Nonlinearity and disorder: Classification and stability of nonlinear impurity modes
DEFF Research Database (Denmark)
Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole
2001-01-01
We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schrödinger equation and describe three types of no...
Stabilization of switched nonlinear systems with unstable modes
Yang, Hao; Cocquempot, Vincent
2014-01-01
This book provides its reader with a good understanding of the stabilization of switched nonlinear systems (SNS), systems that are of practical use in diverse situations: design of fault-tolerant systems in space- and aircraft; traffic control; and heat propagation control of semiconductor power chips. The practical background is emphasized throughout the book; interesting practical examples frequently illustrate the theoretical results with aircraft and spacecraft given particular prominence. Stabilization of Switched Nonlinear Systems with Unstable Modes treats several different subclasses of SNS according to the characteristics of the individual system (time-varying and distributed parameters, for example), the state composition of individual modes and the degree and distribution of instability in its various modes. Achievement and maintenance of stability across the system as a whole is bolstered by trading off between individual modes which may be either stable or unstable, or by exploiting areas of part...
Linear Feedback Stabilization of Nonlinear Systems with an Uncontrollable Critical Mode
1992-11-17
mode that is uncontrollable. The results complement previous work on the synthesis of nonlinear stabilizing control laws. The present work addresses...analysis and stabilizing control design employ results on stability of bifurcations of parametrized systems.
Nonlinear {omega}*-stabilization of the m = 1 mode in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Rogers, B. [Univ. of Maryland, College Park, MD (United States). Inst. for Plasma Research; Zakharov, L. [Princeton Univ., NJ (United States). Plasma Physics Lab.
1995-08-01
Earlier studies of sawtooth oscillations in Tokamak Fusion Test Reactor supershots (Levinton et al, Phys. Rev. Lett. 72, 2895 (1994); Zakharov, et al, Plasma Phys. and Contr. Nucl. Fus. Res., Proc. 15th Int. Conf., Seville 1994, Vienna) have found an apparent contradiction between conventional linear theory and experiment: even in sawtooth-free discharges, the theory typically predicts instability due to a nearly ideal m = 1 mode. Here, the nonlinear evolution of such mode is analyzed using numerical simulations of a two-fluid magnetohydrodynamic (MHD) model. We find the mode saturates nonlinearly at a small amplitude provided the ion and electron drift-frequencies {omega}*{sub i,e} are somewhat above the linear stability threshold of the collisionless m = 1 reconnecting mode. The comparison of the simulation results to m = 1 mode activity in TFTR suggests additional, stabilizing effects outside the present model are also important.
On Stability of Flat Band Modes in a Rhombic Nonlinear Optical Waveguide Array
Maimistov, Andrey I
2016-01-01
The quasi-one-dimensional rhombic array of the waveguides is considered. In the nonlinear case the system of equations describing coupled waves in the waveguides has the solutions that represent the superposition of the flat band modes. The property of stability of these solutions is considered. It was found that the flat band solution is unstable until the power threshold be attained.
Yi-You Hou; Zhang-Lin Wan
2014-01-01
This paper considers the problem of the robust stability for the nonlinear system with time-varying delay and parameters uncertainties. Based on the H∞ theorem, Lyapunov-Krasovskii theory, and linear matrix inequality (LMI) optimization technique, the H∞ quasi-sliding mode controller and switching function are developed such that the nonlinear system is asymptotically stable in the quasi-sliding mode and satisfies the disturbance attenuation (H∞-norm performance). The effectiveness and accura...
Ayten, B.; Westerhof, E.; ASDEX Upgrade team,
2014-01-01
Due to the smallness of the volumes associated with the flux surfaces around the O-point of a magnetic island, the electron cyclotron power density applied inside the island for the stabilization of neoclassical tearing modes (NTMs) can exceed the threshold for non-linear effects as derived
Directory of Open Access Journals (Sweden)
Yi-You Hou
2014-01-01
Full Text Available This paper considers the problem of the robust stability for the nonlinear system with time-varying delay and parameters uncertainties. Based on the H∞ theorem, Lyapunov-Krasovskii theory, and linear matrix inequality (LMI optimization technique, the H∞ quasi-sliding mode controller and switching function are developed such that the nonlinear system is asymptotically stable in the quasi-sliding mode and satisfies the disturbance attenuation (H∞-norm performance. The effectiveness and accuracy of the proposed methods are shown in numerical simulations.
Robust stabilization of underactuated nonlinear systems: A fast terminal sliding mode approach.
Khan, Qudrat; Akmeliawati, Rini; Bhatti, Aamer Iqbal; Khan, Mahmood Ashraf
2017-01-01
This paper presents a fast terminal sliding mode based control design strategy for a class of uncertain underactuated nonlinear systems. Strategically, this development encompasses those electro-mechanical underactuated systems which can be transformed into the so-called regular form. The novelty of the proposed technique lies in the hierarchical development of a fast terminal sliding attractor design for the considered class. Having established sliding mode along the designed manifold, the close loop dynamics become finite time stable which, consequently, result in high precision. In addition, the adverse effects of the chattering phenomenon are reduced via strong reachability condition and the robustness of the system against uncertainties is confirmed theoretically. A simulation as well as experimental study of an inverted pendulum is presented to demonstrate the applicability of the proposed technique.
Ayten, B
2013-01-01
Due to the smallness of the volumes associated with the flux surfaces around the O-point of a magnetic island, the electron cyclotron power density applied inside the island for the stabilization of neoclassical tearing modes (NTMs) can exceed the threshold for non-linear effects as derived previously by Harvey et al, Phys. Rev. Lett. 62 (1989) 426. We study the non-linear electron cyclotron current drive (ECCD) efficiency through bounce-averaged, quasi-linear Fokker-Planck calculations in the magnetic geometry as created by the islands. The calculations are performed for the parameters of a typical NTM stabilization experiment on ASDEX Upgrade. A particular feature of these experiments is that the rays of the EC wave beam propagate tangential to the flux surfaces in the power deposition region. The calculations show significant non-linear effects on the ECCD efficiency, when the ECCD power is increased from its experimental value of 1 MW to a larger value of 4 MW. The nonlinear effects are largest in case of...
Indian Academy of Sciences (India)
P K Karmakar
2011-06-01
The pulsational mode of gravitational collapse (PMGC) in a hydrostatically bounded dust molecular cloud is responsible for the evolution of tremendous amount of energy during star formation. The source of free energy for this gravito-electrostatic instability lies in the associated self-gravity of the dispersed phase of relatively huge dust grains of solid matter over the gaseous phase of background plasma. The nonlinear stability of the same PMGC in an inﬁnite dusty plasma model (plane geometry approximation for large wavelength ﬂuctuation in the absence of curvature effects) is studied in a hydrostatic kind of homogeneous equilibrium conﬁguration. By the standard reductive perturbation technique, a Korteweg–de Vries (KdV) equation for investigating the nonlinear evolution of the lowest order perturbed self-gravitational potential is developed in a time-stationary (steady-state) form, which is studied analytically as well as numerically. Different nonlinear structures (soliton-like and soliton chain-like) are found to exist in different situations. Astrophysical situations, relevant to it, are brieﬂy discussed.
Mode decomposition of nonlinear eigenvalue problems and application in flow stability
Institute of Scientific and Technical Information of China (English)
高军; 罗纪生
2014-01-01
Direct numerical simulations are carried out with different disturbance forms introduced into the inlet of a flat plate boundary layer with the Mach number 4.5. According to the biorthogonal eigenfunction system of the linearized Navier-Stokes equations and the adjoint equations, the decomposition of the direct numerical simulation results into the discrete normal mode is easily realized. The decomposition coefficients can be solved by doing the inner product between the numerical results and the eigenfunctions of the adjoint equations. For the quadratic polynomial eigenvalue problem, the inner product operator is given in a simple form, and it is extended to an N th-degree polynomial eigenvalue problem. The examples illustrate that the simplified mode decomposition is available to analyze direct numerical simulation results.
A nonlinear variable structure stabilizer for power system stability
Energy Technology Data Exchange (ETDEWEB)
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)
1994-09-01
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.
Gu, Zhiping
This paper extends Riccati transfer matrix method to the transient and stability analysis of large scale rotor-bearing systems with strong nonlinear elements, and proposes a mode summation-transfer matrix method, in which the field transfer matrix of a distributed mass uniform shaft segment is obtained with the aid of the idea of mode summation and Newmark beta formulation, and the Riccati transfer matrix method is adopted to stablize the boundary value problem of the nonlinear systems. In this investigation, the real nonlinearity of the strong nonlinear elements is considered, not linearized, and the advantages of the Riccati transfer matrix are retained. So, this method is especially applicable to analyze the transient response and stability of large-scale rotor-bear systems with strong nonlinear elements. One example, a single-spool rotating system with strong nonlinear elements, is given. The obtained results show that this method is superior to that of Gu and Chen (1990) in accuracy, stability, and economy.
Nonlinear dynamics by mode superposition
Energy Technology Data Exchange (ETDEWEB)
Nickell, R.E.
1976-01-01
A mode superposition technique for approximately solving nonlinear initial-boundary-value problems of structural dynamics is discussed, and results for examples involving large deformation are compared to those obtained with implicit direct integration methods such as the Newmark generalized acceleration and Houbolt backward-difference operators. The initial natural frequencies and mode shapes are found by inverse power iteration with the trial vectors for successively higher modes being swept by Gram-Schmidt orthonormalization at each iteration. The subsequent modal spectrum for nonlinear states is based upon the tangent stiffness of the structure and is calculated by a subspace iteration procedure that involves matrix multiplication only, using the most recently computed spectrum as an initial estimate. Then, a precise time integration algorithm that has no artificial damping or phase velocity error for linear problems is applied to the uncoupled modal equations of motion. Squared-frequency extrapolation is examined for nonlinear problems as a means by which these qualities of accuracy and precision can be maintained when the state of the system (and, thus, the modal spectrum) is changing rapidly. The results indicate that a number of important advantages accrue to nonlinear mode superposition: (a) there is no significant difference in total solution time between mode superposition and implicit direct integration analyses for problems having narrow matric half-bandwidth (in fact, as bandwidth increases, mode superposition becomes more economical), (b) solution accuracy is under better control since the analyst has ready access to modal participation factors and the ratios of time step size to modal period, and (c) physical understanding of nonlinear dynamic response is improved since the analyst is able to observe the changes in the modal spectrum as deformation proceeds.
Spiralling solitons and multipole localized modes in nonlocal nonlinear media
DEFF Research Database (Denmark)
Buccoliero, Daniel; Lopez-Aguayo, Servando; Skupin, Stefan
2007-01-01
We analyze the propagation of rotating multi-soliton localized structures in optical media with spatially nonlocal nonlinearity. We demonstrate that nonlocality stabilizes the azimuthal breakup of rotating dipole as well as multipole localized soliton modes. We compare the results for two differe...... models of nonlocal nonlinearity and suggest that the stabilization mechanism is a generic property of a spatial nonlocal nonlinear response independent of its particular functional form.......We analyze the propagation of rotating multi-soliton localized structures in optical media with spatially nonlocal nonlinearity. We demonstrate that nonlocality stabilizes the azimuthal breakup of rotating dipole as well as multipole localized soliton modes. We compare the results for two different...
NONLINEAR STABILITY FOR EADY'S MODEL
Institute of Scientific and Technical Information of China (English)
LIU Yong-ming; QIU Ling-cun
2005-01-01
Poincaré type integral inequality plays an important role in the study of nonlinear stability ( in the sense of Arnold's second theorem) for three-dimensional quasigeostophic flow. The nonlinear stability of Eady's model is one of the most important cases in the application of the method. But the best nonlinear stability criterion obtained so far and the linear stability criterion are not coincident. The two criteria coincide only when the period of the channel is infinite.additional conservation law of momentum and by rigorous estimate of integral inequality. So the new nonlinear stability criterion was obtained, which shows that for Eady 's model in the periodic channel, the linear stable implies the nonlinear stable.
Optimal second order sliding mode control for nonlinear uncertain systems.
Das, Madhulika; Mahanta, Chitralekha
2014-07-01
In this paper, a chattering free optimal second order sliding mode control (OSOSMC) method is proposed to stabilize nonlinear systems affected by uncertainties. The nonlinear optimal control strategy is based on the control Lyapunov function (CLF). For ensuring robustness of the optimal controller in the presence of parametric uncertainty and external disturbances, a sliding mode control scheme is realized by combining an integral and a terminal sliding surface. The resulting second order sliding mode can effectively reduce chattering in the control input. Simulation results confirm the supremacy of the proposed optimal second order sliding mode control over some existing sliding mode controllers in controlling nonlinear systems affected by uncertainty.
Practical stability of nonlinear systems
Lakshmikantham, Vangipuram; Martynyuk, Anatolii Andreevich
1990-01-01
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.
Stability analysis of nonlinear systems
Lakshmikantham, Vangipuram; Martynyuk, Anatoly A
2015-01-01
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.
Fuzzy Sliding Mode Control for Discrete Nonlinear Systems
Institute of Scientific and Technical Information of China (English)
F.Qiao.Q.M.Zhu; A.Winfield; C.Melhuish
2003-01-01
Sliding mode control is introduced into classical model free fuzzy logic control for discrete time nonlinear systems with uncertainty to the design of a novel fuzzy sliding mode control to meet the requirement of necessary and sufficient reaching conditions of sliding mode control. The simulation results show that the proposed controller outperforms the original fuzzy sliding mode controller and the classical fuzzy logic controller in stability, convergence and robustness.
Discrete dissipative localized modes in nonlinear magnetic metamaterials.
Rosanov, Nikolay N; Vysotina, Nina V; Shatsev, Anatoly N; Shadrivov, Ilya V; Powell, David A; Kivshar, Yuri S
2011-12-19
We analyze the existence, stability, and propagation of dissipative discrete localized modes in one- and two-dimensional nonlinear lattices composed of weakly coupled split-ring resonators (SRRs) excited by an external electromagnetic field. We employ the near-field interaction approach for describing quasi-static electric and magnetic interaction between the resonators, and demonstrate the crucial importance of the electric coupling, which can completely reverse the sign of the overall interaction between the resonators. We derive the effective nonlinear model and analyze the properties of nonlinear localized modes excited in one-and two-dimensional lattices. In particular, we study nonlinear magnetic domain walls (the so-called switching waves) separating two different states of nonlinear magnetization, and reveal the bistable dependence of the domain wall velocity on the external field. Then, we study two-dimensional localized modes in nonlinear lattices of SRRs and demonstrate that larger domains may experience modulational instability and splitting.
Discrete-time nonlinear sliding mode controller
African Journals Online (AJOL)
user
: Discrete-time delay system, Sliding mode control, nonlinear sliding ... The concept of the sliding mode control in recent years has drawn the ...... His area of interest is dc-dc converters, electrical vehicle and distributed generation application.
Localized modes in nonlinear binary kagome ribbons
Belicev, P. P.; Gligoric, G.; Radosavljevic, A; Maluckov, A.; Stepic, M.; Vicencio, R. A.; Johansson, Magnus
2015-01-01
The localized mode propagation in binary nonlinear kagome ribbons is investigated with the premise to ensure controlled light propagation through photonic lattice media. Particularity of the linear system characterized by the dispersionless flat band in the spectrum is the opening of new minigaps due to the "binarism." Together with the presence of nonlinearity, this determines the guiding mode types and properties. Nonlinearity destabilizes the staggered rings found to be nondiffracting in t...
Nonlinear magnetohydrodynamics of edge localized mode precursors
Energy Technology Data Exchange (ETDEWEB)
Guo, Z. B., E-mail: guozhipku@gmail.com [State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing (China); WCI Center for Fusion Theory, NFRI, Gwahangno 113, Yusung-gu, Daejeon 305-333 (Korea, Republic of); Wang, Lu [SEEE, Huazhong University of Science and Technology, Wuhan, Hubei 430074 (China); Wang, X. G. [State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing (China)
2015-02-15
A possible origin of edge-localized-mode (ELM) precursors based on nonlinear ideal peeling-ballooning mode is reported. Via nonlinear variational principle, a nonlinear evolution equation of the radial displacement is derived and solved, analytically. Besides an explosive growth in the initial nonlinear phase, it is found that the local displacement evolves into an oscillating state in the developed nonlinear phase. The nonlinear frequency of the ELM precursors scales as ω{sub pre}∼x{sup 1/3}ξ{sup ^}{sub ψ,in}{sup 2/3}n, with x position in radial direction, ξ{sup ^}{sub ψ,in} strength of initial perturbation, and n toroidal mode number.
Nonlinear modes of clarinet-like musical instruments
Noreland, Daniel; Vergez, Christophe; Bouc, Robert
2009-01-01
The concept of nonlinear modes is applied in order to analyze the behavior of a model of woodwind reed instruments. Using a modal expansion of the impedance of the instrument, and by projecting the equation for the acoustic pressure on the normal modes of the air column, a system of second order ordinary differential equations is obtained. The equations are coupled through the nonlinear relation describing the volume flow of air through the reed channel in response to the pressure difference across the reed. The system is treated using an amplitude-phase formulation for nonlinear modes, where the frequency and damping functions, as well as the invariant manifolds in the phase space, are unknowns to be determined. The formulation gives, without explicit integration of the underlying ordinary differential equation, access to the transient, the limit cycle, its period and stability. The process is illustrated for a model reduced to three normal modes of the air column.
Nonlinear modes of clarinet-like musical instruments
Noreland, Daniel; Bellizzi, Sergio; Vergez, Christophe; Bouc, Robert
2009-07-01
The concept of nonlinear modes is applied in order to analyze the behavior of a model of woodwind reed instruments. Using a modal expansion of the impedance of the instrument, and by projecting the equation for the acoustic pressure on the normal modes of the air column, a system of second-order ordinary differential equations is obtained. The equations are coupled through the nonlinear relation describing the volume flow of air through the reed channel in response to the pressure difference across the reed. The system is treated using an amplitude-phase formulation for nonlinear modes, where the frequency and damping functions, as well as the invariant manifolds in the phase space, are unknowns to be determined. The formulation gives, without explicit integration of the underlying ordinary differential equation, access to the transient, the limit cycle, its period and stability. The process is illustrated for a model reduced to three normal modes of the air column.
Seismic base isolation by nonlinear mode localization
Energy Technology Data Exchange (ETDEWEB)
Wang, Y. [University of Illinois, Department of Civil and Environmental Engineering, Urbana, IL (United States); Washington University, Department of Civil and Environmental Engineering, St. Louis, MO (United States); McFarland, D.M. [University of Illinois, Department of Aerospace Engineering, Urbana, IL (United States); Vakakis, A.F. [National Technical University of Athens, Division of Mechanics (Greece); Bergman, L.A. [University of Illinois, Department of Mechanical and Industrial Engineering, Urbana, IL (United States)
2005-03-01
In this paper, the performance of a nonlinear base-isolation system, comprised of a nonlinearly sprung subfoundation tuned in a 1:1 internal resonance to a flexible mode of the linear primary structure to be isolated, is examined. The application of nonlinear localization to seismic isolation distinguishes this study from other base-isolation studies in the literature. Under the condition of third-order smooth stiffness nonlinearity, it is shown that a localized nonlinear normal mode (NNM) is induced in the system, which confines energy to the subfoundation and away from the primary or main structure. This is followed by a numerical analysis wherein the smooth nonlinearity is replaced by clearance nonlinearity, and the system is excited by ground motions representing near-field seismic events. The performance of the nonlinear system is compared with that of the corresponding linear system through simulation, and the sensitivity of the isolation system to several design parameters is analyzed. These simulations confirm the existence of the localized NNM, and show that the introduction of simple clearance nonlinearity significantly reduces the seismic energy transmitted to the main structure, resulting in significant attenuation in the response. (orig.)
Composite fuzzy sliding mode control of nonlinear singularly perturbed systems.
Nagarale, Ravindrakumar M; Patre, B M
2014-05-01
This paper deals with the robust asymptotic stabilization for a class of nonlinear singularly perturbed systems using the fuzzy sliding mode control technique. In the proposed approach the original system is decomposed into two subsystems as slow and fast models by the singularly perturbed method. The composite fuzzy sliding mode controller is designed for stabilizing the full order system by combining separately designed slow and fast fuzzy sliding mode controllers. The two-time scale design approach minimizes the effect of boundary layer system on the full order system. A stability analysis allows us to provide sufficient conditions for the asymptotic stability of the full order closed-loop system. The simulation results show improved system performance of the proposed controller as compared to existing methods. The experimentation results validate the effectiveness of the proposed controller.
Mode matching for optimal plasmonic nonlinear generation
O'Brien, Kevin; Suchowski, Haim; Rho, Jun Suk; Kante, Boubacar; Yin, Xiaobo; Zhang, Xiang
2013-03-01
Nanostructures and metamaterials have attracted interest in the nonlinear optics community due to the possibility of engineering their nonlinear responses; however, the underlying physics to describe nonlinear light generation in nanostructures and the design rules to maximize the emission are still under debate. We study the geometry dependence of the second harmonic and third harmonic emission from gold nanostructures, by designing arrays of nanostructures whose geometry varies from bars to split ring resonators. We fix the length (and volume) of the nanostructure on one axis, and change the morphology from a split ring resonator on the other axis. We observed that the optimal second harmonic generation does not occur at the morphology indicated by a nonlinear oscillator model with parameters derived from the far field transmission and is not maximized by a spectral overlap of the plasmonic modes; however, we find a near field overlap integral and mode matching considerations accurately predict the optimal geometry.
Nonlinear Bogolyubov-Valatin transformations: 2 modes
Scharnhorst, K
2010-01-01
Extending our earlier study of nonlinear Bogolyubov-Valatin transformations (canonical transformations for fermions) for one fermionic mode, in the present paper we perform a thorough study of general (nonlinear) canonical transformations for two fermionic modes. We find that the Bogolyubov-Valatin group for n=2 fermionic modes which can be implemented by means of unitary SU(2^n = 4) transformations is isomorphic to SO(6;R)/Z_2. The investigation touches on a number of subjects. As a novelty from a mathematical point of view, we study the structure of nonlinear basis transformations in a Clifford algebra [specifically, in the Clifford algebra C(0,4)] entailing (supersymmetric) transformations among multivectors of different grades. A prominent algebraic role in this context is being played by biparavectors (products of Dirac matrices, quadriquaternions, sedenions) and spin bivectors (antisymmetric complex matrices). The studied biparavectors are equivalent to Eddington's E-numbers and can be understood in ter...
Lagrangian Space Nonlinear $E$-mode clustering
Yu, Hao-Ran; Zhu, Hong-Ming
2016-01-01
We study the nonlinear $E$-mode clustering in Lagrangian space by using large scale structure (LSS) $N$-body simulations and use the displacement field information in Lagrangian space to recover the primordial linear density field. We find that, compared to Eulerian nonlinear density fields, the $E$-mode displacement fields in Lagrangian space improves the cross-correlation scale $k$ with initial density field by factor of 6 $\\sim$ 7, containing 2 orders of magnitude more primordial information. This illustrates ability of potential density reconstruction algorithms, to improve the baryonic acoustic oscillation (BAO) measurements from current and future large scale structure surveys.
Stability of fractional positive nonlinear systems
Directory of Open Access Journals (Sweden)
Kaczorek Tadeusz
2015-12-01
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.
GA-Based Fuzzy Sliding Mode Controller for Nonlinear Systems
Directory of Open Access Journals (Sweden)
W. L. Chiang
2008-11-01
Full Text Available Generally, the greatest difficulty encountered when designing a fuzzy sliding mode controller (FSMC or an adaptive fuzzy sliding mode controller (AFSMC capable of rapidly and efficiently controlling complex and nonlinear systems is how to select the most appropriate initial values for the parameter vector. In this paper, we describe a method of stability analysis for a GA-based reference adaptive fuzzy sliding model controller capable of handling these types of problems for a nonlinear system. First, we approximate and describe an uncertain and nonlinear plant for the tracking of a reference trajectory via a fuzzy model incorporating fuzzy logic control rules. Next, the initial values of the consequent parameter vector are decided via a genetic algorithm. After this, an adaptive fuzzy sliding model controller, designed to simultaneously stabilize and control the system, is derived. The stability of the nonlinear system is ensured by the derivation of the stability criterion based upon Lyapunov's direct method. Finally, an example, a numerical simulation, is provided to demonstrate the control methodology.
Neural Feedback Passivity of Unknown Nonlinear Systems via Sliding Mode Technique.
Yu, Wen
2015-07-01
Passivity method is very effective to analyze large-scale nonlinear systems with strong nonlinearities. However, when most parts of the nonlinear system are unknown, the published neural passivity methods are not suitable for feedback stability. In this brief, we propose a novel sliding mode learning algorithm and sliding mode feedback passivity control. We prove that for a wide class of unknown nonlinear systems, this neural sliding mode control can passify and stabilize them. This passivity method is validated with a simulation and real experiment tests.
Adaptive Fractional Fuzzy Sliding Mode Control for Multivariable Nonlinear Systems
Junhai Luo; Heng Liu
2014-01-01
This paper presents a robust adaptive fuzzy sliding mode control method for a class of uncertain nonlinear systems. The fractional order calculus is employed in the parameter updating stage. The underlying stability analysis as well as parameter update law design is carried out by Lyapunov based technique. In the simulation, two examples including a comparison with the traditional integer order counterpart are given to show the effectiveness of the proposed method. The main contribution of th...
ON NONLINEAR STABILITY IN NONPARALLEL BOUNDARY LAYER FLOW
Institute of Scientific and Technical Information of China (English)
TANG Deng-bin; WANG Wei-zhi
2004-01-01
The nonlinear stability problem in nonparallel boundary layer flow for two-dimensional disturbances was studied by using a newly presented method called Parabolic Stability Equations (PSE). A series of new modes generated by the nonlinear interaction of disturbance waves were tabulately analyzed, and the Mean Flow Distortion (MFD) was numerically given. The computational techniques developed, including the higher-order spectral method and the more effective algebraic mapping, increased greatly the numerical accuracy and the rate of convergence. With the predictor-corrector approach in the marching procedure, the normalization condition was satisfied, and the stability of numerical calculation could be ensured. With different initial amplitudes, the nonlinear stability of disturbance wave was studied. The results of examples show good agreement with the data given by the DNS using the full Navier-Stokes equations.
Localized modes in nonlinear binary kagome ribbons.
Beličev, P P; Gligorić, G; Radosavljević, A; Maluckov, A; Stepić, M; Vicencio, R A; Johansson, M
2015-11-01
The localized mode propagation in binary nonlinear kagome ribbons is investigated with the premise to ensure controlled light propagation through photonic lattice media. Particularity of the linear system characterized by the dispersionless flat band in the spectrum is the opening of new minigaps due to the "binarism." Together with the presence of nonlinearity, this determines the guiding mode types and properties. Nonlinearity destabilizes the staggered rings found to be nondiffracting in the linear system, but can give rise to dynamically stable ringlike solutions of several types: unstaggered rings, low-power staggered rings, hour-glass-like solutions, and vortex rings with high power. The type of solutions, i.e., the energy and angular momentum circulation through the nonlinear lattice, can be controlled by suitable initial excitation of the ribbon. In addition, by controlling the system "binarism" various localized modes can be generated and guided through the system, owing to the opening of the minigaps in the spectrum. All these findings offer diverse technical possibilities, especially with respect to the high-speed optical communications and high-power lasers.
Localized modes in nonlinear photonic kagome nanoribbons
Energy Technology Data Exchange (ETDEWEB)
Molina, Mario I., E-mail: mmolina@uchile.cl [Departamento de Física, MSI – Nucleus for Advanced Optics, and Center for Optics and Photonics (CEFOP), Facultad de Ciencias, Universidad de Chile, Santiago (Chile)
2012-10-01
We examine localization of light in nonlinear (Kerr) kagome lattices in the shape of narrow strips of varying width. For the narrowest ribbon, the band structure features a flat band leading to linear dynamical trapping of an initially localized excitation. We also find a geometry-induced bistability of the nonlinear modes as the width of the strip is changed. A crossover from one to two dimensions localization behavior is observed as the width is increased, attaining two-dimensional behavior for relatively narrow ribbons.
A spectral characterization of nonlinear normal modes
Cirillo, G. I.; Mauroy, A.; Renson, L.; Kerschen, G.; Sepulchre, R.
2016-09-01
This paper explores the relationship that exists between nonlinear normal modes (NNMs) defined as invariant manifolds in phase space and the spectral expansion of the Koopman operator. Specifically, we demonstrate that NNMs correspond to zero level sets of specific eigenfunctions of the Koopman operator. Thanks to this direct connection, a new, global parametrization of the invariant manifolds is established. Unlike the classical parametrization using a pair of state-space variables, this parametrization remains valid whenever the invariant manifold undergoes folding, which extends the computation of NNMs to regimes of greater energy. The proposed ideas are illustrated using a two-degree-of-freedom system with cubic nonlinearity.
Nonlinear Boundary Stabilization of Nonuniform Timoshenko Beam
Institute of Scientific and Technical Information of China (English)
Qing-xu Yan; Hui-chao Zou; De-xing Feng
2003-01-01
In this paper, the stabilization problem of nonuniform Timoshenko beam by some nonlinear boundary feedback controls is considered. By virtue of nonlinear semigroup theory, energy-perturbed approach and exponential multiplier method, it is shown that the vibration of the beam under the proposed control action decays exponentially or in negative power of time t as t →∞.
Weakly nonlinear stability of vicsous vortices in three-dimensional boundary layers
Bassom, Andrew P.; Otto, S. R.
1993-01-01
Attention is given to the weakly nonlinear stability of essentially viscous vortices in 3D boundary layers. These modes are unstable in the absence of crossflow, but the imposition of small crossflow has a stabilizing effect. Bassom and Hall (1991) demonstrated the existence of neutrally stable vortices for certain crossflow/wave number combinations, and the weakly nonlinear stability properties of these disturbances are described. It is shown that the effect of crossflow is to stabilize the nonlinear modes, and the present calculations allow stable finite-amplitude vortices to be found. Predictions are made concerning the likelihood of observing some of these viscous modes within a practical setting.
Qualitative stability of nonlinear networked systems
Angulo, Marco Tulio; Slotine, Jean-Jacques
2016-01-01
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.
Nonlinear Integral Sliding Mode Control for a Second Order Nonlinear System
Directory of Open Access Journals (Sweden)
Xie Zheng
2015-01-01
Full Text Available A nonlinear integral sliding-mode control (NISMC scheme is proposed for second order nonlinear systems. The new control scheme is characterized by a nonlinear integral sliding manifold which inherits the desired properties of the integral sliding manifold, such as robustness to system external disturbance. In particular, compared with four kinds of sliding mode control (SMC, the proposed control scheme is able to provide better transient performances. Furthermore, the proposed scheme ensures the zero steady-state error in the presence of a constant disturbance or an asymptotically constant disturbance is proved by Lyapunov stability theory and LaSalle invariance principle. Finally, both the theoretical analysis and simulation examples demonstrate the validity of the proposed scheme.
Heli Hu; Dan Zhao; Qingling Zhang
2013-01-01
The sliding mode control and optimization are investigated for a class of nonlinear neutral systems with the unmatched nonlinear term. In the framework of Lyapunov stability theory, the existence conditions for the designed sliding surface and the stability bound ${\\alpha }^{\\ast }$ are derived via twice transformations. The further results are to develop an efficient sliding mode control law with tuned parameters to attract the state trajectories onto the sliding surface in finit...
Nonlinear Bogolyubov-Valatin transformations: Two modes
Scharnhorst, K.; van Holten, J.-W.
