    Srinivasan, V; Sukavanam, N


    This paper is concerned with asymptotic stability and stabilizability of a class of nonlinear dynamical systems with fixed delay in state variable. New sufficient conditions are established in terms of the system parameters such as the eigenvalues of the linear operator, delay parameter, and bounds on the nonlinear parts. Finally, examples are given to testify the effectiveness of the proposed theory.

  20. Power System Security and Stability Control Company


    Branch Company Profile Power System Security and Stability Control Company is called "NARI Stability" to externals. It has a scientific research team, led by Prof. Yusheng Xue, who is an international renowned expert on stability technology, and an academician of the Chinese Academy of Engineering. Based on support and service of security and stability control technology and equipment,

  1. Bifurcations and Stability Boundary of a Power System

    Ying-hui Gao


    A single-axis ux decay model including an excitation control model proposed in [12,14,16] is studied. As the bifurcation parameter P m (input power to the generator) varies, the system exhibits dynamics emerging from static and dynamic bifurcations which link with system collapse. We show that the equilibrium point of the system undergoes three bifurcations: one saddle-node bifurcation and two Hopf bifurcations. The state variables dominating system collapse are different for different critical points, and the excitative control may play an important role in delaying system from collapsing. Simulations are presented to illustrate the dynamical behavior associated with the power system stability and collapse. Moreover, by computing the local quadratic approximation of the 5-dimensional stable manifold at an order 5 saddle point, an analytical expression for the approximate stability boundary is worked out.

  2. The nu Andromedae System: Models and Stability

    Stepinski, Tomasz F.; Malhotra, Renu; Black, David C.


    Radial velocity observations of the F8 V star nu Andromedae taken at Lick and at Whipple Observatories have revealed evidence of three periodicities in the line-of-sight velocity of the star. These periodicities have been interpreted as evidence for at least three low-mass companions (LMCs) revolving around nu Andromedae. The mass and orbital parameters inferred for these companions raise questions about the dynamical stability of the system. We report here results from our independent analysis of the published radial velocity data, as well as new unpublished data taken at Lick Observatory. Our results confirm the finding of three periods in the data. Our best fits to the data, on the assumption that these periods arise from the gravitational perturbations of companions in Keplerian orbits, are also generally in agreement but with some differences from the earlier findings. We find that the available data do not constrain well the orbital eccentricity of the middle companion in a three-companion model of the data. We also find that in order for our best-fit model to the Lick data to be dynamically stable over the lifetime of the star (approximately 2 billion years), the system must have a mean inclination to the plane of the sky greater than 13 deg. The corresponding minimum inclination for the best fit to the Whipple data set is 19 deg. These values imply that the maximum mass for the outer companion can be no greater than about 20 Jupiter masses. Our analysis of the stability of the putative systems also places constraints on the relative inclinations of the orbital planes of the companions. We comment on global versus local (i.e., method of steepest descent) means of finding best-fit orbits from radial velocity data sets.

  3. Proteolytic stability in colloidal systems.

    Maste, M.C.L.


    Proteolytic enzymes in liquid detergents suffer from lack of stability in the sense that activity diminishes with time. Although the phenomenon could be attributed to several factors, the influence of colloidal surfaces on the enzymatic stability was investigated. Besides the types of surfaces that

  4. System design description PFP thermal stabilization

    LARKIN, K.A.


    The purpose of this document is to provide a system design description and design basis for the Plutonium Finishing Plant (PFP) Thermal Stabilization project. The sources of material for this project are residues scraped from glovebox floors and materials already stored in vault storage that need further stabilizing. Stabilizing this material will promote long term storage and reduced worker exposure. This document addresses: functional design, equipment, and safety requirements for thermal stabilization of plutonium residues and oxides.

  5. Stability analysis of single planet systems and their habitable zones

    Kopparapu, Ravi kumar


    We study the dynamical stability of planetary systems consisting of one hypothetical terrestrial mass planet ($1 $ or $10 \\mearth$) and one massive planet ($10 \\mearth - 10 \\mjup$). We consider masses and orbits that cover the range of observed planetary system architectures (including non-zero initial eccentricities), determine the stability limit through N-body simulations, and compare it to the analytic Hill stability boundary. We show that for given masses and orbits of a two planet system, a single parameter, which can be calculated analytically, describes the Lagrange stability boundary (no ejections or exchanges) but which diverges significantly from the Hill stability boundary. However, we do find that the actual boundary is fractal, and therefore we also identify a second parameter which demarcates the transition from stable to unstable evolution. We show the portions of the habitable zones of $\\rho$ CrB, HD 164922, GJ 674, and HD 7924 which can support a terrestrial planet. These analyses clarify th...

  6. Stabilization of third-order bilinear systems using constant controls

    A. E. Golubev


    Full Text Available This paper deals with the zero equilibrium stabilization for dynamical systems that have control input singularities. A dynamical system with scalar control input is called nonregular if the coefficient of input becomes null on a subset of the phase space that contains the origin. One of the classes of nonregular dynamical systems is represented by bilinear systems. In case of second-order bilinear systems the necessary and sufficient conditions for the zero equilibrium stabilizability are known in the literature. However, in general case the stabilization problem in the presence of control input singularities has not been solved yet.In this note we solve the problem of the zero equilibrium stabilization for the third-order bilinear dynamical systems given in a canonical form. The solution is found in the class of constant controls. The necessary and sufficient conditions are obtained for the zero equilibrium stabilizability of the bilinear systems in question.The dependence of the zero equilibrium stabilizability on system parameter values is analyzed. The general criteria of stabilizability by means of constant controls are given for the bilinear systems in question. In case when all the system parameters have nonzero values the necessary and sufficient stabilizability conditions are proved. The case when some of the parameters are equal to zero is also considered.Further research can be focused on extending the obtained results to a higher-order case of bilinear and affine dynamical systems. The solution of the considered stabilization problem should also be found not only within constant controls but also in a class of state feedbacks, particularly, in the case when stabilizing constant control does not exist.One of the potential application areas for the obtained theoretical results is automatic control of technical plants like unmanned aerial vehicles and mobile robots.

  7. Dynamics of Information Systems

    Hirsch, Michael J; Murphey, Robert


    Our understanding of information and information dynamics has outgrown classical information theory. This book presents the research explaining the importance of information in the evolution of a distributed or networked system. It presents techniques for measuring the value or significance of information within the context of a system

  8. Dynamic Systems Modeling

    Sorin Dan ŞANDOR


    Full Text Available System Dynamics was introduced by Jay W. Forrester in the 1960s. Since then the methodology was adopted in many areas of natural or social sciences. This article tries to present briefly how this methodology works, both as Systems Thinking and as Modelling with Vensim computer software.

  9. Relationship between Core Stability Muscle Endurance and Static and Dynamic Balance in Basketball Players

    farzaneh saki; masumeh Baghban


    Objective: Balancing is the most basic function of the neuromuscular system in performing all simple and complex activities that contribute to health-related physical fitness. Core stability may be a contributing factor to static and dynamic balance. The aim of this study was to investigate the relationship between core stability muscle endurance and static and dynamic balance in basketball players. Methods: 100 basketball players (50 female and 50 male players) were selected randomly bas...

  10. On Stability of the Mechanical Lagrangian Systems

    Valer Niminet


    Full Text Available

    We consider MLS (mechanical Lagrangian systems with
    external forces. We give some conditions of stability and dissipativity and show that the energy of the system decreases on the integral curves.

    Key words: LMS, stability, dissipative system.

  11. The stability of protoplanet systems

    Yoshinaga, K; Makino, J


    The authors investigated the stability of 10 protoplanet systems using three-dimensional N-body simulations. They found that the time scale of instability T depends strongly on the initial random velocities nu (eccentricities e and inclinations i) and orbital separations Delta a. For zero initial random velocities, they confirmed the result of Chambers et al. (1996, Icarus 119, 261-268) that T is proportional to exp( Delta a). For finite random velocities, they found that T depends strongly on the initial random velocities. The relation between T and Delta a is still expressed as log T=b+c Delta a. However, both b and c depend on initial random velocities and the slope, b, becomes smaller for larger nu . Even for relatively small initial eccentricities such as e~2r/sub H//a, where r/sub H/ is the Hill radius, the time scale can be reduced by a factor of 10 compared with the case of the zero random velocity. Therefore, the time scale of the formation of inner planets might be much shorter than what implied by ...

  12. Stabilization of model-based networked control systems

    Miranda, Francisco; Abreu, Carlos; Mendes, Paulo M.


    A class of networked control systems called Model-Based Networked Control Systems (MB-NCSs) is considered. Stabilization of MB-NCSs is studied using feedback controls and simulation of stabilization for different feedbacks is made with the purpose to reduce the network trafic. The feedback control input is applied in a compensated model of the plant that approximates the plant dynamics and stabilizes the plant even under slow network conditions. Conditions for global exponential stabilizability and for the choosing of a feedback control input for a given constant time between the information moments of the network are derived. An optimal control problem to obtain an optimal feedback control is also presented.

  13. Optimal Coordinated Design of Multiple Damping Controllers Based on PSS and UPFC Device to Improve Dynamic Stability in the Power System

    A. N. Hussain


    Full Text Available Unified Power Flow Controller (UPFC device is applied to control power flow in transmission lines. Supplementary damping controller can be installed on any control channel of the UPFC inputs to implement the task of Power Oscillation Damping (POD controller. In this paper, we have presented the simultaneous coordinated design of the multiple damping controllers between Power System Stabilizer (PSS and UPFC-based POD or between different multiple UPFC-based POD controllers without PSS in a single-machine infinite-bus power system in order to identify the design that provided the most effective damping performance. The parameters of the damping controllers are optimized utilizing a Chaotic Particle Swarm Optimization (CPSO algorithm based on eigenvalue objective function. The simulation results show that the coordinated design of the multiple damping controllers has high ability in damping oscillations compared to the individual damping controllers. Furthermore, the coordinated design of UPFC-based POD controllers demonstrates the superiority over the coordinated design of PSS and UPFC-based POD controllers for enhancing greatly the stability of the power system.

  14. Dynamic blade row compression component model for stability studies

    Tesch, W. A.; Steenken, W. G.


    This paper describes a generalized dynamic model which has been developed for use in compression component aerodynamic stability studies. The model is a one-dimensional, pitch-line, blade row, lumped volume system. Arbitrary placement of blade free volumes upstream, within, and downstream of the compression component as well as the removal of bleed flow from the exit of any rotor or stator are model options. The model has been applied to a two-stage fan and an eight-stage compressor. The clean inlet pressure ratio/flow maps and the surge line have been reproduced, thereby validating the capability of the dynamic model to reproduce the steady-flow characteristics of the compression component. A method for determining the onset of an aerodynamic instability which is associated with surge is described. Sinusoidally time-varying inlet and exit boundary conditions have been applied to the eight stage compressor as examples of the manner in which this model may be used for stability studies.

  15. Stochastic stability properties of jump linear systems

    Feng, Xiangbo; Loparo, Kenneth A.; Ji, Yuandong; Chizeck, Howard J.


    Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties. It is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability, and a testable necessary and sufficient condition for second moment stability is derived. The Lyapunov exponent method for the study of almost sure sample stability is discussed, and a theorem which characterizes the Lyapunov exponents of jump linear systems is presented.

  16. Role of Intrinsic and Reflexive Dynamics in the Control of Spinal Stability

    Moorhouse, Kevin Michael


    Role of Intrinsic and Reflexive Dynamics in the Control of Spinal Stability Kevin M. Moorhouse Abstract Spinal stability describes the ability of the neuromuscular system to maintain equilibrium in the presence of kinematic and control variability, and may play an important role in the etiology of low-back disorders (LBDs). The primary mechanism for the neuromuscular control of spinal stability is the recruitment and control of active paraspinal muscle stiffness (i.e., trunk stif...

  17. A new transient stability margin based on dynamic security region and its applications


    A new transient stability margin is proposed based on a new expression of dynamic security region (DSR) which is developed from the existing expression of DSR. Applications of the DSR based transient stability margin to contingency ranking and screening are discussed. Simulations in the 10-machine 39-bus New England system are performed to show the effectiveness of the proposed DSR based tran-sient stability margin.

  18. Dynamical stability of a many-body Kapitza pendulum

    Citro, Roberta, E-mail: [Dipartimento di Fisica “E. R. Caianiello” and Spin-CNR, Universita’ degli Studi di Salerno, Via Giovanni Paolo II, I-84084 Fisciano (Italy); Dalla Torre, Emanuele G., E-mail: [Department of Physics, Bar Ilan University, Ramat Gan 5290002 (Israel); Department of Physics, Harvard University, Cambridge, MA 02138 (United States); D’Alessio, Luca [Department of Physics, The Pennsylvania State University, University Park, PA 16802 (United States); Department of Physics, Boston University, Boston, MA 02215 (United States); Polkovnikov, Anatoli [Department of Physics, Boston University, Boston, MA 02215 (United States); Babadi, Mehrtash [Department of Physics, Harvard University, Cambridge, MA 02138 (United States); Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125 (United States); Oka, Takashi [Department of Applied Physics, University of Tokyo, Tokyo, 113-8656 (Japan); Demler, Eugene [Department of Physics, Harvard University, Cambridge, MA 02138 (United States)


    We consider a many-body generalization of the Kapitza pendulum: the periodically-driven sine–Gordon model. We show that this interacting system is dynamically stable to periodic drives with finite frequency and amplitude. This finding is in contrast to the common belief that periodically-driven unbounded interacting systems should always tend to an absorbing infinite-temperature state. The transition to an unstable absorbing state is described by a change in the sign of the kinetic term in the Floquet Hamiltonian and controlled by the short-wavelength degrees of freedom. We investigate the stability phase diagram through an analytic high-frequency expansion, a self-consistent variational approach, and a numeric semiclassical calculation. Classical and quantum experiments are proposed to verify the validity of our results.

  19. Semipredictable dynamical systems

    García-Morales, Vladimir


    A new class of deterministic dynamical systems, termed semipredictable dynamical systems, is presented. The spatiotemporal evolution of these systems have both predictable and unpredictable traits, as found in natural complex systems. We prove a general result: The dynamics of any deterministic nonlinear cellular automaton (CA) with p possible dynamical states can be decomposed at each instant of time in a superposition of N layers involving p0, p1, …, pN - 1 dynamical states each, where the pk ∈ N , k ∈ [ 0 , N - 1 ] are divisors of p. If the divisors coincide with the prime factors of p this decomposition is unique. Conversely, we also prove that N CA working on symbols p0, p1, …, pN - 1 can be composed to create a graded CA rule with N different layers. We then show that, even when the full spatiotemporal evolution can be unpredictable, certain traits (layers) can exactly be predicted. We present explicit examples of such systems involving compositions of Wolfram's 256 elementary CA and a more complex CA rule acting on a neighborhood of two sites and 12 symbols and whose rule table corresponds to the smallest Moufang loop M12(S3, 2).

  20. A unified proof of dynamic stability of interior ESS for projection dynamics

    Joosten, Reinoud A.M.G.; Roorda, Berend


    We present a unified proof of dynamic stability for interior evolutionarily stable strategies for two recently introduced projection dynamics using the angle between certain vectors as a Lyapunov function.


    Uğur YÜCEL


    Full Text Available In various industrial applications there is a need for higher speed, yet reliably operating rotating machinery. A key factor in achieving this type of machinery continues to be the ability to accurately predict the dynamic response and stability of a rotor-bearing system. This paper introduces and explains the nature of rotordynamic phenomena from comparatively simple analytic models. Starting with the most simple rotor model that is supported in two rigid bearings at its ends, the more realistic and more involved cases are considered by incorporating the effects of flexible bearings. Knowledge of these phenomena is fundamental to an understanding of the behavior of complex models, which corresponds to the real rotors of turbomachines.

  2. Dynamic system classifier

    Pumpe, Daniel; Müller, Ewald; Enßlin, Torsten A


    Stochastic differential equations describe well many physical, biological and sociological systems, despite the simplification often made in their derivation. Here the usage of simple stochastic differential equations to characterize and classify complex dynamical systems is proposed within a Bayesian framework. To this end, we develop a dynamic system classifier (DSC). The DSC first abstracts training data of a system in terms of time dependent coefficients of the descriptive stochastic differential equation. Thereby the DSC identifies unique correlation structures within the training data. For definiteness we restrict the presentation of DSC to oscillation processes with a time dependent frequency {\\omega}(t) and damping factor {\\gamma}(t). Although real systems might be more complex, this simple oscillator captures many characteristic features. The {\\omega} and {\\gamma} timelines represent the abstract system characterization and permit the construction of efficient signal classifiers. Numerical experiment...

  3. Dynamic system classifier

    Pumpe, Daniel; Greiner, Maksim; Müller, Ewald; Enßlin, Torsten A.


    Stochastic differential equations describe well many physical, biological, and sociological systems, despite the simplification often made in their derivation. Here the usage of simple stochastic differential equations to characterize and classify complex dynamical systems is proposed within a Bayesian framework. To this end, we develop a dynamic system classifier (DSC). The DSC first abstracts training data of a system in terms of time-dependent coefficients of the descriptive stochastic differential equation. Thereby the DSC identifies unique correlation structures within the training data. For definiteness we restrict the presentation of the DSC to oscillation processes with a time-dependent frequency ω (t ) and damping factor γ (t ) . Although real systems might be more complex, this simple oscillator captures many characteristic features. The ω and γ time lines represent the abstract system characterization and permit the construction of efficient signal classifiers. Numerical experiments show that such classifiers perform well even in the low signal-to-noise regime.

  4. Complexity in Dynamical Systems

    Moore, Cristopher David

    The study of chaos has shown us that deterministic systems can have a kind of unpredictability, based on a limited knowledge of their initial conditions; after a finite time, the motion appears essentially random. This observation has inspired a general interest in the subject of unpredictability, and more generally, complexity; how can we characterize how "complex" a dynamical system is?. In this thesis, we attempt to answer this question with a paradigm of complexity that comes from computer science, we extract sets of symbol sequences, or languages, from a dynamical system using standard methods of symbolic dynamics; we then ask what kinds of grammars or automata are needed a generate these languages. This places them in the Chomsky heirarchy, which in turn tells us something about how subtle and complex the dynamical system's behavior is. This gives us insight into the question of unpredictability, since these automata can also be thought of as computers attempting to predict the system. In the culmination of the thesis, we find a class of smooth, two-dimensional maps which are equivalent to the highest class in the Chomsky heirarchy, the turning machine; they are capable of universal computation. Therefore, these systems possess a kind of unpredictability qualitatively different from the usual "chaos": even if the initial conditions are known exactly, questions about the system's long-term dynamics are undecidable. No algorithm exists to answer them. Although this kind of unpredictability has been discussed in the context of distributed, many-degree-of -freedom systems (for instance, cellular automata) we believe this is the first example of such phenomena in a smooth, finite-degree-of-freedom system.

  5. Attachment is a dynamic system

    Zlatka Cugmas


    Full Text Available On the basis of the study of recent scientific literature about the development of attachment, the author answers the following questions: which are the postulates the theory of attachment has about the stability of the patterns of attachment, which level of stability in the patterns of attachment from infancy to adulthood these studies illuminate and which factors significantly influence the (instability of the patterns of attachment in time. The theory of attachment assumes that normal circumstances elicit stability. Changes, however, can be the result of important events influencing the sensitivity of the object of attachment. Agreement has not yet been reached regarding the percentage of stability in the patterns of attachment. There is more agreement regarding attachment in adulthood than that in childhood. The results depend on the size and characteristics of the subjects of the research, the measuring instruments, type of data analysis etc. The author concludes that attachment is a dynamic system influenced by significant changes in life (the cognitive development of the child, external care, parents' divorce, different stressful situations. As the influence of stressful events on the individual person' s quality of attachment is examined, it is necessary to consider also his/her temperamental characteristics, role of other people in their lives, etc.

  6. A unifying energy-based approach to stability of power grids with market dynamics

    Stegink, Tjerk; De Persis, Claudio; van der Schaft, Arjan


    In this paper a unifying energy-based approach is provided to the modeling and stability analysis of power systems coupled with market dynamics. We consider a standard model of the power network with a third-order model for the synchronous generators involving voltage dynamics. By applying the prima

  7. Complexified dynamical systems

    Bender, Carl M [Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Holm, Darryl D [Department of Mathematics, Imperial College, London SW7 2AZ (United Kingdom); Hook, Daniel W [Blackest Laboratory, Imperial College, London SW7 2BZ (United Kingdom)


    Many dynamical systems, such as the Lotka-Volterra predator-prey model and the Euler equations for the free rotation of a rigid body, are PT symmetric. The standard and well-known real solutions to such dynamical systems constitute an infinitessimal subclass of the full set of complex solutions. This paper examines a subset of the complex solutions that contains the real solutions, namely those having PT symmetry. The condition of PT symmetry selects out complex solutions that are periodic. (fast track communication)

  8. Static and dynamic stability analysis of the space shuttle vehicle-orbiter

    Chyu, W. J.; Cavin, R. K.; Erickson, L. L.