2011-11-01
Extending our earlier study of nonlinear Bogolyubov-Valatin transformations (canonical transformations for fermions) for one fermionic mode, in the present paper, we perform a thorough study of general (nonlinear) canonical transformations for two fermionic modes. We find that the Bogolyubov-Valatin group for n=2 fermionic modes, which can be implemented by means of unitary SU(2n=4) transformations, is isomorphic to SO(6;R)/Z2. The investigation touches on a number of subjects. As a novelty from a mathematical point of view, we study the structure of nonlinear basis transformations in a Clifford algebra [specifically, in the Clifford algebra C(0,4)] entailing (supersymmetric) transformations among multivectors of different grades. A prominent algebraic role in this context is being played by biparavectors (linear combinations of products of Dirac matrices, quadriquaternions, sedenions) and spin bivectors (antisymmetric complex matrices). The studied biparavectors are equivalent to Eddington's E-numbers and can be understood in terms of the tensor product of two commuting copies of the division algebra of quaternions H. From a physical point of view, we present a method to diagonalize any arbitrary two-fermion Hamiltonians. Relying on Jordan-Wigner transformations for two-spin- {1}/{2} and single-spin- {3}/{2} systems, we also study nonlinear spin transformations and the related problem of diagonalizing arbitrary two-spin- {1}/{2} and single-spin- {3}/{2} Hamiltonians. Finally, from a calculational point of view, we pay due attention to explicit parametrizations of SU(4) and SO(6;R) matrices (of respective sizes 4×4 and 6×6) and their mutual relation.
A Stability Theory in Nonlinear Programming
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
We propose a new method for finding the local optimal points ofthe constrained nonlinear programming by Ordinary Differential Equations (ODE), and prove asymptotic stability of the singular points of partial variables in this paper. The condition of overall uniform, asymptotic stability is also given.
Mode-locking in nonlinear rotordynamics
van der Heijden, G. H. M.
1995-05-01
We present a computer-assisted study of the dynamics of two nonlinearly coupled driven oscillators with rotational symmetry which arise in rotordynamics (the nonlinearity coming from bearing clearance). The nonlinearity causes a splitting of the twofold degenerate natural frequency of the associated linear model, leading to three interacting frequencies in the system. Partial mode-locking then yields a biinfinite series of attracting invariant 2-tori carrying (quasi-) periodic motion. Due to the resonance nature, the (quasi-) periodic solutions become periodic in a corotating coordinate system. They can be viewed as entrainments of periodic solutions of the associated linear problem. One presumably infinite family is generated by (scaled) driving frequencies ω = 1+2/ n, n = 1,2,3,...; another one is generated by frequencies ω = m, m = 4,5,6,... Both integers n and m can be related to discrete symmetry properties of the particular periodic solutions. Under a perturbation that breaks the rotational symmetry, more complicated behavior is possible. In particular, a second rational relation between the frequencies can be established, resulting in fully mode-locked periodic motion.
Adaptive stabilization for cascade nonlinear systems
Institute of Scientific and Technical Information of China (English)
陈岚萍; 王洪元; 吴波
2004-01-01
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.
Stability analysis of nonlinear systems with slope restricted nonlinearities.
Liu, Xian; Du, Jiajia; Gao, Qing
2014-01-01
The problem of absolute stability of Lur'e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.
Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities
Directory of Open Access Journals (Sweden)
Xian Liu
2014-01-01
Full Text Available The problem of absolute stability of Lur’e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.
Nonlinear ion trap stability analysis
Energy Technology Data Exchange (ETDEWEB)
Mihalcea, Bogdan M; Visan, Gina G, E-mail: bmihal@infim.r [Institute for Laser, Plasma and Radiation Physics (INFLPR), Atomistilor Str. Nr. 409, 077125 Magurele-Bucharest, Jud. Ilfov (Romania)
2010-09-01
This paper investigates the dynamics of an ion confined in a nonlinear Paul trap. The equation of motion for the ion is shown to be consistent with the equation describing a damped, forced Duffing oscillator. All perturbing factors are taken into consideration in the approach. Moreover, the ion is considered to undergo interaction with an external electromagnetic field. The method is based on numerical integration of the equation of motion, as the system under investigation is highly nonlinear. Phase portraits and Poincare sections show that chaos is present in the associated dynamics. The system of interest exhibits fractal properties and strange attractors. The bifurcation diagrams emphasize qualitative changes of the dynamics and the onset of chaos.
Thermally induced nonlinear mode coupling in high power fiber amplifiers
DEFF Research Database (Denmark)
Johansen, Mette Marie; Hansen, Kristian Rymann; Alkeskjold, Thomas T.;
2013-01-01
Thermally induced nonlinear mode coupling leads to transverse mode instability (TMI) in high power fiber amplifiers. A numerical model including altering mode profiles from thermal effects and waveguide perturbations predicts a TMI threshold of ~200W.......Thermally induced nonlinear mode coupling leads to transverse mode instability (TMI) in high power fiber amplifiers. A numerical model including altering mode profiles from thermal effects and waveguide perturbations predicts a TMI threshold of ~200W....
Quadratic stabilization of switched nonlinear systems
Institute of Scientific and Technical Information of China (English)
DONG YaLi; FAN JiaoJiao; MEI ShengWei
2009-01-01
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.
Terminal Sliding Modes In Nonlinear Control Systems
Venkataraman, Subramanian T.; Gulati, Sandeep
1993-01-01
Control systems of proposed type called "terminal controllers" offers increased precision and stability of robotic operations in presence of unknown and/or changing parameters. Systems include special computer hardware and software implementing novel control laws involving terminal sliding modes of motion: closed-loop combination of robot and terminal controller converge, in finite time, to point of stable equilibrium in abstract space of velocity and/or position coordinates applicable to particular control problem.
Adaptive Fractional Fuzzy Sliding Mode Control for Multivariable Nonlinear Systems
Directory of Open Access Journals (Sweden)
Junhai Luo
2014-01-01
Full Text Available This paper presents a robust adaptive fuzzy sliding mode control method for a class of uncertain nonlinear systems. The fractional order calculus is employed in the parameter updating stage. The underlying stability analysis as well as parameter update law design is carried out by Lyapunov based technique. In the simulation, two examples including a comparison with the traditional integer order counterpart are given to show the effectiveness of the proposed method. The main contribution of this paper consists in the control performance is better for the fractional order updating law than that of traditional integer order.
The Nonlinear Instability Modes of Dished Shallow Shells under Circular Line Loads
Liu Chang-Jiang; Zheng Zhou-Lian; Huang Cong-Bing; He Xiao-Ting; Sun Jun-Yi; Chen Shan-Lin
2011-01-01
This paper investigated the nonlinear stability problem of dished shallow shells under circular line loads. We derived the dimensionless governing differential equations of dished shallow shell under circular line loads according to the nonlinear theory of plates and shells and solved the governing differential equations by combing the free-parameter perturbation method (FPPM) with spline function method (SFM) to analyze the nonlinear instability modes of dished shallow shell under circular l...
On the difficulty of determining tearing mode stability
Energy Technology Data Exchange (ETDEWEB)
Bishop, C.M.; Connor, J.W.; Hastie, R.J.; Cowley, S.C. (AEA Technology, Culham (United Kingdom))
1991-04-01
The effect of local pressure gradients and of a local flattening of the pressure profile (p' {yields} 0) around the resonant surface of a tearing mode is investigated in toroidal geometry. It is shown that the stability index {Delta}', calculated from the ideal outer region, is modified by local profile changes in a way reminiscent of the favourable curvature stabilization of linear and non-linear tearing mode layer theory. If the width of the region of pressure flattening is of the order of the linear resistive layer width, the stabilization from the ideal outer region compensates for the loss of pressure gradient stabilization from the layer, and the overall stability of the mode is largely unaffected. For pressure flattening over a larger region, however, the mode can be strongly destabilized. Since the flattening region may then still be too small to resolve experimentally, this result implies the essential difficulty of determining the tearing mode stability of experimental profiles. (Author).
Breatherlike impurity modes in discrete nonlinear lattices
DEFF Research Database (Denmark)
Hennig, D.; Rasmussen, Kim; Tsironis, G. P.
1995-01-01
We investigate the properties of a disordered generalized discrete nonlinear Schrodinger equation, containing both diagonal and nondiagonal nonlinear terms. The equation models a Linear host lattice doped with nonlinear impurities. We find different types of impurity states that form itinerant...
Nonlinear r-modes in rapidly rotating relativistic stars.
Stergioulas, N; Font, J A
2001-02-12
The r-mode instability in rotating relativistic stars has been shown recently to have important astrophysical implications, provided that r-modes are not saturated at low amplitudes by nonlinear effects or by dissipative mechanisms. Here, we present the first study of nonlinear r-modes in isentropic, rapidly rotating relativistic stars, via 3D general-relativistic hydrodynamical evolutions. We find that (1) on dynamical time scales, there is no strong nonlinear coupling of r-modes to other modes at amplitudes of order one-the maximum r-mode amplitude is of order unity. (2) r-modes and inertial modes in isentropic stars are predominantly discrete modes. (3) The kinematical drift associated with r-modes appears to be present in our simulations, but confirmation requires more precise initial data.
Robustness and robust stability of the active sliding mode synchronization
Energy Technology Data Exchange (ETDEWEB)
Naseh, Majid Reza [Electrical Engineering Department, Islamic Azad University, Birjand Branch (Iran, Islamic Republic of)], E-mail: naseh@ee.src.aiu.ir; Haeri, Mohammad [Advanced Control System Lab., Electrical Engineering Department, Sharif University Technology, Tehran (Iran, Islamic Republic of)], E-mail: haeri@sina.sharif.edu
2009-01-15
We have developed relations between uncertainties and signals bounds in one side and the control parameters on the other side in the case of the active sliding mode synchronization. Using Lyapunov stability theorem, we have determined uncertainties levels for which synchronization is achieved for a given set of the control parameters. We have run a nonlinear programming algorithm to determine the control parameters for specific range of the uncertainties. Finally, numerical simulations are presented to verify the derived relations.
Nonlinear localized modes in PT-symmetric Rosen-Morse potential well
Midya, Bikashkali
2013-01-01
We report the existence and properties of localized modes described by nonlinear Schroedinger equation with complex PT-symmetric Rosen-Morse potential well. Exact analytical expressions of the localized modes are found in both one dimensional and two-dimensional geometry with self-focusing and self-defocusing Kerr nonlinearity. Linear stability analysis reveals that these localized modes are unstable for all real values of the potential parameters although corresponding linear Schroedinger eigenvalue problem possesses unbroken PT-symmetry. This result has been verified by the direct numerical simulation of the governing equation. The transverse power flow density associated with these localized modes has also been examined.
Quasinormal modes of four-dimensional topological nonlinear charged Lifshitz black holes
Energy Technology Data Exchange (ETDEWEB)
Becar, Ramon [Universidad Cato lica de Temuco, Departamento de Ciencias Matematicas y Fisicas, Temuco (Chile); Gonzalez, P.A. [Universidad Diego Portales, Facultad de Ingenieria, Santiago (Chile); Vasquez, Yerko [Universidad de La Serena, Departamento de Fisica, Facultad de Ciencias, La Serena (Chile)
2016-02-15
We study scalar perturbations of four- dimensional topological nonlinear charged Lifshitz black holes with spherical and plane transverse sections, and we find numerically the quasinormal modes for scalar fields. Then we study the stability of these black holes under massive and massless scalar field perturbations. We focus our study on the dependence of the dynamical exponent, the nonlinear exponent, the angular momentum, and the mass of the scalar field in the modes. It is found that the modes are overdamped, depending strongly on the dynamical exponent and the angular momentum of the scalar field for a spherical transverse section. In contrast, for plane transverse sections the modes are always overdamped. (orig.)
Nonlinear localized modes in PT-symmetric optical media with competing gain and loss
Midya, Bikashkali
2014-01-01
The existence and stability of the nonlinear spatial localized modes are investigated in parity-time symmetric optical media characterized by a generic complex hyperbolic refractive index distribution with competing gain and loss profile. The exact analytical expressions of the localized modes are found for all values of the competing parameter and in the presence of both the self-focusing and self-defocusing Kerr nonlinearity. The effect of competing gain/loss profile on the stability structure of these localized modes are discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. The spatial localized modes in two-dimensional geometry as well as the transverse power-flow density associated with these localized modes are also examined.
Numerical computation of nonlinear normal modes in mechanical engineering
Renson, L.; Kerschen, G.; Cochelin, B.
2016-03-01
This paper reviews the recent advances in computational methods for nonlinear normal modes (NNMs). Different algorithms for the computation of undamped and damped NNMs are presented, and their respective advantages and limitations are discussed. The methods are illustrated using various applications ranging from low-dimensional weakly nonlinear systems to strongly nonlinear industrial structures.
Nonlinear normal modes and their application in structural dynamics
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available Recent progress in the area of nonlinear modal analysis for structural systems is reported. Systematic methods are developed for generating minimally sized reduced-order models that accurately describe the vibrations of large-scale nonlinear engineering structures. The general approach makes use of nonlinear normal modes that are defined in terms of invariant manifolds in the phase space of the system model. An efficient Galerkin projection method is developed, which allows for the construction of nonlinear modes that are accurate out to large amplitudes of vibration. This approach is successfully extended to the generation of nonlinear modes for systems that are internally resonant and for systems subject to external excitation. The effectiveness of the Galerkin-based construction of the nonlinear normal modes is also demonstrated for a realistic model of a rotating beam.
Characterization of Non-Linearized Spacecraft Relative Motion using Nonlinear Normal Modes
2016-04-20
Non-Linearized Spacecraft Relative Motion using Nonlinear Normal Modes 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 62601F...AFRL-RV-PS- AFRL-RV-PS- TR-2015-0182 TR-2015-0182 CHARACTERIZATION OF NON-LINEARIZED SPACECRAFT RELATIVE MOTION USING NONLINEAR NORMAL MODES Eric...STATEMENT. THOMAS LOVELL PAUL HAUSGEN, Ph.D. Program Manager Technical Advisor, Spacecraft Component Technology JOHN BEAUCHEMIN Chief Engineer
Phase mixing and nonlinearity in geodesic acoustic modes
Energy Technology Data Exchange (ETDEWEB)
Hung, C. P.; Hassam, A. B. [University of Maryland at College Park, College Park, Maryland 20742 (United States)
2013-09-15
Phase mixing and nonlinear resonance detuning of geodesic acoustic modes in a tokamak plasma are examined. Geodesic acoustic modes (GAMs) are tokamak normal modes with oscillations in poloidal flow constrained to lie within flux surfaces. The mode frequency is sonic, dependent on the local flux surface temperature. Consequently, mode oscillations between flux surfaces get rapidly out of phase, resulting in enhanced damping from the phase mixing. Damping rates are shown to scale as the negative 1/3 power of the large viscous Reynolds number. The effect of convective nonlinearities on the normal modes is also studied. The system of nonlinear GAM equations is shown to resemble the Duffing oscillator, which predicts resonance detuning of the oscillator. Resonant amplification is shown to be suppressed nonlinearly. All analyses are verified by numerical simulation. The findings are applied to a recently proposed GAM excitation experiment on the DIII-D tokamak.
On stability of randomly switched nonlinear systems
Chatterjee, Debasish
2007-01-01
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...
Nonlinear tearing mode study using the almost ideal magnetohydrodynamics (MHD) constraint
Energy Technology Data Exchange (ETDEWEB)
Ren, C.; Callen, J.D. [Univ. of Wisconsin, Madison, WI (United States); Jensen, T.H. [General Atomics, San Diego, CA (United States)
1998-12-31
The tearing mode is an important resistive magnetohydrodynamics (MHD) mode. It perturbs the initial equilibrium magnetic flux surfaces through magnetic field line reconnection to form new flux surfaces with magnetic islands. In the study of the tearing mode, usually the initial equilibria are one dimensional with two ignorable coordinates and the perturbed equilibria are two dimensional with one ignorable coordinate. The tearing mode can be linearly unstable and its growth saturates at a fine amplitude. The neoclassical tearing mode theory shows that the mode can be nonlinearly driven by the bootstrap current even when it is linearly stable to the classical tearing mode. It is important to study the nonlinear behavior of the tearing mode. As an intrinsically nonlinear approach, the use of the almost ideal MHD constraint is suited to study the nonlinear properties of the tearing mode. In this paper, as a validation of the method, the authors study two characteristics of the tearing mode using the almost ideal MHD constraint: (1) the linear stability condition for the initial one dimensional equilibrium; and (2) the final saturation level for the unstable case. In this work, they only consider the simplest case where no gradient of pressure or current density exists at the mode resonant surface.
Finite time control for MIMO nonlinear system based on higher-order sliding mode.
Liu, Xiangjie; Han, Yaozhen
2014-11-01
Considering a class of MIMO uncertain nonlinear system, a novel finite time stable control algorithm is proposed based on higher-order sliding mode concept. The higher-order sliding mode control problem of MIMO nonlinear system is firstly transformed into finite time stability problem of multivariable system. Then continuous control law, which can guarantee finite time stabilization of nominal integral chain system, is employed. The second-order sliding mode is used to overcome the system uncertainties. High frequency chattering phenomenon of sliding mode is greatly weakened, and the arbitrarily fast convergence is reached. The finite time stability is proved based on the quadratic form Lyapunov function. Examples concerning the triple integral chain system with uncertainty and the hovercraft trajectory tracking are simulated respectively to verify the effectiveness and the robustness of the proposed algorithm.
Kuehl, Joseph
2016-11-01
The parabolized stability equations (PSE) have been developed as an efficient and powerful tool for studying the stability of advection-dominated laminar flows. In this work, a new "wavepacket" formulation of the PSE is presented. This method accounts for the influence of finite-bandwidth-frequency distributions on nonlinear stability calculations. The methodology is motivated by convolution integrals and is found to appropriately represent nonlinear energy transfer between primary modes and harmonics, in particular nonlinear feedback, via a "nonlinear coupling coefficient." It is found that traditional discrete mode formulations overestimate nonlinear feedback by approximately 70%. This results in smaller maximum disturbance amplitudes than those observed experimentally. The new formulation corrects this overestimation, accounts for the generation of side lobes responsible for spectral broadening and results in disturbance saturation amplitudes consistent with experiment. A Mach 6 flared-cone example is presented. Support from the AFOSR Young Investigator Program via Grant FA9550-15-1-0129 is gratefully acknowledges.
Stability, Nonlinearity and Reliability of Electrostatically Actuated MEMS Devices
Directory of Open Access Journals (Sweden)
Di Chen
2007-05-01
Full Text Available Electrostatic micro-electro-mechanical system (MEMS is a special branch with a wide range of applications in sensing and actuating devices in MEMS. This paper provides a survey and analysis of the electrostatic force of importance in MEMS, its physical model, scaling effect, stability, nonlinearity and reliability in detail. It is necessary to understand the effects of electrostatic forces in MEMS and then many phenomena of practical importance, such as pull-in instability and the effects of effective stiffness, dielectric charging, stress gradient, temperature on the pull-in voltage, nonlinear dynamic effects and reliability due to electrostatic forces occurred in MEMS can be explained scientifically, and consequently the great potential of MEMS technology could be explored effectively and utilized optimally. A simplified parallel-plate capacitor model is proposed to investigate the resonance response, inherent nonlinearity, stiffness softened effect and coupled nonlinear effect of the typical electrostatically actuated MEMS devices. Many failure modes and mechanisms and various methods and techniques, including materials selection, reasonable design and extending the controllable travel range used to analyze and reduce the failures are discussed in the electrostatically actuated MEMS devices. Numerical simulations and discussions indicate that the effects of instability, nonlinear characteristics and reliability subjected to electrostatic forces cannot be ignored and are in need of further investigation.
Stability of switched nonlinear systems via extensions of LaSalle's invariance principle
Institute of Scientific and Technical Information of China (English)
WANG JinHuan; CHENG DaiZhan
2009-01-01
This paper studies the extension of LaSalle's invariance principle for switched nonlinear systems. Unlike most existing results in which each switching mode in the system needs to be asymptotically stable, this paper allows the switching modes to be only stable. Under certain ergodicity assumptions of the switching signals, two extensions of LaSalle's invariance principle for global asymptotic stability of switched nonlinear systems are obtained using the method of common joint Lyapunov function.
Tearing mode stability calculations with pressure flattening
Ham, C J; Cowley, S C; Hastie, R J; Hender, T C; Liu, Y Q
2013-01-01
Calculations of tearing mode stability in tokamaks split conveniently into an external region, where marginally stable ideal MHD is applicable, and a resonant layer around the rational surface where sophisticated kinetic physics is needed. These two regions are coupled by the stability parameter. Pressure and current perturbations localized around the rational surface alter the stability of tearing modes. Equations governing the changes in the external solution and - are derived for arbitrary perturbations in axisymmetric toroidal geometry. The relationship of - with and without pressure flattening is obtained analytically for four pressure flattening functions. Resistive MHD codes do not contain the appropriate layer physics and therefore cannot predict stability directly. They can, however, be used to calculate -. Existing methods (Ham et al. 2012 Plasma Phys. Control. Fusion 54 025009) for extracting - from resistive codes are unsatisfactory when there is a finite pressure gradient at the rational surface ...
Nonlinear localized modes in PT-symmetric optical media with competing gain and loss
Energy Technology Data Exchange (ETDEWEB)
Midya, Bikashkali, E-mail: bikash.midya@gmail.com [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India); Roychoudhury, Rajkumar, E-mail: rroychoudhury123@gmail.com [Advanced Center for Nonlinear and Complex Phenomena, Kolkata 700075 (India)
2014-02-15
The existence and stability of the nonlinear spatial localized modes are investigated in parity-time symmetric optical media characterized by a generic complex hyperbolic refractive index distribution with competing gain and loss profile. The exact analytical expression of the localized modes are found for all values of the competing parameter and in the presence of both the self-focusing and self-defocusing Kerr nonlinearity. The effects of competing gain/loss profile on the stability structure of these localized modes are discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. The spatial localized modes in two-dimensional geometry as well as the transverse power-flow density associated with these localized modes are also examined. -- Highlights: • Existence of localized modes is investigated in PT-symmetric complex potentials. • Exact analytical expression of the localized modes is obtained. • Effect of gain/loss profile on the stability of these localized modes is discussed. • Localized modes in 2D and associated transverse power-flow density are also examined.
Beam stability & nonlinear dynamics. Formal report
Energy Technology Data Exchange (ETDEWEB)
Parsa, Z. [ed.
1996-12-31
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.
Multi-bi- and tri-stability using nonlinear plasmonic Fano resonators
Amin, Muhammad
2013-09-01
A plasmonic Fano resonator embedding Kerr nonlinearity is used to achieve multi-bi- and tri-stability. Fano resonance is obtained by inducing higher-order plasmon modes on metallic surfaces via geometrical symmetry breaking. The presence of the multiple higher order plasmon modes provides the means for producing multi-bi- or tri-stability in the response of the resonator when it is loaded with a material with Kerr nonlinearity. The multi-stability in the response of the proposed resonator enables its use in three-state all optical memory and switching applications. © 2013 IEEE.
Stability of Nonlinear Stochastic Discrete-Time Systems
2013-01-01
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.
Nonlinear asymmetric tearing mode evolution in cylindrical geometry
Teng, Q.; Ferraro, N.; Gates, D. A.; Jardin, S. C.; White, R. B.
2016-10-01
The growth of a tearing mode is described by reduced MHD equations. For a cylindrical equilibrium, tearing mode growth is governed by the modified Rutherford equation, i.e., the nonlinear Δ'(w ) . For a low beta plasma without external heating, Δ'(w ) can be approximately described by two terms, Δ'ql(w ), ΔA'(w ) [White et al., Phys. Fluids 20, 800 (1977); Phys. Plasmas 22, 022514 (2015)]. In this work, we present a simple method to calculate the quasilinear stability index Δql' rigorously, for poloidal mode number m ≥2 . Δql' is derived by solving the outer equation through the Frobenius method. Δ'ql is composed of four terms proportional to: constant Δ'0 , w, w ln w , and w2. ΔA' is proportional to the asymmetry of island that is roughly proportional to w. The sum of Δql' and ΔA' is consistent with the more accurate expression calculated perturbatively [Arcis et al., Phys. Plasmas 13, 052305 (2006)]. The reduced MHD equations are also solved numerically through a 3D MHD code M3D-C1 [Jardin et al., Comput. Sci. Discovery 5, 014002 (2012)]. The analytical expression of the perturbed helical flux and the saturated island width agree with the simulation results. It is also confirmed by the simulation that the ΔA' has to be considered in calculating island saturation.
Sliding mode identifier for parameter uncertain nonlinear dynamic systems with nonlinear input
Institute of Scientific and Technical Information of China (English)
张克勤; 庄开宇; 苏宏业; 褚健; 高红
2002-01-01
This paper presents a sliding mode(SM) based identifier to deal with the parameter idenfification problem for a class of parameter uncertain nonlinear dynamic systems with input nonlinearity. A sliding mode controller (SMC) is used to ensure the global reaching condition of the sliding mode for the nonlinear system;an identifier is designed to identify the uncertain parameter of the nonlinear system. A numerical example is studied to show the feasibility of the SM controller and the asymptotical convergence of the identifier.
Sliding Mode Control for Nonlinear System Based on T-S Model
Institute of Scientific and Technical Information of China (English)
WU Zhong-qiang
2002-01-01
Using T-S model as an approximation for nonlinear system, the nonlinear system has been fuzzy into local linear model. The variable structure controller designed by using Lyapunov theory insures the stability of system. The sliding mode controller is designed by using unit vector style, and it suit the uncertain elements satisfying matching condition or do not satisfy matching condition. The effect of the scheme has been tasted with a simulation of an inverted pendulum.
Modulational stability and dark solitons in periodic quadratic nonlinear media
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2000-01-01
We show that stable dark solitons exist in quadratic nonlinear media with periodic linear and nonlinear susceptibilities. We investigate the modulational stability of plane waves in such systems, a necessary condition for stable dark solitons....
Three-dimensional modes of a symmetric nonlinear plane waveguide
Akhmediev, N. N.; Nabiev, R. F.; Popov, Yu. M.
1989-01-01
The three-dimensional problem of a symmetric nonlinear plane waveguide, which consist of a linear medium layer surrounded by nonlinear media, is investigated. The stationary solution of this problem is a mode whose field is falling to zero at infinity in all directions perpendicular to the propagation direction. The even, odd and assymetrical solutions of the problem are obtained.
Optimal Sliding Mode Controllers for Attitude Stabilization of Flexible Spacecraft
Directory of Open Access Journals (Sweden)
Chutiphon Pukdeboon
2011-01-01
Full Text Available The robust optimal attitude control problem for a flexible spacecraft is considered. Two optimal sliding mode control laws that ensure the exponential convergence of the attitude control system are developed. Integral sliding mode control (ISMC is applied to combine the first-order sliding mode with optimal control and is used to control quaternion-based spacecraft attitude manoeuvres with external disturbances and an uncertainty inertia matrix. For the optimal control part the state-dependent Riccati equation (SDRE and optimal Lyapunov techniques are employed to solve the infinite-time nonlinear optimal control problem. The second method of Lyapunov is used to guarantee the stability of the attitude control system under the action of the proposed control laws. An example of multiaxial attitude manoeuvres is presented and simulation results are included to verify the usefulness of the developed controllers.
Nonlinear physical systems spectral analysis, stability and bifurcations
Kirillov, Oleg N
2013-01-01
Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems.Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynam
Rotational stabilization of q < 1 modes
Energy Technology Data Exchange (ETDEWEB)
Waelbroeck, F.L.; Aydemir, A.Y. [Univ. of Texas, Austin, TX (United States)
1996-12-31
Analyses of high performance discharges with central safety factor below unity have shown that the ideal Magnetohydrodynamic stability threshold for the n=1 kink mode is often violated with impunity. For TFTR (Tokamak Fusion Test Reactor) supershots, the experimental observations can be explained by diamagnetic stabilization of the reconnecting model provided that the fluid free energy is suitably reduced by trapped particle effects. For the broader profiles typical of other high confinement regimes, however, diamagnetic effects cannot account for the experimental results. Furthermore, there is evidence that the Mercier stability condition can also be violated in some cases. Here, we show that toroidal rotation of the plasma can stabilize the kink mode even in the presence of resistivity in configurations that would otherwise be ideally unstable. Two effects can be distinguished. The first effect consists in a reduction of the ideal driving energy. This can be understood in view of the fact that, to a good approximation, the internal kink is a rigid body displacement combining a tilt of the plasma inside the q = 1 surface with a translation along the tilt axis. In the presence of rotation, this displacement must be accompanied by a precessional motion so as to conserve angular momentum. The kinetic energy of the precessional motion must be extracted from the energy driving the displacement. The second effect of rotation is to resolve the Alfven singularity. This is a consequence of the pressure perturbation caused by the equilibrium variation of the entropy within the flux surfaces. It results in the stabilization of resistive as well as weak ideal instabilities, including Mercier modes. For rotationally stabilized equilibria, it also implies the presence of a neutrally stable mode with frequency of the order of the growth rate of the internal kink.
Relationships between nonlinear normal modes and response to random inputs
Schoneman, Joseph D.; Allen, Matthew S.; Kuether, Robert J.
2017-02-01
The ability to model nonlinear structures subject to random excitation is of key importance in designing hypersonic aircraft and other advanced aerospace vehicles. When a structure is linear, superposition can be used to construct its response to a known spectrum in terms of its linear modes. Superposition does not hold for a nonlinear system, but several works have shown that a system's dynamics can still be understood qualitatively in terms of its nonlinear normal modes (NNMs). This work investigates the connection between a structure's undamped nonlinear normal modes and the spectrum of its response to high amplitude random forcing. Two examples are investigated: a spring-mass system and a clamped-clamped beam modeled within a geometrically nonlinear finite element package. In both cases, an intimate connection is observed between the smeared peaks in the response spectrum and the frequency-energy dependence of the nonlinear normal modes. In order to understand the role of coupling between the underlying linear modes, reduced order models with and without modal coupling terms are used to separate the effect of each NNM's backbone from the nonlinear couplings that give rise to internal resonances. In the cases shown here, uncoupled, single-degree-of-freedom nonlinear models are found to predict major features in the response with reasonable accuracy; a highly inexpensive approximation such as this could be useful in design and optimization studies. More importantly, the results show that a reduced order model can be expected to give accurate results only if it is also capable of accurately predicting the frequency-energy dependence of the nonlinear modes that are excited.
New results in global stabilization for stochastic nonlinear systems
Institute of Scientific and Technical Information of China (English)
Tao BIAN; Zhong-Ping JIANG
2016-01-01
This paper presents new results on the robust global stabilization and the gain assignment problems for stochastic nonlinear systems. Three stochastic nonlinear control design schemes are developed. Furthermore, a new stochastic gain assignment method is developed for a class of uncertain interconnected stochastic nonlinear systems. This method can be combined with the nonlinear small-gain theorem to design partial-state feedback controllers for stochastic nonlinear systems. Two numerical examples are given to illustrate the effectiveness of the proposed methodology.
Bifurcation and stability for a nonlinear parabolic partial differential equation
Chafee, N.
1973-01-01
Theorems are developed to support bifurcation and stability of nonlinear parabolic partial differential equations in the solution of the asymptotic behavior of functions with certain specified properties.
Robust stabilization of general nonlinear systems with structural uncertainty
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This paper deals with the robust stabilization and passivity of general nonlinear systems with structural uncertainty. By using Lyapunov function, it verifies that under some conditions the robust passivity implies the zero-state detectability, Furthermore, it also implies the robust stabilization for such nonlinear systems. We then establish a stabilization method for the nonlinear systems with structural uncertainty. The smooth state feedback law can be constructed with the solution of an equation. Finally, it is worth noting that the main contribution of the paper establishes the relation between robust passivity and feedback stabilization for the general nonlinear systems with structural uncertainty. The simulation shows the effectiveness of the method.
Parametric localized modes in quadratic nonlinear photonic structures
DEFF Research Database (Denmark)
Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole;
2001-01-01
We analyze two-color spatially localized nonlinear modes formed by parametrically coupled fundamental and second-harmonic fields excited at quadratic (or chi2) nonlinear interfaces embedded in a linear layered structure-a quadratic nonlinear photonic crystal. For a periodic lattice of nonlinear...... interfaces, we derive an effective discrete model for the amplitudes of the fundamental and second-harmonic waves at the interfaces (the so-called discrete chi2 equations) and find, numerically and analytically, the spatially localized solutions-discrete gap solitons. For a single nonlinear interface...... in a linear superlattice, we study the properties of two-color localized modes, and describe both similarities to and differences from quadratic solitons in homogeneous media....
Integral sliding mode control for a class of nonlinear neutral systems with time-varying delays
Institute of Scientific and Technical Information of China (English)
Lou Xu-Yang; Cui Bao-Tong
2008-01-01
This paper focuses on sliding mode control problems for a class of nonlinear neutral systems with time-varying delays. An integral sliding surface is firstly constructed. Then it finds a useful criteria to guarantee the global stability for the nonlinear neutral systems with time-varying delays in the specified switching surface, whose condition is formulated as linear matrix inequality. The synthesized sliding mode controller guarantees the reachability of the specified sliding surface. Finally, a numerical simulation validates the effectiveness and feasibility of the proposed technique.
Weakly Nonlinear Stability Analysis of a Thin Magnetic Fluid during Spin Coating
Directory of Open Access Journals (Sweden)
Cha'o-Kuang Chen
2010-01-01
Full Text Available This paper investigates the stability of a thin electrically conductive fluid under an applied uniform magnetic filed during spin coating. A generalized nonlinear kinematic model is derived by the long-wave perturbation method to represent the physical system. After linearizing the nonlinear evolution equation, the method of normal mode is applied to study the linear stability. Weakly nonlinear dynamics of film flow is studied by the multiple scales method. The Ginzburg-Landau equation is determined to discuss the necessary conditions of the various critical flow states, namely, subcritical stability, subcritical instability, supercritical stability, and supercritical explosion. The study reveals that the rotation number and the radius of the rotating circular disk generate similar destabilizing effects but the Hartmann number gives a stabilizing effect. Moreover, the optimum conditions can be found to alter stability of the film flow by controlling the applied magnetic field.
Nonlinear r-Modes in Neutron Stars Instability of an unstable mode
Gressman, P T; Suen, W M; Stergioulas, N; Friedman, J L; Gressman, Philip; Lin, Lap-Ming; Suen, Wai-Mo; Friedman, John L.
2002-01-01
We study the dynamical evolution of a large amplitude r-mode by numerical simulations. R-modes in neutron stars are unstable growing modes, driven by gravitational radiation reaction. In these simulations, r-modes of amplitude unity or above are destroyed by a catastrophic decay: A large amplitude r-mode gradually leaks energy into other fluid modes, which in turn act nonlinearly with the r-mode, leading to the onset of the rapid decay. As a result the r-mode suddenly breaks down into a differentially rotating configuration. The catastrophic decay does not appear to be related to shock waves at the star's surface. The limit it imposes on the r-mode amplitude is significantly smaller than that suggested by previous fully nonlinear numerical simulations.
Chattering-Free Sliding-Mode Control for Electromechanical Actuator with Backlash Nonlinearity
Directory of Open Access Journals (Sweden)
Dongqi Ma
2017-01-01
Full Text Available Considering the backlash nonlinearity and parameter time-varying characteristics in electromechanical actuators, a chattering-free sliding-mode control strategy is proposed in this paper to regulate the rudder angle and suppress unknown external disturbances. Different from most existing backlash compensation methods, a special continuous function is addressed to approximate the backlash nonlinear dead-zone model. Regarding the approximation error, unmodeled dynamics, and unknown external disturbances as a disturbance-like term, a strict feedback nonlinear model is established. Based on this nonlinear model, a chattering-free nonsingular terminal sliding-mode controller is proposed to achieve the rudder angle tracking with a chattering elimination and tracking dynamic performance improvement. A Lyapunov-based proof ensures the asymptotic stability and finite-time convergence of the closed-loop system. Experimental results have verified the effectiveness of the proposed method.
The Nonlinear Instability Modes of Dished Shallow Shells under Circular Line Loads
Directory of Open Access Journals (Sweden)
Liu Chang-Jiang
2011-01-01
Full Text Available This paper investigated the nonlinear stability problem of dished shallow shells under circular line loads. We derived the dimensionless governing differential equations of dished shallow shell under circular line loads according to the nonlinear theory of plates and shells and solved the governing differential equations by combing the free-parameter perturbation method (FPPM with spline function method (SFM to analyze the nonlinear instability modes of dished shallow shell under circular line loads. By analyzing the nonlinear instability modes and combining with concrete computational examples, we obtained the variation rules of the maximum deflection area of initial instability with different geometric parameters and loading action positions and discussed the relationship between the initial instability area and the maximum deflection area of initial instability. The results obtained from this paper provide some theoretical basis for engineering design and instability prediction and control of shallow-shell structures.
Nonlinear vibrations and stability of aerostatic bearing
Directory of Open Access Journals (Sweden)
Kozánek J.
2008-12-01
Full Text Available Bearings based on aerostatic principle belong to the new machine elements advantageous for low- and high-speed applications, but their dynamic and stability properties are not yet sufficiently known. This paper presents a new elaborated method and gained results of theoretical investigation of dynamic properties of aerostatic bearing in general dimensionless form. It is aimed also as a supporting tool for diagnostic and identification methods used at developing of new bearings proposed by TECHLAB, Prague for industrial applications. Mathematical model expresses nonlinear and evolutive properties in the entire area of bearing clearance, contains sufficient number of free parameters in functions of restoring and damping forces and can therefore describe all types of motions occurring in gas bearings as periodic, quasi-periodic, including beats and instability, which can leads to chaotic and self-excited vibrations. The influence of non-diagonal elements of stiffness and damping matrices of linearized model on the spectral properties and the stability of system is investigated, too.
Stability analysis of embedded nonlinear predictor neural generalized predictive controller
Directory of Open Access Journals (Sweden)
Hesham F. Abdel Ghaffar
2014-03-01
Full Text Available Nonlinear Predictor-Neural Generalized Predictive Controller (NGPC is one of the most advanced control techniques that are used with severe nonlinear processes. In this paper, a hybrid solution from NGPC and Internal Model Principle (IMP is implemented to stabilize nonlinear, non-minimum phase, variable dead time processes under high disturbance values over wide range of operation. Also, the superiority of NGPC over linear predictive controllers, like GPC, is proved for severe nonlinear processes over wide range of operation. The necessary conditions required to stabilize NGPC is derived using Lyapunov stability analysis for nonlinear processes. The NGPC stability conditions and improvement in disturbance suppression are verified by both simulation using Duffing’s nonlinear equation and real-time using continuous stirred tank reactor. Up to our knowledge, the paper offers the first hardware embedded Neural GPC which has been utilized to verify NGPC–IMP improvement in realtime.
Stability Analysis for Class of Switched Nonlinear Systems
DEFF Research Database (Denmark)
Shaker, Hamid Reza; How, Jonathan P.
2010-01-01
Stability analysis for a class of switched nonlinear systems is addressed in this paper. Two linear matrix inequality (LMI) based sufficient conditions for asymptotic stability are proposed for switched nonlinear systems. These conditions are analogous counterparts for switched linear systems which...
ABSOLUTE STABILITY OF GENERAL LURIE DISCRETE NONLINEAR CONTROL SYSTEMS
Institute of Scientific and Technical Information of China (English)
GAN Zuoxin; HAN Jingqing; ZHAO Suxia; WU Yongxian
2002-01-01
In the present paper, the absolute stability of general Lurie discrete nonlinear control systems has been discussed by Lyapunov function approach. A sufficient condition of absolute stability for the general Lurie discrete nonlinear control systems is derived, and some necessary and sufficient conditions are obtained in special cases. Meanwhile, we give a simple example to illustrate the effectiveness of the results.
Adaptive Fuzzy Integral Sliding-Mode Regulator for Induction Motor Using Nonlinear Sliding Surface
Directory of Open Access Journals (Sweden)
Yong-Kun Lu
2015-02-01
Full Text Available An adaptive fuzzy integral sliding-mode controller using nonlinear sliding surface is designed for the speed regulator of a field-oriented induction motor drive in this paper. Combining the conventional integral sliding surface with fractional-order integral, a nonlinear sliding surface is proposed for the integral sliding-mode speed control, which can overcome the windup problem and the convergence speed problem. An adaptive fuzzy control term is utilized to approximate the uncertainty. The stability of the controller is analyzed by Lyapunov stability theory. The effectiveness of the proposed speed regulator is demonstrated by the simulation results in comparison with the conventional integral sliding-mode controller based on boundary layer.
Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative
2011-01-01
This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function. Then, the fractional differential inequalities and comparison method are applied to the analysis of the stability of fractional differential systems. In addition, some other sufficient conditions on stability are also presented.
Stability Analysis and Design for Nonlinear Singular Systems
Yang, Chunyu; Zhou, Linna
2013-01-01
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...
The K-Stability of Nonlinear Delay Systems
Institute of Scientific and Technical Information of China (English)
章毅; 张毅; 王联
1994-01-01
In this paper,we study the K-stability theory of nonlinear delay systems.In the more general case,we establish two nonlinear delay differential inequalities.Therefore,to study the X-stability,a powerful method is provided.By making use of the foregoing inequalities,we analyse and investigate some K-stabiiity conditions of nonlinear delay systems.Finally,some examples are given to illustrate our theory.
Contribution to stability analysis of nonlinear control systems
Directory of Open Access Journals (Sweden)
varc Ivan
2003-12-01
Full Text Available The Popov criterion for the stability of nonlinear control systems is considered. The Popov criterion gives sufficient conditions for stability of nonlinear systems in the frequency domain. It has a direct graphical interpretation and is convenient for both design and analysis. In the article presented, a table of transfer functions of linear parts of nonlinear systems is constructed. The table includes frequency response functions and offers solutions to the stability of the given systems. The table makes a direct stability analysis of selected nonlinear systems possible. The stability analysis is solved analytically and graphically.Then it is easy to find out if the nonlinear system is or is not stable; the task that usually ranks among the difficult task in engineering practice.
Full-State Linearization and Stabilization of SISO Markovian Jump Nonlinear Systems
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Zhongwei Lin
2013-01-01
Full Text Available This paper investigates the linearization and stabilizing control design problems for a class of SISO Markovian jump nonlinear systems. According to the proposed relative degree set definition, the system can be transformed into the canonical form through the appropriate coordinate changes followed with the Markovian switchings; that is, the system can be full-state linearized in every jump mode with respect to the relative degree set n,…,n. Then, a stabilizing control is designed through applying the backstepping technique, which guarantees the asymptotic stability of Markovian jump nonlinear systems. A numerical example is presented to illustrate the effectiveness of our results.
Intrinsic localized modes and nonlinear impurity modes in curved Fermi-Pasta-Ulam chain
Indian Academy of Sciences (India)
Ranja Sarkar; Bishwajyoti Dey
2008-06-01
We explore the nature of intrinsic localized modes (ILMs) in a curved FermiPasta-Ulam (FPU) chain and the effects of geometry and second-neighbor interaction on the localization and movability properties of such modes. We determine analytically the structure of the localized modes induced by an isotopic light-mass impurity in this chain. We further demonstrate that a nonlinear impurity mode may be treated as a bound state of an ILM with the impurity.
NOLB: Nonlinear Rigid Block Normal Mode Analysis Method
Hoffmann, Alexandre; Grudinin, Sergei
2017-01-01
International audience; We present a new conceptually simple and computationally efficient method for non-linear normal mode analysis called NOLB. It relies on the rotations-translations of blocks (RTB) theoretical basis developed by Y.-H. Sanejouand and colleagues. We demonstrate how to physically interpret the eigenvalues computed in the RTB basis in terms of angular and linear velocities applied to the rigid blocks and how to construct a non-linear extrapolation of motion out of these velo...
Stabilization of a class of switched nonlinear systems
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The stabilization of a class of switched nonlinear systems is investigated in the paper. The systems concerned are of (generalized) switched Byrnes-Isidori canonical form, which has all switched models in (generalized) ByrnesIsidori canonical form. First, a stability result of switched systems is obtained. Then it is used to solve the stabilization problem of the switched nonlinear control systems. In addition, necessary and sufficient conditions are obtained for a switched affine nonlinear system to be feedback equivalent to (generalized) switched Byrnes-Isidori canonical systems are presented.Finally, as an application the stability of switched lorenz systems is investigated.
Nonlinear saturation of trapped electron modes via perpendicular particle diffusion.
Merz, F; Jenko, F
2008-01-25
In magnetized fusion plasmas, trapped electron mode (TEM) turbulence constitutes, together with ion temperature gradient (ITG) turbulence, the dominant source of anomalous transport on ion scales. While ITG modes are known to saturate via nonlinear zonal flow generation, this mechanism is shown to be of little importance for TEM turbulence in the parameter regime explored here. Instead, a careful analysis of the statistical properties of the ExB nonlinearity in the context of gyrokinetic turbulence simulations reveals that perpendicular particle diffusion is the dominant saturation mechanism. These findings allow for the construction of a rather realistic quasilinear model of TEM induced transport.
W-Stability of Multistable Nonlinear Discrete-Time Systems
Directory of Open Access Journals (Sweden)
Zhishuai Ding
2012-01-01
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.
Nonlinear Mirror Modes in Space Plasmas
Sulem, P -L
2011-01-01
Since the first observations by Kaufmann et al.\\ (1970), special attention has been paid to static pressure-balanced structures in the form of magnetic holes or humps observed in regions of the solar wind and of planetary magnetosheaths where the $\\beta$ parameter is relatively large and the ion perpendicular temperature exceeds the parallel one. Although alternative interpretations have been proposed, these structures are usually viewed as associated with the mirror instability discovered in 1957 by Vedenov and Sagdeev. After reviewing observational results provided by satellite missions, high-resolution numerical simulations of the Vlasov--Maxwell equations together with asymptotic and phenomenological models of the nonlinear dynamics near the instability threshold are discussed. The constraining effect of the mirror instability on the temperature anisotropy associated with a dominant perpendicular ion heating observed in the solar wind is reported, and recent simulations of this phenomenon based on an elab...
Indian Academy of Sciences (India)
Shyamal Mondal; Satya Pratap Singh; Sourabh Mukhopadhyay; Aditya Date; Kamal Hussain; Shouvik Mukherjee; Prasanta Kumar Datta
2014-02-01
A comparative study in terms of optimized output power and stability is made on cascaded second-order nonlinear optical mode-locking with KTP, BBO and LBO crystals for both 1064 nm and 532 nm. Large nonlinear optical phase shift achieved in a non-phase-matched second harmonic generating crystal, is transformed into amplitude modulation through soft aperturing the nonlinear cavity mode variation at the laser gain medium to mode-lock a Nd:YVO4 laser. The laser delivers stable dual wavelength cw mode-locked pulse train with pulse duration 10.3 ps and average power of 1.84 W and 255 mW at 1064 nm and 532 nm respectively for the optimum performance in type-II KTP crystal. The exceptional stability achieved with KTP is accounted by simulating the mode-size variation with phase mismatch.
Mode stability on the real axis
Andersson, Lars; Paganini, Claudio; Whiting, Bernard F
2016-01-01
A generalization of the mode stability result of Whiting (1989) for the Teukolsky equation is proved for the case of real frequencies. The main result of the paper states that a separated solution of the Teukolsky equation governing massless test fields on the Kerr spacetime, which is purely outgoing at infinity, and purely ingoing at the horizon, must vanish. This has the consequence, that for real frequencies, there are linearly independent fundamental solutions of the radial Teukolsky equation which are purely ingoing at the horizon, and purely outgoing at infinity, respectively. This fact yields a representation formula for solutions of the inhomogenous Teukolsky equation.
Sliding mode identifier for parameter uncertain nonlinear dynamic systems with nonlinear input
Institute of Scientific and Technical Information of China (English)
张克勤; 庄开宇; 苏宏业; 褚健; 高红
2002-01-01
This paper presents a sliding mode (SM) based identifier to deal wit h the parameter identification problem for a class of parameter uncertain nonlin ear dynamic systems with input nonlinearity. A sliding mode controller (SMC) is used to ensure the global reaching condition of the sliding mode for the nonline ar system; an identifier is designed to identify the uncertain parameter of the nonlinear system. A numerical example is studied to show the feasibility of the SM controller and the asymptotical convergence of the identifier.
The nonlinear evolution of modes on unstable stratified shear layers
Blackaby, Nicholas; Dando, Andrew; Hall, Philip
1993-06-01
The nonlinear development of disturbances in stratified shear flows (having a local Richardson number of value less than one quarter) is considered. Such modes are initially fast growing but, like related studies, we assume that the viscous, non-parallel spreading of the shear layer results in them evolving in a linear fashion until they reach a position where their amplitudes are large enough and their growth rates have diminished sufficiently so that amplitude equations can be derived using weakly nonlinear and non-equilibrium critical-layer theories. Four different basic integro-differential amplitude equations are possible, including one due to a novel mechanism; the relevant choice of amplitude equation, at a particular instance, being dependent on the relative sizes of the disturbance amplitude, the growth rate of the disturbance, its wavenumber, and the viscosity of the fluid. This richness of choice of possible nonlinearities arises mathematically from the indicial Frobenius roots of the governing linear inviscid equation (the Taylor-Goldstein equation) not, in general, differing by an integer. The initial nonlinear evolution of a mode will be governed by an integro-differential amplitude equations with a cubic nonlinearity but the resulting significant increase in the size of the disturbance's amplitude leads on to the next stage of the evolution process where the evolution of the mode is governed by an integro-differential amplitude equations with a quintic nonlinearity. Continued growth of the disturbance amplitude is expected during this stage, resulting in the effects of nonlinearity spreading to outside the critical level, by which time the flow has become fully nonlinear.
Fuzzy Sliding Mode Controller Design Using Takagi-Sugeno Modelled Nonlinear Systems
Directory of Open Access Journals (Sweden)
S. Bououden
2013-01-01
Full Text Available Adaptive fuzzy sliding mode controller for a class of uncertain nonlinear systems is proposed in this paper. The unknown system dynamics and upper bounds of the minimum approximation errors are adaptively updated with stabilizing adaptive laws. The closed-loop system driven by the proposed controllers is shown to be stable with all the adaptation parameters being bounded. The performance and stability of the proposed control system are achieved analytically using the Lyapunov stability theory. Simulations show that the proposed controller performs well and exhibits good performance.
Tearing Mode Stability with Sheared Toroidal Flows
White, Ryan; Coppi, Bruno
2016-10-01
Toroidal plasma flow induced by neutral beam heating has been found to increase the stability of tearing modes in tokamak plasmas. The need to extrapolate current (experimentally-based) knowledge of tearing mode onset to future machines, requiresa better understanding of the essential physics. We consider the physics of flow near the rational surfaces. For realistic flow profiles, the velocity shear near the rational surface can be treated as a perturbation, and is found to amplify the dominant stabilizing effect of magnetic curvature. This effect can be seen using a cylindrical model if large-aspect-ratio corrections to the magnetic curvature are incorporated. On the other hand, the physical effects of toroidal rotation are completely absent in a cylinder, and require a fully-toroidal calculation to study. The toroidal rotation near the rational surface is found to couple to a geometrical parameter which vanishes for up-down symmetric profiles. Physically, the dominant effects of rotation arise from a Coriolis force, leading to flow directional dependence. This work is supported by the US DOE.
Wall mode stabilization at slow plasma rotation
Hu, Bo; Betti, Riccardo; Reimerdes, Holger; Garofalo, Andrea; Manickam, Janardhan
2007-11-01
Unstable pressure-driven external kink modes, which become slowly growing resistive wall modes (RWMs) in the presence of a resistive wall, can lead to tokamak plasma disruptions at high beta. It has been shown that RWMs are stabilized by fast plasma rotation (about 1-2% of the Alfv'en frequency) in experiments. Conventional theories attribute the RWM suppression to the dissipation induced by the resonances between plasma rotation and ion bounce/transit or shear Alfv'en frequencies [1]. In those theories, the kinetic effects associated with the plasma diamagnetic frequencies and trapped-particle precession drift frequencies are neglected. It has been observed in recent experiments [2,3] that the RWM suppression also occurs at very slow plasma rotation (about 0.3% of the Alfv'en frequency), where the conventional dissipation is too small to fully suppress the RWMs. Here it is shown, that the trapped-particle kinetic contribution associated with the precession motion [4] is large enough to stabilize the RWM in DIII-D at low rotation. Work supported by the US-DoE OFES. [1] A. Bondeson and M. S. Chu, Physics of Plasmas, 3,3013 (1996). [2] H. Reimerdes et al., Physical Review Letters, 98,055001 (2007). [3] M. Takechi et al., Physical Review Letters, 98,055002 (2007). [4] B. Hu and R. Betti, Physical Review Letters, 93,105002 (2004).
Nonlinear plastic modes in disordered solids.
Gartner, Luka; Lerner, Edan
2016-01-01
We propose a theoretical framework within which a robust micromechanical definition of precursors to plastic instabilities, often termed soft spots, naturally emerges. They are shown to be collective displacements (modes) z[over ̂] that correspond to local minima of a barrier function b(z[over ̂]), which depends solely on inherent structure information. We demonstrate how some heuristic searches for local minima of b(z[over ̂]) can a priori detect the locus and geometry of imminent plastic instabilities with remarkable accuracy, at strains as large as γ_{c}-γ∼10^{-2} away from the instability strain γ_{c}. Our findings suggest that the a priori detection of the entire field of soft spots can be effectively carried out by a systematic investigation of the landscape of b(z[over ̂]).
Uncertain Unified Chaotic Systems Control with Input Nonlinearity via Sliding Mode Control
Directory of Open Access Journals (Sweden)
Zhi-ping Shen
2016-01-01
Full Text Available This paper studies the stabilization problem for a class of unified chaotic systems subject to uncertainties and input nonlinearity. Based on the sliding mode control theory, we present a new method for the sliding mode controller design and the control law algorithm for such systems. In order to achieve the goal of stabilization unified chaotic systems, the presented controller can make the movement starting from any point in the state space reach the sliding mode in limited time and asymptotically reach the origin along the switching surface. Compared with the existing literature, the controller designed in this paper has many advantages, such as small chattering, good stability, and less conservative. The analysis of the motion equation and the simulation results all demonstrate that the method is effective.
Robust stabilization for a class of nonlinear networked control systems
Institute of Scientific and Technical Information of China (English)
Jinfeng GAO; Hongye SU; Xiaofu JI; Jian CHU
2008-01-01
The problem of robust stabilization for a class of uncertain networked control systems(NCSs)with nonlinearities satisfying a given sector condition is investigated in this paper.By introducing a new model of NCSs with parameter uncertainty,network.induced delay,nonlinearity and data packet dropout in the transmission,a strict linear matrix inequality(LMI)criterion is proposed for robust stabilization of the uncenmn nonlinear NCSs based on the Lyapunov stability theory.The maximum allowable transfer interval(MATI)can be derived by solving the feasibility problem of the corresponding LMI.Some numerical examples are provided to demonstrate the applicability of the proposed algorithm.
Edge localized mode rotation and the nonlinear dynamics of filaments
Energy Technology Data Exchange (ETDEWEB)
Morales, J. A.; Bécoulet, M.; Garbet, X.; Dif-Pradalier, G.; Huijsmans, G. T. A.; Fil, A.; Nardon, E.; Passeron, C.; Latu, G. [CEA, IRFM, 13108 St. Paul-Lez-Durance (France); Orain, F.; Hoelzl, M. [Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching (Germany); Pamela, S. [CCFE, Culham Science Centre, Abingdon, Oxon OX14 3DB (United Kingdom); Cahyna, P. [Institute of Plasma Physics ASCR, Za Slovankou 1782/3, 182 00 Prague 8 (Czech Republic)
2016-04-15
Edge Localized Modes (ELMs) rotating precursors were reported few milliseconds before an ELM crash in several tokamak experiments. Also, the reversal of the filaments rotation at the ELM crash is commonly observed. In this article, we present a mathematical model that reproduces the rotation of the ELM precursors as well as the reversal of the filaments rotation at the ELM crash. Linear ballooning theory is used to establish a formula estimating the rotation velocity of ELM precursors. The linear study together with nonlinear magnetohydrodynamic simulations give an explanation to the rotations observed experimentally. Unstable ballooning modes, localized at the pedestal, grow and rotate in the electron diamagnetic direction in the laboratory reference frame. Approaching the ELM crash, this rotation decreases corresponding to the moment when the magnetic reconnection occurs. During the highly nonlinear ELM crash, the ELM filaments are cut from the main plasma due to the strong sheared mean flow that is nonlinearly generated via the Maxwell stress tensor.
Edge localized mode rotation and the nonlinear dynamics of filaments
Morales, J. A.; Bécoulet, M.; Garbet, X.; Orain, F.; Dif-Pradalier, G.; Hoelzl, M.; Pamela, S.; Huijsmans, G. T. A.; Cahyna, P.; Fil, A.; Nardon, E.; Passeron, C.; Latu, G.
2016-04-01
Edge Localized Modes (ELMs) rotating precursors were reported few milliseconds before an ELM crash in several tokamak experiments. Also, the reversal of the filaments rotation at the ELM crash is commonly observed. In this article, we present a mathematical model that reproduces the rotation of the ELM precursors as well as the reversal of the filaments rotation at the ELM crash. Linear ballooning theory is used to establish a formula estimating the rotation velocity of ELM precursors. The linear study together with nonlinear magnetohydrodynamic simulations give an explanation to the rotations observed experimentally. Unstable ballooning modes, localized at the pedestal, grow and rotate in the electron diamagnetic direction in the laboratory reference frame. Approaching the ELM crash, this rotation decreases corresponding to the moment when the magnetic reconnection occurs. During the highly nonlinear ELM crash, the ELM filaments are cut from the main plasma due to the strong sheared mean flow that is nonlinearly generated via the Maxwell stress tensor.
Symmetry, stability, and computation of degenerate lasing modes
Liu, David; Ge, Li; Hernandez, Felipe; Pick, Adi; Burkhardt, Stephan; Liertzer, Matthias; Rotter, Stefan; Johnson, Steven G
2016-01-01
We present a general method to obtain the stable lasing solutions for the steady-state ab-initio lasing theory (SALT) for the case of a degenerate symmetric laser in two dimensions (2d). We find that under most regimes (with one pathological exception), the stable solutions are clockwise and counterclockwise circulating modes, generalizing previously known results of ring lasers to all 2d rotational symmetry groups. Our method uses a combination of semi-analytical solutions close to lasing threshold and numerical solvers to track the lasing modes far above threshold. Near threshold, we find closed-form expressions for both circulating modes and other types of lasing solutions as well as for their linearized Maxwell--Bloch eigenvalues, providing a simple way to determine their stability without having to do a full nonlinear numerical calculation. Above threshold, we show that a key feature of the circulating mode is its "chiral" intensity pattern, which arises from spontaneous symmetry-breaking of mirror symme...
Optical surface modes in the presence of nonlinearity and disorder
Molina, M I; Tsironis, G P
2011-01-01
We investigate numerically the effect of the competition of disorder, nonlinearity, and boundaries on the Anderson localization of light waves in finite-size, one-dimensional waveguide arrays. Using the discrete Anderson - nonlinear Schr\\"odinger equation, the propagation of the mode amplitudes up to some finite distance is monitored. The analysis is based on the calculated localization length and the participation number, two standard measures for the statistical description of Anderson localization. For relatively weak disorder and nonlinearity, a higher disorder strength is required to achieve the same degree of localization at the edge than in the interior of the array, in agreement with recent experimental observations in the linear regime. However, for relatively strong disorder and/or nonlinearity, this behavior is reversed and it is now easier to localize an excitation at the edge than in the interior.
Stabilization of nonlinear excitations by disorder
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Johansson, M.
1998-01-01
Using analytical and numerical techniques we analyze the static and dynamical properties of solitonlike excitations in the presence of parametric disorder in the one-dimensional nonlinear Schrodinger equation with a homogeneous power nonlinearity. Both the continuum and the discrete problem are i...
Komech, A I; Stuart, D
2008-01-01
The long-time asymptotics is analyzed for finite energy solutions of the 1D Schr\\"odinger equation coupled to a nonlinear oscillator; mathematically the system under study is a nonlinear Schr\\"odinger equation, whose nonlinear term includes a Dirac delta. The coupled system is invariant with respect to the phase rotation group U(1). This article, which extends the results of a previous one, provides a proof of asymptotic stability of solitary wave solutions in the case that the linearization contains a single discrete oscillatory mode satisfying a non-degeneracy assumption of the type known as the Fermi Golden Rule.
Nonlinear Control Strategies for Bioprocesses: Sliding Mode Control versus Vibrational Control
Selisteanu, Dan; Petre, Emil; Popescu, Dorin; Bobasu, Eugen
2008-01-01
In this work, two nonlinear high-frequency control strategies for bioprocesses are proposed: a feedback sliding mode control law and a vibrational control strategy. In order to implement these strategies, a prototype bioprocess that is carried out in a Continuous Stirred Tank Bioreactor was considered. First, a discontinuous feedback law was designed using the exact linearization and by imposing a SMC that stabilizes the output of the bioprocess. When some state variables used in the control ...
Fuzzy fractional order sliding mode controller for nonlinear systems
Delavari, H.; Ghaderi, R.; Ranjbar, A.; Momani, S.
2010-04-01
In this paper, an intelligent robust fractional surface sliding mode control for a nonlinear system is studied. At first a sliding PD surface is designed and then, a fractional form of these networks PDα, is proposed. Fast reaching velocity into the switching hyperplane in the hitting phase and little chattering phenomena in the sliding phase is desired. To reduce the chattering phenomenon in sliding mode control (SMC), a fuzzy logic controller is used to replace the discontinuity in the signum function at the reaching phase in the sliding mode control. For the problem of determining and optimizing the parameters of fuzzy sliding mode controller (FSMC), genetic algorithm (GA) is used. Finally, the performance and the significance of the controlled system two case studies (robot manipulator and coupled tanks) are investigated under variation in system parameters and also in presence of an external disturbance. The simulation results signify performance of genetic-based fuzzy fractional sliding mode controller.
Stability of Nonlinear Force-Free Magnetic Fields
Institute of Scientific and Technical Information of China (English)
胡友秋
2001-01-01
Based on the magnetohydrodynamic energy principle, it is proved that Gold-Hoyle's nonlinear force-free magnetic field is unstable. This disproves the sufficient criterion for stability of nonlinear force-free magnetic fields given by Kriiger that a nonlinear force-free field is stable if the maximum absolute value of the force-free factor is smaller than the lowest eigenvalue associated with the domain of interest.
Weakly nonlinear stability of ultra-thin slipping films
Institute of Scientific and Technical Information of China (English)
HU Guohui
2005-01-01
A weakly nonlinear theory is presented to study the effects of slippage on the stability of the ultra-thin polymer films.The nonlinear mathematical model is constructed for perturbations of small finite amplitude based on hydrodynamic equations with the long wave approximation. Results reveal that the nonlinearity always accelerates the rupture of the films. The influences of the slip length, film thickness, and initial amplitude of perturbations on the rupture of the films are investigated.