    The longitudinal static and dynamic stability of a Space Shuttle Vehicle-Orbiter (SSV Orbiter) model is analyzed using the FLEXSTAB computer program. Nonlinear effects are accounted for by application of a correction technique in the FLEXSTAB system; the technique incorporates experimental force and pressure data into the linear aerodynamic theory. A flexible Orbiter model is treated in the static stability analysis for the flight conditions of Mach number 0.9 for rectilinear flight (1 g) and for a pull-up maneuver (2.5 g) at an altitude of 15.24 km. Static stability parameters and structural deformations of the Orbiter are calculated at trim conditions for the dynamic stability analysis, and the characteristics of damping in pitch are investigated for a Mach number range of 0.3 to 1.2. The calculated results for both the static and dynamic stabilities are compared with the available experimental data.

  9. Stabilization of Slowly Varying Switched Linear Systems

    ZHANG Bing; LIANG Tong


    The stabilization problem of systems that switch among a finite set of slowly varying linear systems with arbitrary switching frequency is discussed.It is shown that if the entries of the pointwise stabilizing feedback gain matrix are continuously differentiable functions of the entries of the system coefficient matrices,then the closed-loop system is uniformly asymptotically stable if the rate of time variation of the system coefficient matrices is sufficiently small.

  10. Comparing the Power System Stabilizer Based on Sliding Mode Control with the Fuzzy Power System Stabilizer for Single Machine Infinite Bus System (SMIB

    Atabak Kolabi


    Full Text Available This study compares the power system stabilizer based on sliding mode control with the fuzzy power system stabilizer for Single Machine Infinite Bus System (SMIB. Using the sliding mode control, a range is obtained for the changes in system parameters; and a stabilizer is designed to have a proper performance in this wide range. The purpose of designing the sliding mode stabilizer and fuzzy stabilizer is the increased stability and improving the dynamic response of the single machine system connected to the infinite bus in different working conditions. In this study, simulation results are compared in case of conventional PSS, no PSS, PSS based on sliding mode control and PSS based fuzzy logic. The results of simulations performed on the model of nonlinear system shows good performance of sliding mode controller and the Fuzzy controller. SMIB system was selected because of its simple structure, which is very useful in understanding the effects and implications of the PSS.

  11. Criteria for the Degree of Stability of the Linear Constant Systems

    王广彬; 潘宝珍; 侯文渊


    There are various applications of the stability theory of the first-order dynamical systems. And the stability of the non-linear control systems can be determined by its linear part. In practice, it is not enough to know the stability of the dynamical systems. Sometimes we must know the degree of stability of these systems. In this paper, we present some criteria for the degree of stability of the linear constant systems, by using the entries of the coefficient matrix A only.

  12. Dynamic stabilization of Rayleigh-Taylor instability in ablation fronts

    Piriz A.R.


    Full Text Available Dynamic stabilization of Rayleigh-Taylor instability in an ablation front is studied by considering the simplest possible modulations in the acceleration. Explicit analytical expressions for the instability growth rate and for the boundaries of the stability region are obtained by considering a sequence of Dirac deltas. Besides, general square waves allow for studying the effect of the driving asymmetries on the stability region as well as the optimization process. The essential role of compressibility is phenomenologically addressed in order to find the constraints it imposes on the stability region.

  13. Power System Stability Enhancement Using Fact Devices

    Mr. B. T. Ramakrishna Rao


    Full Text Available The development of the modern power system has led to an increasing complexity in the study of power systems, and also presents new challenges to power system stability, and in particular, to the aspects of transient stability and small-signal stability. So Power system engineers are currently facing challenges to increase the power transfer capabilities of existing transmission system. This is where the Flexible AC Transmission Systems (FACTS technology comes into effect with relatively low investment, compared to new transmission or generation facilities. Flexible AC transmission system (FACTS devices use power electronics components to maintain controllability and capability of electrical power system. The paper aims towards the performance of UPFC is compared with other FACTS devices such as Static Synchronous Series Compensator (SSSC, Thyristor Controlled Series Capacitor (TCSC, and Static Var Compensator (SVC respectively. The simulation results demonstrate the effectiveness of the UPFC on transient stability of the system.

  14. The electric power engineering handbook power system stability and control

    Grisby, Leonard L


    With contributions from worldwide leaders in the field, Power System Stability and Control, Third Edition (part of the five-volume set, The Electric Power Engineering Handbook) updates coverage of recent developments and rapid technological growth in essential aspects of power systems. Edited by L.L. Grigsby, a respected and accomplished authority in power engineering, and section editors Miroslav Begovic, Prabha Kundur, and Bruce Wollenberg, this reference presents substantially new and revised content. Topics covered include: * Power System Protection * Power System Dynamics and Stability *

  15. Research on Optimization, Dynamics and Stability of Stairclimbing Wheelchair

    Shashank Shekhar Sahoo


    Full Text Available Since the invention of the wheel, man has always sought to reduce effort to get things done easily. Ultimately, it has resulted in the invention of the Robot, an Engineering Marvel. Up until now, the major factor that hampers widespread usage of robots is locomotion and maneuverability. They are not fit enough to conform even to the most commonplace terrain such as stairs. To overcome this, we are proposing a stair climbing wheelchair robot that looks a lot like a normal wheelchair but with additional stair-climbing functionality to adjust itself according to the height of the step The primarily goal of the prescribed manuscript herewith is to analyze the functional requirements, optimization methods, dynamics and stability during a tracked robotic wheelchair’s climbing of stairs mechanism. At first, the mechanical structure of the wheelchair is designed and the hardware composition of its full control system is devised. Secondly, based on the analysis of its stairs‐climbing process, the dynamical model of stairs‐climbing is established by using the classical mechanics method. Next, through simulation and experiments, the effectiveness of the dynamical model, its stability evaluation and performance parameters is verified. Such procedures will help in establishing a strong fundamental foundation steps to design and develop a standalone semi-autonomous wheelchair that will help and enable a physically challenged person by leg to climb difficult terrains like staircase and speed-breakers with ease and comfort. This design encompasses Renesas’s Arduino compatible GR-KAEDE boards, servo motors, high torque DC motors and various peripheral devices as incorporated in design diagram. We have also extended the application of wheelchair by integrating collision avoidance mechanism.

  16. Gyroscopic stabilization of non-conservative systems

    Kirillov, Oleg N. [Dynamics Group, Department of Mechanical Engineering, Technical University of Darmstadt, Hochschulstr. 1, 64289 Darmstadt (Germany) and Institute of Mechanics, Moscow State Lomonosov University, Michurinskii pr. 1, 119192 Moscow (Russian Federation)]. E-mail:


    Gyroscopic stabilization of a linear conservative system, which is statically unstable, can be either improved or destroyed by weak damping and circulatory forces. This is governed by Whitney umbrella singularity of the boundary of the asymptotic stability domain of the perturbed system.


    QI Zhao-hui(齐朝晖); Alexander P. Seyranian


    The criterion for the points in the parameter space being on the stability boundary of linear Hamiltonian system depending on arbitrary numbers of parameters was given, through the sensitivity analysis of eigenvalues and eigenvectors. The results show that multiple eigenvalues with Jordan chain take a very important role in the stability of Hamiltonian systems.

  18. Stability and stabilization of linear systems with saturating actuators

    Tarbouriech, Sophie; Gomes da Silva Jr, João Manoel; Queinnec, Isabelle


    Gives the reader an in-depth understanding of the phenomena caused by the more-or-less ubiquitous problem of actuator saturation. Proposes methods and algorithms designed to avoid, manage or overcome the effects of actuator saturation. Uses a state-space approach to ensure local and global stability of the systems considered. Compilation of fifteen years' worth of research results.

  19. Stability Limits in Resonant Planetary Systems

    Barnes, Rory


    The relationship between the boundaries for Hill and Lagrange stability in orbital element space is modified in the case of resonantly interacting planets. Hill stability requires the ordering of the planets to remain constant while Lagrange stability also requires all planets to remain bound to the central star. The Hill stability boundary is defined analytically, but no equations exist to define the Lagrange boundary, so we perform numerical experiments to estimate the location of this boundary. To explore the effect of resonances, we consider orbital element space near the conditions in the HD 82943 and 55 Cnc systems. Previous studies have shown that, for non-resonant systems, the two stability boundaries are nearly coincident. However the Hill stability formula are not applicable to resonant systems, and our investigation shows how the two boundaries diverge in the presence of a mean-motion resonance, while confirming that the Hill and Lagrange boundaries are similar otherwise. In resonance the region of...

  20. Fuzzy stability and synchronization of hyperchaos systems

    Wang Junwei [School of Mathematics and Computational Science, Zhongshan University Guangzhou 510275 (China)], E-mail:; Xiong Xiaohua [School of Mathematics and Computational Science, Zhongshan University Guangzhou 510275 (China); Department of Computer Science, Jiangxi Normal University, Nanchang 330027 (China); Zhao Meichun [School of Mathematics and Computational Science, Zhongshan University Guangzhou 510275 (China); Department of Mathematics, Guangdong University of Finance, Gunangzhou 510521 (China); Zhang Yanbin [School of Mathematics and Computational Science, Zhongshan University Guangzhou 510275 (China)


    This paper studies stability and synchronization of hyperchaos systems via a fuzzy-model-based control design methodology. First, we utilize a Takagi-Sugeno fuzzy model to represent a hyperchaos system. Second, we design fuzzy-model-based controllers for stability and synchronization of the system, based on so-called 'parallel distributed compensation (PDC)'. Third, we reduce a question of stabilizing and synchronizing hyperchaos systems to linear matrix inequalities (LMI) so that convex programming techniques can solve these LMIs efficiently. Finally, the generalized Lorenz hyperchaos system is employed to illustrate the effectiveness of our designing controller.

  1. Effective stability for generalized Hamiltonian systems

    CONG; Fuzhong; LI; Yong


    An effective stability result for generalized Hamiltonian systems is obtained by applying the simultaneous approximation technique due to Lochak. Among these systems,dimensions of action variables and angle variables might be distinct.

  2. Robust integral stabilization of regular linear systems

    XU Chengzheng; FENG Dexing


    We consider regular systems with control and observation. We prove some necessary and sufficient condition for an exponentially stable regular system to admit an integral stabilizing controller. We propose also some robust integral controllers when they exist.

  3. Power system dynamics and control

    Kwatny, Harry G


    This monograph explores a consistent modeling and analytic framework that provides the tools for an improved understanding of the behavior and the building of efficient models of power systems. It covers the essential concepts for the study of static and dynamic network stability, reviews the structure and design of basic voltage and load-frequency regulators, and offers an introduction to power system optimal control with reliability constraints. A set of Mathematica tutorial notebooks providing detailed solutions of the examples worked-out in the text, as well as a package that will enable readers to work out their own examples and problems, supplements the text. A key premise of the book is that the design of successful control systems requires a deep understanding of the processes to be controlled; as such, the technical discussion begins with a concise review of the physical foundations of electricity and magnetism. This is followed by an overview of nonlinear circuits that include resistors, inductors, ...

  4. Global stabilization of a Lorenz system

    李世华; 田玉平


    In this paper,using feedback linearizing technique,we show that a Lorenz system can be considered as a cascade system.Moreover,this system satisfies the assumptions of global stabilization of cascade systems.Thus continuous state feedback control laws are proposed to globally stabilize the Lorenz system at the equilibrium point.Simulation results are presented to verify our method.This method can be further generalized to other chaotic systems such as Chen system,coupled dynamos system,etc.

  5. Stability of dynamic response of suspension bridges

    Capsoni, Antonio; Ardito, Raffaele; Guerrieri, Andrea


    The potential occurrence of internal parametric resonance phenomena has been recently indicated as a potential contributory cause of the appearance of critical dynamic states in long-span suspension bridges. At the same time, suspension bridges, in view of their flexibility, are prone to aeroelastic response, such as vortex shedding, torsional divergence and flutter. In this paper, a non-linear dynamic model of a suspension bridge is devised, with the purpose of providing a first attempt toward a unified framework for the study of aeroelastic and internal resonance instabilities. Inspired by the pioneering work of Herrmann and Hauger, the analyses have been based on a linearized formulation that is able to represent the main structural non-linear effects and the coupling given by aerodynamic forces. The results confirm that the interaction between aeroelastic effects and non-linear internal resonance leads to unstable conditions for wind speeds which can be lower than the critical threshold for standard aeroelastic predictions.

  6. Adaptive stabilization for cascade nonlinear systems

    陈岚萍; 王洪元; 吴波


    An adaptive controller of full state feedback for certain cascade nonlinear systems achieving input-to-state stability with respect to unknown bounded disturbance is designed using backstepping and control Lyapunov function (CLF)techniques. We show that unknown bounded disturbance can be estimated by update laws, which requires less information on unknown disturbance, as a part of stabilizing control. The design method achieves the desired property: global robust stability. Our contribution is illustrated with the example of a disturbed pendulum.

  7. V-NIP Ceaser: Video Stabilization System

    Manzoor, Kamran; Ahmed, Atique; Ahmad, Sohail; Manzoor, Umar; Nefti, Samia

    In this paper, we propose a practical and robust approach of video stabilization that produces full-frame stabilized videos with good visual quality. While most previous methods end up with producing low resolution stabilized videos, our completion method produces full-frame videos by temporally filling in missing frame parts by locally aligning required data from neighboring frames. The proposed system has been evaluated on large number of real life videos; results were very promising and support the implementation of the solution.

  8. Dynamic security assessment processing system

    Tang, Lei

    The architecture of dynamic security assessment processing system (DSAPS) is proposed to address online dynamic security assessment (DSA) with focus of the dissertation on low-probability, high-consequence events. DSAPS upgrades current online DSA functions and adds new functions to fit into the modern power grid. Trajectory sensitivity analysis is introduced and its applications in power system are reviewed. An index is presented to assess transient voltage dips quantitatively using trajectory sensitivities. Then the framework of anticipatory computing system (ACS) for cascading defense is presented as an important function of DSAPS. ACS addresses various security problems and the uncertainties in cascading outages. Corrective control design is automated to mitigate the system stress in cascading progressions. The corrective controls introduced in the dissertation include corrective security constrained optimal power flow, a two-stage load control for severe under-frequency conditions, and transient stability constrained optimal power flow for cascading outages. With state-of-the-art computing facilities to perform high-speed extended-term time-domain simulation and optimization for large-scale systems, DSAPS/ACS efficiently addresses online DSA for low-probability, high-consequence events, which are not addressed by today's industrial practice. Human interference is reduced in the computationally burdensome analysis.

  9. Relationship between Core Stability Muscle Endurance and Static and Dynamic Balance in Basketball Players

    farzaneh saki


    Full Text Available Objective: Balancing is the most basic function of the neuromuscular system in performing all simple and complex activities that contribute to health-related physical fitness. Core stability may be a contributing factor to static and dynamic balance. The aim of this study was to investigate the relationship between core stability muscle endurance and static and dynamic balance in basketball players. Methods: 100 basketball players (50 female and 50 male players were selected randomly based on the including criteria.To evaluate core stability muscle strength, a set of tests from core stability exercises was used. Static and dynamic balance were evaluated by Bass Stick and Y balance test respectively. Normality of the data was evaluated using the Kolmogorov Smirnoff test. Data analysis was performed by Spearman product moment coefficient test and independent samples t test. Significant level of p&le0/05 was used in all statistical analyses. Results: Results of t-test showed no significant difference between static balance in boys and girls, while significant differences were observed between dynamic balance and core stability in males and females. In other words, core stability and dynamic balance in boys were more than girls. Also, the results of correlation analysis showed a significant relationship between core stability and dynamic balance (p=0.00 However, no significant relationship was observed between core stability and static balance (p=0.451. Conclusion: Due to the correlation between muscle endurance and dynamic balance in the present study, it can be implied that core stability exercises can improve balance.

  10. Robust decentralized adaptive stabilization for a class of interconnected systems

    Zhaojing WU; Xuejun XIE; Siying ZHANG


    The robust decentralized adaptive output-feedback stabilization for a class of interconnected systems with static and dynamic interconnections by using the MT-filters and backstepping design method is studied. By introducing a new filtered tramformation, the adaptive laws were derived for measurement. Under the assumption of the nonlinear growth conditions imposed on the nonlinear interconnections and by constructing the error system and using a new proof method, the global stability of the closed-loop system was effectively analyzed, and the exponential convergence of all the signals except for parameter estimates were guaranteed.

  11. Optical-Mechanical System for Stabilizing an Inverted Pendulum

    Kuzyakov, O. N.; Andreeva, M. A.


    Controlling open-loop unstable systems is a common benchmark for designing the algorithms to maintain the equilibrium state of anthropomorphous technical devices used within control theory. In this connection, considerable attention is currently being focused on the problem of stabilizing the inverted pendulum system. In this work, the execution of swinging-up the pendulum and, subsequently, maintaining its upward equilibrium state is presented with the help of the laboratory bench TP-802 by Festo Didactics and the movement control device. The configuration of dynamic system for stabilizing the inverted pendulum is offered. The algorithms to swing-up the pendulum and balance it around its upright position are offered as well.

  12. Gyroscopic stabilization and indefimite damped systems

    Pommer, Christian

    a class of feasibel skew-Hermitian matrices A depending on the choise of M. The theory can be applied to dynamical systems of the form x''(t) + ( dD + g G) x'(t) + K x(t) = 0 where G is a skew symmetric gyrocopic matrix, D is a symmetric indefinite damping matrix and K > 0 is a positive definite stiffness......An important issue is how to modify a given unstable matrix in such a way that the resulting matrix is stable. We investigate in general under which condition a matrix M+A is stable,where M is an arbitrary matrix and A is skew-Hermitian. We show that if trace(M) > 0 it is always possible to find...... matrix. d and g are scaling factors used to control the stability of the system. It is quite astonnishing that when the damping matrix D is indefinite the system can under certain conditions be stable even if there are no gyroscopic forces G present The Lyapunov matrix equation is used to predict...

  13. Stabilization of chaotic and non-permanent food-web dynamics

    Williams, R. J.; Martinez, N. D.


    Several decades of dynamical analyses of food-web networks[CITE] have led to important insights into the effects of complexity, omnivory and interaction strength on food-web stability[CITE]. Several recent insights[CITE] are based on nonlinear bioenergetic consumer-resource models[CITE] that display chaotic behavior in three species food chains[CITE] which can be stabilized by omnivory[CITE] and weak interaction of a fourth species[CITE]. We slightly relax feeding on low-density prey in these models by modifying standard food-web interactions known as “typeII” functional responses[CITE]. This change drastically alters the dynamics of realistic systems containing up to ten species. Our modification stabilizes chaotic dynamics in three species systems and reduces or eliminates extinctions and non-persistent chaos[CITE] in ten species systems. This increased stability allows analysis of systems with greater biodiversity than in earlier work and suggests that dynamic stability is not as severe a constraint on the structure of large food webs as previously thought. The sensitivity of dynamical models to small changes in the predator-prey functional response well within the range of what is empirically observed suggests that functional response is a crucial aspect of species interactions that must be more precisely addressed in empirical studies.

  14. Generalized Hill-Stability Criteria for Hierarchical Three-Body Systems at Arbitrary Inclinations

    Grishin, Evgeni; Zenati, Yossef; Michaely, Erez


    A fundamental aspect of the three-body problem is the stability of triple systems. Most stability studies have focused on the co-planar three-body problem, deriving analytic criteria for the dynamical stability of such pro/retrograde systems. Numerical studies of inclined systems phenomenologically mapped their stability regions, but neither explain their physical origin, nor provided satisfactory fit for the dependence of stability on the inclination. Here we present a novel approach to study the stability of hierarchical three-body systems at arbitrary inclinations. This approach accounts not only for the instantaneous stability of such systems, but also for the secular stability and evolution through Lidov-Kozai cycles and evection. Thereby we are able to generalize the Hill-stability criteria to arbitrarily inclined triple systems, and explain the existence of quasi-stable regimes and characterize the inclination dependence of their stability. We complement the analytic treatment with an extensive numeric...

  15. Interactive Dynamic-System Simulation

    Korn, Granino A


    Showing you how to use personal computers for modeling and simulation, Interactive Dynamic-System Simulation, Second Edition provides a practical tutorial on interactive dynamic-system modeling and simulation. It discusses how to effectively simulate dynamical systems, such as aerospace vehicles, power plants, chemical processes, control systems, and physiological systems. Written by a pioneer in simulation, the book introduces dynamic-system models and explains how software for solving differential equations works. After demonstrating real simulation programs with simple examples, the author

  16. Some results on stability of difference systems

    Xiao-Song Yang


    Full Text Available This paper presents some new results on existence and stability of equilibrium or periodic points for difference systems. First sufficient conditions of existence of asymptotically stable equilibrium point as well as the asymptotic stability of given equilibrium point are given for second order or delay difference systems. Then some similar results on existence of asymptotically stable periodic (equilibrium points to general difference systems are presented.

  17. Nanodomain stabilization dynamics in plasma membranes of biological cells

    Das, Tamal; Maiti, Tapas K.; Chakraborty, Suman


    We discover that a synergistically amplifying role of stabilizing membrane proteins and continuous lipid recycling can explain the physics governing the stability, polydispersity, and dynamics of lipid raft domains in plasma membranes of biological cells. We establish the conjecture using a generalized order parameter based on theoretical formalism, endorsed by detailed scaling arguments and domain mapping. Quantitative agreements with morphological distributions of raft complexes, as obtained from Förster resonance energy transfer based visualization, support the present theoretical conjecture.

  18. 基于振荡能量流的双馈风力发电系统动态稳定控制%A Dynamic Stability Control Strategy of Doubly-Fed Wind Power System Based on Transient Energy Flow

    周香珍; 张顺


    提出了一种改善双馈风电场并网系统动态稳定性的控制策略。系统的振荡能量和暂态能量具有一致性,消耗振荡能量的元件能够加速系统不平衡能量的衰减,具有正阻尼。以此为基础,研究了以消耗振荡能量为目标的双馈风电场动态稳定控制方法,并讨论了机组运行极限对控制效果的影响,分析了风电场无功补偿的必要性。控制策略利用双馈风电机组快速有功、无功调节特性,暂存系统不平衡能量,并为系统提供无功补偿,改善系统的动态响应,提高系统稳定性。在DigSILENT/Power Factory中进行了仿真分析,验证了所提出控制策略的有效性及其对电网稳定性的贡献。%A novel control strategy to enhance the dynamic stability of grid-connected wind farm based on doubly-fed induction generator ( DFIG ) was presented. The oscillation energy of system was consistent with its transient energy,the element dissipating energy had positive contribution to the attenuation of unbalancing energy and had positive damping. Then a dynamic stability control strategy based on oscillation energy consumption was studied, the impacts of DFIG operation limits on the control were also discussed, and analyzing the necessity of reactive power compensation for wind farm. The control strategy storage unbalanced energy temporarily and provided fast reactive power compensation by making use of the DFIG fast active and reactive power regulation characteristic, it could improve the dynamic stability of the system. A testing system including a DFIG-based wind farm was realized using DigSILENT/Power Factory, the strategy validation and the contribution to power system stability enhancement were verified by simulation.

  19. Stability Criterion for Discrete-Time Systems

    K. Ratchagit


    Full Text Available This paper is concerned with the problem of delay-dependent stability analysis for discrete-time systems with interval-like time-varying delays. The problem is solved by applying a novel Lyapunov functional, and an improved delay-dependent stability criterion is obtained in terms of a linear matrix inequality.

  20. On formalism and stability of switched systems

    Leth, John-Josef; Wisniewski, Rafal


    In this paper, we formulate a uniform mathematical framework for studying switched systems with piecewise linear partitioned state space and state dependent switching. Based on known results from the theory of differential inclusions, we devise a Lyapunov stability theorem suitable for this class...... of switched systems. With this, we prove a Lyapunov stability theorem for piecewise linear switched systems by means of a concrete class of Lyapunov functions. Contrary to existing results on the subject, the stability theorems in this paper include Filippov (or relaxed) solutions and allow infinite switching...

  1. System design description PFP thermal stabilization



    The purpose of this document is to provide a system design description and design basis for the Plutonium Finishing P1ant (PFP) Thermal Stabilization project. The sources of material for this project are residues scraped from glovebox floors and materials already stored in vault storage that need further stabilizing to meet the 3013 storage requirements. Stabilizing this material will promote long term storage and reduced worker exposure. This document addresses: function design, equipment, and safety requirements for thermal stabilization of plutonium residues and oxides.

  2. Heisenberg picture approach to the stability of quantum Markov systems

    Pan, Yu, E-mail:, E-mail:; Miao, Zibo, E-mail:, E-mail: [Research School of Engineering, Australian National University, Canberra, ACT 0200 (Australia); Amini, Hadis, E-mail: [Edward L. Ginzton Laboratory, Stanford University, Stanford, California 94305 (United States); Gough, John, E-mail: [Institute of Mathematics and Physics, Aberystwyth University, SY23 3BZ Wales (United Kingdom); Ugrinovskii, Valery, E-mail: [School of Engineering and Information Technology, University of New South Wales at ADFA, Canberra, ACT 2600 (Australia); James, Matthew R., E-mail: [ARC Centre for Quantum Computation and Communication Technology, Research School of Engineering, Australian National University, Canberra, ACT 0200 (Australia)


    Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, which extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks.

  3. Heisenberg picture approach to the stability of quantum Markov systems

    Pan, Yu; Amini, Hadis; Miao, Zibo; Gough, John; Ugrinovskii, Valery; James, Matthew R.


    Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, which extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks.

  4. Impulsive dynamics and stabilization of a single wheel robot

    Ou Yongsheng; Wu Xinyu; Xu Yangsheng


    The impulsive motion of a dynamically stabilized robot-Gyrover, which is a single-wheel gyroscopically stabilized robot is studied. A method based on the D' Alembert-Lagrange principle is proposed to develop the impulsive dynamic model of the single wheel robot. This method that can be used to find ways to investigate a single wheel mobile robot rolling on a rough terrain is tested using the experimental platform Gyrover. The conditions of falling over without actuators are addressed. Simulations that validate the analysis are provided as well.

  5. Pedicle Screw-Based Posterior Dynamic Stabilization: Literature Review

    Dilip K. Sengupta


    Full Text Available Posterior dynamic stabilization (PDS indicates motion preservation devices that are aimed for surgical treatment of activity related mechanical low back pain. A large number of such devices have been introduced during the last 2 decades, without biomechanical design rationale, or clinical evidence of efficacy to address back pain. Implant failure is the commonest complication, which has resulted in withdrawal of some of the PDS devices from the market. In this paper the authors presented the current understanding of clinical instability of lumbar motions segment, proposed a classification, and described the clinical experience of the pedicle screw-based posterior dynamic stabilization devices.


    李根国; 朱正佑; 程昌钧


    The dynamic stability of simple supported viscoelastic column, subjected to a periodic axial force, is investigated. The viscoelastic material was assumed to obey the fractional derivative constitutive relation. The governing equation of motion was derived as a weakly singular Volterra integro-partial-differential equation, and it was simplified into a weakly singular Volterra integro-ordinary-differential equation by the Galerkin method. In terms of the averaging method, the dynamical stability was analyzed. A new numerical method is proposed to avoid storing all history data. Numerical examples are presented and the numerical results agree with the analytical ones.

  7. Estimation of multiply digital process control system extractive distillation stability

    V. S. Kudryashov


    Full Text Available An approach to stability analysis of digital control systems associated non-stationary object on the example of the rectification process. Object modeling with cross-connections and the control scheme of the described system, discrete transfer functions in the shift operators. The equations of connection for each output of the closed-loop system. To solve this problem developed an algorithm for estimating the margin of stability of multivariable digital control systems based on the discrete root criterion, comprising the following main stages: obtaining of the characteristic polynomial of the closed-loop system for each output; computation of eigenvalues of the system matrix in the state space to determine roots of the characteristic equation and the stability of the system; determination of the stability and margin of stability by the deviation of maximum module of the root from the boundary of the high variability. To obtain the characteristic polynomial of a as discrete models of controllers and channels of IP object-use the transfer function of the first order with transport delay. The simulation was performed at different parameters of the control object, which is characterized by a stable and an unstable state of the system. VA-den analysis of the numerical values of the roots and character of their location on the complex plane, which to you-water that the system is stable or unstable. To confirm the obtained results were calculated and presented dynamic characteristics of the closed-loop system under different conditions, which confirm the initial assessment, the root criterion. To determine the factor stability of multivariable digital systems is proposed to use the deviation of the maximum root of the characteristic equation from the stability boundary. The obtained results apply to the class of symmetric multivariable control objects. The approach to assessing the sustainability of multivariable system regulation can be effectively

  8. Reduction Principles and the Stabilization of Closed Sets for Passive Systems

    El-Hawwary, Mohamed I


    In this paper we explore the stabilization of closed invariant sets for passive systems, and present conditions under which a passivity-based feedback asymptotically stabilizes the goal set. Our results rely on novel reduction principles allowing one to extrapolate the properties of stability, attractivity, and asymptotic stability of a dynamical system from analogous properties of the system on an invariant subset of the state space.

  9. Stationary dynamical systems

    Furstenberg, Hillel


    Following works of Furstenberg and Nevo and Zimmer we present an outline of a theory of stationary (or m-stationary) dynamical systems for a general acting group G equipped with a probability measure m. Our purpose is two-fold: First to suggest a more abstract line of development, including a simple structure theory. Second, to point out some interesting applications; one of these is a Szemeredi type theorem for SL(2,R).

  10. Research on Dynamics and Stability in the Stairs-Climbing of a Tracked Mobile Robot

    Weijun Tao


    Full Text Available Aiming at the functional requirement of climbing up the stairs, the dynamics and stability during a tracked mobile robot's climbing of stairs is studied. First, from the analysis of its cross-country performance, the mechanical structure of the tracked mobile robot is designed and the hardware composition of its control system is given. Second, based on the analysis to its stairs-climbing process, the dynamical model of stairs-climbing is established by using the classical mechanics method. Next, the stability conditions for its stairs-climbing are determined and an evaluation method of its stairs-climbing stability is proposed, based on a mechanics analysis on the robot's backwards tumbling during the stairs-climbing process. Through simulation and experiments, the effectiveness of the dynamical model and the stability evaluation method of the tracked mobile robot in stairs-climbing is verified, which can provide design and analysis foundations for the tracked mobile robots' stairs-climbing.

  11. Network dynamics and systems biology

    Norrell, Johannes A.

    The physics of complex systems has grown considerably as a field in recent decades, largely due to improved computational technology and increased availability of systems level data. One area in which physics is of growing relevance is molecular biology. A new field, systems biology, investigates features of biological systems as a whole, a strategy of particular importance for understanding emergent properties that result from a complex network of interactions. Due to the complicated nature of the systems under study, the physics of complex systems has a significant role to play in elucidating the collective behavior. In this dissertation, we explore three problems in the physics of complex systems, motivated in part by systems biology. The first of these concerns the applicability of Boolean models as an approximation of continuous systems. Studies of gene regulatory networks have employed both continuous and Boolean models to analyze the system dynamics, and the two have been found produce similar results in the cases analyzed. We ask whether or not Boolean models can generically reproduce the qualitative attractor dynamics of networks of continuously valued elements. Using a combination of analytical techniques and numerical simulations, we find that continuous networks exhibit two effects---an asymmetry between on and off states, and a decaying memory of events in each element's inputs---that are absent from synchronously updated Boolean models. We show that in simple loops these effects produce exactly the attractors that one would predict with an analysis of the stability of Boolean attractors, but in slightly more complicated topologies, they can destabilize solutions that are stable in the Boolean approximation, and can stabilize new attractors. Second, we investigate ensembles of large, random networks. Of particular interest is the transition between ordered and disordered dynamics, which is well characterized in Boolean systems. Networks at the

  12. Computational Methods for Dynamic Stability and Control Derivatives

    Green, Lawrence L.; Spence, Angela M.; Murphy, Patrick C.


    Force and moment measurements from an F-16XL during forced pitch oscillation tests result in dynamic stability derivatives, which are measured in combinations. Initial computational simulations of the motions and combined derivatives are attempted via a low-order, time-dependent panel method computational fluid dynamics code. The code dynamics are shown to be highly questionable for this application and the chosen configuration. However, three methods to computationally separate such combined dynamic stability derivatives are proposed. One of the separation techniques is demonstrated on the measured forced pitch oscillation data. Extensions of the separation techniques to yawing and rolling motions are discussed. In addition, the possibility of considering the angles of attack and sideslip state vector elements as distributed quantities, rather than point quantities, is introduced.

  13. Innovation networking between stability and political dynamics

    Koch, Christian


    of the contribution is to challenge and transcend these notions and develop an understanding of innovation networks as an interplay between stable and dynamic elements, where political processes in innovation are much more than a disruptive and even a counterproductive feature. It reviews the growing number......This contribution views innovation as a social activity of building networks, using software product development in multicompany alliances and networks as example. Innovation networks are frequently understood as quite stable arrangements characterised by high trust among the participants. The aim...... of studies that highlight the political aspect of innovation. The paper reports on a study of innovation processes conducted within the EU—TSER-programme and a study made under the banner of management of technology. Intensive field studies in two constellations of enterprises were carried out. One...

  14. Global analysis of Ivlev's type predator-prey dynamic systems

    XIAO Hai-bin


    Consider a class of Ivlev's type predator-prey dynamic systems with prey and predator both having linear density restricts. By using the qualitative methods of ODE,the global stability of positive equilibrium and existence and uniqueness of non-small amplitude stable limit cycle are obtained. Especially under certain conditions, it shows that existence and uniqueness of non-small amplitude stable limit cycle is equivalent to the local un-stability of positive equilibrium and the local stability of positive equilibrium implies its global stability. That is to say, the global dynamic of the system is entirely determined by the local stability of the positive equilibrium.

  15. Stability Analysis of Neural Networks-Based System Identification

    Talel Korkobi


    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.

  16. On Nonnegative Solutions of Fractional q-Linear Time-Varying Dynamic Systems with Delayed Dynamics

    M. De la Sen


    Full Text Available This paper is devoted to the investigation of nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic linear time-varying systems involving delayed dynamics with delays. The dynamic systems are described based on q-calculus and Caputo fractional derivatives on any order.

  17. Dynamical systems theory for music dynamics

    Boon, J P


    Abstract:We show that, when music pieces are cast in the form of time series of pitch variations, the concepts and tools of dynamical systems theory can be applied to the analysis of {\\it temporal dynamics} in music. (i) Phase space portraits are constructed from the time series wherefrom the dimensionality is evaluated as a measure of the {\\pit global} dynamics of each piece. (ii) Spectral analysis of the time series yields power spectra (\\sim f^{-\

  18. Dynamic control of the space tethered system

    Malashin, A. A.; Smirnov, N. N.; Bryukvina, O. Yu.; Dyakov, P. A.


    We discuss the problem of simultaneous dynamical stabilization and suppression of transverse and longitudinal vibrations of the space tethered system deployed along a certain trajectory. The dynamics of the system is described by a system of nonlinear partial differential equations for the longitudinal and transverse waves and we consider a non-classical version of the problem with one moving boundary. We formulate a mathematical model and perform the analytic and numerical analysis of the boundary control problem based on the Lyapunov method. A scheme of the deployment mechanism is suggested. It includes a control torque and transverse displacement of the boundary and ensures stable deployment of the whole system.



    In this article, criteria of eventual stability are established for impulsive differential systems using piecewise continuous Lyapunov functions. The sufficient conditions that are obtained significantly depend on the moments of impulses. An example is discussed to illustrate the theorem.

  20. The Kinetic Stabilizer: A Route to Simpler Tandem Mirror Systems?

    Post, R


    This paper discusses a new approach to an MHD stabilizing technique for magnetic fusion systems of the axisymmetric ''open-ended'' variety. The concept is adaptable to tandem-mirror systems and would result in a major simplification of such systems, accompanied by a substantial improvement in their confinement characteristics, The paper first discusses the present impetus to find a simpler and less expensive route to fusion than that offered by the mainline approach, the tokamak. The history of magnetic fusion research shows that closed and open systems exhibit very different confinement characteristics. Closed systems, such as the tokamak, the stellarator, or the reversed-field pinch have cross-field transport that is dominated by plasma turbulence. By contrast, there are examples of open-systems where turbulence, if present at all, was at such low levels that the transport agreed with ''classical'' predictions. The clearest examples are ones in which the field geometry was axiymmetric. However axisymmetric mirror systems are subject to MHD instability. Thus in the years following the famous Ioffe experiment, most open systems have employed asymmetric magnetic fields, with attendant problems of complexity and enhanced cross-field transport. This paper proposes a new means of stabilizing axisymmetric mirror-based systems. The idea, called the ''Kinetic Stabilizer'' has roots in experiments performed with the axisymmetric Gas Dynamic Trap at Novosibirsk. In these experiments, performed in a high collisionality plasma regime, it was shown that the presence of the effluent plasma in the positive-curvature expanding-field region outside the mirrors was effective in stabilizing a high-beta (30 percent) confined plasma against MHD modes. In the plasmas of tandem-mirror systems the density of the effluent plasma is too low to employ this method of stabilization. The Kinetic Stabilizer solves this problem by using

  1. Stability and boundary stabilization of 1-D hyperbolic systems

    Bastin, Georges


    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...

  2. Butschli Dynamic Droplet System

    Armstrong, R.; Hanczyc, M.


    of a technology with living properties. Otto Butschli first described the system in 1898, when he used alkaline water droplets in olive oil to initiate a saponification reaction. This simple recipe produced structures that moved and exhibited characteristics that resembled, at least superficially, the amoeba. We......Dynamical oil-water systems such as droplets display lifelike properties and may lend themselves to chemical programming to perform useful work, specifically with respect to the built environment. We present Butschli water-in-oil droplets as a model for further investigation into the development...... to the oil phase), qualify this system as an example of living technology. The analysis of the Butschli droplets suggests that a set of conditions may precede the emergence of lifelike characteristics and exemplifies the richness of this rudimentary chemical system, not only for artificial life...

  3. Dynamics of mechanical systems with variable mass

    Belyaev, Alexander


    The book presents up-to-date and unifying formulations for treating dynamics of different types of mechanical systems with variable mass. The starting point is overview of the continuum mechanics relations of balance and jump for open systems from which extended Lagrange and Hamiltonian formulations are derived. Corresponding approaches are stated at the level of analytical mechanics with emphasis on systems with a position-dependent mass and at the level of structural mechanics. Special emphasis is laid upon axially moving structures like belts and chains, and on pipes with an axial flow of fluid. Constitutive relations in the dynamics of systems with variable mass are studied with particular reference to modeling of multi-component mixtures. The dynamics of machines with a variable mass are treated in detail and conservation laws and the stability of motion will be analyzed. Novel finite element formulations for open systems in coupled fluid and structural dynamics are presented.

  4. Stability and response bounds of non-conservative linear systems

    Kliem, Wolfhard; Pommer, Christian


    This paper develops a stability theorem and response bounds for non-conservative systems of the form MX + (D + G)x + (K + N)x = f(t), with hermitian positive-definite matrices M, D and K, and skew-hermitian matrices G and N. To this end, we first find a Lyapunov function by solving the Lyapunov...... matrix equation. Then, if a system satisfies the condition of the stability theorem, the associated Lyapunov function can be used to obtain response bounds for the norms as well as for the individual coordinates of the solution. Examples from rotor dynamics illustrate the results....

  5. Quadratic stabilization for uncertain stochastic systems

    Jun'e FENG; Weihai ZHANG


    This paper discusses the robust quadratic stabilization control problem for stochastic uncertain systems,where the uncertain matrix is norm bounded,and the external disturbance is a stochastic process.Two kinds of controllers are designed,which include state feedback case and output feedback case.The conditions for the robust quadratic stabilization of stochastic uncertain systems are given via linear matrix inequalities.The detailed design methods are presented.Numerical examples show the effectiveness of our results.

  6. Weak and strong stabilization of linear systems

    Mohamed OUZAHRA; Hamid BOURRAY; Asmae KAMAL; Rachid El AYADI


    We study the problem of stabilizing a distributed linear system on a subregion of its geometrical domain. We are concerned with two methods: the first approach enables us to characterize a stabilizing control via the steady state Riccati equation, and the second one is based on decomposing the state space into two suitable subspaces and studying the projections of the initial system onto such subspaces. The obtained results are performed through various examples.

  7. Invariance and stability for bounded uncertain systems.

    Peng, T. K. C.


    The positive limit sets of the solutions of a contingent differential equation are shown to possess an invariance property. In this connection the 'invariance principle' in the theory of Lyapunov stability is extended to systems with unknown, bounded, time-varying parameters, and thus to a large and important class of nonautonomous systems. Asymptotic stability criteria are obtained and applied to guaranteed cost control problems.

  8. Stability of fractional positive nonlinear systems

    Kaczorek Tadeusz


    Full Text Available The conditions for positivity and stability of a class of fractional nonlinear continuous-time systems are established. It is assumed that the nonlinear vector function is continuous, satisfies the Lipschitz condition and the linear part is described by a Metzler matrix. The stability conditions are established by the use of an extension of the Lyapunov method to fractional positive nonlinear systems.

  9. Nonlinear Slewing Spacecraft Control Based on Exergy, Power Flow, and Static and Dynamic Stability

    Robinett, Rush D.; Wilson, David G.


    This paper presents a new nonlinear control methodology for slewing spacecraft, which provides both necessary and sufficient conditions for stability by identifying the stability boundaries, rigid body modes, and limit cycles. Conservative Hamiltonian system concepts, which are equivalent to static stability of airplanes, are used to find and deal with the static stability boundaries: rigid body modes. The application of exergy and entropy thermodynamic concepts to the work-rate principle provides a natural partitioning through the second law of thermodynamics of power flows into exergy generator, dissipator, and storage for Hamiltonian systems that is employed to find the dynamic stability boundaries: limit cycles. This partitioning process enables the control system designer to directly evaluate and enhance the stability and performance of the system by balancing the power flowing into versus the power dissipated within the system subject to the Hamiltonian surface (power storage). Relationships are developed between exergy, power flow, static and dynamic stability, and Lyapunov analysis. The methodology is demonstrated with two illustrative examples: (1) a nonlinear oscillator with sinusoidal damping and (2) a multi-input-multi-output three-axis slewing spacecraft that employs proportional-integral-derivative tracking control with numerical simulation results.