Nonlinear modes and symmetry breaking in rotating double-well potentials
Li, Yongyao; Malomed, Boris A
2012-01-01
We study modes trapped in a rotating ring carrying the self-focusing (SF) or defocusing (SDF) cubic nonlinearity and double-well potential $\\cos^{2}\\theta $, where $\\theta $ is the angular coordinate. The model, based on the nonlinear Schr\\"{o}dinger (NLS) equation in the rotating reference frame, describes the light propagation in a twisted pipe waveguide, as well as in other optical settings, and also a Bose-Einstein condensate (BEC)trapped in a torus and dragged by the rotating potential. In the SF and SDF regimes, five and four trapped modes of different symmetries are found, respectively. The shapes and stability of the modes, and transitions between them are studied in the first rotational Brillouin zone. In the SF regime, two symmetry-breaking transitions are found, of subcritical and supercritical types. In the SDF regime, an antisymmetry-breaking transition occurs. Ground-states are identified in both the SF and SDF systems.
On absolute stability of nonlinear systems with small delays
Directory of Open Access Journals (Sweden)
M. I. Gil
1998-01-01
Full Text Available Nonlinear nonautonomous retarded systems with separated autonomous linear parts and continuous nonlinear ones are considered. It is assumed that deviations of the argument are sufficiently small. Absolute stability conditions are derived. They are formulated in terms of eigenvalues of auxiliary matrices.
Asymptotic stability and stabilizability of nonlinear systems with delay.
Srinivasan, V; Sukavanam, N
2016-11-01
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.
Uniform Stability of Damped Nonlinear Vibrations of an Elastic String
Indian Academy of Sciences (India)
Ganesh C Gorain; Sujit K Bose
2003-11-01
Here we are concerned about uniform stability of damped nonlinear transverse vibrations of an elastic string fixed at its two ends. The vibrations governed by nonlinear integro-differential equation of Kirchoff type, is shown to possess energy uniformly bounded by exponentially decaying function of time. The result is achieved by considering an energy-like Lyapunov functional for the system.
Energy Technology Data Exchange (ETDEWEB)
Olazabal-Loume, M; Breil, J; Hallo, L; Ribeyre, X [CELIA, UMR 5107 Universite Bordeaux 1-CNRS-CEA, 351 cours de la Liberation, 33405 Talence (France); Sanz, J, E-mail: olazabal@celia.u-bordeaux1.f [ETSI Aeronauticos, Universidad Politecnica de Madrid, Madrid 28040 (Spain)
2011-01-15
The linear and non-linear sensitivity of the 180 kJ baseline HiPER target to high-mode perturbations, i.e. surface roughness, is addressed using two-dimensional simulations and a complementary analysis by linear and non-linear ablative Rayleigh-Taylor models. Simulations provide an assessment of an early non-linear stage leading to a significant deformation of the ablation surface for modes of maximum linear growth factor. A design using a picket prepulse evidences an improvement in the target stability inducing a delay of the non-linear behavior. Perturbation evolution and shape, evidenced by simulations of the non-linear stage, are analyzed with existing self-consistent non-linear theory.
Mode stability on the real axis
Andersson, Lars; Ma, Siyuan; Paganini, Claudio; Whiting, Bernard F.
2017-07-01
A generalization of the mode stability result of Whiting [J. Math. Phys. 30, 1301-1305 (1989)] for the Teukolsky equation is proved for the case of real frequencies. The main result of the paper states that a separated solution of the Teukolsky equation governing massless test fields on the Kerr spacetime, which is purely outgoing at infinity, and purely ingoing at the horizon, must vanish. This has the consequence that for real frequencies, there are linearly independent fundamental solutions of the radial Teukolsky equation Rhor,Rout, which are purely ingoing at the horizon and purely outgoing at infinity, respectively. This fact yields a representation formula for solutions of the inhomogeneous Teukolsky equation and was recently used by Shlapentokh-Rothman [Ann. Henri Poincaré 16, 289-345 (2015)] for the scalar wave equation.
Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative
Directory of Open Access Journals (Sweden)
Fengrong Zhang
2011-01-01
Full Text Available This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function. Then, the fractional differential inequalities and comparison method are applied to the analysis of the stability of fractional differential systems. In addition, some other sufficient conditions on stability are also presented.
Global stabilization of nonlinear systems with uncertain structure
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The global stabilization problem of nonlinear systems with uncertain structure is dealt with. Based on control Lyapunov function (CLF), a sufficient and necessary condition for Lyapunov stabilization is given. From the condition,several simply sufficient conditions for the globally asymptotical stability are deduced. A state feedback control law is designed to globally asymptotically stabilize the equilibrium of the closed system. Last, a simulation shows the effectiveness of the method.
Nonsingular Terminal Sliding Mode Control of Uncertain Second-Order Nonlinear Systems
Directory of Open Access Journals (Sweden)
Minh-Duc Tran
2015-01-01
Full Text Available This paper presents a high-performance nonsingular terminal sliding mode control method for uncertain second-order nonlinear systems. First, a nonsingular terminal sliding mode surface is introduced to eliminate the singularity problem that exists in conventional terminal sliding mode control. By using this method, the system not only can guarantee that the tracking errors reach the reference value in a finite time with high-precision tracking performance but also can overcome the complex-value and the restrictions of the exponent (the exponent should be fractional number with an odd numerator and an odd denominator in traditional terminal sliding mode. Then, in order to eliminate the chattering phenomenon, a super-twisting higher-order nonsingular terminal sliding mode control method is proposed. The stability of the closed-loop system is established using the Lyapunov theory. Finally, simulation results are presented to illustrate the effectiveness of the proposed method.
Non-linear ultimate strength and stability limit state analysis of a wind turbine blade
DEFF Research Database (Denmark)
Rosemeier, Malo; Berring, Peter; Branner, Kim
2016-01-01
flap-wise loading has been compared with a linear response to determine the blade's resistance in the ultimate strength and stability limit states. The linear analysis revealed an unrealistic failure mechanism and failure mode. Further, it did not capture the highly non-linear response of the blade...... of an imperfection. The more realistic non-linear approaches yielded more optimistic results than the mandatory linear bifurcation analysis. Consequently, the investigated blade designed after the lesser requirements was sufficient. Using the non-linear approaches, considering inter-fibre failure as the critical...... failure mode, yielded still a significant safety margin for the designer (7–28%). The non-linear response was significantly dependent on the scaling of the imperfection. Eurocode's method of applying an imperfection appeared more realistic than the GL method. Since the considered blade withstood 135...
Kerr-lens Mode Locking Without Nonlinear Astigmatism
Yefet, Shi; Pe'er, Avi
2013-01-01
We demonstrate a Kerr-lens mode locked folded cavity using a planar (non-Brewster) Ti:sapphire crystal as a gain and Kerr medium, thus cancelling the nonlinear astigmatism caused by a Brewster cut Kerr medium. Our method uses a novel cavity folding in which the intra-cavity laser beam propagates in two perpendicular planes such that the astigmatism of one mirror is compensated by the other mirror, enabling the introduction of an astigmatic free, planar-cut gain medium. We demonstrate that this configuration is inherently free of nonlinear astigmatism, which in standard cavity folding needs a special power specific compensation.
Reliability optimization of friction-damped systems using nonlinear modes
Krack, Malte; Tatzko, Sebastian; Panning-von Scheidt, Lars; Wallaschek, Jörg
2014-06-01
A novel probabilistic approach for the design of mechanical structures with friction interfaces is proposed. The objective function is defined as the probability that a specified performance measure of the forced vibration response is achieved subject to parameter uncertainties. The practicability of the approach regarding the extensive amount of required design evaluations is strictly related to the computational efficiency of the nonlinear dynamic analysis. Therefore, it is proposed to employ a recently developed parametric reduced order model (ROM) based on nonlinear modes of vibration, which can facilitate a decrease of the computational burden by several orders of magnitude.
Stabilization of vortex beams in Kerr media by nonlinear absorption
Porras, Miguel A.; Carvalho, Márcio; Leblond, Hervé; Malomed, Boris A.
2016-11-01
We elaborate a solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form robust tubular filaments in transparent dielectrics as common as air, water, and optical glasses at sufficiently high intensities. We also show that the tubular, rotating, and specklelike filamentation regimes, previously observed in experiments with axicon-generated Bessel beams, can be explained as manifestations of the stability or instability of a specific nonlinear Bessel-vortex state, which is fully identified.
Stabilization of vortex beams in Kerr media by nonlinear absorption
Porras, Miguel A; Leblond, Hervé; Malomed, Boris A
2016-01-01
We elaborate a new solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form robust tubular filaments in transparent dielectrics as common as air, water and optical glasses at sufficiently high intensities. We also show that the tubular, rotating and speckle-like filamentation regimes, previously observed in experiments with axicon-generated Bessel beams, can be explained as manifestations of the stability or instability of a specific nonlinear Bessel-vortex state, which is fully identified.
Remarks on the relationship between ℒp stability and internal stability of nonlinear systems
Wang, Xu; Grip, H°avard Fjær; Saberi, Ali A.; Stoorvogel, Anton A.; Saberi, Ingmar
2013-01-01
In this paper, we investigate the relationship between ℒp stability and internal stability of nonlinear systems. It is shown that under certain conditions, ℒp stability without finite gain implies attractivity of the equilibrium, and that local ℒp stability with finite gain implies local asymptotic
Remarks on the relationship between ℒp stability and internal stability of nonlinear systems
Wang, Xu; Grip, H°avard Fjær; Saberi, Ali; Stoorvogel, Anton A.; Saberi, Ingmar
2011-01-01
In this paper, we investigate the relationship between ℒp stability and internal stability of nonlinear systems. It is shown that under certain conditions, ℒp stability without finite gain implies attractivity of the equilibrium, and that local ℒp stability with finite gain implies local asymptotic
Low-cost sliding mode control of WECS based on DFIG with stability analysis
DJOUDI, ABDELHAK; CHEKIREB, Hachemi; BERKOUK, EL MADJID; Bacha, Seddik
2015-01-01
The aim of this work is to developing sliding mode control of active and reactive stator powers produced by a wind energy conversion system (WECS), based on doubly fed induction generator (DFIG). A flux estimation model and rotor current sensor are no longer required. The controller is developed from the DFIG nonlinear-coupled model. Moreover, the global stability and the DFIG states' boundedness when our low-cost sliding mode control is applied are established analytically. It is reveal...
Terminal Sliding Mode Control with Adaptive Law for Uncertain Nonlinear System
Directory of Open Access Journals (Sweden)
Zhanshan Zhao
2015-01-01
Full Text Available A novel nonsingular terminal sliding mode controller is proposed for a second-order system with unmodeled dynamics uncertainties and external disturbances. We need not achieve the knowledge for boundaries of uncertainties and external disturbances in advance. The adaptive control gains are obtained to estimate the uncertain parameters and external disturbances which are unknown but bounded. The closed loop system stability is ensured with robustness and adaptation by the Lyapunov stability theorem in finite time. An illustrative example of second-order nonlinear system with unmodeled dynamics and external disturbances is given to demonstrate the effectiveness of the presented scheme.
Multistable internal resonance in electroelastic crystals with nonlinearly coupled modes
Kirkendall, Christopher R.; Kwon, Jae W.
2016-03-01
Nonlinear modal interactions have recently become the focus of intense research in micro- and nanoscale resonators for their use to improve oscillator performance and probe the frontiers of fundamental physics. However, our understanding of modal coupling is largely restricted to clamped-clamped beams, and lacking in systems with both geometric and material nonlinearities. Here we report multistable energy transfer between internally resonant modes of an electroelastic crystal plate and use a mixed analytical-numerical approach to provide new insight into these complex interactions. Our results reveal a rich bifurcation structure marked by nested regions of multistability. Even the simple case of two coupled modes generates a host of topologically distinct dynamics over the parameter space, ranging from the usual Duffing bistability to complex multistable behaviour and quasiperiodic motion.
PV Degradation Curves: Non-Linearities and Failure Modes
Energy Technology Data Exchange (ETDEWEB)
Jordan, Dirk C.; Silverman, Timothy J.; Sekulic, Bill; Kurtz, Sarah R.
2016-09-03
Photovoltaic (PV) reliability and durability have seen increased interest in recent years. Historically, and as a preliminarily reasonable approximation, linear degradation rates have been used to quantify long-term module and system performance. The underlying assumption of linearity can be violated at the beginning of the life, as has been well documented, especially for thin-film technology. Additionally, non-linearities in the wear-out phase can have significant economic impact and appear to be linked to different failure modes. In addition, associating specific degradation and failure modes with specific time series behavior will aid in duplicating these degradation modes in accelerated tests and, eventually, in service life prediction. In this paper, we discuss different degradation modes and how some of these may cause approximately linear degradation within the measurement uncertainty (e.g., modules that were mainly affected by encapsulant discoloration) while other degradation modes lead to distinctly non-linear degradation (e.g., hot spots caused by cracked cells or solder bond failures and corrosion). The various behaviors are summarized with the goal of aiding in predictions of what may be seen in other systems.
ASYMPTOTIC STABILITY OF SINGULAR NONLINEAR DIFFERENTIAL SYSTEMS WITH UNBOUNDED DELAYS
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
In this paper,the asymptotic stability of singular nonlinear differential systems with unbounded delays is considered.The stability criteria are derived based on a kind of Lyapunov-functional and some technique of matrix inequalities.The criteria are described as matrix equation and matrix inequalities,which are computationally flexible and efficient.Two examples are given to illustrate the results.
Control Lyapunov Stabilization of Nonlinear Systems with Structural Uncertainty
Institute of Scientific and Technical Information of China (English)
CAI Xiu-shan; HAN Zheng-zhi; TANG Hou-jun
2005-01-01
This paper deals with global stabilization problem for the nonlinear systems with structural uncertainty.Based on control Lyapunov function, a sufficient and necessary condition for the globally and asymptotically stabilizing the equailibrium of the closed system is given. Moreovery, an almost smooth state feedback control law is constructed. The simulation shows the effectiveness of the method.
Nonlinear Interaction of Transversal Modes in a CO2 Laser
Lopez-Ruiz, Ricardo; Mindlin, G. B.; Perez-Garcia, C.; Tredicce, J. R.
2002-01-01
We show the possibility of achieving experimentally a Takens-Bogdanov bifurcation for the nonlinear interaction of two transverse modes ($l = \\pm 1$) in a $CO_2$ laser. The system has a basic O(2) symmetry which is perturbed by some symmetry-breaking effects that still preserve the $Z_2$ symmetry. The pattern dynamics near this codimension two bifurcation under such symmetries is described. This dynamics changes drastically when the laser properties are modified.
Stochastic Stability Analysis for Markovian Jump Neutral Nonlinear Systems
Directory of Open Access Journals (Sweden)
Bo Wang
2012-10-01
Full Text Available In this paper, the stability problem is studied for a class of Markovian jump neutral nonlinear systems with time-varying delay. By Lyapunov-Krasovskii function approach, a novel mean-square exponential stability criterion is derived for the situations that the system's transition rates are completely accessible, partially accessible and non-accessible, respectively. Moreover, the developed stability criterion is extended to the systems with different bounded sector nonlinear constraints. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed methods.
Robust Stabilization of a Class of passive Nonlinear Systems
Joshi, Suresh M.; Kelkar, Atul G.
1996-01-01
The problem of feedback stabilization is considered for a class of nonlinear, finite dimensional, time invariant passive systems that are affine in control. Using extensions of the Kalman-Yakubovch lemma, it is shown that such systems can be stabilized by a class of finite demensional, linear, time-invariant controllers which are strictly positive real in the weak or marginal sense. The stability holds regardless of model uncertainties, and is therefore, robust.
Directory of Open Access Journals (Sweden)
Atabak Kolabi
2013-01-01
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.
Chattering free adaptive fuzzy terminal sliding mode control for second order nonlinear system
Institute of Scientific and Technical Information of China (English)
Jinkun LIU; Fuchun SUN
2006-01-01
A novel fuzzy terminal sliding mode control (FTSMC) scheme is proposed for position tracking of a class of second-order nonlinear uncertain system. In the proposed scheme, we integrate input-output linearization technique to cancel the nonlinearities. By using a function-augmented sliding hyperplane, it is guaranteed that the output tracking error converges to zero in finite time which can be set arbitrarily. The proposed scheme eliminates reaching phase problem, so that the closed-loop system always shows invariance property to parameter uncertainties. Fuzzy logic systems are used to approximate the unknown system functions and switch item. Robust adaptive law is proposed to reduce approximation errors between true nonlinear functions and fuzzy systems, thus chattering phenomenon can be eliminated. Stability of the proposed control scheme is proved and the scheme is applied to an inverted pendulum system. Simulation studies are provided to confirm performance and effectiveness of the proposed control approach.
The non-linear evolution of edge localized modes
Energy Technology Data Exchange (ETDEWEB)
Wenninger, Ronald
2013-01-09
Edge localized modes (ELMs) are instabilities in the edge of tokamak plasmas in the high confinement regime (H-mode). Without them the edge transport in ordinary H-mode plasmas is too low to establish a stationary situation. However in a future device large unmitigated ELMs are believed to cause divertor power flux densities far in excess of tolerable material limits. Hence the size of energy loss per ELM and the resulting ELM frequency must be controlled. To proceed in understanding how the ELM size is determined and how ELM mitigation methods work it is necessary to characterize the non-linear evolution of pedestal erosion. In order to achieve this experimental data is compared to the results of ELM simulations with the code JOREK (reduced MHD, non-linear) applying a specially developed synthetic magnetic diagnostic. The experimental data are acquired by several fast sampling diagnostics at the experiments ASDEX Upgrade and TCV at a large number of toroidal/poloidal positions. A central element of the presented work is the detailed characterization of dominant magnetic perturbations during ELMs. These footprints of the instability can be observed most intensely in close temporal vicinity to the onset of pedestal erosion. Dominant magnetic perturbations are caused by current perturbations located at or inside the last closed flux surface. In ASDEX Upgrade under certain conditions dominant magnetic perturbations like other H-mode edge instabilities display a similarity to solitons. Furthermore - as expected - they are often observed to be correlated to a perturbation of electron temperature. In TCV it is possible to characterize the evolution of the toroidal structure of dominant magnetic perturbations. Between growing above the level of background fluctuations and the maximum perturbation level for all time instance a similar toroidal structure is observed. This rigid mode-structure is an indication for non-linear coupling. Most frequently the dominant toroidal
Nonlinear dynamics of hidden modes in a system with internal symmetry
Perchikov, Nathan; Gendelman, O. V.
2016-09-01
We consider a discrete dynamical system with internal degrees of freedom (DOF). Due to the symmetry between the internal DOFs, certain internal modes cannot be excited by external forcing (in a case of linear interactions) and thus are considered "hidden". If such a system is weakly asymmetric, the internal modes remain approximately "hidden" from the external excitation, given that small damping is taken into account. However, already in the case of weak cubic nonlinearity, these hidden modes can be excited, even as the exact symmetry is preserved. This excitation occurs through parametric resonance. Floquet analysis reveals instability patterns for the explored modes. To perform this analysis with the required accuracy, we suggest a special method for obtaining the Fourier series of the unperturbed solution for the nonlinear normal mode. This method does not require explicit integration of the arising quadratures. Instead, it employs expansion of the solution at the stage of the implicit quadrature in terms of Chebyshev polynomials. The emerging implicit equations are solved by using a fixed-point iteration scheme. Poincaré sections help to clarify the correspondence between the loss of stability of the modes and the global structure of the dynamical flow. In particular, the conditions for intensive energy exchange in the system are characterized.
Universal fuzzy integral sliding-mode controllers for stochastic nonlinear systems.
Gao, Qing; Liu, Lu; Feng, Gang; Wang, Yong
2014-12-01
In this paper, the universal integral sliding-mode controller problem for the general stochastic nonlinear systems modeled by Itô type stochastic differential equations is investigated. One of the main contributions is that a novel dynamic integral sliding mode control (DISMC) scheme is developed for stochastic nonlinear systems based on their stochastic T-S fuzzy approximation models. The key advantage of the proposed DISMC scheme is that two very restrictive assumptions in most existing ISMC approaches to stochastic fuzzy systems have been removed. Based on the stochastic Lyapunov theory, it is shown that the closed-loop control system trajectories are kept on the integral sliding surface almost surely since the initial time, and moreover, the stochastic stability of the sliding motion can be guaranteed in terms of linear matrix inequalities. Another main contribution is that the results of universal fuzzy integral sliding-mode controllers for two classes of stochastic nonlinear systems, along with constructive procedures to obtain the universal fuzzy integral sliding-mode controllers, are provided, respectively. Simulation results from an inverted pendulum example are presented to illustrate the advantages and effectiveness of the proposed approaches.
Nonlinear stability of cosmological solutions in massive gravity
De Felice, Antonio; Lin, Chunshan; Mukohyama, Shinji
2013-01-01
We investigate nonlinear stability of two classes of cosmological solutions in massive gravity: isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) solutions and anisotropic FLRW solutions. For this purpose we construct the linear cosmological perturbation theory around axisymmetric Bianchi type--I backgrounds. We then expand the background around the two classes of solutions, which are fixed points of the background evolution equation, and analyze linear perturbations on top of it. This provides a consistent truncation of nonlinear perturbations around these fixed point solutions and allows us to analyze nonlinear stability in a simple way. In particular, it is shown that isotropic FLRW solutions exhibit nonlinear ghost instability. On the other hand, anisotropic FLRW solutions are shown to be ghost-free for a range of parameters and initial conditions.
Self-stabilized and dispersion-compensated passively mode-locked Yb:Yttrium aluminum garnet laser
Agnesi, A.; Guandalini, A.; Reali, G.
2005-04-01
Self-stabilized passive mode-locking of a diode-pumped Yb:yttrium aluminum garnet laser with a semiconductor saturable absorber was achieved using an off-phase-matching second-harmonic crystal. According to the numerical model, such a condition is accomplished by self-defocusing in the nonlinear crystal in the presence of positive intracavity dispersion. Robust mode locking with Fourier-limited 1.0-ps pulses was obtained, whereas mode locking, unassisted by the nonlinear crystal, yielded 2.2-ps pulses, with the laser operating near the edge of the stability region in order to minimize the saturation energy of the semiconductor device.
On the non-linear stability of scalar field cosmologies
Energy Technology Data Exchange (ETDEWEB)
Alho, Artur; Mena, Filipe C [Centro de Matematica, Universidade do Minho, 4710-057 Braga (Portugal); Kroon, Juan A Valiente, E-mail: aalho@math.uminho.pt, E-mail: fmena@math.uminho.pt, E-mail: jav@maths.qmul.ac.uk [School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS (United Kingdom)
2011-09-22
We review recent work on the stability of flat spatially homogeneous and isotropic backgrounds with a self-interacting scalar field. We derive a first order quasi-linear symmetric hyperbolic system for the Einstein-nonlinear-scalar field system. Then, using the linearized system, we show how to obtain necessary and sufficient conditions which ensure the exponential decay to zero of small non-linear perturbations.
Stabilization of solitons under competing nonlinearities by external potentials
Energy Technology Data Exchange (ETDEWEB)
Zegadlo, Krzysztof B., E-mail: zegadlo@if.pw.edu.pl; Karpierz, Miroslaw A. [Faculty of Physics, Warsaw University of Technology, Warsaw, ul. Koszykowa 75, PL-00-662 Warszawa (Poland); Wasak, Tomasz; Trippenbach, Marek [Faculty of Physics, University of Warsaw, ul. Hoza 69, PL-00-681 Warszawa (Poland); Malomed, Boris A. [Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)
2014-12-15
We report results of the analysis for families of one-dimensional (1D) trapped solitons, created by competing self-focusing (SF) quintic and self-defocusing (SDF) cubic nonlinear terms. Two trapping potentials are considered, the harmonic-oscillator (HO) and delta-functional ones. The models apply to optical solitons in colloidal waveguides and other photonic media, and to matter-wave solitons in Bose-Einstein condensates loaded into a quasi-1D trap. For the HO potential, the results are obtained in an approximate form, using the variational and Thomas-Fermi approximations, and in a full numerical form, including the ground state and the first antisymmetric excited one. For the delta-functional attractive potential, the results are produced in a fully analytical form, and verified by means of numerical methods. Both exponentially localized solitons and weakly localized trapped modes are found for the delta-functional potential. The most essential conclusions concern the applicability of competing Vakhitov-Kolokolov (VK) and anti-VK criteria to the identification of the stability of solitons created under the action of the competing SF and SDF terms.
Tunable rotary orbits of matter-wave nonlinear modes in attractive Bose-Einstein condensates
Energy Technology Data Exchange (ETDEWEB)
He, Y J; Wang, H Z [State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-Sen University, Guangzhou, 510275 (China); Malomed, Boris A [Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel); Mihalache, Dumitru [Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), 407 Atomistilor, Magurele-Bucharest 077125 (Romania)], E-mail: stswhz@mail.sysu.edu.cn
2008-03-14
We demonstrate that by spatially modulating the Bessel optical lattice where a Bose-Einstein condensate is loaded, we get tunable rotary orbits of nonlinear lattice modes. We show that the radially expanding or shrinking Bessel lattice can drag the nonlinear localized modes to orbits of either larger or smaller radii and the rotary velocity of nonlinear modes can be changed accordingly. The localized modes can even be transferred to the Bessel lattice core when the localized modes' rotations are stopped. Effects beyond the quasi-particle approximation such as destruction of the nonlinear modes by nonadiabatic dragging are also explored.
Nonlinear Slewing Spacecraft Control Based on Exergy, Power Flow, and Static and Dynamic Stability
Robinett, Rush D.; Wilson, David G.
2009-10-01
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.
Nonlinear stabilization of tokamak microturbulence by fast ions
Citrin, J; Garcia, J; Haverkort, J W; Hogeweij, G M D; Jenko, F; Johnson, T; Mantica, P; Pueschel, M J; Told, D; contributors, JET-EFDA
2013-01-01
Nonlinear electromagnetic stabilization by suprathermal pressure gradients found in specific regimes is shown to be a key factor in reducing tokamak microturbulence, augmenting significantly the thermal pressure electromagnetic stabilization. Based on nonlinear gyrokinetic simulations investigating a set of ion heat transport experiments on the JET tokamak, described by Mantica et al. [Phys. Rev. Lett. 107 135004 (2011)], this result explains the experimentally observed ion heat flux and stiffness reduction. These findings are expected to improve the extrapolation of advanced tokamak scenarios to reactor relevant regimes.
Stability properties of nonlinear dynamical systems and evolutionary stable states
Energy Technology Data Exchange (ETDEWEB)
Gleria, Iram, E-mail: iram@fis.ufal.br [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)
2017-03-18
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.
Stabilization of nonlinear systems based on robust control Lyapunov function
Institute of Scientific and Technical Information of China (English)
CAI Xiu-shan; HAN Zheng-zhi; LU Gan-yun
2007-01-01
This paper deals with the robust stabilization problem for a class of nonlinear systems with structural uncertainty. Based on robust control Lyapunov function, a sufficient and necessary condition for a function to be a robust control Lyapunov function is given. From this condition, simply sufficient condition for the robust stabilization (robust practical stabilization) is deduced. Moreover, if the equilibrium of the closed-loop system is unique, the existence of such a robust control Lyapunov function will also imply robustly globally asymptotical stabilization. Then a continuous state feedback law can be constructed explicitly. The simulation shows the effectiveness of the method.
Stabilization of tearing modes to suppress major disruptions in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Holmes, J.A.; Carreras, B.; Hicks, H.R.; Lynch, S.J.; Waddell, B.V.
1979-02-01
It is shown, for q-profiles which lead to a disruption, that the control of the amplitude of the 2/1 tearing mode avoids the disruption. Q-profiles measured in T-4 and PLT before a major disruption were studied. Two methods of controlling the 2/1 mode amplitude have been considered: (1) Feedback stabilization with the feedback signal locked in phase with the 2/1 mode. (2) Heating slightly outside the q = 2 surface. In both cases it is only necessary to decrease the 2/1 mode amplitude to suppress the disruption. It is not always necessary to stabilize the unstable modes fully.
Directory of Open Access Journals (Sweden)
Cha'o-Kuang Chen
2009-01-01
Full Text Available The main object of this paper is to study the weakly nonlinear hydrodynamic stability of the thin Newtonian fluid flowing on a rotating circular disk. A long-wave perturbation method is used to derive the nonlinear evolution equation for the film flow. The linear behaviors of the spreading wave are investigated by normal mode approach, and its weakly nonlinear behaviors are explored by the method of multiple scales. The Ginzburg-Landau equation is determined to discuss the necessary condition for the existence of such flow pattern. The results indicate that the superctitical instability region increases, and the subcritical stability region decreases with the increase of the rotation number or the radius of circular disk. It is found that the rotation number and the radius of circular disk not only play the significant roles in destabilizing the flow in the linear stability analysis but also shrink the area of supercritical stability region at high Reynolds number in the weakly nonlinear stability analysis.
Stabilization of a Nonlinear Delay System
Directory of Open Access Journals (Sweden)
Walid Arouri
2012-01-01
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. Thats 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.
Sinou, Jean-Jacques; Thouverez, Fabrice; Jezequel, Louis
2006-01-01
International audience; Herein, a novel non-linear procedure for producing non-linear behaviour and stable limit cycle amplitudes of non-linear systems subjected to super-critical Hopf bifurcation point is presented. This approach, called Complex Non-Linear Modal Analysis (CNLMA), makes use of the non-linear unstable mode which governs the non-linear dynamic of structural systems in unstable areas. In this study, the computational methodology of CNLMA is presented for the systematic estimatio...
Global Stabilization of Nonlinear Systems with Byrnes-Isidori Normal Form
Institute of Scientific and Technical Information of China (English)
WU Yu-qiang; YU Xing-huo
2002-01-01
The global stabilization of nonlinear cascade systems with partially linear composite dynamics is discussed in this paper using continuous terminal sliding modes (TSM). A two phase control strategy is proposed. The first phase is to use a linear control, called pre-TSM control, to bring the system state into a region where the TSM control is not singular. The second phase is to employ the TSM control in the region such that the equilibrium of the linear subsystem is reached in a finite time whose value is tunable by parameter setting of the TSMs. The finite time convergence of the proposed control strategy enables elimination of the effect of asymptotic convergence on the nonlinear systems. Although the proposed control strategy is sliding mode based, the control signal is continuous except at a single discontinuous point.Chattering phenomenon commonly associated with sliding mode control does not occur.
Compositional Finite-Time Stability analysis of nonlinear systems
DEFF Research Database (Denmark)
Tabatabaeipour, Mojtaba; Blanke, Mogens
2014-01-01
for the system but with bounded disturbance. Sufficient conditions for finite-time stability and finite-time boundedness of nonlinear systems as well as a computational method based on sum of squares programming to check the conditions are given. The problem of finite-time stability for a system that consists......This paper, investigates finite-time stability and finite-time boundedness for nonlinear systems with polynomial vector fields. Finite-time stability requires the states of the system to remain a given bounded set in a finite-time interval and finite-time boundedness considers the same problem...... of an interconnection of subsystems is also considered and we show how to decompose the problem into subproblems for each subsystem with coupling constraints. A solution to the problem using sum of squares programming and dual decomposition is presented. The method is demonstrated through some examples....
Non-Linear Aeroelastic Stability of Wind Turbines
DEFF Research Database (Denmark)
Zhang, Zili; Sichani, Mahdi Teimouri; Li, Jie;
2013-01-01
As wind turbines increase in magnitude without a proportional increase in stiffness, the risk of dynamic instability is believed to increase. Wind turbines are time dependent systems due to the coupling between degrees of freedom defined in the fixed and moving frames of reference, which may...... trigger off internal resonances. Further, the rotational speed of the rotor is not constant due to the stochastic turbulence, which may also influence the stability. In this paper, a robust measure of the dynamic stability of wind turbines is suggested, which takes the collective blade pitch control...... and non-linear aero-elasticity into consideration. The stability of the wind turbine is determined by the maximum Lyapunov exponent of the system, which is operated directly on the non-linear state vector differential equations. Numerical examples show that this approach is promising for stability...
Stabilization of nonlinear systems by similarity transformations
Directory of Open Access Journals (Sweden)
Irina E. Zuber
1998-01-01
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.
Energy Technology Data Exchange (ETDEWEB)
Itasse, Maxime, E-mail: Maxime.Itasse@onera.fr; Brazier, Jean-Philippe, E-mail: Jean-Philippe.Brazier@onera.fr; Léon, Olivier, E-mail: Olivier.Leon@onera.fr; Casalis, Grégoire, E-mail: Gregoire.Casalis@onera.fr [Onera - The French Aerospace Lab, F-31055 Toulouse (France)
2015-08-15
Nonlinear evolution of disturbances in an axisymmetric, high subsonic, high Reynolds number hot jet with forced eigenmodes is studied using the Parabolized Stability Equations (PSE) approach to understand how modes interact with one another. Both frequency and azimuthal harmonic interactions are analyzed by setting up one or two modes at higher initial amplitudes and various phases. While single mode excitation leads to harmonic growth and jet noise amplification, controlling the evolution of a specific mode has been made possible by forcing two modes (m{sub 1}, n{sub 1}), (m{sub 2}, n{sub 2}), such that the difference in azimuth and in frequency matches the desired “target” mode (m{sub 1} − m{sub 2}, n{sub 1} − n{sub 2}). A careful setup of the initial amplitudes and phases of the forced modes, defined as the “killer” modes, has allowed the minimizing of the initially dominant instability in the near pressure field, as well as its estimated radiated noise with a 15 dB loss. Although an increase of the overall sound pressure has been found in the range of azimuth and frequency analyzed, the present paper reveals the possibility to make the initially dominant instability ineffective acoustically using nonlinear interactions with forced eigenmodes.
On the nonlinear stability of mKdV breathers
DEFF Research Database (Denmark)
Alejo Plana, Miguel Angel; Muñoz, Claudio
2012-01-01
Breather modes of the mKdV equation on the real line are known to be elastic under collisions with other breathers and solitons. This fact indicates very strong stability properties of breathers. In this communication we describe a rigorous, mathematical proof of the stability of breathers under...
Relationship between the magnitude of singular value and nonlinear stability
Institute of Scientific and Technical Information of China (English)
穆穆; 郭欢; 王佳峰; 李勇
2001-01-01
The relationship between the magnitude of singular value and nonlinear stability or instability of the basic flow is investigated. The results show that there is a good corresponding relationship between them. The magnitude of singular value decreases as the stability (or instability) of the basic flow increases (or decreases). In the stable case, the magnitude of the maximum singular value is much smaller than in the unstable case.
Asymptotic Stability of Uniformly Bounded Nonlinear Switched Systems
Jouan, Philippe; Naciri, Said
2012-01-01
We study the asymptotic stability properties of nonlinear switched systems under the assumption of the existence of a common weak Lyapunov function. We consider the class of nonchaotic inputs, which generalize the different notions of inputs with dwell-time, and the class of general ones. For each of them we provide some sufficient conditions for asymptotic stability in terms of the geometry of certain sets. The results, which extend those of Balde, Jouan about linear systems, are illustrated...
Stabilization of discrete nonlinear systems based on control Lyapunov functions
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
The stabilization of discrete nonlinear systems is studied.Based on control Lyapunov functions,asufficient and necessary condition for a quadratic function to be a control Lyapunov function is given.From this condition,a continuous state feedback law is constructed explicitly.It can globally asymptotically stabilize the equilibrium of the closed-loop system.A simulation example shows the effectiveness of the proposed method.
Sliding-mode control design for nonlinear systems using probability density function shaping.
Liu, Yu; Wang, Hong; Hou, Chaohuan
2014-02-01
In this paper, we propose a sliding-mode-based stochastic distribution control algorithm for nonlinear systems, where the sliding-mode controller is designed to stabilize the stochastic system and stochastic distribution control tries to shape the sliding surface as close as possible to the desired probability density function. Kullback-Leibler divergence is introduced to the stochastic distribution control, and the parameter of the stochastic distribution controller is updated at each sample interval rather than using a batch mode. It is shown that the estimated weight vector will converge to its ideal value and the system will be asymptotically stable under the rank-condition, which is much weaker than the persistent excitation condition. The effectiveness of the proposed algorithm is illustrated by simulation.
NOLB : Non-linear rigid block normal mode analysis method.
Hoffmann, Alexandre; Grudinin, Sergei
2017-04-05
We present a new conceptually simple and computationally efficient method for non-linear normal mode analysis called NOLB. It relies on the rotations-translations of blocks (RTB) theoretical basis developed by Y.-H. Sanejouand and colleagues. We demonstrate how to physically interpret the eigenvalues computed in the RTB basis in terms of angular and linear velocities applied to the rigid blocks and how to construct a non-linear extrapolation of motion out of these velocities. The key observation of our method is that the angular velocity of a rigid block can be interpreted as the result of an implicit force, such that the motion of the rigid block can be considered as a pure rotation about a certain center. We demonstrate the motions produced with the NOLB method on three different molecular systems and show that some of the lowest frequency normal modes correspond to the biologically relevant motions. For example, NOLB detects the spiral sliding motion of the TALE protein, which is capable of rapid diffusion along its target DNA. Overall, our method produces better structures compared to the standard approach, especially at large deformation amplitudes, as we demonstrate by visual inspection, energy and topology analyses, and also by the MolProbity service validation. Finally, our method is scalable and can be applied to very large molecular systems, such as ribosomes. Standalone executables of the NOLB normal mode analysis method are available at https://team.inria.fr/nano-d/software/nolb-normal-modes. A graphical user interfaces created for the SAMSON software platform will be made available at https: //www.samson-connect.net.
Signatures of nonlinear mode interactions in the pulsating hot B subdwarf star KIC 10139564
Zong, W.; Charpinet, S.; Vauclair, G.
2016-10-01
Context. The unprecedented photometric quality and time coverage offered by the Kepler spacecraft has opened up new opportunities to search for signatures of nonlinear effects that affect oscillation modes in pulsating stars. Aims: The data accumulated on the pulsating hot B subdwarf KIC 10139564 are used to explore in detail the stability of its oscillation modes, focusing in particular on evidences of nonlinear behaviors. Methods: We analyzed 38 months of contiguous short-cadence data, concentrating on mode multiplets induced by the star rotation and on frequencies forming linear combinations that show intriguing behaviors during the course of the observations. Results: We find clear signatures that point toward nonlinear effects predicted by resonant mode coupling mechanisms. These couplings can induce various mode behaviors for the components of multiplets and for frequencies related by linear relationships. We find that a triplet at 5760 μHz, a quintuplet at 5287 μHz and a (ℓ > 2) multiplet at 5412 μHz, all induced by rotation, show clear frequency and amplitude modulations which are typical of the so-called intermediate regime of a resonance between the components. One triplet at 316 μHz and a doublet at 394 μHz show modulated amplitude and constant frequency which can be associated with a narrow transitory regime of the resonance. Another triplet at 519 μHz appears to be in a frequency-locked regime where both frequency and amplitude are constant. Additionally, three linear combinations of frequencies near 6076 μHz also show amplitude and frequency modulations, which are likely related to a three-mode direct resonance of the type ν0 ~ ν1 + ν2. Conclusions: The identified frequency and amplitude modulations are the first clear-cut signatures of nonlinear resonant couplings occurring in pulsating hot B subdwarf stars. However, the observed behaviors suggest that the resonances occurring in these stars usually follow more complicated patterns than
A steady-state solver and stability calculator for nonlinear internal wave flows
Viner, Kevin C.; Epifanio, Craig C.; Doyle, James D.
2013-10-01
A steady solver and stability calculator is presented for the problem of nonlinear internal gravity waves forced by topography. Steady-state solutions are obtained using Newton's method, as applied to a finite-difference discretization in terrain-following coordinates. The iteration is initialized using a boundary-inflation scheme, in which the nonlinearity of the flow is gradually increased over the first few Newton steps. The resulting method is shown to be robust over the full range of nonhydrostatic and rotating parameter space. Examples are given for both nonhydrostatic and rotating flows, as well as flows with realistic upstream shear and static stability profiles. With a modest extension, the solver also allows for a linear stability analysis of the steady-state wave fields. Unstable modes are computed using a shifted-inverse method, combined with a parameter-space search over a set of realistic target values. An example is given showing resonant instability in a nonhydrostatic mountain wave.
Nonlinear tearing mode in inhomogeneous plasma: I. Unmagnetized islands
Energy Technology Data Exchange (ETDEWEB)
Waelbroeck, F L [Institute for Fusion Studies, University of Texas, Austin, TX 78712-0262 (United States)
2007-06-15
A theory of the nonlinear growth and propagation of magnetic islands in the semi-collisional regime is presented. The theory includes the effects of finite electron temperature gradients and uses a fluid model with cold ions in slab geometry to describe islands that are unmagnetized in the sense that their width is less than {rho}{sub s}, the ion Larmor radius calculated with the electron temperature. The polarization integral and the natural phase velocity are both calculated. It is found that increasing the electron temperature gradient reduces the natural phase velocity below the electron diamagnetic frequency and thus causes the polarization current to become stabilizing.
The linear and nonlinear stability of thread-annular flow.
Walton, Andrew G
2005-05-15
The surgical technique of thread injection of medical implants is modelled by the axial pressure-gradient-driven flow between concentric cylinders with a moving core. The linear stability of the flow to both axisymmetric and asymmetric perturbations is analysed asymptotically at large Reynolds number, and computationally at finite Reynolds number. The existence of multiple regions of instability is predicted and their dependence upon radius ratio and thread velocity is determined. A discrepancy in critical Reynolds numbers and cut-off velocity is found to exist between experimental results and the predictions of the linear theory. In order to account for this discrepancy, the high Reynolds number, nonlinear stability properties of the flow are analysed and a nonlinear, equilibrium critical layer structure is found, which leads to an enhanced correction to the basic flow. The predictions of the nonlinear theory are found to be in good agreement with the experimental data.
The Local Stability of Solutions for a Nonlinear Equation
Directory of Open Access Journals (Sweden)
Haibo Yan
2014-01-01
Full Text Available The approach of Kruzkov’s device of doubling the variables is applied to establish the local stability of strong solutions for a nonlinear partial differential equation in the space L1(R by assuming that the initial value only lies in the space L1(R∩L∞(R.
Discontinuous stabilization of nonlinear systems : Quantized and switching controls
Ceragioli, Francesca; De Persis, Claudio
2007-01-01
In this paper we consider the classical problem of stabilizing nonlinear systems in the case the control laws take values in a discrete set. First, we present a robust control approach to the problem. Then, we focus on the class of dissipative systems and rephrase classical results available for thi
Asymptotic Stability of Interconnected Passive Non-Linear Systems
Isidori, A.; Joshi, S. M.; Kelkar, A. G.
1999-01-01
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.
Nonlinear theory of combustion stability in liquid rocket engine based on chemistry dynamics
Institute of Scientific and Technical Information of China (English)
黄玉辉; 王振国; 周进
2002-01-01
Detailed models of combustion instability based on chemistry dynamics are developed. The results show that large activation energy goes against the combustion stability. The heat transfer coefficient between the wall and the combust gas is an important bifurcation parameter for the combustion instability. The acoustics modes of the chamber are in competition and cooperation with each other for limited vibration energy. Thermodynamics criterion of combustion stability can be deduced from the nonlinear thermodynamics. Correlations of the theoretical results and historical experiments indicate that chemical kinetics play a critical role in the combustion instability.
NONLINEAR THEORY OF DYNAMIC STABILITY FOR LAMINATED COMPOSITE CYLINDRICAL SHELLS
Institute of Scientific and Technical Information of China (English)
周承倜; 王列东
2001-01-01
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.
Exponential Stability of Stochastic Nonlinear Dynamical Price System with Delay
Directory of Open Access Journals (Sweden)
Wenli Zhu
2013-01-01
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.
Stability of gyro with harmonic nonlinearity in spinning vehicle
Singh, S. N.
1983-03-01
The stability analysis of a rate gyro mounted in a vehicle which is spinning with uncertain angular velocity about the spin axis of the gyro is presented. The complete nonlinear equation of the motion of the gimbal is considered, retaining the fundamental and second harmonic nonlinear terms which are functions of the angular velocity of the vehicle about the spin axis of the gyro. Using the circle criterion for the case of time-varying angular momentum and the Lyapunov approach for the case of uncertain constant angular velocity, conditions for asymptotic stability and global asymptotic stability are obtained. Stable regions in parameter space of the gyro and state space are obtained, and analytical relations for the selection of gyro parameters are derived.
ANALYSIS OF NONLINEAR DYNAMIC STABILITY OF LIQUID-CONVEYING PIPES
Institute of Scientific and Technical Information of China (English)
张立翔; 黄文虎
2002-01-01
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.
Competing stability modes in vortex structure formation
Garrett, Stephen; Gostelow, J. Paul; Rona, Aldo; McMullan, W. Andrew
2015-11-01
Nose cones and turbine blades have rotating components and represent very practical geometries for which the behavior of vortex structures is not completely understood. These two different physical cases demonstrate a common theme of competition between mode and vortex types. The literature concerning boundary-layer transition over rotating cones presents clear evidence of an alternative instability mode leading to counter-rotating vortex pairs, consistent with a centrifugal instability. This is in contrast to co-rotating vortices present over rotating disks that arise from crossflow effects. It is demonstrated analytically that this mode competes with the crossflow mode and is dominant only over slender cones. Predictions are aligned with experimental measurements over slender cones. Concurrent experimental work on the flow over swept cylinders shows that organized fine-scale streamwise vorticity occurs more frequently on convex surfaces than is appreciated. The conventional view of purely two-dimensional laminar boundary layers following blunt leading edges is not realistic and such boundary layers need to be treated three-dimensionally, particularly when sweep is present. The vortical structures are counter-rotating for normal cylinders and co-rotating under high sweep conditions. Crossflow instabilities may have a major role to play in the transition process but the streamline curvature mode is still present, and seemingly unchanged, when the boundary layer becomes turbulent.
Mukamel, Shaul
2003-08-01
Computing response functions by following the time evolution of superoperators in Liouville space (whose vectors are ordinary Hilbert space operators) offers an attractive alternative to the diagrammatic perturbative expansion of many-body equilibrium and nonequilibrium Green's functions. The bookkeeping of time ordering is naturally maintained in real (physical) time, allowing the formulation of Wick's theorem for superoperators, giving a factorization of higher order response functions in terms of two fundamental Green's functions. Backward propagations and analytic continuations using artificial times (Keldysh loops and Matsubara contours) are avoided. A generating functional for nonlinear response functions unifies quantum field theory and the classical mode coupling formalism of nonlinear hydrodynamics and may be used for semiclassical expansions. Classical response functions are obtained without the explicit computation of stability matrices.
Stabilization of the resistive shell mode in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Fitzpatrick, R.; Aydemir, A.
1995-02-01
The stability of current-driven external-kink modes is investigated in a tokamak plasma surrounded by an external shell of finite electrical conductivity. According to conventional theory, the ideal mode can be stabilized by placing the shell sufficiently close to the plasma, but the non-rotating ``resistive shell mode,`` which grows on the characteristic L/R time of the shell, always persists. It is demonstrated, using both analytic and numerical techniques, that a combination of strong edge plasma rotation and dissipation somewhere inside the plasma is capable of stabilizing the resistive shell mode. This stabilization mechanism does not necessarily depend on toroidicity or presence of resonant surfaces inside the plasma.
Extension to nonlinear stability theory of the circular Couette flow
Yau, Pun Wong; Wang, Shixiao; Rusak, Zvi
2016-11-01
A nonlinear stability analysis of the viscous circular Couette flow to axisymmetric perturbations under axial periodic boundary conditions is developed. The analysis is based on investigating the properties of a reduced Arnol'd energy-Casimir function Ard of Wang (2009). We show that all the inviscid flow effects as well as all the viscous-dependent terms related to the flow boundaries vanish. The evolution of ΔArd depends solely on the viscous effects of the perturbation's dynamics inside the flow domain. The requirement for the temporal decay of ΔArd leads to novel sufficient conditions for the nonlinear stability of the circular Couette flow in response to axisymmetric perturbations. Comparisons with historical studies show that our results shed light on the experimental measurements of Wendt (1933) and significantly extend the classical nonlinear stability results of Serrin (1959) and Joseph & Hung (1971). When the flow is nonlinearly stable and evolves axisymmetrically for all time, then it always decays asymptotically in time to the circular Couette flow determined uniquely by the setup of the rotating cylinders. This study provides new physical insights into a classical flow problem that was studied for decades.
Nonlinear high-order mode locking in stochastic sensory neurons
Rowe, Michael; Afghan, Muhammad; Neiman, Alexander
2004-03-01
Excitable systems demonstrate various mode locking regimes when driven by periodic external signals. With noise taken into account, such regimes represent complex nonlinear responses which depend crucially on the frequency and amplitude of the periodic drive as well as on the noise intensity. We study this using a computational model of a stochastic Hodgkin-Huxley neuron in combination with the turtle vestibular sensory system as an experimental model. A bifurcation analysis of the model is performed. Extracellular recordings from primary vestibular afferent neurons with two types of stimuli are used in the experimental study. First, mechanical stimuli applied to the labyrinth allow us to study the responses of the entire system, including transduction by the hair cells and spike generation in the primary afferents. Second, a galvanic stimuli applied directly to an afferent are used to study the responses of afferent spike generator directly. The responses to galvanic stimuli reveal multiple high-order mode locking regimes which are well reproduced in numerical simulation. Responses to mechanical stimulation are characterized by larger variability so that fewer mode-locking regimes can be observed.
Stabilizing model predictive control for constrained nonlinear distributed delay systems.
Mahboobi Esfanjani, R; Nikravesh, S K Y
2011-04-01
In this paper, a model predictive control scheme with guaranteed closed-loop asymptotic stability is proposed for a class of constrained nonlinear time-delay systems with discrete and distributed delays. A suitable terminal cost functional and also an appropriate terminal region are utilized to achieve asymptotic stability. To determine the terminal cost, a locally asymptotically stabilizing controller is designed and an appropriate Lyapunov-Krasoskii functional of the locally stabilized system is employed as the terminal cost. Furthermore, an invariant set for locally stabilized system which is established by using the Razumikhin Theorem is used as the terminal region. Simple conditions are derived to obtain terminal cost and terminal region in terms of Bilinear Matrix Inequalities. The method is illustrated by a numerical example.
Stability properties of a general class of nonlinear dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Gleria, I.M. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail: iram@ucb.br; Figueiredo, A. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail: annibal@helium.fis.unb.br; Rocha, T.M. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail: marciano@helium.fis.unb.br
2001-05-04
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)
Xinghua Liu; Hongsheng Xi
2013-01-01
The exponential stability of neutral Markovian jump systems with interval mode-dependent time-varying delays, nonlinear perturbations, and partially known transition rates is investigated. A novel augmented stochastic Lyapunov functional is constructed, which employs the improved bounding technique and contains triple-integral terms to reduce conservativeness; then the delay-range-dependent and rate-dependent exponential stability criteria are developed by Lyapunov stability theory, reciproca...
Linear and nonlinear stability analysis in BWRs applying a reduced order model
Energy Technology Data Exchange (ETDEWEB)
Olvera G, O. A.; Espinosa P, G.; Prieto G, A., E-mail: omar_olverag@hotmail.com [Universidad Autonoma Metropolitana, Unidad Iztapalapa, San Rafael Atlixco No. 186, Col. Vicentina, 09340 Ciudad de Mexico (Mexico)
2016-09-15
Boiling Water Reactor (BWR) stability studies are generally conducted through nonlinear reduced order models (Rom) employing various techniques such as bifurcation analysis and time domain numerical integration. One of those models used for these studies is the March-Leuba Rom. Such model represents qualitatively the dynamic behavior of a BWR through a one-point reactor kinetics, a one node representation of the heat transfer process in fuel, and a two node representation of the channel Thermal hydraulics to account for the void reactivity feedback. Here, we study the effect of this higher order model on the overall stability of the BWR. The change in the stability boundaries is determined by evaluating the eigenvalues of the Jacobian matrix. The nonlinear model is also integrated numerically to show that in the nonlinear region, the system evolves to stable limit cycles when operating close to the stability boundary. We also applied a new technique based on the Empirical Mode Decomposition (Emd) to estimate a parameter linked with stability in a BWR. This instability parameter is not exactly the classical Decay Ratio (Dr), but it will be linked with it. The proposed method allows decomposing the analyzed signal in different levels or mono-component functions known as intrinsic mode functions (Imf). One or more of these different modes can be associated to the instability problem in BWRs. By tracking the instantaneous frequencies (calculated through Hilbert Huang Transform (HHT) and the autocorrelation function (Acf) of the Imf linked to instability. The estimation of the proposed parameter can be achieved. The current methodology was validated with simulated signals of the studied model. (Author)
Yang, T C
2014-02-01
This paper applies the mode coupling equation to calculate the mode-coupling matrix for nonlinear internal waves appearing as a train of solitons. The calculation is applied to an individual soliton up to second order expansion in sound speed perturbation in the Dyson series. The expansion is valid so long as the fractional sound speed change due to a single soliton, integrated over range and depth, times the wavenumber is smaller than unity. Scattering between the solitons are included by coupling the mode coupling matrices between the solitons. Acoustic fields calculated using this mode-coupling matrix formulation are compared with that obtained using a parabolic equation (PE) code. The results agree very well in terms of the depth integrated acoustic energy at the receivers for moving solitary internal waves. The advantages of using the proposed approach are: (1) The effects of mode coupling can be studied as a function of range and time as the solitons travel along the propagation path, and (2) it allows speedy calculations of sound propagation through a packet or packets of solitons saving orders of magnitude computations compared with the PE code. The mode coupling theory is applied to at-sea data to illustrate the underlying physics.
QUANTITATIVE METHODOLOGY FOR STABILITY ANALYSIS OF NONLINEAR ROTOR SYSTEMS
Institute of Scientific and Technical Information of China (English)
ZHENG Hui-ping; XUE Yu-sheng; CHEN Yu-shu
2005-01-01
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.
Pashaei, Shabnam; Badamchizadeh, Mohammadali
2016-07-01
This paper investigates the stabilization and disturbance rejection for a class of fractional-order nonlinear dynamical systems with mismatched disturbances. To fulfill this purpose a new fractional-order sliding mode control (FOSMC) based on a nonlinear disturbance observer is proposed. In order to design the suitable fractional-order sliding mode controller, a proper switching surface is introduced. Afterward, by using the sliding mode theory and Lyapunov stability theory, a robust fractional-order control law via a nonlinear disturbance observer is proposed to assure the existence of the sliding motion in finite time. The proposed fractional-order sliding mode controller exposes better control performance, ensures fast and robust stability of the closed-loop system, eliminates the disturbances and diminishes the chattering problem. Finally, the effectiveness of the proposed fractional-order controller is depicted via numerical simulation results of practical example and is compared with some other controllers.
Nonlinear interface optical switch structure for dual mode switching revisited
Bussjager, Rebecca J.; Osman, Joseph M.; Chaiken, Joseph
1998-07-01
There is a need for devices which will allow integration of photonic/optical computing subsystems into electronic computing architectures. This presentation reviews the nonlinear interface optical switch (NIOS) concept and then describes a new effect, the erasable optical memory (EOM) effect. We evaluate an extension of the NIOS device to allow simultaneous optical/electronic, i.e. dual mode, switching of light utilizing the EOM effect. Specific devices involve the fabrication of thin film tungsten (VI) oxide (WO3) and tungsten (V) oxide (W2O5) on the hypotenuse of glass (BK-7), fused silica (SiO2) and zinc selenide (ZnSe) right angle prisms. Chemical reactions and temporal response tests were performed and are discussed.
Nonlinear nano-scale localized breather modes in a discrete weak ferromagnetic spin lattice
Energy Technology Data Exchange (ETDEWEB)
Kavitha, L., E-mail: louiskavitha@yahoo.co.in [Department of Physics, School of Basic and Applied Sciences, Central University of Tamil Nadu (CUTN), Thiruvarur 610 101, Tamil Nadu (India); Max-Planck Institute for the Physics of Complex Systems, Dresden (Germany); The Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Parasuraman, E. [Department of Physics, Periyar University, Salem 636 011, Tamil Nadu (India); Center for Nanoscience and Nanotechnology, Periyar University, Salem 636 011, Tamil Nadu (India); Gopi, D. [Department of Chemistry, Periyar University, Salem 636 011, Tamil Nadu (India); Center for Nanoscience and Nanotechnology, Periyar University, Salem 636 011, Tamil Nadu (India); Prabhu, A. [Department of Physics, Periyar University, Salem 636 011, Tamil Nadu (India); Vicencio, Rodrigo A. [Departamento de Física and MSI-Nucleus on Advanced Optics, Center for Optics and Photonics (CEFOP), Facultad de Ciencias, Universidad de Chile, Santiago 7800003 (Chile); Max-Planck Institute for the Physics of Complex Systems, Dresden (Germany)
2016-03-01
We investigate the propagation dynamics of highly localized discrete breather modes in a weak ferromagnetic spin lattice with on-site easy axis anisotropy due to crystal field effect. We derive the discrete nonlinear equation of motion by employing boson mappings and p-representation. We explore the onset of modulational instability both analytically in the framework of linear stability analysis and numerically by means of molecular dynamics (MD) simulations, and a perfect agreement was demonstrated. It is also explored that how the antisymmetric nature of the canted ferromagnetic lattice supports highly localized discrete breather (DBs) modes as shown in the stability/instability windows. The energy exchange between low amplitude discrete breathers favours the growth of higher amplitude DBs, resulting eventually in the formation of few long-lived high amplitude DBs. - Highlights: • The effects of DM and anisotropy interaction on the DB modes are studied. • The antisymmetric nature of the canted ferromagnetic medium supports the DB modes. • Dynamics of ferromagnetic chain is governed by boson mappings and p-representation.
Underlying conservation and stability laws in nonlinear propagation of axicon-generated Bessel beams
Porras, Miguel A; Losada, Juan Carlos
2015-01-01
In light filamentation induced by axicon-generated, powerful Bessel beams, the spatial propagation dynamics in the nonlinear medium determines the geometry of the filament channel and hence its potential applications. We show that the observed steady and unsteady Bessel beam propagation regimes can be understood in a unified way from the existence of an attractor and its stability properties. The attractor is identified as the nonlinear unbalanced Bessel beam (NL-UBB) whose inward H\\"ankel beam amplitude equals the amplitude of the linear Bessel beam that the axicon would generate in linear propagation. A simple analytical formula that determines de NL-UBB attractor is given. Steady or unsteady propagation depends on whether the attracting NL-UBB has a small, exponentially growing, unstable mode. In case of unsteady propagation, periodic, quasi-periodic or chaotic dynamics after the axicon reproduces similar dynamics after the development of the small unstable mode into the large perturbation regime.
Phase stabilization of Kerr frequency comb internally without nonlinear optical interferometry
Huang, S -W; Yang, J; Yu, M; Kwong, D -L; Wong, C W
2016-01-01
Optical frequency comb (OFC) technology has been the cornerstone for scientific breakthroughs such as precision frequency metrology, redefinition of time, extreme light-matter interaction, and attosecond sciences. While the current mode-locked laser-based OFC has had great success in extending the scientific frontier, its use in real-world applications beyond the laboratory setting remains an unsolved challenge. Microresonator-based OFCs, or Kerr frequency comb, have recently emerged as a candidate solution to the challenge because of their preferable size, weight, and power consumption (SWaP). On the other hand, the current phase stabilization technology requires either external optical references or power-demanding nonlinear processes, overturning the SWaP benefit of Kerr frequency combs. Introducing a new concept in phase control, here we report an internally phase stabilized Kerr frequency comb without the need of any optical references or nonlinear processes. We describe the comb generation analytically ...
Fang, Xiaohui; Wai, P K A; Lu, Chao; Chen, Jinhua
2014-02-10
A pulse-width-tunable 10 GHz flattop pulse (FTP) train is generated based on the combined action of active mode locking and nonlinear polarization rotation pulse shaping. Although the setup was previously used for other applications, the mechanism of FTP generation based on it is first analyzed and confirmed in the experiment. An FTP with pulse width tunable from 12 to 20 ps by changing polarization controllers is generated within the wavelength tuning range of 20 nm. The generated pulse reveals good stability, with the side mode suppression ratio of 65 dB, timing jitter of 92 fs, and amplitude fluctuation of 0.36%.
Chen, Yong; Yan, Zhenya
2017-01-01
The effect of derivative nonlinearity and parity-time-symmetric (PT -symmetric) potentials on the wave propagation dynamics is explored in the derivative nonlinear Schrödinger equation, where the physically interesting Scarf-II and harmonic-Hermite-Gaussian potentials are chosen. We study numerically the regions of unbroken and broken linear PT -symmetric phases and find some stable bright solitons of this model in a wide range of potential parameters even though the corresponding linear PT -symmetric phases are broken. The semielastic interactions between particular bright solitons and exotic incident waves are illustrated such that we find that particular nonlinear modes almost keep their shapes after interactions even if the exotic incident waves have evidently been changed. Moreover, we exert the adiabatic switching on PT -symmetric potential parameters such that a stable nonlinear mode with the unbroken linear PT -symmetric phase can be excited to another stable nonlinear mode belonging to the broken linear PT -symmetric phase.
FUZZY STABILITY ANALYSIS OF MODE COUPLING CHATTER ON CUTTING PROCESS
Institute of Scientific and Technical Information of China (English)
1998-01-01
The influence of fuzzy uncertainty factors is considered on the analysis of chatter occurring during machine tool cutting process. Using fuzzy mathematics analysis methods, a detailed discussion over fuzzy stability analysis problems is presented related to the mode coupling chatter with respect to intrinsic structure fuzzy factors, and the possibility distribution of the fuzzy stability cutting range and the confidence level expressions of the fuzzy stability cutting width are given.
Robust Stabilization of Nonlinear Systems with Uncertain Varying Control Coefficient
Directory of Open Access Journals (Sweden)
Zaiyue Yang
2014-01-01
Full Text Available This paper investigates the stabilization problem for a class of nonlinear systems, whose control coefficient is uncertain and varies continuously in value and sign. The study emphasizes the development of a robust control that consists of a modified Nussbaum function to tackle the uncertain varying control coefficient. By such a method, the finite-time escape phenomenon has been prevented when the control coefficient is crossing zero and varying its sign. The proposed control guarantees the asymptotic stabilization of the system and boundedness of all closed-loop signals. The control performance is illustrated by a numerical simulation.
Stability Analysis of Some Nonlinear Anaerobic Digestion Models
Directory of Open Access Journals (Sweden)
Ivan Simeonov
2010-04-01
Full Text Available Abstract: The paper deals with local asymptotic stability analysis of some mass balance dynamic models (based on one and on two-stage reaction schemes of the anaerobic digestion (AD in CSTR. The equilibrium states for models based on one (with Monod, Contois and Haldane shapes for the specific growth rate and on two-stage (only with Monod shapes for both the specific growth rate of acidogenic and methanogenic bacterial populations reaction schemes have been determined solving sets of nonlinear algebraic equations using Maples. Their stability has been analyzed systematically, which provides insight and guidance for AD bioreactors design, operation and control.
Robust stabilization of uncertain nonholonomic systems with strong nonlinear drifts
Institute of Scientific and Technical Information of China (English)
Yuqiang WU; Xiuyun ZHENG
2008-01-01
This paper investigates the robust stabilization of the nonholonomic control systems with strongly nonlinear uncertainties.In order to make the state scaling effective and to prevent the fiflite time escape phenomenon from happening.the switching control strategy based on the state measurement of the first subsystem is employed to achieve the asymptotic stabilization.The recurslve integrator backstepping technique is applied to the design of the robust controller.The simulation example demonstrates the efficiency and robust features of the proposed method.