  10. Uncertain dynamical systems: A differential game approach

    Gutman, S.


    A class of dynamical systems in a conflict situation is formulated and discussed, and the formulation is applied to the study of an important class of systems in the presence of uncertainty. The uncertainty is deterministic and the only assumption is that its value belongs to a known compact set. Asymptotic stability is fully discussed with application to variable structure and model reference control systems.


    WANG Hong-li; FENG Jian-feng; SHEN Fei; SUN Jing


    A food chain made up of two typical algae and a zooplankton was considered. Based on ecological eutrophication, interaction of the algal and the prey of the zooplankton, a nutrient nonlinear dynamic system was constructed. Using the methods of the modern nonlinear dynamics, the bifurcation behaviors and stability of the model equations by changing the control parameter r were discussed. The value of r for bifurcation point was calculated, and the stability of the limit cycle was also discussed. The result shows that through quasi-periodicity bifurcation the system is lost in chaos.

  12. Stability Analysis on Speed Control System of Autonomous Underwater Vehicle

    LI Ye; PANG Yong-jie; WAN Lei; WANG Fang; LIAO Yu-lei


    The stability of the motion control system is one of the decisive factors of the control quality for Autonomous Underwater Vehicle (AUV).The divergence of control,which the unstable system may be brought about,is fatal to the operation of AUV.The stability analysis of the PD and S-surface speed controllers based on the Lyapunov' s direct method is proposed in this paper.After decoupling the six degree-of-freedom (DOF) motions of the AUV,the axial dynamic behavior is discussed and the condition is deduced,in which the parameters selection within stability domain can guarantee the system asymptotically stable.The experimental results in a tank and on the sea have successfully verified the algorithm reliability,which can be served as a good reference for analyzing other AUV nonlinear control systems.

  13. Nanojets: Electrification Energetics Dynamics Stability and Breakup


    computer algorithms to the point that we could simulate...been no prior atomistic simulations in these areas. A significant component or our progress to date has been the development of parallel computer ... algorithms that can efficiently model systems as complex as a colloid thruster, yet be flexible enough to allow modeling of other interesting phenomena involving the electrodynamics of dielectric and charged

  14. Dynamic flight stability of a hovering model dragonfly.

    Liang, Bin; Sun, Mao


    The longitudinal dynamic flight stability of a model dragonfly at hovering flight is studied, using the method of computational fluid dynamics to compute the stability derivatives and the techniques of eigenvalue and eigenvector analysis for solving the equations of motion. Three natural modes of motion are identified for the hovering flight: one unstable oscillatory mode, one stable fast subsidence mode and one stable slow subsidence mode. The flight is dynamically unstable owing to the unstable oscillatory mode. The instability is caused by a pitch-moment derivative with respect to horizontal velocity. The damping force and moment derivatives (with respect to horizontal and vertical velocities and pitch-rotational velocity, respectively) weaken the instability considerably. The aerodynamic interaction between the forewing and the hindwing does not have significant effect on the stability properties. The dragonfly has similar stability derivatives, hence stability properties, to that of a one-wing-pair insect at normal hovering, but there are differences in how the derivatives are produced because of the highly inclined stroke plane of the dragonfly.

  15. Dynamic stability of deformable elements of one class of aeroelastic constructions

    Velmisov, Petr A.; Ankilov, Andrey V.; Semenova, Elizaveta P.


    At designing of the constructions and the devices interacting with the flow of gas or liquid, it is necessary to solve the problems associated with the investigation of the stability required for their functioning and operational reliability. The definition of stability of an elastic body corresponds to the Lyapunov's concept of stability of dynamical system. A mathematical model of the device relating to the vibration technique, which is intended for intensification of technological processes, for example, the process of mixing, is considered. The action of these devices is based on the oscillations of elastic elements at the flowing around gas or liquid flow. The dynamic stability of the elastic element, located inside of the flow channel with the subsonic flow of gas or liquid (in an ideal model of a compressible environment) is investigated. The model is described by coupled system of partial differential equations for the unknown functions - the potential of the gas velocity and deformation of the elastic element. On the basis of the construction of functional, the sufficient conditions of the dynamical stability, imposing restrictions on the free-stream velocity of the gas, the flexural stiffness of the elastic element, and other parameters of the mechanical system are obtained. The examples of construction of the stability regions for particular parameters of the mechanical system are presented.

  16. Adaptive Stabilization for Uncertain Nonholonomic Dynamic Mobile Robots Based on Visual Servoing Feedback

    YANG Fang; WANG Chao-Li


    The stabilization problem of nonholonomic dynamic mobile robots with a fixed (ceiling-mounted) camera is addressed in this paper.First,a camera-object visual servding kinematic model is introduced by utilizing the pin-hole camera model and a kinematic stabilizing controller is given for the kinematic model.Then,an adaptive sliding mode controller is designed to stabilize uncertain dynamic mobile robot in the presence of parametric uncertainties associated with the camera system.The proposed controller is robust not only to structured uncertainty such as mass variation but also to unstructured one such as disturbances.The stability of the proposed control system and the boundedness of estimated parameters are rigorously proved by Lyapunov method.Simulation results are presented to illustrate the performance of the control law.

  17. Stability of Surface Nanobubbles: A Molecular Dynamics Study

    Maheshwari, Shantanu; Hoef, van der Martin; Zhang, Xuehua; Lohse, Detlef


    The stability and growth or dissolution of a single surface nanobubble on a chemically patterned surface are studied by molecular dynamics simulations of binary mixtures consisting of Lennard-Jones (LJ) particles. Our simulations reveal how pinning of the three-phase contact line on the surface can

  18. Dynamic Transfer Schemes and Stability of International Climate Coalitions

    Nagashima, M.N.; Dellink, R.B.; Ierland, van E.C.


    This paper examines the formation and stability of coalitions in international climate agreements with a combined game-theoretic and integrated assessment model. The empirical model comprises twelve regions and investigates partial coalition formation in a one-shot cartel game. We argue that a dynam

  19. Brane/antibrane dynamics and KKLT stability

    Polchinski, Joseph


    String theory has few or no stable nonsupersymmetric or de Sitter vacua, only metastable ones. Antibranes are a simple source of supersymmetry breaking, as in the KKLT model, but various arguments have been given that these fail to produce the desired vacua. Proper analysis of the system requires identifying the correct effective field theories at various scales. We find that it reproduces the KKLT conclusions. This is an expanded version of a talk presented at SUSY 2015, Lake Tahoe.

  20. Near periodicity in dynamical systems



    The notion of near periodicity is shown to be equivalent to that of weak near periodicity in dynamical systems. A sufficient condition for the positive near periodicity of a point in dynamical systems is given. The structure of nearly periodic dynamical systems is discussed, and a condition is proved to be necessary and sufficient for a dynamical system on a local compact space to be positively nearly periodic.

  1. BioFlex Dynamic Stabilization System in Treatment of Lumbar Degenerative Diseases%BioFlex动态稳定系统治疗腰椎退行性变疾病

    黄升峰; 李展振; 张海存; 吴沧陆; 黄明


    BioFlex动态稳定系统是目前临床运用较多的后路非融合系统之一,具有容易安装、对组织损伤小、去除病变并保留手术节段功能等优点,治疗腰椎退行性变疾病疗效肯定。%BioFlex dynamic stabilization system is one of the currently most used posterior non-fusion systems, which has some advantages such as easy installing, slight tissue damage, lesions removing and the functions of operated segments can be kept, and significant curative effect would be got when it's used in treatment of lumbar degenerative diseases.

  2. Toluene stability Space Station Rankine power system

    Havens, V. N.; Ragaller, D. R.; Sibert, L.; Miller, D.


    A dynamic test loop is designed to evaluate the thermal stability of an organic Rankine cycle working fluid, toluene, for potential application to the Space Station power conversion unit. Samples of the noncondensible gases and the liquid toluene were taken periodically during the 3410 hour test at 750 F peak temperature. The results obtained from the toluene stability loop verify that toluene degradation will not lead to a loss of performance over the 30-year Space Station mission life requirement. The identity of the degradation products and the low rates of formation were as expected from toluene capsule test data.

  3. Gyroscopic Stabilization of Indefinite Damped Systems

    Kliem, Wolfhard; Müller, Peter C.


    Modelling of mechanical systems with sliding bearings, or with dry friction, can lead to linear systems with an indefinite damping matrix. We ask under what conditions such a system is unstable (the indefiniteness of the damping matrix is not enough) and under what conditions we can stabilize...

  4. Study on dynamic anti-sliding stability of a high gravity dam considering complex dam foundation

    Deng-hong CHEN; Cheng-bin DU


    There existed some limitations when analyzing the anti-sliding seismic stability of dam-foundation system by traditional pseudo-static method and response spectrum method. The dynamic strength reduction method was used to study on the deep anti-sliding stability of a high gravity dam considering complex dam foundation under strong earthquake-induced ground action. The static analysis was firstly carried out by reducing the shear strength parameters of the dam foundation’s rock mass with equal...

  5. Dynamics and Stability of Rolling Viscoelastic Tires

    Potter, Trevor [Univ. of California, Berkeley, CA (United States)


    Current steady state rolling tire calculations often do not include treads because treads destroy the rotational symmetry of the tire. We describe two methodologies to compute time periodic solutions of a two-dimensional viscoelastic tire with treads: solving a minimization problem and solving a system of equations. We also expand on work by Oden and Lin on free spinning rolling elastic tires in which they disovered a hierachy of N-peak steady state standing wave solutions. In addition to discovering a two-dimensional hierarchy of standing wave solutions that includes their N-peak hiearchy, we consider the eects of viscoelasticity on the standing wave solutions. Finally, a commonplace model of viscoelasticity used in our numerical experiments led to non-physical elastic energy growth for large tire speeds. We show that a viscoelastic model of Govindjee and Reese remedies the problem.

  6. The validity and reliability of a dynamic neuromuscular stabilization-heel sliding test for core stability.

    Cha, Young Joo; Lee, Jae Jin; Kim, Do Hyun; You, Joshua Sung H


    Core stabilization plays an important role in the regulation of postural stability. To overcome shortcomings associated with pain and severe core instability during conventional core stabilization tests, we recently developed the dynamic neuromuscular stabilization-based heel sliding (DNS-HS) test. The purpose of this study was to establish the criterion validity and test-retest reliability of the novel DNS-HS test. Twenty young adults with core instability completed both the bilateral straight leg lowering test (BSLLT) and DNS-HS test for the criterion validity study and repeated the DNS-HS test for the test-retest reliability study. Criterion validity was determined by comparing hip joint angle data that were obtained from BSLLT and DNS-HS measures. The test-retest reliability was determined by comparing hip joint angle data. Criterion validity was (ICC2,3) = 0.700 (pcore stability measures. Test-retest reliability was (ICC3,3) = 0.953 (pcore stability measures. Test-retest reliability data suggests that DNS-HS core stability was a reliable test for core stability. Clinically, the DNS-HS test is useful to objectively quantify core instability and allow early detection and evaluation.

  7. Dynamical stability and evolution of the discs of Sc galaxies

    Fuchs, B


    We examine the local stability of galactic discs against axisymmetric density perturbations with special attention to the different dynamics of the stellar and gaseous components. In particular the discs of the Milky Way and of NGC 6946 are studied. The Milky Way is shown to be stable, whereas the inner parts of NGC 6946, a typical Sc galaxy from the Kennicutt (1989) sample, are dynamically unstable. The ensuing dynamical evolution of the composite disc is studied by numerical simulations. The evolution is so fierce that the stellar disc heats up dynamically on a short time scale to such a degree, which seems to contradict the morphological appearance of the galaxy. The star formation rate required to cool the disc dynamically is estimated. Even if the star formation rate in NGC 6946 is at present high enough to meet this requirement, it is argued that the discs of Sc galaxies cannot sustain such a high star formation rate for longer periods.


    ZHENG Hui-ping; XUE Yu-sheng; CHEN Yu-shu


    Rotor-bearings systems applied widely in industry are nonlinear dynamic systems of multi-degree-of-freedom. Modem concepts on design and maintenance call for quantitative stability analysis. Using trajectory based stability-preserving and dimensional-reduction, a quanttative stability analysis method for rotor systems is presented. At first, an n-dimensional nonlinear non-autonomous rotor system is decoupled into n subsystems after numerical integration. Each of them has only onedegree-of-freedom and contains time-varying parameters to represent all other state variables. In this way, n-dimensional trajectory is mapped into a set of one-dimensional trajectories. Dynamic central point (DCP) of a subsystem is then defined on the extended phase plane, namely, force-position plane. Characteristics of curves on the extended phase plane and the DCP's kinetic energy difference sequence for general motion in rotor systems are studied. The corresponding stability margins of trajectory are evaluated quantitatively. By means of the margin and its sensitivity analysis, the critical parameters of the period doubling bifurcation and the Hopf bifurcation in a flexible rotor supported by two short journal beatings with nonlinear suspensionare are determined.

  9. International Conference on Dynamical Systems : Theory and Applications


    The book is a collection of contributions devoted to analytical, numerical and experimental techniques of dynamical systems, presented at the international conference "Dynamical Systems: Theory and Applications," held in Lódz, Poland on December 7-10, 2015. The studies give deep insight into new perspectives in analysis, simulation, and optimization of dynamical systems, emphasizing directions for future research. Broadly outlined topics covered include: bifurcation and chaos in dynamical systems, asymptotic methods in nonlinear dynamics, dynamics in life sciences and bioengineering, original numerical methods of vibration analysis, control in dynamical systems, stability of dynamical systems, vibrations of lumped and continuous sytems, non-smooth systems, engineering systems and differential equations, mathematical approaches to dynamical systems, and mechatronics.

  10. International Conference on Dynamical Systems : Theory and Applications


    The book is the second volume of a collection of contributions devoted to analytical, numerical and experimental techniques of dynamical systems, presented at the international conference "Dynamical Systems: Theory and Applications," held in Lódz, Poland on December 7-10, 2015. The studies give deep insight into new perspectives in analysis, simulation, and optimization of dynamical systems, emphasizing directions for future research. Broadly outlined topics covered include: bifurcation and chaos in dynamical systems, asymptotic methods in nonlinear dynamics, dynamics in life sciences and bioengineering, original numerical methods of vibration analysis, control in dynamical systems, stability of dynamical systems, vibrations of lumped and continuous sytems, non-smooth systems, engineering systems and differential equations, mathematical approaches to dynamical systems, and mechatronics.

  11. Robust stability test for 2-D continuous-discrete systems with interval parameters



    It is revealed that the dynamic stability of 2-D recursive continuous-discrete systems with interval parameters involves the problem of robust Hurwitz-Schur stability of bivariate polynomials family. It is proved that the HurwitzSchur stability of the denominator polynomials of the systems is necessary and sufficient for the asymptotic stability of the 2-D hybrid systems. The 2-D hybrid transformation, i.e. 2-D Laplace-Z transformation, has been proposed to solve the stability analysis of the 2-D continuous-discrete systems, to get the 2-D hybrid transfer functions of the systems. The edge test for the Hurwitz-Schur stability of interval bivariate polynomials is introduced. The Hurwitz-Schur stability of the interval family of 2-D polynomials can be guaranteed by the stability of its finite edge polynomials of the family. An algorithm about the stability test of edge polynomials is given.

  12. The design of image stabilization control system

    Lin, Zhe; Wu, Chunnan; Yu, Fei; Kang, Xiaojun


    For high resolution satellite remote sensing cameras, the line of sight (LOS) moving during the image exposure period will cause the modulation transfer function (MTF) degradation and image blurring. Image stabilization component is used to improve image quality by actively removing the apparent motion induced by vibration, tracking error and attitude instability. In this paper, the image stabilization component is considered as a kind of closed loop servo control system, and the image stabilization effect is converted into servo control performance for research. Firstly, the image stabilization servo loop scheme and transfer function model are constructed and the LOS jitter is considered as the output of a stochastic system derived by white-Gaussian noise. Based on the proposed model, the demand boundary of jitter rejection function is described, and the design criterion to be satisfied is obtained according to the requirement of image stabilization performance. And then, a discrete Kalman estimation algorithm is introduced into image stabilization servo loop to filter out the noise caused by pixel-shift sensor (PSS) and compensate for the delay due to the PSS measurement. Based on the given design criterion, the control law is designed by using the output of Kalman filter. The computer simulation is achieved to show that the proposed control strategy can significantly improve the image stabilization performance.

  13. Stability and Transport in Magnetic Confinement Systems

    Weiland, Jan


    Stability and Transport in Magnetic Confinement Systems provides an advanced introduction to the fields of stability and transport in tokamaks. It serves as a reference for researchers with its highly-detailed theoretical background, and contains new results in the areas of analytical nonlinear theory of transport using kinetic theory and fluid closure. The use of fluid descriptions for advanced stability and transport problems provide the reader with a better understanding of this topic. In addition, the areas of nonlinear kinetic theory and fluid closure gives the researcher the basic knowledge of a highly relevant area to the present development of transport physics.

  14. Dynamic Stability of Viscoelastic Plates with Finite Deformation and Shear Effects

    李晶晶; 程昌钧; 等


    Based on Reddy's theory of plates with higher-order shear deformations and the Boltzmann superposition principles,the governing equations were established for dynamic stability of viscoelastic plates with finite deformations taking account of shear effects,The Galerkin method was applied to simplify the set of equations.The numerical methods in nonlinear dynamics were used to solve the simplified system.It could e seen that there are plenty of dynamic properties for this kind of viscoelastic plates under transverse harmonic loads.The influences of the transverse shear deformations and material parameter on the dynamic behavior of nonlinear viscoelatic plates were investigated.

  15. A new strategy for transient stability using augmented generator control and local dynamic braking

    Dorsey, J.; Jiang, H.; Habetler, T. [Georgia Inst. of Tech., Atlanta, GA (United States); Qu, Z. [University of Central Florida, Orlando, FL (United States)


    A decentralized automatic control strategy for significantly improving the transient stability of a large power system is introduced. The strategy combines local dynamic braking and a straightforward augmentation of the existing turbine / governor control system that uses only local feedback. The brake resistor, which employs thick film, metal oxide technology, has no inductance and is of very low resistance, allowing its use during fault to show a generator`s acceleration. Simulation results using the 39 Bus New England system show that the strategy dramatically increases the global stability of a power system. (author) 15 refs., 7 figs., 1 tab.

  16. Dynamics of stochastic systems

    Klyatskin, Valery I


    Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. The well known example of Brownian particle suspended in fluid and subjected to random molecular bombardment laid the foundation for modern stochastic calculus and statistical physics. Other important examples include turbulent transport and diffusion of particle-tracers (pollutants), or continuous densities (''''oil slicks''''), wave propagation and scattering in randomly inhomogeneous media, for instance light or sound propagating in the turbulent atmosphere.Such models naturally render to statistical description, where the input parameters and solutions are expressed by random processes and fields.The fundamental problem of stochastic dynamics is to identify the essential characteristics of system (its state and evolution), and relate those to the input parameters of ...

  17. Cosmological dynamical systems

    Leon, Genly


    In this book are studied, from the perspective of the dynamical systems, several Universe models. In chapter 1 we give a bird's eye view on cosmology and cosmological problems. Chapter 2 is devoted to a brief review on some results and useful tools from the qualitative theory of dynamical systems. They provide the theoretical basis for the qualitative study of concrete cosmological models. Chapters 1 and 2 are a review of well-known results. Chapters 3, 4, 5 and 6 are devoted to our main results. In these chapters are extended and settled in a substantially different, more strict mathematical language, several results obtained by one of us in arXiv:0812.1013 [gr-qc]; arXiv:1009.0689 [gr-qc]; arXiv:0904.1577[gr-qc]; and arXiv:0909.3571 [hep-th]. In chapter 6, we provide a different approach to the subject discussed in astro-ph/0503478. Additionally, we perform a Poincar\\'e compactification process allowing to construct a global phase space containing all the cosmological information in both finite and infinite...

  18. Recent Advances in Heliogyro Solar Sail Structural Dynamics, Stability, and Control Research

    Wilkie, W. Keats; Warren, Jerry E.; Horta, Lucas G.; Lyle, Karen H.; Juang, Jer-Nan; Gibbs, S. Chad; Dowell, Earl H.; Guerrant, Daniel V.; Lawrence, Dale


    Results from recent NASA sponsored research on the structural dynamics, stability, and control characteristics of heliogyro solar sails are summarized. Specific areas under investigation include coupled nonlinear finite element analysis of heliogyro membrane blade with solar radiation pressure effects, system identification of spinning membrane structures, and solarelastic stability analysis of heliogyro solar sails, including stability during blade deployment. Recent results from terrestrial 1-g blade dynamics and control experiments on "rope ladder" membrane blade analogs, and small-scale in vacuo system identification experiments with hanging and spinning high-aspect ratio membranes will also be presented. A low-cost, rideshare payload heliogyro technology demonstration mission concept is used as a mission context for these heliogyro structural dynamics and solarelasticity investigations, and is also described. Blade torsional dynamic response and control are also shown to be significantly improved through the use of edge stiffening structural features or inclusion of modest tip masses to increase centrifugal stiffening of the blade structure. An output-only system identification procedure suitable for on-orbit blade dynamics investigations is also developed and validated using ground tests of spinning sub-scale heliogyro blade models. Overall, analytical and experimental investigations to date indicate no intractable stability or control issues for the heliogyro solar sail concept.