The numerical stability of nonlinear floating body calculations
Park, Jong-Hwan
1992-01-01
The numerical stability of nonlinear body-wave interaction problems is investigated by applying potential flow assumptions to oscillating, non-wallsided two-dimensional and three-dimensional axisymmetric bodies. This body-wave interaction problem is solved using a mixed two-step Eulerian-Lagrangian method. In the first step, Laplace's equation is solved to determine the unknown potential values on the body and the unknown derivatives of the potentials on the free surface. In the second step, free surface boundary conditions are applied using the results of the first step to find the evolved free surface location and new potential values on the new location. Each step has particular mathematical characteristics (elliptic or parabolic-like), so that each step requires different numerical schemes. Consequently, the numerical stability of this body-wave interaction problem contains the characteristics of both of these two steps. The major contributions made to this body-wave interaction problem are the effects of the various parameters (i.e. time increments, panel length, etc.) and the different forms of the Boundary Integral Method (BIM) on numerical stability and accuracy. The far-field truncation requirement is met by matching the linear outer solution to the nonlinear inner solution at the truncation boundary. The intersection point is traced by the extrapolation method with a special boundary condition at the intersection point. To determine the evolution of the free surface according to a Lagrangian model, a regridding scheme is utilized to prevent the concentration of the Lagrangian markers in the vicinity of high gradients. A parameter for the numerical stability of free surface waves, the Free Surface Stability (FSS) number, is defined as a function of the time step size and the discretized panel length. The various stability regions are investigated by changing the FSS number, Green's function constant c, and numerical schemes. A nonlinear stability analysis
Paradoxical stabilization of forced oscillations by strong nonlinear friction
Esirkepov, Timur Zh.; Bulanov, Sergei V.
2017-08-01
In a dissipative dynamic system driven by an oscillating force, a strong nonlinear highly oscillatory friction force can create a quasi-steady tug, which is always directed opposite to the ponderomotive force induced due to a spatial inhomogeneity of oscillations. When the friction-induced tug exceeds the ponderomotive force, the friction stabilizes the system oscillations near the maxima of the oscillation spatial amplitude of the driving force.
Nonlinear mode decomposition: A noise-robust, adaptive decomposition method
Iatsenko, Dmytro; McClintock, Peter V. E.; Stefanovska, Aneta
2015-09-01
The signals emanating from complex systems are usually composed of a mixture of different oscillations which, for a reliable analysis, should be separated from each other and from the inevitable background of noise. Here we introduce an adaptive decomposition tool—nonlinear mode decomposition (NMD)—which decomposes a given signal into a set of physically meaningful oscillations for any wave form, simultaneously removing the noise. NMD is based on the powerful combination of time-frequency analysis techniques—which, together with the adaptive choice of their parameters, make it extremely noise robust—and surrogate data tests used to identify interdependent oscillations and to distinguish deterministic from random activity. We illustrate the application of NMD to both simulated and real signals and demonstrate its qualitative and quantitative superiority over other approaches, such as (ensemble) empirical mode decomposition, Karhunen-Loève expansion, and independent component analysis. We point out that NMD is likely to be applicable and useful in many different areas of research, such as geophysics, finance, and the life sciences. The necessary matlab codes for running NMD are freely available for download.
Nonlinear mode decomposition: a noise-robust, adaptive decomposition method.
Iatsenko, Dmytro; McClintock, Peter V E; Stefanovska, Aneta
2015-09-01
The signals emanating from complex systems are usually composed of a mixture of different oscillations which, for a reliable analysis, should be separated from each other and from the inevitable background of noise. Here we introduce an adaptive decomposition tool-nonlinear mode decomposition (NMD)-which decomposes a given signal into a set of physically meaningful oscillations for any wave form, simultaneously removing the noise. NMD is based on the powerful combination of time-frequency analysis techniques-which, together with the adaptive choice of their parameters, make it extremely noise robust-and surrogate data tests used to identify interdependent oscillations and to distinguish deterministic from random activity. We illustrate the application of NMD to both simulated and real signals and demonstrate its qualitative and quantitative superiority over other approaches, such as (ensemble) empirical mode decomposition, Karhunen-Loève expansion, and independent component analysis. We point out that NMD is likely to be applicable and useful in many different areas of research, such as geophysics, finance, and the life sciences. The necessary matlab codes for running NMD are freely available for download.
Adaptive terminal sliding mode control for high-order nonlinear dynamic systems
Institute of Scientific and Technical Information of China (English)
庄开宇; 苏宏业; 张克勤; 褚健
2003-01-01
An adaptive terminal sliding mode control (SMC) technique is proposed to deal with the tracking problem for a class of high-order nonlinear dynamic systems. It is shown that a function augmented sliding hyperplane can be used to develop a new terminal sliding mode for high-order nonlinear systems. A terminal SMC controller based on Lyapunov theory is designed to force the state variables of the closed-loop system to reach and remain on the terminal sliding mode, so that the output tracking error then converges to zero in finite time which can be set arbitrarily. An adaptive mechanism is introduced to estimate the unknown parameters of the upper bounds of system uncertainties. The estimates are then used as controller parameters so that the effects of uncertain dynamics can be eliminated. It is also shown that the stability of the closed-loop system can be guaranteed with the proposed control strategy. The simulation of a numerical example is provided to show the effectiveness of the new method.
Nonlinear adaptive control based on fuzzy sliding mode technique and fuzzy-based compensator.
Nguyen, Sy Dzung; Vo, Hoang Duy; Seo, Tae-Il
2017-09-01
It is difficult to efficiently control nonlinear systems in the presence of uncertainty and disturbance (UAD). One of the main reasons derives from the negative impact of the unknown features of UAD as well as the response delay of the control system on the accuracy rate in the real time of the control signal. In order to deal with this, we propose a new controller named CO-FSMC for a class of nonlinear control systems subjected to UAD, which is constituted of a fuzzy sliding mode controller (FSMC) and a fuzzy-based compensator (CO). Firstly, the FSMC and CO are designed independently, and then an adaptive fuzzy structure is discovered to combine them. Solutions for avoiding the singular cases of the fuzzy-based function approximation and reducing the calculating cost are proposed. Based on the solutions, fuzzy sliding mode technique, lumped disturbance observer and Lyapunov stability analysis, a closed-loop adaptive control law is formulated. Simulations along with a real application based on a semi-active train-car suspension are performed to fully evaluate the method. The obtained results reflected that vibration of the chassis mass is insensitive to UAD. Compared with the other fuzzy sliding mode control strategies, the CO-FSMC can provide the best control ability to reduce unwanted vibrations. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Fan, Quan-Yong; Yang, Guang-Hong
2016-01-01
This paper is concerned with the problem of integral sliding-mode control for a class of nonlinear systems with input disturbances and unknown nonlinear terms through the adaptive actor-critic (AC) control method. The main objective is to design a sliding-mode control methodology based on the adaptive dynamic programming (ADP) method, so that the closed-loop system with time-varying disturbances is stable and the nearly optimal performance of the sliding-mode dynamics can be guaranteed. In the first step, a neural network (NN)-based observer and a disturbance observer are designed to approximate the unknown nonlinear terms and estimate the input disturbances, respectively. Based on the NN approximations and disturbance estimations, the discontinuous part of the sliding-mode control is constructed to eliminate the effect of the disturbances and attain the expected equivalent sliding-mode dynamics. Then, the ADP method with AC structure is presented to learn the optimal control for the sliding-mode dynamics online. Reconstructed tuning laws are developed to guarantee the stability of the sliding-mode dynamics and the convergence of the weights of critic and actor NNs. Finally, the simulation results are presented to illustrate the effectiveness of the proposed method.
Stability of thermal modes in cool prominence plasmas
Soler, Roberto; Parenti, Susanna
2012-01-01
Context: Magnetohydrodynamic thermal modes may play an important role in the formation, plasma condensation, and evolution of solar prominences. Unstable thermal modes due to unbalance between radiative losses and heating can lead to rapid plasma cooling and condensation. An accurate description of the radiative loss function is therefore crucial for this process. Aims: We study the stability of thermal modes in unbounded and uniform plasmas with properties akin to those in solar prominences. Effects due to partial ionization are taken into account. Three different parametrizations of the radiative loss function are used. Methods: By means of a normal mode analysis, we investigate linear nonadiabatic perturbations superimposed on the equilibrium state. We find an approximate instability criterion for thermal modes, while the exact linear growth rate is obtained by numerically solving the general dispersion relation. The stability of thermal disturbances is compared for the three different loss functions consi...
Geometrical Nonlinear Aeroelastic Stability Analysis of a Composite High-Aspect-Ratio Wing
Directory of Open Access Journals (Sweden)
Chang Chuan Xie
2008-01-01
Full Text Available A composite high-aspect-ratio wing of a high-altitude long-endurance (HALE aircraft was modeled with FEM by MSC/NASTRAN, and the nonlinear static equilibrium state is calculated under design load with follower force effect, but without load redistribution. Assuming the little vibration amplitude of the wing around the static equilibrium state, the system is linearized and the natural frequencies and mode shapes of the deformed structure are obtained. Planar doublet lattice method is used to calculate unsteady aerodynamics in frequency domain ignoring the bending effect of the deflected wing. And then, the aeroelastic stability analysis of the system under a given load condition is successively carried out. Comparing with the linear results, the nonlinear displacement of the wing tip is higher. The results indicate that the critical nonlinear flutter is of the flap/chordwise bending type because of the chordwise bending having quite a large torsion component, with low critical speed and slowly growing damping, which dose not appear in the linear analysis. Furthermore, it is shown that the variation of the nonlinear flutter speed depends on the scale of the load and on the chordwise bending frequency. The research work indicates that, for the very flexible HALE aircraft, the nonlinear aeroelastic stability is very important, and should be considered in the design progress. Using present FEM software as the structure solver (e.g. MSC/NASTRAN, and the unsteady aerodynamic code, the nonlinear aeroelastic stability margin of a complex system other than a simple beam model can be determined.
Regimes of stability of accelerator modes
Hihinashvili, R; Avizrats, Y S; Iomin, A; Fishman, S; Guarneri, I; Hihinashvili, Rebecca; Oliker, Tali; Avizrats, Yaniv S.; Iomin, Alexander; Fishman, Shmuel; Guarneri, Italo
2006-01-01
The phase diagram of a simple area-preserving map, which was motivated by the quantum dynamics of cold atoms, is explored analytically and numerically. Periodic orbits of a given winding ratio are found to exist within wedge-shaped regions in the phase diagrams, which are analogous to the Arnol'd tongues which have been extensively studied for a variety of dynamical systems, mostly dissipative ones. A rich variety of bifurcations of various types are observed, as well as period doubling cascades. Stability of periodic orbits is analyzed in detail.
Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems with Jumps
Directory of Open Access Journals (Sweden)
Minsong Zhang
2014-01-01
Full Text Available This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs and linear matrix inequalities (LMIs. Numerical examples are given to illustrate the effectiveness of the proposed methodology.
Study of the stability of polarization mode dispersion in fibre
Institute of Scientific and Technical Information of China (English)
付松年; 吴重庆; 刘海涛; 沈平; 董晖
2003-01-01
Polarization mode dispersion (PMD) is the ultimate limitation to high bit-rate fibre communication system. The stability of PMD is very important to its measurement and compensation. This paper puts forward a method to measure the stability of PMD by measuring the stability of the state of polarization (SOP) and introduces the conception of time evolution vector (TEV) of SOP. We observe the fact that the regularity of the principal state of polarization changing with time is the same as other SOPs', if we neglect the dependence of TEV on wavelength. We also measure the SOP's stability of some fibres with different lengths, and obtain results of PMD changing with time.
Directory of Open Access Journals (Sweden)
Fei Chen
2013-01-01
Full Text Available This paper deals with the finite-time stabilization problem for discrete-time Markov jump nonlinear systems with time delays and norm-bounded exogenous disturbance. The nonlinearities in different jump modes are parameterized by neural networks. Subsequently, a linear difference inclusion state space representation for a class of neural networks is established. Based on this, sufficient conditions are derived in terms of linear matrix inequalities to guarantee stochastic finite-time boundedness and stochastic finite-time stabilization of the closed-loop system. A numerical example is illustrated to verify the efficiency of the proposed technique.
Design for robust stabilization of nonlinear systems with uncertain parameters
Institute of Scientific and Technical Information of China (English)
赖旭芝; 文静; 吴敏
2004-01-01
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.
Integral Terminal Sliding Mode Control for a Class of Nonaffine Nonlinear Systems with Uncertainty
Qiang Zhang; Hongliang Yu; Xiaohong Wang
2013-01-01
This paper is concerned with an integral terminal sliding mode tracking control for a class of uncertain nonaffine nonlinear systems. Firstly, the nonaffine nonlinear systems is approximated to facilitate the desired control design via a novel dynamic modeling technique. Next, for the unmeasured disturbance of nonlinear systems, integral terminal sliding mode disturbance observer is presented. The developed disturbance observer can guarantee the disturbance approximation error to converge to ...
Stability of the resistive wall mode in JET
Energy Technology Data Exchange (ETDEWEB)
Chapman, I T; Gimblett, C G; Gryaznevich, M P; Hender, T C; Howell, D F; Liu, Y Q; Pinches, S D [EURATOM/UKAEA Fusion Association, Culham Science Centre, Abingdon, Oxfordshire OX14 3DB (United Kingdom)], E-mail: ian.chapman@ukaea.org.uk
2009-05-15
The kinetic effects influencing the stability of the resistive wall mode (RWM) are investigated by applying a drift kinetic code to calculate the change in the potential energy of the mode in the presence of thermal and energetic particles. The analysis is carried out for typical JET high-{beta} plasmas. It is found that the strongest kinetic damping of the RWM arises due to mode resonance with the precession motion of the trapped thermal particles. The stability of the RWM in JET plasmas is also probed by using active MHD spectroscopy. The frequency spectrum of the plasma response to oscillating externally applied fields has been measured and fitted to parameter models in order to infer the stability of the RWM. A new model retaining information about the plasma response is presented to describe the resonant field amplification in the presence of a stable RWM.
Slope stability analysis using limit equilibrium method in nonlinear criterion.
Lin, Hang; Zhong, Wenwen; Xiong, Wei; Tang, Wenyu
2014-01-01
In slope stability analysis, the limit equilibrium method is usually used to calculate the safety factor of slope based on Mohr-Coulomb criterion. However, Mohr-Coulomb criterion is restricted to the description of rock mass. To overcome its shortcomings, this paper combined Hoek-Brown criterion and limit equilibrium method and proposed an equation for calculating the safety factor of slope with limit equilibrium method in Hoek-Brown criterion through equivalent cohesive strength and the friction angle. Moreover, this paper investigates the impact of Hoek-Brown parameters on the safety factor of slope, which reveals that there is linear relation between equivalent cohesive strength and weakening factor D. However, there are nonlinear relations between equivalent cohesive strength and Geological Strength Index (GSI), the uniaxial compressive strength of intact rock σ ci , and the parameter of intact rock m i . There is nonlinear relation between the friction angle and all Hoek-Brown parameters. With the increase of D, the safety factor of slope F decreases linearly; with the increase of GSI, F increases nonlinearly; when σ ci is relatively small, the relation between F and σ ci is nonlinear, but when σ ci is relatively large, the relation is linear; with the increase of m i , F decreases first and then increases.
Enhanced adaptive fuzzy sliding mode control for uncertain nonlinear systems
Roopaei, Mehdi; Zolghadri, Mansoor; Meshksar, Sina
2009-09-01
In this article, a novel Adaptive Fuzzy Sliding Mode Control (AFSMC) methodology is proposed based on the integration of Sliding Mode Control (SMC) and Adaptive Fuzzy Control (AFC). Making use of the SMC design framework, we propose two fuzzy systems to be used as reaching and equivalent parts of the SMC. In this way, we make use of the fuzzy logic to handle uncertainty/disturbance in the design of the equivalent part and provide a chattering free control for the design of the reaching part. To construct the equivalent control law, an adaptive fuzzy inference engine is used to approximate the unknown parts of the system. To get rid of the chattering, a fuzzy logic model is assigned for reaching control law, which acting like the saturation function technique. The main advantage of our proposed methodology is that the structure of the system is unknown and no knowledge of the bounds of parameters, uncertainties and external disturbance are required in advance. Using Lyapunov stability theory and Barbalat's lemma, the closed-loop system is proved to be stable and convergence properties of the system is assured. Simulation examples are presented to verify the effectiveness of the method. Results are compared with some other methods proposed in the past research.
Alippi, A.; Biagioni, A.; Germano, M.; Passeri, D.
2008-06-01
Local probing of nonlinear generation of harmonic vibrations has been done on bone plate samples and the evaluation of the nonlinear term is derived from a limited number of cases of bovine thigh bones, that shows that a low level of nonlinearity is present in bone structures. This is consistent with the assumption that in low level nonlinear samples the distribution of harmonic vibrations matches the corresponding power distribution of the fundamental mode.
Geometrical nonlinear stability analyses of cable-truss domes
Institute of Scientific and Technical Information of China (English)
高博青; 卢群鑫; 董石麟
2003-01-01
The nonlinear finite element method is used to analyze the geometrical nonlinear stability of cable-truss domes with different cable distributions. The results indicate that the critical load increases evidently when cables, especially diagonal cables, are distributed in the structure. The critical loads of the structure at different rise-span ratios are also discussed in this paper. It was shown that the effect of the tensional cable is more evident at small rise-span ratio. The buckling of the structure is characterized by a global collapse at small rise-span ratio; that the torsional buckling of the radial truss occurs at big rise-span ratio; and that at proper rise-span ratio, the global collapse and the lateral buckling of the truss occur nearly simultaneously.
Stability Analysis of Continuous Waves in Nonlocal Random Nonlinear Media
Directory of Open Access Journals (Sweden)
Maxim A. Molchan
2007-08-01
Full Text Available On the basis of the competing cubic-quintic nonlinearity model, stability (instability of continuous waves in nonlocal random non-Kerr nonlinear media is studied analytically and numerically. Fluctuating media parameters are modeled by the Gaussian white noise. It is shown that for different response functions of a medium nonlocality suppresses, as a rule, both the growth rate peak and bandwidth of instability caused by random parameters. At the same time, for a special form of the response functions there can be an ''anomalous'' subjection of nonlocality to the instability development which leads to further increase of the growth rate. Along with the second-order moments of the modulational amplitude, higher-order moments are taken into account.
Geometrical nonlinear stability analyses of cable-truss domes
Institute of Scientific and Technical Information of China (English)
高博青; 卢群鑫; 董石麟
2003-01-01
The nonlinear finite element method is used to analyze the geometrical nonlinear stability of cabletruss domes with different cable distributions. The results indicate that the critical load increases evidently when cables, especially diagonal cables, are distributed in the structure. The critical loads of the structure at different rise-span ratios are also discussed in this paper. It was shown that the effect of the tensional cable is more evident at small rise-span ratio. The buckling of the structure is characterized by a global collapse at small rlse-span ratio ; that the torsional buckling of the radial truss occurs at big rise-span ratio; and that at proper rise-span ratio, the global collapse and the lateral buckling of the truss occur nearly simultaneously.
Transient stability improvement by nonlinear controllers based on tracking
Energy Technology Data Exchange (ETDEWEB)
Ramirez, Juan M. [Centro de Investigacion y Estudios Avanzados, Guadalajara, Mexico. Av. Cientifica 1145. Col. El Bajio. Zapopan, Jal. 45015 (Mexico); Arroyave, Felipe Valencia; Correa Gutierrez, Rosa Elvira [Universidad Nacional de Colombia, Sede Medellin. Facultad de Minas, Escuela de Mecatronica (Colombia)
2011-02-15
This paper deals with the control problem in multi-machine electric power systems, which represent complex great scale nonlinear systems. Thus, the controller design is a challenging problem. These systems are subjected to different perturbations, such as short circuits, connection and/or disconnection of loads, lines, or generators. Then, the utilization of controllers which guarantee good performance under those perturbations is required in order to provide electrical energy to the loads with admissible stability margins. The proposed controllers are based on a systematic strategy, which calculate nonlinear controllers for generating units in a power plant, both for voltage and velocity regulation. The formulation allows designing controllers in a multi-machine power system without intricate calculations. Results on a power system of the open research indicate the proposition's suitability. The problem is formulated as a tracking problem. The designed controllers may be implemented in any electric power system. (author)
Stability analysis of a class of fractional order nonlinear systems with order lying in (0, 2).
Zhang, Ruoxun; Tian, Gang; Yang, Shiping; Cao, Hefei
2015-05-01
This paper investigates the stability of n-dimensional fractional order nonlinear systems with commensurate order 0 nonlinear systems with order lying in (0, 2). According to this theory, stabilizing a class of fractional order nonlinear systems only need a linear state feedback controller. Simulation results demonstrate the effectiveness of the proposed theory.
Adaptive steady-state stabilization for nonlinear dynamical systems
Braun, David J.
2008-07-01
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.
Nonlinear Coherent Directional Coupler: Coupled Mode Theory and BPM Simulation
National Research Council Canada - National Science Library
Kumbhakar, Dharmadas
2012-01-01
.... The coupling lengths derived from this simulation are compared with coupled mode theories. BPM results for the critical power follow the trend of the coupled mode theories, but it lies in between two coupled mode theories...
Physics and stabilization of resistive wall modes in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Bondeson, A [Department of Electromagnetics, EURATOM-VR/Fusion Association, Chalmers University of Technology, Goeteborg (Sweden); Liu, Y Q [Department of Electromagnetics, EURATOM-VR/Fusion Association, Chalmers University of Technology, Goeteborg (Sweden); Gregoratto, D [Department of Electromagnetics, EURATOM-VR/Fusion Association, Chalmers University of Technology, Goeteborg (Sweden); Fransson, C M [Department of Signals and Systems, Chalmers University of Technology, Goeteborg (Sweden); Gribov, Y [Physics Unit, ITER Naka Joint Work Site, Naka, Ibaraki (Japan)
2003-12-01
The theory of resistive wall modes (RWMs) is discussed and compared with experimental results. Special attention is given to the possibilities of stabilizing the RWM by plasma rotation and active feedback. A simple cylindrical model is used to illustrate various aspects of active control. Fully toroidal computations are also presented, including predictions for RWM stabilization in ITER. According to ideal MHD, robust control of RWM should be straightforward. Theory for stabilization by rotation is discussed, and a semikinetic model is introduced, which compares favourably with experiment. The semikinetic model produces somewhat lower rotation thresholds than previous models.
A Nonlinear Coupled-Mode System for Water Waves over a General Bathymetry
Athanassoulis, G. A.; Belibassakis, K. A.
2003-04-01
in the local-mode series References Athanassoulis, G. A. Belibassakis, K. A.: A Consistent Coupled-Mode Theory for the Propagation of Small-Amplitude Water Waves over Variable Bathymetry Regions. J. Fluid Mech. 389, 275--301, 1999. Athanassoulis, G. A. Belibassakis, K. A.: A Complete Modal Expansion of the Wave Potential and Its Application to Linear and Nonlinear Water-Wave Problems, Proc. "Rogue Waves 2000", Brest, France, 29--30 November 2000. Belibassakis, K. A. Athanassoulis, G. A. Extension of second-order Stokes theory to variable bathymetry, J. Fluid Mech. 464, 35--80, 2002. Luke, J. C.: A Variational Principle for a Fluid with a Free Surface. J. Fluid Mech. 27, 395--397, 1967. Petrov, A. A.: Variational Statement of the Problem of Liquid Motion in a Container of Finite Dimensions. PMM, 28 (4), 917--922, 1964. Zakharov, V. E.: Stability of Periodic Waves of Finite Amplitude on the Surface of a Deep Fluid. J. Appl. Math. Tech. Phys., 2 190, 1968.
Stability analysis for nonlinear multi－variable delay perturbation problems
Institute of Scientific and Technical Information of China (English)
WangHongshan; ZhangChengjian
2003-01-01
This paper discusses the stability of theoretical solutions for nonlinear multi-variable delay perturbation problems(MVDPP) of the form x′(t) = f(x(t),x(t - τ1(t)),…,x(t -τm(t)),y(t),y(t - τ1(t)),…,y(t - τm(t))), and gy′(t) = g(x(t),x(t- τ1(t)),…,x(t- τm(t)),y(t),y(t- τ1(t)),…,y(t- τm(t))), where 0 < ε <<1. A sufficient condition of stability for the systems is obtained. Additionally we prove the numerical solutions of the implicit Euler method are stable under this condition.
Stability of the accelerated expansion in nonlinear electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Sharif, M.; Mumtaz, Saadia [University of the Punjab, Department of Mathematics, Lahore (Pakistan)
2017-02-15
This paper is devoted to the phase space analysis of an isotropic and homogeneous model of the universe by taking a noninteracting mixture of the electromagnetic and viscous radiating fluids whose viscous pressure satisfies a nonlinear version of the Israel-Stewart transport equation. We establish an autonomous system of equations by introducing normalized dimensionless variables. In order to analyze the stability of the system, we find corresponding critical points for different values of the parameters. We also evaluate the power-law scale factor whose behavior indicates different phases of the universe in this model. It is concluded that the bulk viscosity as well as electromagnetic field enhances the stability of the accelerated expansion of the isotropic and homogeneous model of the universe. (orig.)
Zhang, Wei-Ya; Li, Yong-Li; Chang, Xiao-Yong; Wang, Nan
2013-09-01
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.
Indian Academy of Sciences (India)
P K Datta; Chandrajit Basu; S Mukhopadhyay; S K Das; G K Samanta; Antonio Agnesi
2004-11-01
A non-linear mirror consisting of a lithium triborate crystal and a dichroic output coupler are used to mode-lock (passively) an Nd : YVO4 laser, pumped by a diode laser array. The laser can operate both in cw mode-locked and simultaneously Q-switched and mode-locked (QML) regime. The peak power of the laser while operating in QML regime is much higher but pulses suffers from poor amplitude stability. The incorporation of an acousto-optic modulator as an active Q-switch enhances the stability of the QML pulse envelope. The second-order non-linearity of powdered crystalline urea is conclusively measured with respect to KDP while the laser is operating in passively Q-switched and passively mode-locked regime as well as in actively Q-switched and passively mode-locked regime.
Optimization of hardening/softening behavior of plane frame structures using nonlinear normal modes
DEFF Research Database (Denmark)
Dou, Suguang; Jensen, Jakob Søndergaard
2016-01-01
/softening behavior of nonlinear mechanical systems. The iterative optimization procedure consists of calculation of nonlinear normal modes, solving an adjoint equation system for sensitivity analysis and an update of design variables using a mathematical programming tool. We demonstrate the method with examples......Devices that exploit essential nonlinear behavior such as hardening/softening and inter-modal coupling effects are increasingly used in engineering and fundamental studies. Based on nonlinear normal modes, we present a gradient-based structural optimization method for tailoring the hardening...
Distributed Adaptive Fuzzy Control for Nonlinear Multiagent Systems Via Sliding Mode Observers.
Shen, Qikun; Shi, Peng; Shi, Yan
2016-12-01
In this paper, the problem of distributed adaptive fuzzy control is investigated for high-order uncertain nonlinear multiagent systems on directed graph with a fixed topology. It is assumed that only the outputs of each follower and its neighbors are available in the design of its distributed controllers. Equivalent output injection sliding mode observers are proposed for each follower to estimate the states of itself and its neighbors, and an observer-based distributed adaptive controller is designed for each follower to guarantee that it asymptotically synchronizes to a leader with tracking errors being semi-globally uniform ultimate bounded, in which fuzzy logic systems are utilized to approximate unknown functions. Based on algebraic graph theory and Lyapunov function approach, using Filippov-framework, the closed-loop system stability analysis is conducted. Finally, numerical simulations are provided to illustrate the effectiveness and potential of the developed design techniques.
Event-triggered sliding mode control for a class of nonlinear systems
Behera, Abhisek K.; Bandyopadhyay, Bijnan
2016-09-01
Event-triggering strategy is one of the real-time control implementation techniques which aims at achieving minimum resource utilisation while ensuring the satisfactory performance of the closed-loop system. In this paper, we address the problem of robust stabilisation for a class of nonlinear systems subject to external disturbances using sliding mode control (SMC) by event-triggering scheme. An event-triggering scheme is developed for SMC to ensure the sliding trajectory remains confined in the vicinity of sliding manifold. The event-triggered SMC brings the sliding mode in the system and thus the steady-state trajectories of the system also remain bounded within a predesigned region in the presence of disturbances. The design of event parameters is also given considering the practical constraints on control execution. We show that the next triggering instant is larger than its immediate past triggering instant by a given positive constant. The analysis is also presented with taking delay into account in the control updates. An upper bound for delay is calculated to ensure stability of the system. It is shown that with delay steady-state bound of the system is increased than that of the case without delay. However, the system trajectories remain bounded in the case of delay, so stability is ensured. The performance of this event-triggered SMC is demonstrated through a numerical simulation.
Schamel, Hans; Mandal, Debraj; Sharma, Devendra
2017-03-01
An outstanding notion for collisionless plasmas is the essential nonlinear character of their coherent structures, which in the stationary, weak amplitude limit are described by a continuum of cnoidal electron and ion hole modes governed by a multiparametric nonlinear dispersion relation. The well-known discrete structure of undamped linear plasma modes is seamlessly embedded in this nonlinear continuum as the microscopic texture of plasma begins to reveal itself in the high temperature collisionless plasma limit. This transforms the linear-threshold-based operating mechanism of plasma turbulence into a fundamental nonlinear, multifaceted one. Based on a comprehensive three-level description of increasing profundity, a proof of this novel dictum is presented, which makes use of the joint properties of such structures, their coherency and stationarity, and uses in succession a fluid, linear Vlasov and a full Vlasov description. It unifies discrete and continuum limits by resolving the inevitable resonant region and shows that coherent electrostatic equilibria are generally controlled by kinetic particle trapping and are hence fundamentally nonlinear. By forging a link between damped and growing wave solutions, these modes render plasma stability complex and difficult to evaluate due to the entangled pattern of the stability boundary in function and parameter space, respectively. A direct consequence is the existence of negative energy modes of arbitrarily small amplitudes in the subcritical region of the two-stream instability as well as the failure of linear Landau (Vlasov, van Kampen) theory, whenever resonant particles are involved, in addressing the onset of instability in a current-carrying plasma. Responsible for this subtle phase space behavior is hence the thresholdless omnipresence of the trapping nonlinearity originating from coherency. A high resolution, exact-mass-ratio, multispecies, and collisionless plasma simulation is employed to illustrate
Global stabilizer of a general class of feedback nonlinear systems and its exponential convergence
Institute of Scientific and Technical Information of China (English)
Runing MA; Jundi DIAN
2005-01-01
We discuss the global stabilization procedure which renders a general class of feedback nonlinear systems exponential convergent. Our stabilizer consists of a nested saturation function, which is a nonlinear combination of satrration functions. Here we prove the exponential convergence of the stabilizer for the first time and give numerical examples to illustrate the efficiency of the result given above.
Absolute stability of nonlinear systems with time delays and applications to neural networks
Directory of Open Access Journals (Sweden)
Xinzhi Liu
2001-01-01
Full Text Available In this paper, absolute stability of nonlinear systems with time delays is investigated. Sufficient conditions on absolute stability are derived by using the comparison principle and differential inequalities. These conditions are simple and easy to check. In addition, exponential stability conditions for some special cases of nonlinear delay systems are discussed. Applications of those results to cellular neural networks are presented.
Univariate and Bivariate Empirical Mode Decomposition for Postural Stability Analysis
Directory of Open Access Journals (Sweden)
Jacques Duchêne
2008-05-01
Full Text Available The aim of this paper was to compare empirical mode decomposition (EMD and two new extended methods of Ã¢Â€Â‰EMD named complex empirical mode decomposition (complex-EMD and bivariate empirical mode decomposition (bivariate-EMD. All methods were used to analyze stabilogram center of pressure (COP time series. The two new methods are suitable to be applied to complex time series to extract complex intrinsic mode functions (IMFs before the Hilbert transform is subsequently applied on the IMFs. The trace of the analytic IMF in the complex plane has a circular form, with each IMF having its own rotation frequency. The area of the circle and the average rotation frequency of IMFs represent efficient indicators of the postural stability status of subjects. Experimental results show the effectiveness of these indicators to identify differences in standing posture between groups.