  19. Stabilization of a Nonlinear Delay System

    Walid Arouri


    Full Text Available Problem statement: The analysis and control of delayed systems are becoming more and more research topics in progress. This is mainly due to the fact that the delay is frequently encountered in technological systems. This can affect their significantly operations. Most control command laws are based on current digital computers and delays are intrinsic to the process or in the control loop caused by the transmission time control sequences, or computing time. The delay may affect one or more states of the considered system. It may also affect the establishment of the command. Several studies have investigated the stability of delay systems under the assumption that the delay is a variable phenomenon; such variation is considered to be bounded or limited to facilitate analysis of the system. In this study we propose a modelling of delayed system by using the multimodels and switched system theory. The analysis of stability is based on the use of second Lyapunov method. The issued stability conditions are expressed as Bilinear Matrix Inequalities impossible to resolve. That’s why we propose the same original relaxations to come over this difficulty, an example of induction machine is given to illustrate over approach. Approach: We propose to use the control theory developed for switched systems to synthesis a control laws for the stabilisation of delays system. Results: We stabilize the induction machine around many operating points despite the non linearities. Conclusion: The developed method is less conservative and less pessimistic than the used classical methods.

  20. A Study on the Stability of a Ballistic System Under Random Excitation

    Yang, Chunyan; Xu, Lina; Huang, Yong


    The stability analysis of a ballistic system is important for its design and performance. The eigenvalue method is presented to get the stability of the linear part of the ballistic system. Combining the eigenvalue method and stochastic dynamical theory, we can get the bifurcation diagram of the pitch angle for the deterministic system and the bifurcation diagram for the system with random disturbance. By comparing the two situations, the dynamic behavior at the feature point was analyzed.

  1. Dynamical behavior and Jacobi stability analysis of wound strings

    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)


    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.)

  2. Application of ISOBAR Dynamic Stabilization System in Treatment of Degenerative Lumbar Disease%腰椎退行性疾病ISOBAR动态固定早期临床观察

    李忠海; 王诗媛; 付强; 马辉; 唐昊; 张秋林


    目的 探讨后路ISOBAR动态稳定系统在腰椎退行性疾病治疗中的应用指征、短期疗效和安全性.方法 将自2008年9月~2009年12月收治腰椎退行性疾病(L4、5)28例,随机分为常规减压加ISOBAR动态固定组(治疗组14例)和传统椎间融合内固定组(对照组14例).结果 所有患者获得6~24个月(平均14.6个月)的随访.术后随访VAS评分及ODI均得到明显改善,与术前相比均有显著性差异(P <0.001).对照组术后L4、5及L2~S1节段的ROM均较术前明显下降(P<0.05),而相邻节段L3、4、L5S1的(活动度)ROM无显著变化(P>0.05).治疗组术后各节段和L2~S1的ROM较术前均无明显变化(P>0.05).结论 ISOBAR动态固定系统治疗单节段腰椎退变性疾病取得了满意的短期临床疗效,但没有充分证据证明动态固定技术可以取代传统的融合技术,手术适应证的合理选择十分重要.%Objective To assess the indication,safety and efficacy of the dynamic stabilization system (the ISOBAR system) in the treatment of degenerative lumbar disease. Methods Between September 2008 and December 2009, 28 consecutive patients seeking medical treatment for one level (L4、5) lumbar degenerative disease in our department were included in this study. They were randomly and evenly assigned into an experimental group of decompression and dynamic stabilization with the ISOBAR system (n=14) and a control group of traditional interbody fusion (n=14). Results All cases were followed up for 14.6 months averagely. The postoperative VAS and ODI showed a significant postoperative reduction of disability during the whole period of follow-up (P 0.05). In the dynamic stabilization group, no signifcant changes of global lumbar spine ROM (L2~S1) and segmental ROM (index level and cranial/caudal adjacent levels) were seen (P >0.05). Conclusion This study shows that monosegmental posterior dynamic stabilization with the ISOBAR system demonstrates excellent outcome

  3. Stability of posterior dynamic stabilization system fixation for the treatment of lumbar disc herniation%后路动态稳定系统内固定治疗腰椎间盘突出症的稳定性评价☆

    丁立祥; 陈迎春; 张亘瑷; 姚琦; 侯宇


    BACKGROUND: Posterior dynamic stabilization system can be used to maintain the vertebral motion segment and reduce the degeneration of vertebral body adjacent segment. OBJECTIVE: To investigate the efficacy and stability of posterior dynamic stabilization system for the treatment of lumbar disc herniation. METHODS: Eighteen patients with degenerative lumbar disease and treated with posterior decompression and posterior dynamic stabilization system internal fixation in the Department of Orthopedics, Beijing Shijitan Hospital Affiliated to Capital Medical University from February 2009 to June 2011 were selected, included 11 male patients and seven female patients, the age was 32-67 years old and averaged in 45 years old. The visual analogue scale score was used for pain assessment and the Oswestry disability index was used for clinical evaluation, the flexion and hyperextension X-ray films were used to measure the activity of lumbar intervertebral disc and the adjacent intervertebral disc after posterior dynamic stabilization system fixation. RESULTS AND CONCLUSION: Al the patients were fol owed-up for 20-45 months, averaged in 38 months. The visual analogue scale score before posterior dynamic stabilization system fixation was 7.1-9.4 points, and averaged 8.3 points, the postoperative score was 0-3.1 points, averaged 1.5 points, the improvement rate of visual analogue scale score was 81.5%. The Oswestry disability index before posterior dynamic stabilization system fixation was 35-81 points (average 60 points) and 0-45 points after fixation (average 22 points), and the improvement rate of Oswestry disability index was 63.3%. There was one case of loosening after posterior dynamic stabilization system fixation, one case had lower extremity nerve symptoms transient increasing and relieved after 3 months. The average range of motion after fixation was 5.3°. The posterior dynamic stabilization system for the treatment of lumbar disc herniation can maintain the range of

  4. Chaos control of chaotic dynamical systems using backstepping design

    Yassen, M.T. [Mathematics Department, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)] e-mail:


    This work presents chaos control of chaotic dynamical systems by using backstepping design method. This technique is applied to achieve chaos control for each of the dynamical systems Lorenz, Chen and Lue systems. Based on Lyapunov stability theory, control laws are derived. We used the same technique to enable stabilization of chaotic motion to a steady state as well as tracking of any desired trajectory to be achieved in a systematic way. Numerical simulations are shown to verify the results.

  5. Robust Stability of Switched Systems

    Sloth, Christoffer; Wisniewski, Rafael


    This paper presents a linear programming-based method for finding Lyapunov functions of switched systems with polynomial vector fields and parametric uncertainties. We propose to utilize a certificate of positivity in the Bernstein basis to find a Lyapunov function. A certificate of positivity...... in the Bernstein basis always exists if a polynomial is positive, and the Bernstein basis is shown to be well conditioned....

  6. On the dynamics of turbulent transport near marginal stability

    Diamond, P.H. [California Univ., San Diego, La Jolla, CA (United States). Dept. of Physics]|[General Atomics, San Diego, CA (United States); Hahm, T.S. [Princeton Univ., NJ (United States). Plasma Physics Lab.


    A general methodology for describing the dynamics of transport near marginal stability is formulated. Marginal stability is a special case of the more general phenomenon of self-organized criticality. Simple, one field models of the dynamics of tokamak plasma self-organized criticality have been constructed, and include relevant features such as sheared mean flow and transport bifurcations. In such models, slow mode (i.e. large scale, low frequency transport events) correlation times determine the behavior of transport dynamics near marginal stability. To illustrate this, impulse response scaling exponents (z) and turbulent diffusivities (D) have been calculated for the minimal (Burgers) and sheared flow models. For the minimal model, z = 1 (indicating ballastic propagation) and D {approximately}(S{sub 0}{sup 2}){sup 1/3}, where S{sub 0}{sup 2} is the noise strength. With an identically structured noise spectrum and flow with shearing rate exceeding the ambient decorrelation rate for the largest scale transport events, diffusion is recovered with z = 2 and D {approximately} (S{sub 0}{sup 2}){sup 3/5}. This indicates a qualitative change in the dynamics, as well as a reduction in losses. These results are consistent with recent findings from {rho} scaling scans. Several tokamak transport experiments are suggested.

  7. Dynamic Phasors-Based Modeling and Stability Analysis of Droop-Controlled Inverters for Microgrid Applications

    Guo, Xiaoqiang; Lu, Zhigang; Wang, Baocheng


    System modeling and stability analysis is one of the most important issues of inverter-dominated microgrids. It is useful to determine the system stability and optimize the control parameters. The complete small signal models for the inverter-dominated microgrids have been developed which are very...... accurate and could be found in literature. However, the modeling procedure will become very complex when the number of inverters in microgrid is large. One possible solution is to use the reduced-order small signal models for the inverter-dominated microgrids. Unfortunately, the reduced-order small signal...... models fail to predict the system instabilities. In order to solve the problem, a new modeling approach for inverter-dominated microgrids by using dynamic phasors is presented in this paper. Our findings indicate that the proposed dynamic phasor model is able to predict accurately the stability margins...

  8. AMD-stability and the classification of planetary systems

    Laskar, J.; Petit, A. C.


    We present here in full detail the evolution of the angular momentum deficit (AMD) during collisions as it was described in Laskar (2000, Phys. Rev. Lett., 84, 3240). Since then, the AMD has been revealed to be a key parameter for the understanding of the outcome of planetary formation models. We define here the AMD-stability criterion that can be easily verified on a newly discovered planetary system. We show how AMD-stability can be used to establish a classification of the multiplanet systems in order to exhibit the planetary systems that are long-term stable because they are AMD-stable, and those that are AMD-unstable which then require some additional dynamical studies to conclude on their stability. The AMD-stability classification is applied to the 131 multiplanet systems from The Extrasolar Planet Encyclopaedia database for which the orbital elements are sufficiently well known. The AMD-stability coefficients of selected planetary systems are available at the CDS via anonymous ftp to ( or via

  9. Dihedral influence on lateral-directional dynamic stability on large aspect ratio tailless flying wing aircraft

    Song Lei; Yang Hua; Zhang Yang; Zhang Haoyu; Huang Jun


    The influence of dihedral layout on lateral-directional dynamic stability of the tailless flying wing aircraft is discussed in this paper. A tailless flying wing aircraft with a large aspect ratio is selected as the object of study, and the dihedral angle along the spanwise sections is divided into three segments. The influence of dihedral layouts is studied. Based on the stability derivatives cal-culated by the vortex lattice method code, the linearized small-disturbance equations of the lateral modes are used to determine the mode dynamic characteristics. By comparing 7056 configurations with different dihedral angle layouts, two groups of stability optimized dihedral layout concepts are created. Flight quality close to Level 2 requirements is achieved in these optimized concepts without any electric stability augmentation system.

  10. Research on Dynamics and Stability in the Stairs-climbing of a Tracked Mobile Robot

    Weijun Tao; Yi Ou; Hutian Feng


    Aiming at the functional requirement of climbing up the stairs, the dynamics and stability during a tracked mobile robot's climbing of stairs is studied. First, from the analysis of its cross-country performance, the mechanical structure of the tracked mobile robot is designed and the hardware composition of its control system is given. Second, based on the analysis to its stairs-climbing process, the dynamical model of stairs-climbing is established by using the classical mechanics method. N...

  11. Dynamics and Adaptive Control for Stability Recovery of Damaged Aircraft

    Nguyen, Nhan; Krishnakumar, Kalmanje; Kaneshige, John; Nespeca, Pascal


    This paper presents a recent study of a damaged generic transport model as part of a NASA research project to investigate adaptive control methods for stability recovery of damaged aircraft operating in off-nominal flight conditions under damage and or failures. Aerodynamic modeling of damage effects is performed using an aerodynamic code to assess changes in the stability and control derivatives of a generic transport aircraft. Certain types of damage such as damage to one of the wings or horizontal stabilizers can cause the aircraft to become asymmetric, thus resulting in a coupling between the longitudinal and lateral motions. Flight dynamics for a general asymmetric aircraft is derived to account for changes in the center of gravity that can compromise the stability of the damaged aircraft. An iterative trim analysis for the translational motion is developed to refine the trim procedure by accounting for the effects of the control surface deflection. A hybrid direct-indirect neural network, adaptive flight control is proposed as an adaptive law for stabilizing the rotational motion of the damaged aircraft. The indirect adaptation is designed to estimate the plant dynamics of the damaged aircraft in conjunction with the direct adaptation that computes the control augmentation. Two approaches are presented 1) an adaptive law derived from the Lyapunov stability theory to ensure that the signals are bounded, and 2) a recursive least-square method for parameter identification. A hardware-in-the-loop simulation is conducted and demonstrates the effectiveness of the direct neural network adaptive flight control in the stability recovery of the damaged aircraft. A preliminary simulation of the hybrid adaptive flight control has been performed and initial data have shown the effectiveness of the proposed hybrid approach. Future work will include further investigations and high-fidelity simulations of the proposed hybrid adaptive Bight control approach.

  12. Data Systems Dynamic Simulator

    Rouff, Christopher; Clark, Melana; Davenport, Bill; Message, Philip


    The Data System Dynamic Simulator (DSDS) is a discrete event simulation tool. It was developed for NASA for the specific purpose of evaluating candidate architectures for data systems of the Space Station era. DSDS provides three methods for meeting this requirement. First, the user has access to a library of standard pre-programmed elements. These elements represent tailorable components of NASA data systems and can be connected in any logical manner. Secondly, DSDS supports the development of additional elements. This allows the more sophisticated DSDS user the option of extending the standard element set. Thirdly, DSDS supports the use of data streams simulation. Data streams is the name given to a technique that ignores packet boundaries, but is sensitive to rate changes. Because rate changes are rare compared to packet arrivals in a typical NASA data system, data stream simulations require a fraction of the CPU run time. Additionally, the data stream technique is considerably more accurate than another commonly-used optimization technique.

  13. Wallis动态稳定系统治疗腰椎间盘突出症临床研究%A clinical study on the Wallis dynamic stabilization system in the treatment of lumbar disc herniation



    Objective To explore the early efficacy of the Wallis interspinous dynamic stabilization system in the treatment of lumbar disc herniation,and whether to reduce early reexamination after lumbar discectomy and to reduce degenerative of lumbar vertebra.Methods 108 patients with lumbar disc herniation received fenestration discectomy and implantation of the Wallis interspinous dynamic stabilization system.The surgical process,surgical duration,amount of intraoperative bleeding,and early postoperative recovery were observed; The VAS scores and JOA scores were used for pre-and post-operative assessment.Results The procedure for implanting Wallis interspinous dynamic stabilization system was simple and had shorter duration.The patients has less injury and quicker postoperative recovery.The VAS score was 3.5 ± 1.0 on day 3 and 2.3 ± 0.5 on day 7 after surgery; the JOA score was 25.1-+ 1.2 on month 1 and 24.5 ± 2.0 on month 6.Conclusions Wallis interspinous dynamic stabilization system is safe,simple,and efficacious in the treatment of lumbar disc herniation complicated by lumbar spinal degeneration.It can effectively reduce the short-term postoperative recurrence of lumbar disc herniation.%目的 研究Wallis棘突间态稳定系统在腰椎间盘突出症治疗中的早期疗效;是否有效减少腰椎间盘摘除术后早期复查、减缓腰椎退变.方法 对108例腰椎间盘突出症患者行开窗髓核摘除术,术中植入Wallis棘突间动态稳定系统,观察手术操作过程、手术用时、术中出血量及术后早期恢复情况,并通过VAS评分、JOA评分进行术前术后评估.结果 Wallis棘突间动态稳定系统植入手术操作简单,用时短,组织损伤小,术后恢复顺利,术后3天VAS评分(3.5±1.0)分,术后7天(2.3±0.5)分,JOA评分术后1个月(25.1±1.2)分,术后6个月(24.5±2.0)分.结论 Wallis棘突间动态稳定系统治疗伴有腰椎退变的腰椎间盘突出症安全简便,早期效果良好,有效减少短期椎间盘术后复发.

  14. Optimal Subinterval Selection Approach for Power System Transient Stability Simulation

    Soobae Kim


    Full Text Available Power system transient stability analysis requires an appropriate integration time step to avoid numerical instability as well as to reduce computational demands. For fast system dynamics, which vary more rapidly than what the time step covers, a fraction of the time step, called a subinterval, is used. However, the optimal value of this subinterval is not easily determined because the analysis of the system dynamics might be required. This selection is usually made from engineering experiences, and perhaps trial and error. This paper proposes an optimal subinterval selection approach for power system transient stability analysis, which is based on modal analysis using a single machine infinite bus (SMIB system. Fast system dynamics are identified with the modal analysis and the SMIB system is used focusing on fast local modes. An appropriate subinterval time step from the proposed approach can reduce computational burden and achieve accurate simulation responses as well. The performance of the proposed method is demonstrated with the GSO 37-bus system.

  15. Duality in Dynamic Fuzzy Systems

    Yoshida, Yuji


    This paper shows the resolvent equation, the maximum principle and the co-balayage theorem for a dynamic fuzzy system. We define a dual system for the dynamic fuzzy system, and gives a duality for Snell's optimal stopping problem by the dual system.

  16. Hybrid dynamical systems observation and control

    Defoort, Michael


    This book is a collection of contributions defining the state of current knowledge and new trends in hybrid systemssystems involving both continuous dynamics and discrete events – as described by the work of several well-known groups of researchers. Hybrid Dynamical Systems presents theoretical advances in such areas as diagnosability, observability and stabilization for various classes of system. Continuous and discrete state estimation and self-triggering control of nonlinear systems are advanced. The text employs various methods, among them, high-order sliding modes, Takagi–Sugeno representation and sampled-data switching to achieve its ends. The many applications of hybrid systems from power converters to computer science are not forgotten; studies of flexible-joint robotic arms and – as representative biological systems – the behaviour of the human heart and vasculature, demonstrate the wide-ranging practical significance of control in hybrid systems. The cross-disciplinary origins of study ...

  17. Modeling and Stability Analysis of Wedge Clutch System

    Jian Yao


    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.

  18. Aeromechanical stability analysis of a multirotor vehicle with application to hybrid heavy lift helicopter dynamics

    Venkatesan, C.; Friedmann, P. P.


    The Hybrid Heavy Lift Helicopter (HHLH) is a potential candidate vehicle aimed at providing heavy lift capability at low cost. This vehicle consists of a buoyant envelope attached to a supporting structure. Four rotor systems are also attached to the supporting structure. Nonlinear equations of motion capable of modeling the dynamics of this multi-rotor/support frame/vehicle system have been developed and used to study the fundamental aeromechanical stability characteristics of this class of vehicles. The mechanism of coupling between the blades, supporting structure and rigid body modes is identified and the effect of buoyancy ratio (buoyant lift/total weight) on the vehicle dynamics is studied. It is shown that dynamics effects have a major role in the design of such vehicles. The analytical model developed is also useful for studying the aeromechanical stability of single rotor and tandem rotor coupled rotor/fuselage systems.

  19. Aeromechanical stability analysis of a multirotor vehicle with application to hybrid heavy lift helicopter dynamics

    Venkatesan, C.; Friedmann, P. P.


    The Hybrid Heavy Lift Helicopter (HHLH) is a potential candidate vehicle aimed at providing heavy lift capability at low cost. This vehicle consists of a buoyant envelope attached to a supporting structure. Four rotor systems are also attached to the supporting structure. Nonlinear equations of motion capable of modeling the dynamics of this multi-rotor/support frame/vehicle system have been developed and used to study the fundamental aeromechanical stability characteristics of this class of vehicles. The mechanism of coupling between the blades, supporting structure and rigid body modes is identified and the effect of buoyancy ratio (buoyant lift/total weight) on the vehicle dynamics is studied. It is shown that dynamics effects have a major role in the design of such vehicles. The analytical model developed is also useful for studying the aeromechanical stability of single rotor and tandem rotor coupled rotor/fuselage systems.

  20. Exponential Stability Criteria for Nonautonomous Difference Systems

    Rigoberto Medina


    Full Text Available The aim of this paper is to characterize the exponential stability of linear systems of difference equations with slowly varying coefficients. Our approach is based on the generalization of the freezing method for difference equations combined with new estimates for the norm of bounded linear operators. The main novelty of this work is that we use estimates for the absolute values of entries of a matrix-valued function, instead of bounds on its eigenvalues. By this method, new explicit stability criteria for linear nonautonomous systems are derived.

  1. 电力系统大扰动下暂态电压稳定的动态特征分析%Dynamic eigen analysis of transient voltage stability under large disturbance for power system

    刘彦呈; 王川; 魏一


    A dynamic eigen analysis method is presented aiming at the defects that current voltage stability research results cannot give the explicit criterion about transient voltage stability information. First, this paper establishes an integrated mathematical model reflecting power system transient process with the consideration of speed-adjusting and excitation-control, i.e., Non-linear Differential Algebraic Equations (NDAE). Second, all the eigen values and left, right eigen vectors are solved by using implicit trapezoidal integration method to build Jacobian matrix dynamically in the process of step-by-step integration of NDAE. Finally, this paper calculates all the participating factors of eigen vectors corresponding with all status variables. Then, transient voltage instability criterion is proposed. Simulation results after comparing the method with time domain simulation demonstrate that the transient voltage instability criterion is correct. The paper provides a novel way to research power system transient voltage stability in terms of combining linear system theory with numerical integration.This work is supported by Natural Science Foundation of Liaoning Province (No. 20092148).%针对目前电力系统电压稳定性研究成果难以给出明确的暂态稳定判定信息的缺陷,提出一种电力系统大扰动下暂态电压稳定的动态特征分析方法.该方法首先建立反映电力系统暂态过渡过程的计及调速与励磁控制的综合数学模型,即非线性微分代数方程组(Non-linear Differential Algebraic Equations,NDAE);其次在运用隐式梯形积分法对NDAE进行逐步积分过程中动态生成Jacobian矩阵,并求解出全部特征根及左,右特征向量;最后计算出各个状态变量与之对应特征向量的相关因子,基于此给出暂态电压失稳的判据.该方法通过与时域仿真法的对比结果证明所提出系统暂态电压失稳判据的正确性,为今后从线性系统理论与数值积分

  2. Stability of Nonlinear Stochastic Discrete-Time Systems


    This paper studies the stability for nonlinear stochastic discrete-time systems. First of all, several definitions on stability are introduced, such as stability, asymptotical stability, and pth moment exponential stability. Moreover, using the method of the Lyapunov functionals, some efficient criteria for stochastic stability are obtained. Some examples are presented to illustrate the effectiveness of the proposed theoretical results.

  3. Stability Criteria for Volterra Integrodynamic System

    Nusrat Yasmin


    Full Text Available We study conditions under which the solutions of linear Volterra integrodynamic system of the form yΔt=Atyt+∫t0tKt,sysΔs are stable on certain time scales. We construct a number of Lyapunov functionals on time scales from which we obtain necessary and sufficient conditions for stability of Volterra integrodynamic system and also we prove several results concerning qualitative behavior of this system.

  4. Experimental Study on the Dynamic Stability of the IXV Configuration

    Gülhan, Ali; Klevanski, Josef; Gawehn, Thomas


    Dynamic stability of the IXV configuration has been investigated using free oscillation measurement technique in the Trisonic Windtunnel (TMK). In the transonic Mach number range an escalating behavior of the pitching moment damping derivative has been observed, although the vehicle is statically stable. At Mach 0.8 the vehicle showed the most unstable behavior. The instability becomes weaker with increasing Mach number. At Mach number 1.1 the vehicle is only slight...

  5. Structural Optimization of Machine Gun Based on Dynamic Stability Concept

    LI Yong-jian; WANG Rui-lin; ZHANG Ben-jun


    Improving the firing accuracy is a final goal of structural optimization of machine guns. The main factors which affect the dispersion accuracy of machine gun are analyzed. Based on the concept of dynamic stability, a structural optimization model is built up, and the sensitivity of dispersion accuracy to design variables is analyzed. The optimization results of a type of machine gun show that the method is valid, feasible, and can be used as a guide to the structural optimization of other automatic weapons.

  6. Dynamical Behavior and Stability Analysis in a Hybrid Epidemiological-Economic Model with Incubation

    Chao Liu


    Full Text Available A hybrid SIR vector disease model with incubation is established, where susceptible host population satisfies the logistic equation and the recovered host individuals are commercially harvested. It is utilized to discuss the transmission mechanism of infectious disease and dynamical effect of commercial harvest on population dynamics. Positivity and permanence of solutions are analytically investigated. By choosing economic interest of commercial harvesting as a parameter, dynamical behavior and local stability of model system without time delay are studied. It reveals that there is a phenomenon of singularity induced bifurcation as well as local stability switch around interior equilibrium when economic interest increases through zero. State feedback controllers are designed to stabilize model system around the desired interior equilibria in the case of zero economic interest and positive economic interest, respectively. By analyzing corresponding characteristic equation of model system with time delay, local stability analysis around interior equilibrium is discussed due to variation of time delay. Hopf bifurcation occurs at the critical value of time delay and corresponding limit cycle is also observed. Furthermore, directions of Hopf bifurcation and stability of the bifurcating periodic solutions are studied. Numerical simulations are carried out to show consistency with theoretical analysis.

  7. Dynamical behavior and Jacobi stability analysis of wound strings

    Lake, Matthew J


    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 t...

  8. uncertain dynamic systems on time scales

    V. Lakshmikantham


    Full Text Available A basic feedback control problem is that of obtaining some desired stability property from a system which contains uncertainties due to unknown inputs into the system. Despite such imperfect knowledge in the selected mathematical model, we often seek to devise controllers that will steer the system in a certain required fashion. Various classes of controllers whose design is based on the method of Lyapunov are known for both discrete [4], [10], [15], and continuous [3–9], [11] models described by difference and differential equations, respectively. Recently, a theory for what is known as dynamic systems on time scales has been built which incorporates both continuous and discrete times, namely, time as an arbitrary closed sets of reals, and allows us to handle both systems simultaneously [1], [2], [12], [13]. This theory permits one to get some insight into and better understanding of the subtle differences between discrete and continuous systems. We shall, in this paper, utilize the framework of the theory of dynamic systems on time scales to investigate the stability properties of conditionally invariant sets which are then applied to discuss controlled systems with uncertain elements. For the notion of conditionally invariant set and its stability properties, see [14]. Our results offer a new approach to the problem in question.

  9. A Non-equilibrium Thermodynamic Framework for the Dynamics and Stability of Ecosystems

    Michaelian, K


    The population dynamics and stability of ecosystems of interacting species is studied from the perspective of non-equilibrium thermodynamics by assuming that species, through their biotic and abiotic interactions, are units of entropy production and exchange in an open thermodynamic system with constant external constraints. Within the context of the linear theory of irreversible thermodynamics, such a system will naturally evolve towards a stable stationary state in which the production of entropy within the ecosystem is at a local minimum value. It is shown that this extremal condition leads to equations for the stationary (steady) state population dynamics of interacting species, more general than those of Lotka-Volterra, and to conditions on the parameters of the community interaction matrix guaranteeing ecosystem stability. The paradoxical stability of real complex ecosystems thus has a simple explanation within the proposed framework. Furthermore, it is shown that the second law of thermodynamics constr...

  10. Inherent robust stability of driver support systems

    王龙; J.; Ackermann


    Presented are the fact that the transfer function from the front steering angle to yaw rate is strictly positive real, irrespective of the uncertain mass and uncertain velocity, how to determine the positivity margin for this transfer function (some stabilization results are obtained), and how to check the positivity of a controller family. Furthermore,by exploiting the intrinsic structure of system equations and uncertainties, a nonconservative PID stabilization criterion for driver support systems is established. Some interesting results on positivity and connections of PID controllers are shown. Finally, some extreme point results on PID α-stabilization are obtained. These results give certain explanations and justifications for the simulation results performed at German Aerospace Research Center.

  11. Synchronization dynamics of two different dynamical systems

    Luo, Albert C.J., E-mail: [Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805 (United States); Min Fuhong [Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805 (United States)


    Highlights: > Synchronization dynamics of two distinct dynamical systems. > Synchronization, de-synchronization and instantaneous synchronization. > A controlled pendulum synchronizing with the Duffing oscillator. > Synchronization invariant set. > Synchronization parameter map. - Abstract: In this paper, synchronization dynamics of two different dynamical systems is investigated through the theory of discontinuous dynamical systems. The necessary and sufficient conditions for the synchronization, de-synchronization and instantaneous synchronization (penetration or grazing) are presented. Using such a synchronization theory, the synchronization of a controlled pendulum with the Duffing oscillator is systematically discussed as a sampled problem, and the corresponding analytical conditions for the synchronization are presented. The synchronization parameter study is carried out for a better understanding of synchronization characteristics of the controlled pendulum and the Duffing oscillator. Finally, the partial and full synchronizations of the controlled pendulum with periodic and chaotic motions are presented to illustrate the analytical conditions. The synchronization of the Duffing oscillator and pendulum are investigated in order to show the usefulness and efficiency of the methodology in this paper. The synchronization invariant domain is obtained. The technique presented in this paper should have a wide spectrum of applications in engineering. For example, this technique can be applied to the maneuvering target tracking, and the others.

  12. Stability and control of dynamic walking for a five-link planar biped robot with feet

    Chenglong FU; Ken CHEN; Jing XIONG; Leon XU


    During dynamic walking of biped robots, the underactuated rotating degree of freedom (DOF) emerges between the support foot and the ground, which makes the biped model hybrid and dimension-variant. This paper addresses the asymptotic orbit stability for dimension-variant hybrid systems (DVHS). Based on the generalized Poincare map, the stability criterion for DVHS is also presented, and the result is then used to study dynamic walking for a five-link planar biped robot with feet. Time-invariant gait planning and nonlinear control strategy for dynamic walking with flat feet is also introduced. Simulation results indicate that an asymptotically stable limit cycle of dynamic walking is achieved by the proposed method.

  13. Local Dynamic Stability Assessment of Motion Impaired Elderly Using Electronic Textile Pants.

    Liu, Jian; Lockhart, Thurmon E; Jones, Mark; Martin, Tom


    A clear association has been demonstrated between gait stability and falls in the elderly. Integration of wearable computing and human dynamic stability measures into home automation systems may help differentiate fall-prone individuals in a residential environment. The objective of the current study was to evaluate the capability of a pair of electronic textile (e-textile) pants system to assess local dynamic stability and to differentiate motion-impaired elderly from their healthy counterparts. A pair of e-textile pants comprised of numerous e-TAGs at locations corresponding to lower extremity joints was developed to collect acceleration, angular velocity and piezoelectric data. Four motion-impaired elderly together with nine healthy individuals (both young and old) participated in treadmill walking with a motion capture system simultaneously collecting kinematic data. Local dynamic stability, characterized by maximum Lyapunov exponent, was computed based on vertical acceleration and angular velocity at lower extremity joints for the measurements from both e-textile and motion capture systems. Results indicated that the motion-impaired elderly had significantly higher maximum Lyapunov exponents (computed from vertical acceleration data) than healthy individuals at the right ankle and hip joints. In addition, maximum Lyapunov exponents assessed by the motion capture system were found to be significantly higher than those assessed by the e-textile system. Despite the difference between these measurement techniques, attaching accelerometers at the ankle and hip joints was shown to be an effective sensor configuration. It was concluded that the e-textile pants system, via dynamic stability assessment, has the potential to identify motion-impaired elderly.

  14. Dynamic stability of communities of amphibians in short-term-flooded forest ecosystems

    O. V. Zhukov


    Full Text Available The estimation of stability of amphibian populations on the basis of data of population dynamics is given. The paper shows an attempt to estimate the direction of dynamic changes of amphibian populations, and defines the rate of the system deviation from the stationary state due to possible influence of the environmental factors by using concepts such as reactivity, degree of reactivity and flexibility of the system when using their indexes. It is found that populations of amphibians are quite stable with regard to quantifying these species. Characteristic feature is the elasticity of the system. It is confirmed by the elasticity of the system species Bufo bufo (Linnaeus, 1758. TypePelobates fuscus (Laurenti, 1768 is defined as a factor of stability of the system in quantitative terms. Dependenceof dynamics of the population on its size is established using the regression equation. Dynamics of groups depends on the action of possible predictors in response to which the population of B. bufo is not changed. The ecosystem is characterized as a place of interaction between biotic factors and factors of abiotic origin, which are due to the external action. Internal factor of the ecosystem stability is the influence of some amphibian populations on the other ones. The system features sustainable and relatively stable number of B. bufo, which does not affect the level of its stability. Stationary state of the grouping is unstable due to dynamic matrix, which describes the behavior of the group in the vicinity of the first stationary state. The second steady state is stableone, and the system returns to the stationary state with the help of wave-like dynamics. On the basis of our study it is established that the number of groups of amphibians remains stable, the systems behave differently, and dynamics of their return to the stationary state is elastic or reactive one. Еcosystems within lime-ash oak forests in the Central floodplain of the Samarariver

  15. Collective dynamics of multicellular systems

    R Maithreye; C Suguna; Somdatta Sinha


    We have studied the collective behaviour of a one-dimensional ring of cells for conditions when the individual uncoupled cells show stable, bistable and oscillatory dynamics. We show that the global dynamics of this model multicellular system depends on the system size, coupling strength and the intrinsic dynamics of the cells. The intrinsic variability in dynamics of the constituent cells are suppressed to stable dynamics, or modified to intermittency under different conditions. This simple model study reveals that cell–cell communication, system size and intrinsic cellular dynamics can lead to evolution of collective dynamics in structured multicellular biological systems that is significantly different from its constituent single-cell behaviour.


    Duraid F. Ahmed


    Full Text Available      The performance of pressure control system and stability analysis was studied for different types of controllers. A theoretical model for closed-loop system is developed and dynamic behavior of the control system was studied by introducing a step change in the pressure of the inlet stream. The results show that the theoretical response is faster than the experimental response due to the lags of the control valve and measuring elements. The pressure control system is stable for all conditions and for different control action because the real parts of roots of characteristics equation are negative but the response at PID controller is oscillatory stable. when PID controller used the response is improve due to eliminate the offset and stabilizing effect of derivative allow the proportional gain to be increased and increasing the speed of response compared to proportional and proportional-integral controllers.  

  17. The effects of interaction compartments on stability for competitive systems.

    Rozdilsky, Ian D; Stone, Lewi; Solow, Andrew


    The interactions between species are unlikely to be randomly arranged, and there is increasing evidence that most interactions occur within small species sub-groups, or compartments, that do not strongly interact with one another. We examine whether arranging the interactions of a competitive system into compartments influences the system properties of linear stability, feasibility, reactivity, and biomass stability, thereby altering the likelihood of species persistence. Model Lotka-Volterra systems of diffuse competition were analysed with interactions arranged randomly and in compartments. It was found, using a variety of dynamical measures, that arranging interactions into compartments enhances the likelihood of species persistence. Since many natural competitive systems appear to have interactions arranged within compartments, this may be an outcome of the positive attributes that this form of organization offers.

  18. Dynamical Systems for Creative Technology

    van Amerongen, J.


    Dynamical Systems for Creative Technology gives a concise description of the physical properties of electrical, mechanical and hydraulic systems. Emphasis is placed on modelling the dynamical properties of these systems. By using a system’s approach it is shown that a limited number of mathematical

  19. Chaos for Discrete Dynamical System

    Lidong Wang


    Full Text Available We prove that a dynamical system is chaotic in the sense of Martelli and Wiggins, when it is a transitive distributively chaotic in a sequence. Then, we give a sufficient condition for the dynamical system to be chaotic in the strong sense of Li-Yorke. We also prove that a dynamical system is distributively chaotic in a sequence, when it is chaotic in the strong sense of Li-Yorke.

  20. Stationary Stability for Evolutionary Dynamics in Finite Populations

    Marc Harper


    Full Text Available We demonstrate a vast expansion of the theory of evolutionary stability to finite populations with mutation, connecting the theory of the stationary distribution of the Moran process with the Lyapunov theory of evolutionary stability. We define the notion of stationary stability for the Moran process with mutation and generalizations, as well as a generalized notion of evolutionary stability that includes mutation called an incentive stable state (ISS candidate. For sufficiently large populations, extrema of the stationary distribution are ISS candidates and we give a family of Lyapunov quantities that are locally minimized at the stationary extrema and at ISS candidates. In various examples, including for the Moran and Wright–Fisher processes, we show that the local maxima of the stationary distribution capture the traditionally-defined evolutionarily stable states. The classical stability theory of the replicator dynamic is recovered in the large population limit. Finally we include descriptions of possible extensions to populations of variable size and populations evolving on graphs.

  1. Landscape Construction in Dynamical Systems

    Tang, Ying; Yuan, Ruoshi; Wang, Gaowei; Ao, Ping

    The idea of landscape has been recently applied to study various of biological problems. We demonstrate that a dynamical structure built into nonlinear dynamical systems allows us to construct such a global optimization landscape, which serves as the Lyapunov function for the ordinary differential equation. We find exact constructions on the landscape for a class of dynamical systems, including a van der Pol type oscillator, competitive Lotka-Volterra systems, and a chaotic system. The landscape constructed provides a new angle for understanding and modelling biological network dynamics.

  2. Motivational Dynamics in Language Learning: Change, Stability, and Context

    Waninge, Freerkien; Dörnyei, Zoltán; De Bot, Kees


    Motivation as a variable in L2 development is no longer seen as the stable individual difference factor it was once believed to be: Influenced by process-oriented models and principles, and especially by the growing understanding of how complex dynamic systems work, researchers have been focusing increasingly on the dynamic and changeable nature…

  3. Dynamic flight stability of a bumblebee in forward flight

    Yan Xiong; Mao Sun


    The longitudinal dynamic flight stability of a bumblebee in forward flight is studied.The method of computational fluid dynamics is used to compute the aerodynamic derivatives and the techniques of eigenvalue and eigenvector analysis are employed for solving the equations of motion.The primary findings are as the following.The forward flight of the bumblebee is not dynamically stable due to the existence of one(or two)unstable or approximately neutrally stable natural modes of motion.At hovering to medium flight speed[flight speed ue=(0-3.5)m s-1;advance ratio J=0-0.44],the flight is weakly unstable or approximately neutrally stable;at high speed(ue=4.5 m s-1;J=0.57),the flight becomes strongly unstable(initial disturbance double its value in only 3.5 wingbeats).

  4. Dynamics and stability of a vertical water bridge

    Namin, Reza Montazeri


    A vertical connection of water is formed when a high voltage electrode is dipped in and pulled out of a container of deionized water. We considered the formation, stability and dynamical characteristics of this vertical water bridge. For the first time in this field, we observed instabilities in the bridge that led to an oscillatory behaviour which is categorized in three dynamical regimes and supplied explanations on the physics behind these varied motions. We report the formation of macroscopic droplets during this motion, which their dynamics revealed that they are electrically charged. In some cases the droplets would be levitating when the electric force opposes the gravity. Also the steady bridge is thoroughly studied regarding its geometry and a set of quantitative data is presented using dimensionless numbers, which brings the possibility of direct quantitative comparison between theory and experiments. Our results shed light on the physics behind this phenomenon and the horizontal water bridge, which...

  5. Response Based Emergency Control System for Power System Transient Stability

    Huaiyuan Wang


    Full Text Available A transient stability control system for the electric power system composed of a prediction method and a control method is proposed based on trajectory information. This system, which is independent of system parameters and models, can detect the transient stability of the electric power system quickly and provide the control law when the system is unstable. Firstly, system instability is detected by the characteristic concave or convex shape of the trajectory. Secondly, the control method is proposed based on the analysis of the slope of the state plane trajectory when the power system is unstable. Two control objectives are provided according to the methods of acquiring the far end point: one is the minimal cost to restore the system to a stable state; the other one is the minimal cost to limit the maximum swing angle. The simulation indicates that the mentioned transient stability control system is efficient.

  6. Stabilizing equilibrium by linear feedback control for controlling chaos in Chen system

    Costa, V A [Departamento de Ciencias Basicas, Facultad de IngenierIa (UNLP), La Plata (Argentina); Gonzalez, G A, E-mail:, E-mail: [Departamento de Matematica, Facultad de Ingenieria (UBA), Buenos Aires (Argentina)


    Stabilization of a chaotic system in one of its unstable equilibrium points by applying small perturbations is studied. A two-stage control strategy based on linear feedback control is applied. Improvement of system performance is addressed by exploiting the ergodicity of the original dynamics and using Lyapunov stability results for control design. Extension to the not complete observability case is also analyzed.

  7. The Next Generation of High-Speed Dynamic Stability Wind Tunnel Testing (Invited)

    Tomek, Deborah M.; Sewall, William G.; Mason, Stan E.; Szchur, Bill W. A.


    Throughout industry, accurate measurement and modeling of dynamic derivative data at high-speed conditions has been an ongoing challenge. The expansion of flight envelopes and non-conventional vehicle design has greatly increased the demand for accurate prediction and modeling of vehicle dynamic behavior. With these issues in mind, NASA Langley Research Center (LaRC) embarked on the development and shakedown of a high-speed dynamic stability test technique that addresses the longstanding problem of accurately measuring dynamic derivatives outside the low-speed regime. The new test technique was built upon legacy technology, replacing an antiquated forced oscillation system, and greatly expanding the capabilities beyond classic forced oscillation testing at both low and high speeds. The modern system is capable of providing a snapshot of dynamic behavior over a periodic cycle for varying frequencies, not just a damping derivative term at a single frequency.

  8. Laser stabilization using saturated absorption in a cavity QED system

    Tieri, D A; Christensen, Bjarke T R; Thomsen, J W; Holland, M J


    We consider the phase stability of a local oscillator (or laser) locked to a cavity QED system comprised of atoms with an ultra-narrow optical transition. The atoms are cooled to millikelvin temperatures and then released into the optical cavity. Although the atomic motion introduces Doppler broadening, the standing wave nature of the cavity causes saturated absorption features to appear, which are much narrower than the Doppler width. These features can be used to achieve an extremely high degree of phase stabilization, competitive with the current state-of-the-art. Furthermore, the inhomogeneity introduced by finite atomic velocities can cause optical bistability to disappear, resulting in no regions of dynamic instability and thus enabling a new regime accessible to experiments where optimum stabilization may be achieved.