Semiclassical mode-coupling factorizations of coherent nonlinear optical response
Jansen, TL; Mukamel, S
2003-01-01
The identification of relevant collective coordinates is crucial for the interpretation of coherent nonlinear spectroscopies of complex molecules and liquids. Using an h expansion of Liouville space generating functions, we show how to factorize multitime nonlinear response functions into products o
On the stability and compressive nonlinearity of a physiologically based model of the cochlea
Energy Technology Data Exchange (ETDEWEB)
Nankali, Amir [Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan (United States); Grosh, Karl [Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan (United States); Department of Biomedical Engineering, University of Michigan, Ann Arbor, Michigan (United States)
2015-12-31
Hearing relies on a series of coupled electrical, acoustical (fluidic) and mechanical interactions inside the cochlea that enable sound processing. A positive feedback mechanism within the cochlea, called the cochlear amplifier, provides amplitude and frequency selectivity in the mammalian auditory system. The cochlear amplifier and stability are studied using a nonlinear, micromechanical model of the Organ of Corti (OoC) coupled to the electrical potentials in the cochlear ducts. It is observed that the mechano-electrical transduction (MET) sensitivity and somatic motility of the outer hair cell (OHC), control the cochlear stability. Increasing MET sensitivity beyond a critical value, while electromechanical coupling coefficient is within a specific range, causes instability. We show that instability in this model is generated through a supercritical Hopf bifurcation. A reduced order model of the system is approximated and it is shown that the tectorial membrane (TM) transverse mode effect on the dynamics is significant while the radial mode can be simplified from the equations. The cochlear amplifier in this model exhibits good agreement with the experimental data. A comprehensive 3-dimensional model based on the cross sectional model is simulated and the results are compared. It is indicated that the global model qualitatively inherits some characteristics of the local model, but the longitudinal coupling along the cochlea shifts the stability boundary (i.e., Hopf bifurcation point) and enhances stability.
Stabilization effect of Weibel modes in relativistic laser fusion plasma
Belghit, Slimen; Sid, Abdelaziz
2016-06-01
In this work, the Weibel instability (WI) due to inverse bremsstrahlung (IB) absorption in a laser fusion plasma has been investigated. The stabilization effect due to the coupling of the self-generated magnetic field by WI with the laser wave field is explicitly shown. In this study, the relativistic effects are taken into account. Here, the basic equation is the relativistic Fokker-Planck (F-P) equation. The main obtained result is that the coupling of self-generated magnetic field with the laser wave causes a stabilizing effect of excited Weibel modes. We found a decrease in the spectral range of Weibel unstable modes. This decreasing is accompanied by a reduction of two orders in the growth rate of instable Weibel modes or even stabilization of these modes. It has been shown that the previous analysis of the Weibel instability due to IB has overestimated the values of the generated magnetic fields. Therefore, the generation of magnetic fields by the WI due to IB should not affect the experiences of an inertial confinement fusion.
Excitations and management of the nonlinear localized gap modes
Indian Academy of Sciences (India)
Bishwajyoti Dey
2015-11-01
We discuss about the theory of nonlinear localized excitations, such as soliton and compactons in the gap of the linear spectrum of the nonlinear systems. We show how the gap originates in the linear spectrum using examples of a few systems, such as nonlinear lattices, Bose–Einstein condensates in optical lattice and systems represented by coupled nonlinear evolution equations. We then analytically show the excitation of solitons and compacton-like solutions in the gap of the linear spectrum of a system of coupled Korteweg–de Vries (KdV) equations with linear and nonlinear dispersions. Finally, we discuss about the theory of Feshbach resonance management and dispersion management of the soliton solutions.
Excitation Thresholds for Nonlinear Localized Modes on Lattices
Weinstein, M I
1999-01-01
Breathers are spatially localized and time periodic solutions of extended Hamiltonian dynamical systems. In this paper we study excitation thresholds for (nonlinearly dynamically stable) ground state breather or standing wave solutions for networks of coupled nonlinear oscillators and wave equations of nonlinear Schrödinger (NLS) type. Excitation thresholds are rigorously characterized by variational methods. The excitation threshold is related to the optimal (best) constant in a class of discr ete interpolation inequalities related to the Hamiltonian energy. We establish a precise connection among $d$, the dimensionality of the lattice, $2\\sigma+1$, the degree of the nonlinearity and the existence of an excitation threshold for discrete nonlinear Schrödinger systems (DNLS). We prove that if $\\sigma\\ge 2/d$, then ground state standing waves exist if and only if the total power is larger than some strictly positive threshold, the context of DNLS. We also discuss upper and lower bounds for excitation threshol...
Energy Technology Data Exchange (ETDEWEB)
Baik, I.C.; Kim, K.H.; Cho, K.Y.; Youn, M.J. [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)
1998-04-01
A DSP-based robust nonlinear speed control of a permanent magnet synchronous motor (PMSM) which is robust to unknown parameter variations and speed measurement error is presented. The model reference adaptive system (MRAS) based adaptation mechanisms for the estimation of slowly varying parameters are derived using the Lyapunov stability theory. For the disturbances or quickly varying parameters, a quasi-linearized and decoupled model including the influence of parameter variations and speed measurement error on the nonlinear speed control of a PMSM is derived. Based on this model, a boundary layer integral sliding mode controller to improve the robustness and performance of the nonlinear speed control of a PMSM is designed and compared with the conventional controller. To show the validity of the proposed control scheme, simulations and experimental works are carried out and compared with the conventional control scheme. (author). 19 refs., 14 figs., 6 tabs.
AMABILI, M.; PELLICANO, F.; PAÏDOUSSIS, M. P.
1999-08-01
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.
Robust Absolute Stability of General Interval Lur'e Type Nonlinear Control Systems
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
In this paper, Lyapunov function method isused to study the robust absolute stability of general interval Lur'e type nonlinear control systems. As a result, algebraically sufficient conditions with interval matrix inequality form are obtained for the general interval Lur'e type nonlinear control systems, thus the relationship between the stability of symmetrical interval matrix and the robust absolute stability of general interval Lur'e type nonlinear control systems is established.
Collapse arrest and soliton stabilization in nonlocal nonlinear media
DEFF Research Database (Denmark)
Bang, Ole; Krolikowski, Wieslaw; Wyller, John
2002-01-01
We investigate the properties of localized waves in cubic nonlinear materials with a symmetric nonlocal nonlinear response of arbitrary shape and degree of nonlocality, described by a general nonlocal nonlinear Schrodinger type equation. We prove rigorously by bounding the Hamiltonian that nonloc......We investigate the properties of localized waves in cubic nonlinear materials with a symmetric nonlocal nonlinear response of arbitrary shape and degree of nonlocality, described by a general nonlocal nonlinear Schrodinger type equation. We prove rigorously by bounding the Hamiltonian...
Energy Technology Data Exchange (ETDEWEB)
Li, Jin [Chongqing University, Department of Physics, Chongqing (China); Lin, Kai [Universidade de Sao Paulo, Instituto de Fisica, CP 66318, Sao Paulo (Brazil); Yang, Nan [Huazhong University of Science and Technology, Department of Physics, Wuhan (China)
2015-03-01
Based on a regular exact black hole (BH) from nonlinear electrodynamics (NLED) coupled to general relativity, we investigate the stability of such BH through the Quasinormal Modes (QNMs) of electromagnetic (EM) field perturbations and its thermodynamics through Hawking radiation. In perturbation theory, we can deduce the effective potential from a nonlinear EM field. The comparison of the potential function between regular and RN BHs could predict similar QNMs. The QNM frequencies tell us the effect of the magnetic charge q, the overtone n, and the angular momentum number l on the dynamic evolution of NLED EM field. Furthermore we also discuss the cases of near-extreme conditions of such a magnetically charged regular BH. The corresponding QNM spectrum illuminates some special properties in the near-extreme cases. For the thermodynamics, we employ the Hamilton-Jacobi method to calculate the near-horizon Hawking temperature of the regular BH and reveal the relationship between the classical parameters of the black hole and its quantum effects. (orig.)
Analysis of Stability and Bifurcation in Nonlinear Mechanics with Dissipation
Directory of Open Access Journals (Sweden)
Claude Stolz
2011-01-01
Full Text Available The analysis of stability and bifurcation is studied in nonlinear mechanics with dissipative mechanisms: plasticity, damage, fracture. The description is based on introduction of a set of internal variables. This framework allows a systematic description of the material behaviour via two potentials: the free energy and the potential of dissipation. In the framework of standard generalized materials the internal state evolution is governed by a variational inequality which depends on the mechanism of dissipation. This inequality is obtained through energetic considerations in an unified description based upon energy and driving forces associated to the dissipative process. This formulation provides criterion for existence and uniqueness of the system evolution. Examples are presented for plasticity, fracture and for damaged materials.
On nonlinear stability in various random normed spaces
Directory of Open Access Journals (Sweden)
Saadati Reza
2011-01-01
Full Text Available Abstract In this article, we prove the nonlinear stability of the quartic functional equation 1 6 f ( x + 4 y + f ( 4 x - y = 3 0 6 9 f x + y 3 + f ( x + 2 y (1 + 1 3 6 f ( x - y - 1 3 9 4 f ( x + y + 4 2 5 f ( y - 1 5 3 0 f ( x (2 (3 in the setting of random normed spaces Furthermore, the interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean space, the theory of fixed point theory, the theory of intuitionistic spaces and the theory of functional equations are also presented in the article.
Multivariable nonlinear control of STATCOM for synchronous generator stabilization
Energy Technology Data Exchange (ETDEWEB)
Sahoo, N.C. [Multimedia Univ., Melaka (Malaysia). Faculty of Engineering and Technology; Panigrahi, B.K.; Panda, G. [Multimedia Univ., Selangor (Malaysia); Dash, P.K. [National Inst. of Technology, Rourkela (India)
2004-01-01
A static synchronous compensator (STATCOM) is a typical flexible ac transmission system device playing a vital role as a stability aid for small and large transient disturbances in an interconnected power system. This article deals with design and evaluation of a feedback linearizing nonlinear controller for STATCOM installed in a single-machine infinite-bus power system. In addition to the coordinated control of ac and dc bus voltages, the proposed controller also provides good damping to the electromechanical oscillation of the synchronous generator under transient disturbances. The efficiency of the control strategy is evaluated by computer simulation studies. The comparative study of these results with the conventional cascade control structure establishes the elegance of the proposed control scheme. (author)
Whispering Gallery Mode Resonator Stabilized Narrow Linewidth Fiber Loop Laser
Sprenger, B; Wang, L J; 10.1364/OL.34.003370
2012-01-01
We demonstrate a narrow line, fiber loop laser using Erbium-doped fiber as the gain material, stabilized by using a microsphere as a transmissive frequency selective element. Stable lasing with a linewidth of 170 kHz is observed, limited by the experimental spectral resolution. A linear increase in output power and a red-shift of the lasing mode were also observed with increasing pump power. Its potential application is also discussed.
On the linear stability of collisionless microtearing modes
Predebon, I
2013-01-01
Microtearing modes are an important drive of turbulent heat transport in present-day fusion plasmas. We investigate their linear stability under very-low collisionality regimes, expected for the next generations of devices, using gyrokinetic and drift-kinetic approaches. At odds with current opinion, we show that collisionless microtearing instabilities may occur in certain experimental conditions, particularly relevant for such devices as reversed field pinches and spherical tokamaks.
Holographic Reversed-Mode Polymer-Stabilized Liquid Crystal Grating
Institute of Scientific and Technical Information of China (English)
MA Ji; SONG Jing; LIU Yong-Gang; RUAN Sheng-Ping; XUAN Li
2005-01-01
@@ We demonstrate the "reversed-mode" polymer-stabilized liquid crystal device. The incidence light goes through the film without the applied voltage and is diffracted with it. Because of relatively high liquid crystal percentage of 94%, the operating voltage of the device is less than 20 V. We explain this phenomenon using the molecularorientation model and the refractive index profile. The device can be used as display, optical switch, optical modulator and especially optical cross-connect deflector.
Nonlinear Mirror and Weibel modes: peculiarities of quasi-linear dynamics
Directory of Open Access Journals (Sweden)
O. A. Pokhotelov
2010-12-01
Full Text Available A theory for nonlinear evolution of the mirror modes near the instability threshold is developed. It is shown that during initial stage the major instability saturation is provided by the flattening of the velocity distribution function in the vicinity of small parallel ion velocities. The relaxation scenario in this case is accompanied by rapid attenuation of resonant particle interaction which is replaced by a weaker adiabatic interaction with mirror modes. The saturated plasma state can be considered as a magnetic counterpart to electrostatic BGK modes. After quasi-linear saturation a further nonlinear scenario is controlled by the mode coupling effects and nonlinear variation of the ion Larmor radius. Our analytical model is verified by relevant numerical simulations. Test particle and PIC simulations indeed show that it is a modification of distribution function at small parallel velocities that results in fading away of free energy driving the mirror mode. The similarity with resonant Weibel instability is discussed.
Nonlinear optics in the LP(02) higher-order mode of a fiber.
Chen, Y; Chen, Z; Wadsworth, W J; Birks, T A
2013-07-29
The distinct disperion properties of higher-order modes in optical fibers permit the nonlinear generation of radiation deeper into the ultraviolet than is possible with the fundamental mode. This is exploited using adiabatic, broadband mode convertors to couple light efficiently from an input fundamental mode and also to return the generated light to an output fundamental mode over a broad spectral range. For example, we generate visible and UV supercontinuum light in the LP(02) mode of a photonic crystal fiber from sub-ns pulses with a wavelength of 532 nm.
STABILITY ANALYSIS OF RUNGE-KUTTA METHODS FOR NONLINEAR SYSTEMS OF PANTOGRAPH EQUATIONS
Institute of Scientific and Technical Information of China (English)
Yue-xin Yu; Shou-fu Li
2005-01-01
This paper is concerned with numerical stability of nonlinear systems of pantograph equations. Numerical methods based on (k, l)-algebraically stable Runge-Kutta methods are suggested. Global and asymptotic stability conditions for the presented methods are derived.
STABILIZATION OF NONLINEAR TIME-VARYING SYSTEMS: A CONTROL LYAPUNOV FUNCTION APPROACH
Institute of Scientific and Technical Information of China (English)
Zhongping JIANG; Yuandan LIN; Yuan WANG
2009-01-01
This paper presents a control Lyapunov function approach to the global stabilization problem for general nonlinear and time-varying systems. Explicit stabilizing feedback control laws are proposed based on the method of control Lyapunov functions and Sontag's universal formula.
Stability analysis of Runge-Kutta methods for nonlinear neutral delay integro-differential equations
Institute of Scientific and Technical Information of China (English)
2007-01-01
The sufficient conditions for the stability and asymptotic stability of Runge-Kutta methods for nonlinear neutral delay integro-differential equations are derived. A numerical test that confirms the theoretical results is given in the end.
Finite-beta effects on the nonlinear evolution of the (m = 1; n = 1) mode in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Holmes, J.A.; Carreras, B.A.; Hicks, H.R.; Lynch, V.E.; Rothe, K.E.
1982-01-01
The stability and evolution of ISX-B-like plasmas are numerically studied using a reduced set of resistive magnetohydrodynamic (MHD) equations. For a sequence of equilibria stable to ideal modes, the n = 1 mode changes from a tearing branch to a pressure-driven branch as ..beta../sup p/ is increased. When this mode is unstable at low beta, it is just the (m = 1;n = 1) tearing mode. Higher n modes also become linearly unstable with increasing ..beta../sub p/; they are essentially pressure driven and have a ballooning character. For low values of beta the instability is best described as a ..beta../sub p/ distortion of the (m = 1;n = 1) tearing mode. This mode drives many other helicities through toroidal and nonlinear couplings. As ..beta../sub p/ is increased, the growth of the m = 1 island slows down in time, going from exponential to linear before reconnection occurs. If ..beta../sub p/ is large enough, the island saturates without reconnection. A broad spectrum of other modes, driven by the (m = 1;n = 1) instability, is produced. These results agree with some observed features of MHD activity in ISX-B.
Singh, S. N.
1982-03-01
Using the invariance principle of LaSalle (1962) sufficient conditions for the existence of linear and nonlinear control laws for local and global asymptotic stability of nonlinear Hamiltonian systems are derived. An instability theorem is also presented which identifies the control laws from the given class which cannot achieve asymptotic stability. Some of the stability results are based on certain results for the univalence of nonlinear maps. A similar approach for the stabilization of bilinear systems which include nonconservative systems in elasticity is used and a necessary and sufficient condition for stabilization is obtained. An application to attitude control of a gyrostat Satellite is presented.
Profile stabilization of tilt mode in a Field Reversed Configuration
Energy Technology Data Exchange (ETDEWEB)
Cobb, J.W.; Tajima, T. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies; Barnes, D.C. [Los Alamos National Lab., NM (United States)
1993-06-01
The possibility of stabilizing the tilt mode in Field Reversed Configurations without resorting to explicit kinetic effects such as large ion orbits is investigated. Various pressure profiles, P({Psi}), are chosen, including ``hollow`` profiles where current is strongly peaked near the separatrix. Numerical equilibria are used as input for an initial value simulation which uses an extended Magnetohydrodynamic (MHD) model that includes viscous and Hall terms. Tilt stability is found for specific hollow profiles when accompanied by high values of separatrix beta, {beta}{sub sep}. The stable profiles also have moderate to large elongation, racetrack separatrix shape, and lower values of 3, average ratio of Larmor radius to device radius. The stability is unaffected by changes in viscosity, but the neglect of the Hall term does cause stable results to become marginal or unstable. Implications for interpretation of recent experiments are discussed.
Stability of Rotor Hopfield Neural Networks With Synchronous Mode.
Kobayashi, Masaki
2016-12-29
A complex-valued Hopfield neural network (CHNN) is a model of a Hopfield neural network using multistate neurons. The stability conditions of CHNNs have been widely studied. A CHNN with a synchronous mode will converge to a fixed point or a cycle of length 2. A rotor Hopfield neural network (RHNN) is also a model of a multistate Hopfield neural network. RHNNs have much higher storage capacity and noise tolerance than CHNNs. We extend the theories regarding the stability of CHNNs to RHNNs. In addition, we investigate the stability of RHNNs with the projection rule. Although a CHNN with projection rule can be trapped at a cycle, an RHNN with projection rule converges to a fixed point. This is one of the great advantages of RHNNs.
NONLINEAR STABILITY OF NATURAL RUNGE-KUTTA METHODS FOR NEUTRAL DELAY DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Cheng-jian Zhang
2002-01-01
This paper first presents the stability analysis of theoretical solutions for a class of nonlinear neutral delay-differential equations (NDDEs). Then the numerical analogous results, of the natural Runge-Kutta (NRK) methods for the same class of nonlinear NDDEs,are given. In particular, it is shown that the (k, l)-algebraic stability of a RK method for ODEs implies the generalized asymptotic stability and the global stability of the induced NRK method.
Nonlinear Dynamical analysis of an AFM tapping mode microcantilever beam
Directory of Open Access Journals (Sweden)
Choura S.
2012-07-01
Full Text Available We focus in this paper on the modeling and dynamical analysis of a tapping mode atomic force microscopy (AFM microcantilever beam. This latter is subjected to a harmonic excitation of its base displacement and to Van der Waals and DMT contact forces at its free end. For AFM design purposes, we derive a mathematical model for accurate description of the AFM microbeam dynamics. We solve the resulting equations of motions and associated boundary conditions using the Galerkin method. We find that using one-mode approximation in tapping mode operating in the neighborhood of the contact region one-mode approximation may lead to erroneous results.
An Enhanced Asymptotic Expansion for the Stability of Nonlinear Elastic Structures
DEFF Research Database (Denmark)
Christensen, Claus Dencker; Byskov, Esben
2010-01-01
A new, enhanced asymptotic expansion applicable to stability of structures made of nonlinear elastic materials is established. The method utilizes “hyperbolic” terms instead of the conventional polynomial terms, covers full kinematic nonlinearity and is applied to nonlinear elastic Euler columns ...
Adaptive Neural-Sliding Mode Control of Active Suspension System for Camera Stabilization
Directory of Open Access Journals (Sweden)
Feng Zhao
2015-01-01
Full Text Available The camera always suffers from image instability on the moving vehicle due to the unintentional vibrations caused by road roughness. This paper presents a novel adaptive neural network based on sliding mode control strategy to stabilize the image captured area of the camera. The purpose is to suppress vertical displacement of sprung mass with the application of active suspension system. Since the active suspension system has nonlinear and time varying characteristics, adaptive neural network (ANN is proposed to make the controller robustness against systematic uncertainties, which release the model-based requirement of the sliding model control, and the weighting matrix is adjusted online according to Lyapunov function. The control system consists of two loops. The outer loop is a position controller designed with sliding mode strategy, while the PID controller in the inner loop is to track the desired force. The closed loop stability and asymptotic convergence performance can be guaranteed on the basis of the Lyapunov stability theory. Finally, the simulation results show that the employed controller effectively suppresses the vibration of the camera and enhances the stabilization of the entire camera, where different excitations are considered to validate the system performance.
Mode interaction in horses, tea, and other nonlinear oscillators: the universal role of symmetry
Weele, van der Jacobus P.; Banning, Erik J.
2001-01-01
This paper is about mode interaction in systems of coupled nonlinear oscillators. The main ideas are demonstrated by means of a model consisting of two coupled, parametrically driven pendulums. On the basis of this we also discuss mode interaction in the Faraday experiment (as observed by Ciliberto
Nonlinear resonances of three modes in a high-T{sub c} superconducting magnetic levitation system
Energy Technology Data Exchange (ETDEWEB)
Sasaki, Masahiko, E-mail: galian@z2.keio.jp; Sakaguchi, Ryunosuke; Sugiura, Toshihiko, E-mail: sugiura@mach.keio.ac.jp
2013-11-15
Highlights: •We studied two nonlinear vibrations of a levitated beam supported by superconductors. •One of the vibrations is combination resonance of the 1st mode and the 3rd mode. •The other vibration is autoparametric resonance of the 2nd mode. •When the amplitude of the 2nd mode is small, the combination resonance is suppressed. •Otherwise, the two resonances can be resonated simultaneously. -- Abstract: In a high-T{sub c} superconducting magnetic levitation system, an object can levitate without control and contact. So it is expected to be applied to magnetically levitated transportation. To use it safely, lightening the levitated object is necessary. But this reduces the bending stiffness of the object. Besides, the system has nonlinearity. Therefore nonlinear elastic vibration can occur. This study focused on how plural nonlinear elastic vibrations of the 1st, 2nd and 3rd modes simultaneously occur. Our numerical calculation and experiment found out that the three modes simultaneously resonate when the amplitude of the 2nd mode is large enough whereas only the 2nd mode resonates when it is small.
Energy Technology Data Exchange (ETDEWEB)
Dhote, Sharvari, E-mail: sharvari.dhote@mail.utoronto.ca; Zu, Jean; Zhu, Yang [Department of Mechanical and Industrial Engineering, University of Toronto, 5 King' s College Road, Toronto, Ontario M5S-3G8 (Canada)
2015-04-20
In this paper, a nonlinear wideband multi-mode piezoelectric vibration-based energy harvester (PVEH) is proposed based on a compliant orthoplanar spring (COPS), which has an advantage of providing multiple vibration modes at relatively low frequencies. The PVEH is made of a tri-leg COPS flexible structure, where three fixed-guided beams are capable of generating strong nonlinear oscillations under certain base excitation. A prototype harvester was fabricated and investigated through both finite-element analysis and experiments. The frequency response shows multiple resonance which corresponds to a hardening type of nonlinear resonance. By adding masses at different locations on the COPS structure, the first three vibration modes are brought close to each other, where the three hardening nonlinear resonances provide a wide bandwidth for the PVEH. The proposed PVEH has enhanced performance of the energy harvester in terms of a wide frequency bandwidth and a high-voltage output under base excitations.
Dikandé, Alain M.; Voma Titafan, J.; Essimbi, B. Z.
2017-10-01
The transition dynamics from continuous-wave to pulse regimes of operation for a generic model of passively mode-locked lasers with saturable absorbers, characterized by an active medium with non-Kerr nonlinearity, are investigated analytically and numerically. The system is described by a complex Ginzburg–Landau equation with a general m:n saturable nonlinearity (i.e {I}m/{(1+{{Γ }}I)}n, where I is the field intensity and m and n are two positive numbers), coupled to a two-level gain equation. An analysis of stability of continuous waves, following the modulational instability approach, provides a global picture of the self-starting dynamics in the system. The analysis reveals two distinct routes depending on values of the couple (m, n), and on the dispersion regime: in the normal dispersion regime, when m = 2 and n is arbitrary, the self-starting requires positive values of the fast saturable absorber and nonlinearity coefficients, but negative values of these two parameters for the family with m = 0. However, when the spectral filter is negative, the laser can self-start for certain values of the input field and the nonlinearity saturation coefficient Γ. The present work provides a general map for the self-starting mechanisms of rare-earth doped figure-eight fiber lasers, as well as Kerr-lens mode-locked solid-state lasers.
Stability of dithered non-linear systems with backlash or hysteresis
Desoer, C. A.; Shahruz, S. M.
1986-01-01
A study is conducted of the effect of dither on the nonlinear element of a single-input single-outout feedback system. Nonlinearities are considered with memory (backlash, hysteresis), in the feedforward loop; a dither of a given amplitude is injected at the input of the nonlinearity. The nonlinearity is followed by a linear element with low-pass characteristic. The stability of the dithered system and an approximate equivalent system (in which the nonlinearity is a smooth function) are compared. Conditions on the input and on the dither frequency are obtained so that the approximate-system stability guarantees that of the given hysteretic system.
Nonlinear localized modes in dipolar Bose–Einstein condensates in two-dimensional optical lattices
Energy Technology Data Exchange (ETDEWEB)
Rojas-Rojas, Santiago, E-mail: srojas@cefop.cl [Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Naether, Uta [Instituto de Ciencia de Materiales de Aragón and Departamento de Física de la Materia Condensada, CSIC-Universidad de Zaragoza, 50009 Zaragoza (Spain); Delgado, Aldo [Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Vicencio, Rodrigo A. [Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago (Chile)
2016-09-16
Highlights: • We study discrete two-dimensional breathers in dipolar Bose–Einstein Condensates. • Important differences in the properties of three fundamental modes are found. • Norm threshold for existence of 2D breathers varies with dipolar interaction. • The Effective Potential Method is implemented for stability analysis. • Uncommon mobility of 2D discrete solitons is observed. - Abstract: We analyze the existence and properties of discrete localized excitations in a Bose–Einstein condensate loaded into a periodic two-dimensional optical lattice, when a dipolar interaction between atoms is present. The dependence of the Number of Atoms (Norm) on the energy of solutions is studied, along with their stability. Two important features of the system are shown, namely, the absence of the Norm threshold required for localized solutions to exist in finite 2D systems, and the existence of regions in the parameter space where two fundamental solutions are simultaneously unstable. This feature enables mobility of localized solutions, which is an uncommon feature in 2D discrete nonlinear systems. With attractive dipolar interaction, a non-trivial behavior of the Norm dependence is obtained, which is well described by an analytical model.
Energy Technology Data Exchange (ETDEWEB)
Bessa, Wallace M. [Universidade Federal do Rio Grande do Norte, Department of Mechanical Engineering, Campus Universitario Lagoa Nova, 59072-970 Natal, RN (Brazil)], E-mail: wmbessa@ufrnet.br; Paula, Aline S. de [Universidade Federal do Rio de Janeiro, COPPE - Department of Mechanical Engineering, P.O. Box 68.503, 21941-972 Rio de Janeiro, RJ (Brazil)], E-mail: alinesp27@gmail.com; Savi, Marcelo A. [Universidade Federal do Rio de Janeiro, COPPE - Department of Mechanical Engineering, P.O. Box 68.503, 21941-972 Rio de Janeiro, RJ (Brazil)], E-mail: savi@mecanica.ufrj.br
2009-10-30
Chaos control may be understood as the use of tiny perturbations for the stabilization of unstable periodic orbits embedded in a chaotic attractor. The idea that chaotic behavior may be controlled by small perturbations of physical parameters allows this kind of behavior to be desirable in different applications. In this work, chaos control is performed employing a variable structure controller. The approach is based on the sliding mode control strategy and enhanced by an adaptive fuzzy algorithm to cope with modeling inaccuracies. The convergence properties of the closed-loop system are analytically proven using Lyapunov's direct method and Barbalat's lemma. As an application of the control procedure, a nonlinear pendulum dynamics is investigated. Numerical results are presented in order to demonstrate the control system performance. A comparison between the stabilization of general orbits and unstable periodic orbits embedded in chaotic attractor is carried out showing that the chaos control can confer flexibility to the system by changing the response with low power consumption.
Directory of Open Access Journals (Sweden)
Xiaoguang Deng
2015-01-01
Full Text Available Based on the nonlinear stability analysis method, the 3D nonlinear finite element model of a composite girder cable-stayed bridge with three pylons is established to research the effect of factors including geometric nonlinearity, material nonlinearity, static wind load, and unbalanced construction load on the structural stability during construction. Besides, the structural nonlinear stability in different construction schemes and the determination of temporary pier position are also studied. The nonlinear stability safety factors are calculated to demonstrate the rationality and safety of construction schemes. The results show that the nonlinear stability safety factors of this bridge during construction meet the design requirement and the minimum value occurs in the maximum double cantilever stage. Besides, the nonlinear stability of the structure in the side of edge-pylon meets the design requirement in the two construction schemes. Furthermore, the temporary pier can improve the structure stability, effectively, and the actual position is reasonable. In addition, the local buckling of steel girder occurs earlier than overall instability under load in some cable tension stages. Finally, static wind load and the unbalanced construction load should be considered in the stability analysis for the adverse impact.
Integral input-to-state stability of nonlinear control systems with delays
Energy Technology Data Exchange (ETDEWEB)
Zhu Wenli [Department of Economics Mathematics, South Western University of Finance and Economics, Chengdu 610074 (China)]. E-mail: zhuwl@swufe.edu.cn; Yi Zhang [Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054 (China)]. E-mail: zhangyi@uestc.edu.cn
2007-10-15
Integral input-to-state stability is an interesting concept that has been recently introduced to nonlinear control systems. This paper generalizes this concept to nonlinear control systems with delays. These delays can be bounded, unbounded, and even infinite. Theorems for integral input-to-state stability are derived by developing the method of Razumikhin technique in the theory of functional differential equations.
Directory of Open Access Journals (Sweden)
Mourad Kchaou
2017-01-01
Full Text Available This paper addresses the problem of sliding mode control (SMC design for a class of uncertain switched descriptor systems with state delay and nonlinear input. An integral sliding function is designed and an adaptive sliding mode controller for the reaching motion is then synthesised such that the trajectories of the resulting closed-loop system can be driven onto a prescribed sliding surface and maintained there for all subsequent times. Moreover, based on a new Lyapunov-Krasovskii functional, a delay-dependent sufficient condition is established such that the admissibility as well as the H∞ performance requirement of the sliding mode dynamics can be guaranteed in the presence of time delay, external disturbances, and nonlinear input which comprises dead-zones and/or sector nonlinearities. The major contributions of this paper of this approach include (i the closed-loop system exhibiting strong robustness against nonlinear dynamics and (ii the control scheme enjoying the chattering-free characteristic. Finally, two representative examples are given to illustrate the theoretical developments.