  9. On the Stability of Bilinear Stochastic Systems


    d’Equations Differentielles Stochastiques Lineaires", Journees Stabilite Asymptotique des Systemes Differentiels a Perturbation Aleatoire. CNRS, 1986. [3...for the Lyapunov numbers associated with this equation are given. Bilinear noise models are, after linear ones, the second simplest case of stochastic...give a condition for the stability with probability one of the d-dimensional Ito equation which describes the behavior of such a system dYs = AYs ds

  10. Improvement of Power System Stability using Artificial Neural Network based HVDC Controls

    Nagu Bhookya


    Full Text Available In this paper, investigation is carried out for the improvement of power system stability by utilizing auxiliary controls for controlling HVDC power flow. The current controller model and the line dynamics are considered in the stability analysis. Transient stability analysis is done on a multi-machine system, where, a neural network controller is developed to improve the stability of the power system and to improve the response time of the controller to the changing conditions in power system. The results show the application of the neural network controller in AC-DC power systems.

  11. Handbook of dynamical systems, v.3

    Takens, F; Broer, H W


    In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli. * Covers recent literature on various topics related to the theory of bifurcations of differentiable dynamical systems* Highlights developments that are the foundation for future research in this field* Provides material in the form of surveys, which are important tools for introducing the bifurcations of differentiable dyn...

  12. Lyapunov Stability of Complementarity and Extended Systems

    Camlibel, M. Kanat; Pang, Jong-Shi; Shen, Jinglai


    A linear complementarity system (LCS) is a piecewise linear dynamical system consisting of a linear time-invariant ordinary differential equation (ODE) parameterized by an algebraic variable that is required to be a solution to a finite-dimensional linear complementarity problem (LCP), whose

  13. Effects of head type on the stability of gemini surfactant foam by molecular dynamics simulation

    Wu, Gang; Yuan, Congtai; Ji, Xianjing; Wang, Hongbing; Sun, Shuangqing; Hu, Songqing


    Molecular dynamics simulations have been carried out to study the stability of gemini surfactant foam with different head groups. The results showed that the interaction strength between the polar head groups of the surfactants and water molecules increased from 12-3S-12 (sulfate) system, 12-3Sn-12 (sulfonate) system to 12-3L-12 (carboxylate) system, and the coordination number of water molecules around head increased. From the perspective of energy, the interface formation energy of 12-3L-12 system was smallest, which means that the foam stability was the best. These results indicated that the different head type had a significant effect on the stability of gemini surfactant foam.

  14. Stability analysis of a simple rheonomic nonholonomic constrained system

    Liu, Chang; Liu, Shi-Xing; Mei, Feng-Xing


    It is a difficult problem to study the stability of the rheonomic and nonholonomic mechanical systems. Especially it is difficult to construct the Lyapunov function directly from the differential equation. But the gradient system is exactly suitable to study the stability of a dynamical system with the aid of the Lyapunov function. The stability of the solution for a simple rheonomic nonholonomic constrained system is studied in this paper. Firstly, the differential equations of motion of the system are established. Secondly, a problem in which the generalized forces are exerted on the system such that the solution is stable is proposed. Finally, the stable solutions of the rheonomic nonholonomic system can be constructed by using the gradient systems. Project supported by the National Natural Science Foundation of China (Grant Nos. 11272050, 11202090, 11472124, 11572034, and 11572145), the Science and Technology Research Project of Liaoning Province, China (Grant No. L2013005), China Postdoctoral Science Foundation (Grant No. 2014M560203), and the Doctor Start-up Fund in Liaoning Province of China (Grant No. 20141050).

  15. Gyroscopic Stabilization of Indefinite Damped Systems

    Kliem, Wolfhard; Müller, Peter C.


    The paper deals with linear systems of differential equationswith symmetric system matrices M,D, and K.The mass matrix M and the stiffness matrix K are both assumed to bepositive definite. The damping matrix D is indefinite. Three questionsare of interest: 1) When is the system unstable? Apparently...... not always,if the matrix D is indefinite. 2) What can we say about conditions whichensure that an unstable system can be stabilized by adding a gyroscopicterm Gdx/dt? 3) What is, in this case, a suitable or optimal matrixG? The questions are answered in the frame of a first order perturbationapproach....

  16. Wind energy conversion. Volume IV. Drive system dynamics

    Martinez-Sanchez, M.; Labuszewski, T.


    The dynamics of the drive system and various approaches to power transmission are described. The effects on performance of using a constant rotor speed as opposed to a rotor speed varying with the wind speed are discussed for various rotor operating schedules and typical wind distributions. The dynamics of the combined rotor, alternator, and drive system are analyzed. Conditions which could lead to electro-dynamic instabilities and desynchronization are discussed as well as means for stabilizing the system. The dynamics of the drive system and important design conditions for various drive systems are discussed, such as location of the alternators, use of hydraulic drive systems and smoothing techniques.

  17. Output Feedback for Stochastic Nonlinear Systems with Unmeasurable Inverse Dynamics

    Xin Yu; Na Duan


    This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability (iISS) in deterministic systems and stochastic input-to-state stability (SISS) in stochastic systems, a concept of stochastic integral input-to-state stability (SiISS) using Lyapunov functions is first introduced. A constructive strategy is proposed to design a dynamic output feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.

  18. Fuzzy Logic System for Slope Stability Prediction

    Tarig Mohamed


    Full Text Available The main goal of this research is to predict the stability of slopes using fuzzy logic system. GeoStudio, a commercially available software was used to compute safety factors for various designs of slope. The general formulation of the software could analyze slope stability using various methods of analysis i.e. Morgenstern-Price, Janbu, Bishop and Ordinary to calculate the safety factors. After analyzing, fuzzy logic was used to predict the slope stability. Fuzzy logic is based on natural language and conceptually easy to understand, flexible, tolerant of imprecise data and able to model nonlinear functions of arbitrary complexity. Several important parameters such as height of slope, unit weight of slope material, angle of slope, coefficient of cohesion and internal angle of friction were used as the input parameters, while the factor of safety was the output parameter. A model to test the stability of the slope was generated from the calculated data. This model presented a relationship between input parameters and stability of the slopes. Results showed that the prediction using fuzzy logic was accurate and close to the target data.

  19. Design and Simulation of ADRC Controller for Dynamic Gyro Video Stabilization System%动力陀螺稳像系统自抗扰控制器设计与仿真

    张君健; 刘晓利; 马增虎


    In order to improve tracking performance and anti-interference performance, a controller based on the active disturbance rejection control (ADRC) theory is designed for the dynamic gyro which is strongly coupled and disturbed. A decoupling feed forward control matrix deal with coupling of channels. Use extended state observer to estimate and compensate the interior and exterior disturbance of system in real time, and ADRC controller is designed by nonlinear state error feedback control principle to realize control of dynamic gyro. Numerical simulation shows that the controller designed by ADRC can meet the need of dynamic gyro, and it has excellent decoupling performance, tracking performance and anti-interference performance for coupling system. It can meet control needs of dynamic gyro video stabilization system.%为了进一步提高系统的跟踪性能与抗干扰性能,运用自抗扰控制(active disturbance rejection control,ADRC)理论对具有交叉耦合以及会受内外干扰的动力陀螺稳像系统设计控制器。采用前馈控制解耦矩阵实现了通道之间的解耦。采用扩张状态观测器对系统的内外干扰进行实时估计和补偿,由非线性状态误差反馈控制律设计了ADRC控制器,实现对动力陀螺稳像系统的控制。数字仿真结果表明:所设计的自抗扰解耦控制器具有良好的解耦性能、跟踪性能、抗干扰性能和抑噪性能,可以满足动力陀螺稳像系统的控制要求。

  20. Lumbar interbody fusion vs dynamic stabilization system for degenerative lumbar disease%腰椎椎间融合术与动态固定术治疗腰椎退行性疾病的临床评价

    马辉; 李忠海; 朱晓东; 白玉树; 王传峰; 吴大江; 陈誉; 李明


    目的 通过比较分析腰椎椎间融合术与动态固定术治疗腰椎退行性疾病的临床疗效和术后并发症,探讨腰椎退行性疾病治疗方法的合理选择.方法 2009年1月~2010年12月,选择32例腰椎退行性疾病(L4/L5)患者,按配对设计分为对照组和治疗组,对照组16例患者均行椎弓根螺钉固定并单枚融合器置入;治疗组16例患者行常规椎板切除减压、髓核摘除和Isobar动态固定.比较观察2组病例的治疗效果、手术时间、出血量、手术并发症等.治疗效果评价采用Oswestry功能障碍指数(Oswestry disability index,ODI)及疼痛视觉模拟量表(visual analogue scale,VAS)评分,手术邻近节段(L3/L4和L5/S1)及腰椎(L2~S1)的活动度(range of motion,ROM)采用过伸过屈动力侧位X线片检查进行评价.结果 所有患者均获6~24个月的随访,平均15.8个月.与术前相比,2组患者术后症状均有明显改善,术后ODI及VAS评分与术前相比差异有统计学意义(P0.05);2组均未出现内固定相关并发症;2组术后邻近节段(L3/L4和L5/S1)的ROM与术前相比差异无统计学意义(P>0.05).腰椎(L2~S1)的ROM,融合组较术前显著下降,差异有统计学意义(P0.05).结论 腰椎椎间融合术与Isobar动态固定术治疗单节段腰椎退变性疾病均可取得满意的短期临床疗效,但理论上动态固定技术内固定失败的风险高于椎间融合术,故采用动态固定技术治疗腰椎退变性疾病应慎重.%Objective To assess the clinical effectiveness and postoperative complications of lumbar interbody fusion and dynamic stabilization system( the Isobar system ) for degenerative lumbar disease, in an attempt to explore an optimal surgical procedure. Methods From January 2009 to December 2010, 32 degenerative disease ( L4/L5 ) cases were randomly and equally assigned to an experimental group of decompression and dynamic stabilization with Isobar system ( n = 16 ) and a control group of

  1. Assessment of current criteria for dynamic stability of container vessels

    Stanca, C.; Ancuta, C.; Acomi, N.; Andrei, C.


    Container vessels sailing through heavy weather are exposed to a significant variation of stability due to specific shape of the hull combined with the action of the waves. Even if the weather forecast is transmitted to vessels, the way of acting it is a matter of officers’ experience. The Maritime Safety Committee, under the International Maritime Organization, has approved the Guidance to the master for avoiding dangerous situations in adverse weather and sea conditions. Adverse weather conditions include wind induced waves or heavy swell. The development of dangerous phenomena such as surf-riding and broaching to, syncronious and parametric rollings is a result of a these adverse conditions which has to be encountered by the vessels. Understanding the dynamic stability of the vessel in the waves and ship's behaviour based on mathematical and physical rules is a difficult task, any effort in order to assess these components are salutary. To avoid excessive acceleration and forces which can damage the hull of the vessel, lashing and integrity of containers, course and speed may need to be changed for the vessel's motion in heavy seas. Specific software have been developed as aids for evaluating the response of the vessel in heavy seas according to parameters variations. The paper aims at assessing of current criteria for dynamic stability of a container vessel model ship in order to determine the ways for avoiding dangerous conditions. The results should be regarded as a supporting tool during the decision making process.

  2. Strategy switching in the stabilization of unstable dynamics.

    Jacopo Zenzeri

    Full Text Available In order to understand mechanisms of strategy switching in the stabilization of unstable dynamics, this work investigates how human subjects learn to become skilled users of an underactuated bimanual tool in an unstable environment. The tool, which consists of a mass and two hand-held non-linear springs, is affected by a saddle-like force-field. The non-linearity of the springs allows the users to determine size and orientation of the tool stiffness ellipse, by using different patterns of bimanual coordination: minimal stiffness occurs when the two spring terminals are aligned and stiffness size grows by stretching them apart. Tool parameters were set such that minimal stiffness is insufficient to provide stable equilibrium whereas asymptotic stability can be achieved with sufficient stretching, although at the expense of greater effort. As a consequence, tool users have two possible strategies for stabilizing the mass in different regions of the workspace: 1 high stiffness feedforward strategy, aiming at asymptotic stability and 2 low stiffness positional feedback strategy aiming at bounded stability. The tool was simulated by a bimanual haptic robot with direct torque control of the motors. In a previous study we analyzed the behavior of naïve users and we found that they spontaneously clustered into two groups of approximately equal size. In this study we trained subjects to become expert users of both strategies in a discrete reaching task. Then we tested generalization capabilities and mechanism of strategy-switching by means of stabilization tasks which consist of tracking moving targets in the workspace. The uniqueness of the experimental setup is that it addresses the general problem of strategy-switching in an unstable environment, suggesting that complex behaviors cannot be explained in terms of a global optimization criterion but rather require the ability to switch between different sub-optimal mechanisms.

  3. Stabilization of nonlinear systems by similarity transformations

    Irina E. Zuber


    Full Text Available For a system x˙=A(x+b(xu, u(x=s∗(xx, x∈ℝn, where the pair (A(x,b(x is given, we obtain the feedback vector s(x to stabilize the corresponding closed loop system. For an arbitrarily chosen constant vector g, a sufficient condition of the existence and an explicit form of a similarity transformation T(A(x,b(x,g is established. The latter transforms matrix A(x into the Frobenius matrix, vector b(x into g, and an unknown feedback vector s(x into the first unit vector. The boundaries of A˜(y,g are determined by the boundaries of {∂kA(x∂xk,∂kb(x∂xk}, k=0,n−1¯. The stabilization of the transformed system is subject to the choice of the constant vector g.

  4. Kinematic variability, fractal dynamics and local dynamic stability of treadmill walking

    Terrier Philippe


    Full Text Available Abstract Background Motorized treadmills are widely used in research or in clinical therapy. Small kinematics, kinetics and energetics changes induced by Treadmill Walking (TW as compared to Overground Walking (OW have been reported in literature. The purpose of the present study was to characterize the differences between OW and TW in terms of stride-to-stride variability. Classical (Standard Deviation, SD and non-linear (fractal dynamics, local dynamic stability methods were used. In addition, the correlations between the different variability indexes were analyzed. Methods Twenty healthy subjects performed 10 min TW and OW in a random sequence. A triaxial accelerometer recorded trunk accelerations. Kinematic variability was computed as the average SD (MeanSD of acceleration patterns among standardized strides. Fractal dynamics (scaling exponent α was assessed by Detrended Fluctuation Analysis (DFA of stride intervals. Short-term and long-term dynamic stability were estimated by computing the maximal Lyapunov exponents of acceleration signals. Results TW did not modify kinematic gait variability as compared to OW (multivariate T2, p = 0.87. Conversely, TW significantly modified fractal dynamics (t-test, p = 0.01, and both short and long term local dynamic stability (T2 p = 0.0002. No relationship was observed between variability indexes with the exception of significant negative correlation between MeanSD and dynamic stability in TW (3 × 6 canonical correlation, r = 0.94. Conclusions Treadmill induced a less correlated pattern in the stride intervals and increased gait stability, but did not modify kinematic variability in healthy subjects. This could be due to changes in perceptual information induced by treadmill walking that would affect locomotor control of the gait and hence specifically alter non-linear dependencies among consecutive strides. Consequently, the type of walking (i.e. treadmill or overground is important to consider in

  5. Finite element analysis of dynamic stability of skeletal structures under periodic loading

    THANA Hemantha Kumar; AMEEN Mohammed


    This paper addresses the dynamic stability problem of columns and frames subjected to axially applied periodic loads. Such a structure can become unstable under certain combinations of amplitudes and frequencies of the imposed load acting on its columns/beams. These are usually shown in the form of plots which describe regions of instability. The finite element method (FEM) is used in this work to analyse dynamic stability problems of columns. Two-noded beam elements are used for this purpose.The periodic loading is decomposed into various harmonics using Fourier series expansion. Computer codes in C++ using object oriented concepts are developed to determine the stability regions of columns subjected to periodic loading. A number of numerical examples are presented to illustrate the working of the program. The direct integration of the equations of motions of the discretised system is carried out using Newmark's method to verify the results.

  6. Structural dynamics in rotating systems

    Kiraly, Louis J.


    Major issues and recent advances in the structural dynamics of rotating systems are summarized. The objectives and benefits of such systems are briefly discussed. Directions for future research are suggested.


    Wei WANG; Changyun WEN; Guanghong YANG


    In this paper, the authors analyze the stability of a class of interconnected systems with subsystem unmodeled dynamics and dynamic interactions employing decentralized adaptive controllers designed by Wen, Zhou, and Wang (2008) in the presence of actuator failures. It will be shown that the global stability of the remaining closed-loop system is still ensured and the outputs are also regulated to zero when some subsystems break down.

  8. Stochastic Stabilization of Itô Stochastic Systems with Markov Jumping and Linear Fractional Uncertainty

    Fei Long


    Full Text Available For a class of Itô stochastic linear systems with the Markov jumping and linear fractional uncertainty, the stochastic stabilization problem is investigated via state feedback and dynamic output feedback, respectively. In order to guarantee the stochastic stability of such uncertain systems, state feedback and dynamic output control law are, respectively, designed by using multiple Lyapunov function technique and LMI approach. Finally, two numerical examples are presented to illustrate our results.

  9. Chaotic Dynamics in Hybrid Systems

    P.J. Collins (Pieter)


    htmlabstractIn this paper we give an overview of some aspects of chaotic dynamics in hybrid systems, which comprise different types of behaviour. Hybrid systems may exhibit discontinuous dependence on initial conditions leading to new dynamical phenomena. We indicate how methods from topological

  10. Chaotic dynamics in hybrid systems

    P.J. Collins (Pieter)


    htmlabstractIn this paper we give an overview of some aspects of chaotic dynamics in hybrid systems, which comprise different types of behaviour. Hybrid systems may exhibit discontinuous dependence on initial conditions leading to new dynamical phenomena. We indicate how methods from topological

  11. A new hyperchaotic dynamical system

    Liu Chong-Xin


    In this paper a new hyperchaotic system is reported. Some basic dynamical properties, such as continuous specare studied. Dynamical behaviours of the new hyperchaotic system are proved by not only numerical simulation and brief theoretical analysis but also an electronic circuit experiment.

  12. Voltage stability analysis of grid-connected wind farms with FACTS: Static and dynamic analysis

    Kevin Zibran Heetun


    Full Text Available Recently, analysis of some major blackouts and failures of power system shows that voltage instability problem has been one of the main reasons of these disturbances and network collapses. In this article, a systematic approach to voltage stability analysis using various techniques for the IEEE 14-bus case study is presented. Static analysis is used to analyze the voltage stability of the system under study, while the dynamic analysis is used to evaluate the performance of compensators. The static techniques used are power flow, V–P curve analysis, and Q–V modal analysis. In this study, Flexible Alternating Current Transmission system (FACTS devices—namely, static synchronous compensators (STATCOMs and static var compensators (SVCs—are used as reactive power compensators, taking into account maintaining the violated voltage magnitudes of the weak buses within the acceptable limits defined in ANSI C84.1. Simulation results validate that both the STATCOMs and the SVCs can be effectively used to enhance the static voltage stability and increasing network loadability margin. Additionally, based on the dynamic analysis results, it has been shown that STATCOMs have superior performance, in dynamic voltage stability enhancement, compared to SVCs.

  13. Use of a portable motion analysis system for knee dynamic stability assessment in anterior cruciate ligament deficiency during single-legged hop landing

    Man-Yi Yeung


    Conclusion: The altered knee kinematics in ACL-deficient patients can be revealed by a portable motion capture system, which may enable the clinical application of kinematic assessment in the evaluation of ACL deficiency.

  14. Uniform exponential stability of linear periodic systems in a Banach space

    David N. Cheban


    Full Text Available This article is devoted to the study of linear periodic dynamical systems, possessing the property of uniform exponential stability. It is proved that if the Cauchy operator of these systems possesses a certain compactness property, then the asymptotic stability implies the uniform exponential stability. We also show applications to different classes of linear evolution equations, such as ordinary linear differential equations in the space of Banach, retarded and neutral functional differential equations, some classes of evolution partial differential equations.

  15. Automatic stabilization of velocity for ultrasonic vibration system


    Describes the structure of a current feedback ultrasonicgeneration system with such characteristic as velocity stabilization and automatic frequency tracking, discusses the velocity stabilization principle, and points out that successful frequency tracking is precondition for velocity stabilization.

  16. Recurrence for random dynamical systems

    Marie, Philippe


    This paper is a first step in the study of the recurrence behavior in random dynamical systems and randomly perturbed dynamical systems. In particular we define a concept of quenched and annealed return times for systems generated by the composition of random maps. We moreover prove that for super-polynomially mixing systems, the random recurrence rate is equal to the local dimension of the stationary measure.



    It is studied how the aluminum foil chatter mark is produced and controlledThe stableness of hydraulic AGC system,fluid vibration of capsule system,and electromechanical coupling of AC/AC VVVF system and dec oupling are also studiedIt is shown that rolling mill design should go to syst em dynamic design from traditional designThe framed drawing of system dynamic design program is presented

  18. Wallis动态稳定系统治疗腰椎退行性疾病%Preliminary observation of Wallis dynamic stabilization system for treatment of lumbar degenerative diseases

    普有登; 汤逊; 周田华; 石健; 姜伟; 张金鹏


    Objective To analyze the early clinical effects of Wallis dynamic stabilization system for the treatment of lumbar degenerative diseases, and to discuss the indications of this technique.Methods The clinical outcomes of 26 patients with lumbar degenerative diseases treated by only Wallis interspinous dynamic stabilization system or combined with posterior lumbar fusion were studied retrospectively.The visual analogue scale (VAS) and Japanese Orthopaedic Association (JOA) scores were recorded pre- and postoperatively.The ratio of JOA was applied to evaluate the curative effect.Results All the cases were followed up for a mean period of 14months ( rangel 6-24 months).Imaging showed all implants no loosening, dislocation or fracture.The VAS scores were 7.62 ± 1.50, 2.42 ± 1.03, 0.85 ± 0.73 at 1 d preoperative, 2 weeks postoperative and the final follow-up respectively.JOA scores were 10.12 ± 2.42, 20.62 ± 2.28, 24.92 ± 2.45 at 1 d preoperative, 2 weeks postoperative and the final follow-up respectively.The JOA improvement rates of 24 cases(92.3% ) were good/excellent at the final follow-up.Conclusion It is benefit to use Wallis interspinous dynamic stabilization system or combination with postreior lumbar fusion for remaining motor function of reserved spinal segments, with the advantage of mini-tissue damage and excellent effects.It is a good choice for the treatment of lumbar degenerative diseases.%目的 分析Wallis棘突间动态稳定系统治疗腰椎退行性疾病的早期效果,并探讨其手术适应证.方法 分析26例单独采用Wallis棘突间动态稳定系统或联合固定融合术治疗腰椎退行性疾病患者的临床疗效和初期随访结果,记录术前及术后疼痛视觉模拟量表(visual analogue scale,VAS)评分(10分法)、下腰痛日本骨科协会(Japanese Orthopaedic Association,JOA)评分(29分法),计算JOA改善率评估手术疗效.结果 经6~24个月(平均14个月)的随访,影像学显示内置物无

  19. Asymptotic Stability of Interconnected Passive Non-Linear Systems

    Isidori, A.; Joshi, S. M.; Kelkar, A. G.


    This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.

  20. Dynamic Stability of Passive Bipedal Walking on Rough Terrain:A Preliminary Simulation Study

    Parsa Nassiri Afshar; Lei Ren


    A simplified 2D passive dynamic model was simulated to walk down on a rough slope surface defined by deterministic profiles to investigate how the walking stability changes with increasing surface roughness.Our results show that the passive walker can walk on rough surfaces subject to surface roughness up to approximately 0.1% of its leg length.This indicates that bipedal walkers based on passive dynamics may possess some intrinsic stability to adapt to rough terrains although the maximum roughness they can tolerate is small.Orbital stability method was used to quantify the walking stability before the walker started to fall over.It was found that the average maximum Floquet multiplier increases with surface roughness in a non-linear form.Although the passive walker remained orbitally stable for all the simulation cases,the results suggest that the possibility of the bipedal model moving away from its limit cycle increases with the surface roughness if subjected to additional perturbations.The number of consecutive steps before falling was used to measure the walking stability after the passive walker started to fall over.The results show that the number of steps before falling decreases exponentially with the increase in surface roughness.When the roughness magnitude approached to 0.73% of the walker's leg length,it fell down to the ground as soon as it entered into the uneven terrain.It was also found that shifting the phase angle of the surface profile has apparent affect on the system stability.This is probably because point contact was used to simulate the heel strikes and the resulted variations in system states at heel strikes may have pronounced impact on the passive gaits,which have narrow basins of attraction.These results would provide insight into how the dynamic stability of passive bipedal walkers evolves with increasing surface roughness.

  1. Stability analysis and controller design for a linear system with Duhem hysteresis nonlinearity

    Ouyang, Ruiyue; Jayawardhana, Bayu


    In this paper, we investigate the stability of feedback interconnections between a linear system and a Duhem hysteresis operator, where the linear system satisfies either counter-clockwise (CCW) or clockwise (CW) inputoutput dynamics [1], [13]. More precisely, depending on the input-output dynamics

  2. Stability Constrained Efficiency Optimization for Droop Controlled DC-DC Conversion System

    Meng, Lexuan; Dragicevic, Tomislav; Guerrero, Josep M.


    implementing tertiary regulation. Moreover, system dynamic is affected when shifting VRs. Therefore, the stability is considered in optimization by constraining the eigenvalues arising from dynamic state space model of the system. Genetic algorithm is used in searching for global efficiency optimum while...

  3. The stabilizing effects of genetic diversity on predator-prey dynamics.

    Steiner, Christopher F; Masse, Jordan


    Heterogeneity among prey in their susceptibility to predation is a potentially important stabilizer of predator-prey interactions, reducing the magnitude of population oscillations and enhancing total prey population abundance. When microevolutionary responses of prey populations occur at time scales comparable to population dynamics, adaptive responses in prey defense can, in theory, stabilize predator-prey dynamics and reduce top-down effects on prey abundance. While experiments have tested these predictions, less explored are the consequences of the evolution of prey phenotypes that can persist in both vulnerable and invulnerable classes. We tested this experimentally using a laboratory aquatic system composed of the rotifer Brachionus calyciflorus as a predator and the prey Synura petersenii, a colony-forming alga that exhibits genetic variation in its propensity to form colonies and colony size (larger colonies are a defense against predators). Prey populations of either low initial genetic diversity and low adaptive capacity or high initial genetic diversity and high adaptive capacity were crossed with predator presence and absence. Dynamics measured over the last 127 days of the 167-day experiment revealed no effects of initial prey genetic diversity on the average abundance or temporal variability of predator populations. However, genetic diversity and predator presence/absence interactively affected prey population abundance and stability; diversity of prey had no effects in the absence of predators but stabilized dynamics and increased total prey abundance in the presence of predators. The size structure of the genetically diverse prey populations diverged from single strain populations in the presence of predators, showing increases in colony size and in the relative abundance of cells found in colonies. Our work sheds light on the adaptive value of colony formation and supports the general view that genetic diversity and intraspecific trait variation of

  4. Stability of Intelligent Transportation Network Dynamics: A Daily Path Flow Adjustment considering Travel Time Differentiation

    Ming-Chorng Hwang


    Full Text Available A theoretic formulation on how traffic time information distributed by ITS operations influences the trajectory of network flows is presented in this paper. The interactions between users and ITS operator are decomposed into three parts: (i travel time induced path flow dynamics (PFDTT; (ii demand induced path flow dynamics (PFDD; and (iii predicted travel time dynamics for an origin-destination (OD pair (PTTDOD. PFDTT describes the collective results of user’s daily route selection by pairwise comparison of path travel time provided by ITS services. The other two components, PTTDOD and PFDD, are concentrated on the evolutions of system variables which are predicted and observed, respectively, by ITS operators to act as a benchmark in guiding the target system towards an expected status faster. In addition to the delivered modelings, the stability theorem of the equilibrium solution in the sense of Lyapunov stability is also provided. A Lyapunov function is developed and employed to the proof of stability theorem to show the asymptotic behavior of the aimed system. The information of network flow dynamics plays a key role in traffic control policy-making. The evaluation of ITS-based strategies will not be reasonable without a well-established modeling of network flow evolutions.

  5. Recurrent Neural Network for Single Machine Power System Stabilizer

    Widi Aribowo


    Full Text Available In this paper, recurrent neural network (RNN is used to design power system stabilizer (PSS due to its advantage on the dependence not only on present input but also on past condition. A RNN-PSS is able to capture the dynamic response of a system without any delays caused by external feedback, primarily by the internal feedback loop in recurrent neuron. In this paper, RNNPSS consists of a RNN-identifier and a RNN-controller. The RNN-Identifier functions as the tracker of dynamics characteristics of the plant, while the RNN-controller is used to damp the system’s low frequency oscillations. Simulation results using MATLAB demonstrate that the RNNPSS can successfully damp out oscillation and improve the performance of the system.

  6. Voltage stability dynamical analysis by comparing static and dynamical loads; Estudio dinamico de estabilidad de tension comparando modelos de carga estatica y carga dinamica

    Aromataris, Luis [Universidad Nacional de Rio Cuarto (UNRC) (Argentina); Arnera, Patricia; Riubrugent, Jean [Universidad Nacional de La Plata, Buenos Aires (Argentina). Facultad de Ingenieria. Instituto de Investigaciones Tecnologicas para Redes y Equipos Electricos


    This work investigate the impact produced by the load model on the voltage stability analysis of an electric system. Qualitative and quantitative analyses are approached in connection with the effects of modeling the electric loads by both dynamical and static way. Also it is highlighted the importance of using dynamical models of load, mainly when it is composed by motors.

  7. Stability Analysis of Closed-loop Water System

    Yongzheng FU; Keqi WU; Yaqiao CAI


    Aiming at closed-loop water system, by the method that shutting certain subcircuit, and solving the piping network, computing flow deviation of other subcircuits, then analyzing the rules of variation of stability with various factors, following conclusions are obtained: When reducing the resistance in main pipes, increasing resistance of subcircuits, system stability can be improved. Centralized regulation by changing power has no influence on system stability; centralized regulation by changing resistances will decrease system stability. Pump characteristics curve influences system stability, stability of the flat characteristic is superior to the steep one. For direct return system (DRS), the stability of subcircuit which is farthest from the heat source is the worst. For reverse return system (RRS), the stability of subcircuit in the middle of the pipe-network has the worst stability.Overall, stability of RRS is inferior to that of DRS.

  8. A switched system approach to stabilization f networked control systems


    A switched system approach is proposed to model networked control systems (NCSs) with communication constraints. This enables us to apply the rich theory of switched systems to analyzing such NCSs. Sufficient conditions are presented on the stabilization of NCSs. Stabilizing state/output feedback controllers can be constructed by using the feasible solutions of some linear matrix inequalities (LMIs). The merit of our proposed approach is that the behavior of the NCSs can be studied by considering switched system without augmenting the system. A simulation example is worked out to illustrate the effectiveness of the proposed approach.

  9. Continuation and stability deduction of resonant periodic orbits in three dimensional systems

    Antoniadou, Kyriaki I; Varvoglis, Harry


    In dynamical systems of few degrees of freedom, periodic solutions consist the backbone of the phase space and the determination and computation of their stability is crucial for understanding the global dynamics. In this paper we study the classical three body problem in three dimensions and use its dynamics to assess the long-term evolution of extrasolar systems. We compute periodic orbits, which correspond to exact resonant motion, and determine their linear stability. By computing maps of dynamical stability we show that stable periodic orbits are surrounded in phase space with regular motion even in systems with more than two degrees of freedom, while chaos is apparent close to unstable ones. Therefore, families of stable periodic orbits, indeed, consist backbones of the stability domains in phase space.

  10. Thermal stability of marks gold nanoparticles: A molecular dynamics simulation

    Jia, Yanlin; Li, Siqi; Qi, Weihong; Wang, Mingpu; Li, Zhou; Wang, Zhixing


    Molecular dynamics (MDs) simulations were used to explore the thermal stability of Au nanoparticles (NPs) with decahedral, cuboctahedral, icosahedral and Marks NPs. According to the calculated cohesive energy and melting temperature, the Marks NPs have a higher cohesive energy and melting temperature compared to these other shapes. The Lindemann index, radial distribution function, deformation parameters, mean square displacement and self-diffusivity have been used to characterize the structure variation during heating. This work may inspire researchers to prepare Marks NPs and apply them in different fields.

  11. Maintaining genome stability in the nervous system.

    McKinnon, Peter J


    Active maintenance of genome stability is a prerequisite for the development and function of the nervous system. The high replication index during neurogenesis and the long life of mature neurons highlight the need for efficient cellular programs to safeguard genetic fidelity. Multiple DNA damage response pathways ensure that replication stress and other types of DNA lesions, such as oxidative damage, do not affect neural homeostasis. Numerous human neurologic syndromes result from defective DNA damage signaling and compromised genome integrity. These syndromes can involve different neuropathology, which highlights the diverse maintenance roles that are required for genome stability in the nervous system. Understanding how DNA damage signaling pathways promote neural development and preserve homeostasis is essential for understanding fundamental brain function.

  12. System Design Description PFP Thermal Stabilization



    The purpose of this document is to provide a system design description (SDD) and design basis for the Plutonium Finishing Plant (PFP) Thermal Stabilization project. The chief objective of the SDD is to document the Structures, Systems, and Components (SSCs) that establish and maintain the facility Safety Envelope necessary for normal safe operation of the facility; as identified in the FSAR, the OSRs, and Safety Assessment Documents (SADs). This safety equipment documentation should satisfy guidelines for the SDD given in WHC-SD-CP-TI-18 1, Criteria for Identification and Control of Equipment Necessary for Preservation of the Safety Envelope and Safe Operation of PFP. The basis for operational, alarm response, maintenance, and surveillance procedures are also identified and justified in this document. This document and its appendices address the following elements of the PFP Thermal Stabilization project: Functional and design requirements; Design description; Safety Envelope Analysis; Safety Equipment Class; and Operational, maintenance and surveillance procedures.

  13. On Causality in Dynamical Systems

    Harnack, Daniel


    Identification of causal links is fundamental for the analysis of complex systems. In dynamical systems, however, nonlinear interactions may hamper separability of subsystems which poses a challenge for attempts to determine the directions and strengths of their mutual influences. We found that asymmetric causal influences between parts of a dynamical system lead to characteristic distortions in the mappings between the attractor manifolds reconstructed from respective local observables. These distortions can be measured in a model-free, data-driven manner. This approach extends basic intuitions about cause-effect relations to deterministic dynamical systems and suggests a mathematically well defined explanation of results obtained from previous methods based on state space reconstruction.

  14. Fast Dynamic Simulation-Based Small Signal Stability Assessment and Control

    Acharya, Naresh [General Electric Company, Fairfield, CT (United States); Baone, Chaitanya [General Electric Company, Fairfield, CT (United States); Veda, Santosh [General Electric Company, Fairfield, CT (United States); Dai, Jing [General Electric Company, Fairfield, CT (United States); Chaudhuri, Nilanjan [General Electric Company, Fairfield, CT (United States); Leonardi, Bruno [General Electric Company, Fairfield, CT (United States); Sanches-Gasca, Juan [General Electric Company, Fairfield, CT (United States); Diao, Ruisheng [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Wu, Di [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Huang, Zhenyu [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Zhang, Yu [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Jin, Shuangshuang [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Zheng, Bin [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Chen, Yousu [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)


    Power grid planning and operation decisions are made based on simulation of the dynamic behavior of the system. Enabling substantial energy savings while increasing the reliability of the aging North American power grid through improved utilization of existing transmission assets hinges on the adoption of wide-area measurement systems (WAMS) for power system stabilization. However, adoption of WAMS alone will not suffice if the power system is to reach its full entitlement in stability and reliability. It is necessary to enhance predictability with "faster than real-time" dynamic simulations that will enable the dynamic stability margins, proactive real-time control, and improve grid resiliency to fast time-scale phenomena such as cascading network failures. Present-day dynamic simulations are performed only during offline planning studies, considering only worst case conditions such as summer peak, winter peak days, etc. With widespread deployment of renewable generation, controllable loads, energy storage devices and plug-in hybrid electric vehicles expected in the near future and greater integration of cyber infrastructure (communications, computation and control), monitoring and controlling the dynamic performance of the grid in real-time would become increasingly important. The state-of-the-art dynamic simulation tools have limited computational speed and are not suitable for real-time applications, given the large set of contingency conditions to be evaluated. These tools are optimized for best performance of single-processor computers, but the simulation is still several times slower than real-time due to its computational complexity. With recent significant advances in numerical methods and computational hardware, the expectations have been rising towards more efficient and faster techniques to be implemented in power system simulators. This is a natural expectation, given that the core solution algorithms of most commercial simulators were developed

  15. High temperature SMES for improving power system stabilities

    CHENG ShiJie; TANG YueJin


    Superconducting magnetic energy storage (SMES) system has been proven very effective to improve power system stabilities. It is realized with superconductivity technology, power electronics and control theory. In order to promote the application of such kind control device and to further investigate the properties of the controller, a detail mathematic model of such control device is developed. Based on the developed model, extensive analysis including time domain simulation is carried out to investigate the characteristic of the SMES to compensate the unba- lanced dynamic active and reactive power of AC power system. The capability of SMES to increase power system transient and small signal perturbation stabilities are analyzed. A prototype SMES is developed, in which the conduction cooling and the high temperature superconductive techniques are used. The performance of the prototype is experimentally investigated in a laboratory environment. Very encouraging results are obtained. After a brief introduction of the SMES control system and the principle of its capability to improve power system stabilities, the details of the mathematic model, the theoretical analysis, the developed device and the experiment test results are all given in this paper.

  16. High temperature SMES for improving power system stabilities


    Superconducting magnetic energy storage (SMES) system has been proven very effective to improve power system stabilities. It is realized with superconductivity technology, power electronics and control theory. In order to promote the applica-tion of such kind control device and to further investigate the properties of the controller, a detail mathematic model of such control device is developed. Based on the developed model, extensive analysis including time domain simulation is carried out to investigate the characteristic of the SMES to compensate the unba- lanced dynamic active and reactive power of AC power system. The capability of SMES to increase power system transient and small signal perturbation stabilities are analyzed. A prototype SMES is developed, in which the conduction cooling and the high temperature superconductive techniques are used. The performance of the prototype is experimentally investigated in a laboratory environment. Very en-couraging results are obtained. After a brief introduction of the SMES control sys-tem and the principle of its capability to improve power system stabilities, the de-tails of the mathematic model, the theoretical analysis, the developed device and the experiment test results are all given in this paper.

  17. Criteria for Stability of Linear Control Systems

    JING Yan-fei; HUANG Ting-zhu


    As it is well known, it is significant to know whether a matrix is an H-matrix or not in stability analysis of linear control systems. However, to distinguish H-matrices is difficult in real applications. In this paper, a practical extension of the sufficient conditions for H-matrices is investigated under some conditions. A larger scale of H-matrices which can be judged by the proposed method is shown by the numerical examples.

  18. Stability of SIRS system with random perturbations

    Lu, Qiuying


    Epidemiological models with bilinear incidence rate λSI usually have an asymptotically stable trivial equilibrium corresponding to the disease-free state, or an asymptotically stable non-trivial equilibrium (i.e. interior equilibrium) corresponding to the endemic state. In this paper, we consider an epidemiological model, which is an SIRS model with or without distributed time delay influenced by random perturbations. We present the stability conditions of the disease-free equilibrium of the associated stochastic SIRS system.

  19. Stability and dynamics of membrane-spanning DNA nanopores

    Maingi, Vishal; Burns, Jonathan R.; Uusitalo, Jaakko J.; Howorka, Stefan; Marrink, Siewert J.; Sansom, Mark S. P.


    Recently developed DNA-based analogues of membrane proteins have advanced synthetic biology. A fundamental question is how hydrophilic nanostructures reside in the hydrophobic environment of the membrane. Here, we use multiscale molecular dynamics (MD) simulations to explore the structure, stability and dynamics of an archetypical DNA nanotube inserted via a ring of membrane anchors into a phospholipid bilayer. Coarse-grained MD reveals that the lipids reorganize locally to interact closely with the membrane-spanning section of the DNA tube. Steered simulations along the bilayer normal establish the metastable nature of the inserted pore, yielding a force profile with barriers for membrane exit due to the membrane anchors. Atomistic, equilibrium simulations at two salt concentrations confirm the close packing of lipid around of the stably inserted DNA pore and its cation selectivity, while revealing localized structural fluctuations. The wide-ranging and detailed insight informs the design of next-generation DNA pores for synthetic biology or biomedicine.

  20. A Dynamic Stability Criterion for Ice Shelves and Tidewater Glaciers

    Bassis, J. N.; Fricker, H. A.; Minster, J.


    The collapse of the Antarctic ice shelves could have dramatic consequences for the mass balance of the Antarctic ice sheet and, as a result, sea level rise. It is therefore imperative to improve our knowledge of the mechanisms that lead to ice shelf retreat. The mechanism that has the potential to remove the largest amounts of mass rapidly is iceberg calving. However, the processes and mechanisms that lead to iceberg calving are still poorly understood. Motivated by the complexity of the short-time scale behavior of ice fracture we seek a dynamic stability criterion that predicts the onset of ice shelf retreat based on dimensional analysis. In our approach, rather than attempt to model the initiation and propagation of individual fractures, we look for a non-dimensional number that describes the overall ice shelf stability. We also make the assumption that the same criterion, valid for ice shelves, also applies to tidewater glaciers. This enables us to test our criterion against a larger set of ice shelves and calving glaciers. Our analysis predicts that retreat will occur when a non-dimensional number that we call the "terminus stability number", decreases below a critical value. We show that this criterion is valid for calving glaciers in Alaska, for several glaciers around Greenland as well as for three Antarctic ice shelves. This stability analysis has much in common with classic hydrodynamic stability theory, where the onset of instability is related to non-dimensional numbers that are largely independent of geometry or other situation specific variables.