Institute of Scientific and Technical Information of China (English)
LI De-Jun; MI Xian-Wu; DENG Ke; TANG Yi
2006-01-01
In the classical lattice theory, solitons and locaLized modes can exist in many one-dimensional nonlinear lattice chains, however, in the quantum lattice theory, whether quantum solitons and localized modes can exist or not in the one-dimensional lattice chains is an interesting problem. By using the number state method and the Hartree approximation combined with the method of multiple scales, we investigate quantum solitons and localized modes in a one-dimensional lattice chain with the nonlinear substrate potential. It is shown that quantum solitons do exist in this nonlinear lattice chain, and at the boundary of the phonon Brillouin zone, quantum solitons become quantum localized modes, phonons are pinned to the lattice of the vicinity at the central position j = j0.
Attractor-repeller pair of topological zero modes in a nonlinear quantum walk
Gerasimenko, Y.; Tarasinski, B.; Beenakker, C. W. J.
2016-02-01
The quantum-mechanical counterpart of a classical random walk offers a rich dynamics that has recently been shown to include topologically protected bound states (zero modes) at boundaries or domain walls. Here we show that a topological zero mode may acquire a dynamical role in the presence of nonlinearities. We consider a one-dimensional discrete-time quantum walk that combines zero modes with a particle-conserving nonlinear relaxation mechanism. The presence of both particle-hole and chiral symmetry converts two zero modes of opposite chirality into an attractor-repeller pair of the nonlinear dynamics. This makes it possible to steer the walker towards a domain wall and trap it there.
Pourmahmood Aghababa, Mohammad
2013-10-01
This paper investigates the problem of robust control of nonlinear fractional-order dynamical systems in the presence of uncertainties. First, a novel switching surface is proposed and its finite-time stability to the origin is proved. Subsequently, using the sliding mode theory, a robust fractional control law is proposed to ensure the existence of the sliding motion in finite time. We use a fractional Lyapunov stability theory to prove the stability of the system in a given finite time. In order to avoid the chattering, which is inherent in conventional sliding mode controllers, we transfer the sign function of the control input into the fractional derivative of the control signal. The proposed chattering-free sliding mode technique is then applied for stabilisation of a broad class of three-dimensional fractional-order chaotic systems via a single variable driving control input. Simulation results reveal that the proposed fractional sliding mode controller works well for chaos control of fractional-order hyperchaotic Chen, chaotic Lorenz and chaotic Arneodo systems with no-chatter control inputs.
Non-linear evolution of double tearing modes in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Fredrickson, E.; Bell, M.; Budny, R.V.; Synakowski, E.
1999-12-17
The delta prime formalism with neoclassical modifications has proven to be a useful tool in the study of tearing modes in high beta, collisionless plasmas. In this paper the formalism developed for the inclusion of neoclassical effects on tearing modes in monotonic q-profile plasmas is extended to plasmas with hollow current profiles and double rational surfaces. First, the classical formalism of tearing modes in the Rutherford regime in low beta plasmas is extended to q profiles with two rational surfaces. Then it is shown that this formalism is readily extended to include neoclassical effects.
Nonlinear Mixing of Collective Modes in Harmonically Trapped Bose-Einstein Condensates
Mizoguchi, Takahiro; Watabe, Shohei; Nikuni, Tetsuro
2016-01-01
We study nonlinear mixing effects among quadrupole modes and scissors modes in a harmonically trapped Bose-Einstein condensate. Using a perturbative technique in conjunction with a variational approach with a Gaussian trial wave function for the Gross-Pitaevskii equation, we find that mode mixing selectively occurs. Our perturbative approach is useful in gaining qualitative understanding of the recent experiment [Yamazaki et al., J. Phys. Soc. Japan 84, 44001 (2015)], exhibiting a beating phe...
Mittag-Leffler Stability Theorem for Fractional Nonlinear Systems with Delay
Directory of Open Access Journals (Sweden)
S. J. Sadati
2010-01-01
Full Text Available Fractional calculus started to play an important role for analysis of the evolution of the nonlinear dynamical systems which are important in various branches of science and engineering. In this line of taught in this paper we studied the stability of fractional order nonlinear time-delay systems for Caputo's derivative, and we proved two theorems for Mittag-Leffler stability of the fractional nonlinear time delay systems.
Delay-dependent robust stabilization for a class of neutral systems with nonlinear perturbations
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This note deals with the problem of stabilization/stability for neutral systems with nonlinear perturbations.A new stabilization/stability scheme is presented.Using improved Lyapunov functionals.less conservative stabilization/stability conditions are derived for such systems based on linear matrix inequalities(LMI).Numerical examples are provided to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature.
Spectral characteristics of Compton backscattering sources. Linear and nonlinear modes
Energy Technology Data Exchange (ETDEWEB)
Potylitsyn, A.P., E-mail: potylitsyn@tpu.ru [National Research Tomsk Polytechnic University, 634050 Tomsk (Russian Federation); National Research Nuclear University MEPhI, 115409 Moscow (Russian Federation); Kolchuzhkin, A.M. [Moscow State University of Technology “STANKIN”, 127994 Moscow (Russian Federation)
2015-07-15
Compton backscattering (CBS) of laser photons by relativistic electrons is widely used to design X-ray and gamma sources with a bandwidth better than 1% using a tight collimation. In order to obtain a reasonable intensity of the resulting beam one has to increase power of a laser pulse simultaneously with narrowing of the waist in the interaction point. It can lead to nonlinearity of CBS process which is affected on spectral characteristics of the collimated gamma beam (so-called “red-shift” of the spectral line, emission of “soft” photons with energy much less than the spectral line energy). In this paper we have analyzed such an influence using Monte-Carlo technique and have shown that even weak nonlinearity should be taken into account if the gamma beam is formed by a narrow aperture.
Nonlinear localized flatband modes with spin-orbit coupling
Gligorić, G; Hadžievski, Lj; Flach, S; Malomed, B
2016-01-01
We report the coexistence and properties of stable compact localized states (CLSs) and discrete solitons (DSs) for nonlinear spinor waves on a flatband network with spin-orbit coupling (SOC). The system can be implemented by means of a binary Bose-Einstein condensate loaded in the corresponding optical lattice. In the linear limit, the SOC opens a minigap between flat and dispersive bands in the system's bandgap structure, and preserves the existence of CLSs at the flatband frequency, simultaneously lowering their symmetry. Adding onsite cubic nonlinearity, the CLSs persist and remain available in an exact analytical form, with frequencies which are smoothly tuned into the minigap. Inside of the minigap, the CLS and DS families are stable in narrow areas adjacent to the FB. Deep inside the semi-infinite gap, both the CLSs and DSs are stable too.
Environmental stability of actively mode locked fibre lasers
Hill, Calum H.; Lee, Stephen T.; Reid, Derryck T.; Baili, Ghaya; Davies, John
2016-10-01
Lasers developed for defence related applications typically encounter issues with reliability and meeting desired specification when taken from the lab to the product line. In particular the harsh environmental conditions a laser has to endure can lead to difficulties. This paper examines a specific class of laser, namely actively mode-locked fibre lasers (AMLFLs), and discusses the impact of environmental perturbations. Theoretical and experimental results have assisted in developing techniques to improve the stability of a mode-locked pulse train for continuous operation. Many of the lessons learned in this research are applicable to a much broader category of lasers. The AMLFL consists of a fibre ring cavity containing a semiconductor optical amplifier (SOA), an isolator, an output coupler, a circulator, a bandpass filter and a modulator. The laser produces a train of 6-ps pulses at 800 nm with a repetition rate in the GHz regime and a low-noise profile. This performance is realisable in a laboratory environment. However, even small changes in temperature on the order of 0.1 °C can cause a collapse of mode-locked dynamics such that the required stability cannot be achieved without suitable feedback. Investigations into the root causes of this failure were performed by changing the temperature of components that constitute the laser resonator and observing their properties. Several different feedback mechanisms have been investigated to improve laser stability in an environment with dynamic temperature changes. Active cavity length control will be discussed along with DC bias control of the Mach-Zehnder modulator (MZM).
Stabilization of solitons under competing nonlinearities by external potentials
Zegadlo, Krzysztof B; Malomed, Boris A; Karpierz, Miroslaw A; Trippenbach, Marek
2014-01-01
We report results of the analysis for families of one-dimensional (1D) trapped solitons, created by competing self-focusing (SF) quintic and self-defocusing (SDF) cubic nonlinear terms. Two trapping potentials are considered, the harmonic-oscillator (HO) and delta-functional ones. The models apply to optical solitons in colloidal waveguides and other photonic media, and to matter-wave solitons in Bose-Einstein condensates (BEC) loaded into a quasi-1D trap. For the HO potential, the results are obtained in an approximate form, using the variational and Thomas-Fermi approximations (VA and TFA), and in a full numerical form, including the ground state and the first antisymmetric excited one. For the delta-functional attractive potential, the results are produced in a fully analytical form, and verified by means of numerical methods. Both exponentially localized solitons and weakly localized trapped modes are found for the delta-functional potential. The most essential conclusions concern the applicability of com...
Nonlinear simulations of particle source effects on edge localized mode
Energy Technology Data Exchange (ETDEWEB)
Huang, J.; Tang, C. J. [College of Physical Science and Technology, Sichuan University, Chengdu 610065 (China); Key Laboratory of High Energy Density Physics and Technology of Ministry of Education, Sichuan University, Chengdu 610064 (China); Chen, S. Y., E-mail: sychen531@163.com [College of Physical Science and Technology, Sichuan University, Chengdu 610065 (China); Key Laboratory of High Energy Density Physics and Technology of Ministry of Education, Sichuan University, Chengdu 610064 (China); Southwestern Institute of Physics, Chengdu 610041 (China); Wang, Z. H. [Southwestern Institute of Physics, Chengdu 610041 (China)
2015-12-15
The effects of particle source (PS) with different intensities and located positions on Edge Localized Mode (ELM) are systematically studied with BOUT++ code. The results show the ELM size strongly decreases with increasing the PS intensity once the PS is located in the middle or bottom of the pedestal. The effects of PS on ELM depend on the located position of PS. When it is located at the top of the pedestal, peeling-ballooning (P-B) modes can extract more free energy from the pressure gradient and grow up to be a large filament at the initial crash phase and the broadening of mode spectrum can be suppressed by PS, which leads to more energy loss. When it is located in the middle or bottom of the pedestal, the extraction of free energy by P-B modes can be suppressed, and a small filament is generated. During the turbulence transport phase, the broader mode spectrum suppresses the turbulence transport when PS is located in the middle, while the zonal flow plays an important role in damping the turbulence transport when PS is located at the bottom.
Institute of Scientific and Technical Information of China (English)
Ahcene Boubakir; Fares Boudjema; Salim Labiod
2009-01-01
The aim of this paper is to develop a neuro-fuzzy-sliding mode controller (NFSMC) with a nonlinear sliding surface for a coupled tank system.The main purpose is to eliminate the chattering phenomenon and to overcome the problem of the equivalent control computation.A first-order nonlinear sliding surface is presented,on which the developed sliding mode controller (SMC) is based.Mathematical proof for the stability and convergence of the system is presented.In order to reduce the chattering in SMC,a fixed boundary layer around the switch surface is used.Within the boundary layer,where the fuzzy logic control is applied,the chattering phenomenon,which is inherent in a sliding mode control,is avoided by smoothing the switch signal.Outside the boundary,the sliding mode control is applied to drive the system states into the boundary layer.Moreover,to compute the equivalent controller,a feed-forward neural network (NN) is used.The weights of the net are updated such that the corrective control term of the NFSMC goes to zero.Then,this NN also alleviates the chattering phenomenon because a big gain in the corrective control term produces a more serious chattering than a small gain.Experimental studies carried out on a coupled tank system indicate that the proposed approach is good for control applications.
Institute of Scientific and Technical Information of China (English)
Mohammad Pourmahmood Aghababa; Hassan Feizi
2012-01-01
This paper deals with the design of a novel nonsingular terminal sliding mode controller for finite-time synchronization of two different chaotic systems with fully unknown parameters and nonlinear inputs.We propose a novel nonsingular terminal sliding surface and prove its finite-time convergence to zero.We assume that both the master's and the slave's system parameters are unknown in advance.Proper adaptation laws are derived to tackle the unknown parameters.An adaptive sliding mode control law is designed to ensure the existence of the sliding mode in finite time.We prove that both reaching and sliding mode phases are stable in finite time.An estimation of convergence time is given.Two illustrative examples show the effectiveness and usefulness of the proposed technique.It is worthwhile noticing that the introduced nonsingular terminal sliding mode can be applied to a wide variety of nonlinear control problems.
Institute of Scientific and Technical Information of China (English)
LI Shoufu
2005-01-01
A series of stability, contractivity and asymptotic stability results of the solutions to nonlinear stiff Volterra functional differential equations (VFDEs) in Banach spaces is obtained, which provides the unified theoretical foundation for the stability analysis of solutions to nonlinear stiff problems in ordinary differential equations(ODEs), delay differential equations(DDEs), integro-differential equations(IDEs) and VFDEs of other type which appear in practice.
Nonlinear Stability of a SIRS Epidemic Model with Convex Incidence Rate
Buonomo, B.; Rionero, S.
2010-09-01
We study an epidemic model for infections with non permanent acquired immunity (SIRS). The incidence rate is assumed to be convex respect to the infective class. By using a peculiar Lyapunov function, we obtain necessary and sufficient conditions for the local nonlinear stability of equilibria. Conditions ensuring the global stability of the endemic equilibrium are also obtained. Our procedure allows to enlarge the class of incidence rates ensuring the Lyapunov nonlinear stability of the endemic equilibrium for SIRS models.
Errouissi, Rachid; Yang, Jun; Chen, Wen-Hua; Al-Durra, Ahmed
2016-08-01
In this paper, a robust nonlinear generalised predictive control (GPC) method is proposed by combining an integral sliding mode approach. The composite controller can guarantee zero steady-state error for a class of uncertain nonlinear systems in the presence of both matched and unmatched disturbances. Indeed, it is well known that the traditional GPC based on Taylor series expansion cannot completely reject unknown disturbance and achieve offset-free tracking performance. To deal with this problem, the existing approaches are enhanced by avoiding the use of the disturbance observer and modifying the gain function of the nonlinear integral sliding surface. This modified strategy appears to be more capable of achieving both the disturbance rejection and the nominal prescribed specifications for matched disturbance. Simulation results demonstrate the effectiveness of the proposed approach.
Tian, Qing; Wu, Lei; Zhang, Jie-Fang; Malomed, Boris A; Mihalache, D; Liu, W M
2011-01-01
We put forward a generic transformation which helps to find exact soliton solutions of the nonlinear Schrödinger equation with a spatiotemporal modulation of the nonlinearity and external potentials. As an example, we construct exact solitons for the defocusing nonlinearity and harmonic potential. When the soliton's eigenvalue is fixed, the number of exact solutions is determined by energy levels of the linear harmonic oscillator. In addition to the stable fundamental solitons, stable higher-order modes, describing array of dark solitons nested in a finite-width background, are constructed too. We also show how to control the instability domain of the nonstationary solitons.
Terminal sliding mode tracking control for a class of SISO uncertain nonlinear systems.
Chen, Mou; Wu, Qing-Xian; Cui, Rong-Xin
2013-03-01
In this paper, the terminal sliding mode tracking control is proposed for the uncertain single-input and single-output (SISO) nonlinear system with unknown external disturbance. For the unmeasured disturbance of nonlinear systems, terminal sliding mode disturbance observer is presented. The developed disturbance observer can guarantee the disturbance approximation error to converge to zero in the finite time. Based on the output of designed disturbance observer, the terminal sliding mode tracking control is presented for uncertain SISO nonlinear systems. Subsequently, terminal sliding mode tracking control is developed using disturbance observer technique for the uncertain SISO nonlinear system with control singularity and unknown non-symmetric input saturation. The effects of the control singularity and unknown input saturation are combined with the external disturbance which is approximated using the disturbance observer. Under the proposed terminal sliding mode tracking control techniques, the finite time convergence of all closed-loop signals are guaranteed via Lyapunov analysis. Numerical simulation results are given to illustrate the effectiveness of the proposed terminal sliding mode tracking control.
Passamonti, A
2011-01-01
We study the damping of the gravitational radiation-driven f-mode instability in ro- tating neutron stars by nonlinear bulk viscosity in the so-called supra-thermal regime. In this regime the dissipative action of bulk viscosity is known to be enhanced as a result of nonlinear contributions with respect to the oscillation amplitude. Our anal- ysis of the f-mode instability is based on a time-domain code that evolves linear perturbations of rapidly rotating polytropic neutron star models. The extracted mode frequency and eigenfunctions are subsequently used in standard energy integrals for the gravitational wave growth and viscous damping. We find that nonlinear bulk vis- cosity has a moderate impact on the size of the f-mode instability window, becoming an important factor and saturating the mode's growth at a relatively large oscillation amplitude. We show that a similar result holds for the damping of the inertial r-mode instability by nonlinear bulk viscosity. In addition, we show that the action of bulk v...
Sakly, Anis; Kermani, Marwen
2015-07-01
This paper is concerned with the problems of stability analysis and stabilization with a state feedback controller through pole placement for a class of both continuous and discrete-time switched nonlinear systems. These systems are modeled by differential or difference equations. Then, a transformation under the arrow form is employed. Note that, the main contribution in this work is twofold: firstly, based on the construction of an appropriated common Lyapunov function, as well the use of the vector norms notion, the recourse to the Kotelyanski lemma, the M-matrix proprieties, the aggregation techniques and the application of the Borne-Gentina criterion, new sufficient stability conditions under arbitrary switching for the autonomous system are deduced. Secondly, this result is extended for designing a state feedback controller by using pole assignment control, which guarantee that the corresponding closed-loop system is globally asymptotically stable under arbitrary switching. The main novelties features of these obtained results are the explicitness and the simplicity in their application. Moreover, they allow us to avoid the search of a common Lyapunov function which is a difficult matter. Finally, as validation to stabilize a shunt DC motor under variable mechanical loads is performed to demonstrate the effectiveness of the proposed results.
Nonlinear and Variable Structure Excitation Controller for Power System Stability
Institute of Scientific and Technical Information of China (English)
Wang Ben; Ronnie Belmans
2006-01-01
A new nonlinear variable structure excitation controller is proposed. Its design combines the differential geometry theory and the variable structure controlling theory. The mathematical model in the form of "an affine nonlinear system" is set up for the control of a large-scale power system. The static and dynamic performances of the nonlinear variable structure controller are simulated. The response of system with the controller proposed is compared to that of the nonlinear optimal controller when the system is subjected to a variety of disturbances. Simulation results show that the nonlinear variable structure excitation controller gives more satisfactorily static and dynamic performance and better robustness.
Nonlinear spatial mode imaging of hybrid photonic crystal fibers
DEFF Research Database (Denmark)
Petersen, Sidsel Rübner; Alkeskjold, Thomas Tanggaard; Laurila, Marko;
2013-01-01
Degenerate spontaneous four wave mixing is studied for the rst time in a large mode area hybrid photonic crystal ber, where light con nement is achieved by combined index- and bandgap guiding. Four wave mixing products are generated on the edges of the bandgaps, which is veri ed by numerical...
The simplex method for nonlinear sliding mode control
Directory of Open Access Journals (Sweden)
Bartolini G.
1998-01-01
Full Text Available General nonlinear control systems described by ordinary differential equations with a prescribed sliding manifold are considered. A method of designing a feedback control law such that the state variable fulfills the sliding condition in finite time is based on the construction of a suitable simplex of vectors in the tangent space of the manifold. The convergence of the method is proved under an obtuse angle condition and a way to build the required simplex is indicated. An example of engineering interest is presented.
Energy Technology Data Exchange (ETDEWEB)
Li, S.; Pons, R. (Autonoma de Barcelona (Spain). Dept. of Fisica); Zhang, Y. (Chongqing Inst. of Posts and Telecommunications, Sichuan (China). Telecommunications Engineering Dept.)
1994-08-01
In this paper, the authors study a laser using a nonlinear Fabry-Perot etalon as a cavity mirror. First, using the semiclassical laser theory and the differential equation for the lossy nonlinear Fabry-Perot etalon, they develop dynamic equations describing this system for single-mode operation. In this model, the frequency-pulling effect, a finite response time of the nonlinear medium, and a finite-cavity round-trip time of the Fabry-Perot etalon are included. Second, based on this model, they analyze the stability of this laser and give some numerical results. The results show that (1) this system can exist in the stable state and in the unstable state; (2) there are not only saddle-node bifurcations but also Hopf bifurcations; (3) the detuning parameter will effect the characteristics of the bistability and the number and distribution of Hopf bifurcation points.
Nonlinear regime of the mode-coupling instability in 2D plasma crystals
Röcker, T B; Zhdanov, S K; Nosenko, V; Ivlev, A V; Thomas, H M; Morfill, G E
2014-01-01
The transition between linear and nonlinear regimes of the mode-coupling instability (MCI) operating in a monolayer plasma crystal is studied. The mode coupling is triggered at the centre of the crystal and a melting front is formed, which travels through the crystal. At the nonlinear stage, the mode coupling results in synchronisation of the particle motion and the kinetic temperature of the particles grows exponentially. After melting of the crystalline structure, the mean kinetic energy of the particles continued to grow further, preventing recrystallisation of the melted phase. The effect could not be reproduced in simulations employing a simple point-like wake model. This shows that at the nonlinear stage of the MCI a heating mechanism is working which was not considered so far.
Simplex sliding mode control for nonlinear uncertain systems via chaos optimization
Energy Technology Data Exchange (ETDEWEB)
Lu, Zhao; Shieh, Leang-San; Chen, Guanrong; Coleman, Norman P
2005-02-01
As an emerging effective approach to nonlinear robust control, simplex sliding mode control demonstrates some attractive features not possessed by the conventional sliding mode control method, from both theoretical and practical points of view. However, no systematic approach is currently available for computing the simplex control vectors in nonlinear sliding mode control. In this paper, chaos-based optimization is exploited so as to develop a systematic approach to seeking the simplex control vectors; particularly, the flexibility of simplex control is enhanced by making the simplex control vectors dependent on the Euclidean norm of the sliding vector rather than being constant, which result in both reduction of the chattering and speedup of the convergence. Computer simulation on a nonlinear uncertain system is given to illustrate the effectiveness of the proposed control method.
Center Frequency Stabilization in Planar Dual-Mode Resonators during Mode-Splitting Control
Naji, Adham; Soliman, Mina H.
2017-03-01
Shape symmetry in dual-mode planar electromagnetic resonators results in their ability to host two degenerate resonant modes. As the designer enforces a controllable break in the symmetry, the degeneracy is removed and the two modes couple, exchanging energy and elevating the resonator into its desirable second-order resonance operation. The amount of coupling is controlled by the degree of asymmetry introduced. However, this mode coupling (or splitting) usually comes at a price. The centre frequency of the perturbed resonator is inadvertently drifted from its original value prior to coupling. Maintaining centre frequency stability during mode splitting is a nontrivial geometric design problem. In this paper, we analyse the problem and propose a novel method to compensate for this frequency drift, based on field analysis and perturbation theory, and we validate the solution through a practical design example and measurements. The analytical method used works accurately within the perturbational limit. It may also be used as a starting point for further numerical optimization algorithms, reducing the required computational time during design, when larger perturbations are made to the resonator. In addition to enabling the novel design example presented, it is hoped that the findings will inspire akin designs for other resonator shapes, in different disciplines and applications.
Center Frequency Stabilization in Planar Dual-Mode Resonators during Mode-Splitting Control
Naji, Adham; Soliman, Mina H.
2017-01-01
Shape symmetry in dual-mode planar electromagnetic resonators results in their ability to host two degenerate resonant modes. As the designer enforces a controllable break in the symmetry, the degeneracy is removed and the two modes couple, exchanging energy and elevating the resonator into its desirable second-order resonance operation. The amount of coupling is controlled by the degree of asymmetry introduced. However, this mode coupling (or splitting) usually comes at a price. The centre frequency of the perturbed resonator is inadvertently drifted from its original value prior to coupling. Maintaining centre frequency stability during mode splitting is a nontrivial geometric design problem. In this paper, we analyse the problem and propose a novel method to compensate for this frequency drift, based on field analysis and perturbation theory, and we validate the solution through a practical design example and measurements. The analytical method used works accurately within the perturbational limit. It may also be used as a starting point for further numerical optimization algorithms, reducing the required computational time during design, when larger perturbations are made to the resonator. In addition to enabling the novel design example presented, it is hoped that the findings will inspire akin designs for other resonator shapes, in different disciplines and applications. PMID:28272422
2011-01-01
International audience; We study theoretically, numerically and experimentally the nonlinear propagation of partially incoherent optical waves in single mode optical fibers. We revisit the traditional treatment of the wave turbulence theory to provide a statistical kinetic description of the integrable scalar NLS equation. In spite of the formal reversibility and of the integrability of the NLS equation, the weakly nonlinear dynamics reveals the existence of an irreversible evolution toward a...
Development of numerical algorithms for practical computation of nonlinear normal modes
2008-01-01
When resorting to numerical algorithms, we show that nonlinear normal mode (NNM) computation is possible with limited implementation effort, which paves the way to a practical method for determining the NNMs of nonlinear mechanical systems. The proposed method relies on two main techniques, namely a shooting procedure and a method for the continuation of NNM motions. In addition, sensitivity analysis is used to reduce the computational burden of the algorithm. A simplified discrete model of a...
Current-mode analog nonlinear function synthesizer structures
Popa, Cosmin Radu
2013-01-01
This book is dedicated to the analysis and design of analog CMOS nonlinear function synthesizer structures, based on original superior-order approximation functions. A variety of analog function synthesizer structures are discussed, based on accurate approximation functions. Readers will be enabled to implement numerous circuit functions with applications in analog signal processing, including exponential, Gaussian or hyperbolic functions. Generalizing the methods for obtaining these particular functions, the author analyzes superior-order approximation functions, which represent the core for developing CMOS analog nonlinear function synthesizers. · Describes novel methods for generating a multitude of circuit functions, based on superior-order improved accuracy approximation functions; · Presents techniques for analog function synthesizers that can be applied easily to a wide variety of analog signal processing circuits; · Enables the design of analog s...
Energy Technology Data Exchange (ETDEWEB)
Assadi, S.
1994-01-01
Linear and nonlinear magnetohydrodynamic (MHD) stability of current-driven modes are studied in the MST reversed field pinch. Measured low frequency (f < 35 kHz) magnetic fluctuations are consistent with the global resistive tearing instabilities predicted by 3-D MHD simulations. At frequencies above 35 kHz, the magnetic fluctuations were detected to be localized and externally resonant. Discrete dynamo events, ``sawtooth oscillations,`` have been observed in the experimental RFP plasmas. This phenomenon causes the plasma to become unstable to m = 1 tearing modes. The modes that may be important in different phases of these oscillations are identified. These results then assist in nonlinear studies and also help to interpret the spectral broadening of the measured data during a discrete dynamo event. Three-wave nonlinear coupling of spectral Fourier modes is measured in the MST by applying bispectral analysis to magnetic fluctuations measured at the plasma edge at 64 toroidal locations and 16 poloidal locations, permitting observation of coupling over 8 poloidal and 32 toroidal modes. Comparison to bispectra predicted by resistive MHD computation indicates reasonably good agreement. However, during the crash phase of the sawtooth oscillation the nonlinear coupling is strongly enhanced, concomitant with a broadened k-spectrum. During the sawtooth formation the plasma is undergoing a pure diffusive process. The dynamo only occurs during the sawtooth crash. High frequency activity prior to a sawtooth crash is caused by nonlinear frequency (small-scale) mode coupling. Growth rate and coupling coefficients of toroidal mode spectra are calculated by statistical modeling. Temporal evolution of edge toroidal mode spectra has been predicted by transfer function analysis. The driving sources of electrostatic fields are different than for the magnetic fields. The characteristics of tearing modes can be altered by external field errors and addition of impurities to the plasma.
Energy Technology Data Exchange (ETDEWEB)
Romera, M.; Monteblanco, E.; Garcia-Sanchez, F.; Buda-Prejbeanu, L. D.; Ebels, U. [Univ. Grenoble Alpes, F-38000 Grenoble (France); CEA, INAC-SPINTEC, F-38000 Grenoble (France); CNRS, SPINTEC, F-38000 Grenoble (France); Delaët, B. [CEA-LETI, MINATEC, DRT/LETI/DIHS, 38054 Grenoble (France)
2015-05-11
The influence of dynamic coupling in between magnetic layers of a standard spin torque nano-oscillator composed of a synthetic antiferromagnet (SyF) as a polarizer and an in-plane magnetized free layer has been investigated. Experiments on spin valve nanopillars reveal non-continuous features such as kinks in the frequency field dependence that cannot be explained without such interactions. Comparison of experiments to numerical macrospin simulations shows that this is due to non-linear interaction between the spin torque (STT) driven mode and a damped mode that is mediated via the third harmonics of the STT mode. It only occurs at large applied currents and thus at large excitation amplitudes of the STT mode. Under these conditions, a hybridized mode characterized by a strong reduction of the linewidth appears. The reduced linewidth can be explained by a reduction of the non-linear contribution to the linewidth via an enhanced effective damping. Interestingly, the effect depends also on the exchange interaction within the SyF. An enhancement of the current range of reduced linewidth by a factor of two and a reduction of the minimum linewidth by a factor of two are predicted from simulation when the exchange interaction strength is reduced by 30%. These results open directions to optimize the design and microwave performances of spin torque nano-oscillators taking advantage of the coupling mechanisms.
Robust stability of discrete-time nonlinear system with time-delay
Institute of Scientific and Technical Information of China (English)
LIU Xin-ge; WU Min
2005-01-01
The robustly asymptotical stability problem for discrete-time nonlinear systems with time-delay was investigated. Positive definite matrix are constructed through Lyapunov functional. With the identity transform, property of matrix inverse and S-procedure, a new sufficient condition independent of the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is established. With Schur complement, another equivalent sufficient condition for robust stability of discrete-time nonlinear systems with time-delay is given. Finally, a sufficient condition dependent on the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is obtained. A unified approach is used to cast the robust stability problem into a convex optimization involving linear matrix inequalities.
Stabilization and regulation of nonlinear systems a robust and adaptive approach
Chen, Zhiyong
2015-01-01
The core of this textbook is a systematic and self-contained treatment of the nonlinear stabilization and output regulation problems. Its coverage embraces both fundamental concepts and advanced research outcomes and includes many numerical and practical examples. Several classes of important uncertain nonlinear systems are discussed. The state-of-the art solution presented uses robust and adaptive control design ideas in an integrated approach which demonstrates connections between global stabilization and global output regulation allowing both to be treated as stabilization problems. Stabilization and Regulation of Nonlinear Systems takes advantage of rich new results to give students up-to-date instruction in the central design problems of nonlinear control, problems which are a driving force behind the furtherance of modern control theory and its application. The diversity of systems in which stabilization and output regulation become significant concerns in the mathematical formulation of practical contr...
Nonlinear Generation of Fluting Perturbations by Kink Mode
Ruderman, M. S.
2017-08-01
We study the excitation of fluting perturbations in a magnetic tube by an initially imposed kink mode. We use the ideal magnetohydrodynamic (MHD) equations in the cold-plasma approximation. We also use the thin-tube approximation and scale the dependent and independent variables accordingly. Then we assume that the dimensionless amplitude of the kink mode is small and use it as an expansion parameter in the regular perturbation method. We obtain the expression for the tube boundary perturbation in the second-order approximation. This perturbation is a superposition of sausage and fluting perturbations. The amplitude of the fluting perturbation takes its maximum at the middle of the tube, and it monotonically decreases with the distance from the middle of the tube.
General complex envelope solutions of coupled-mode optics with quadratic or cubic nonlinearity
Hesketh, Graham D
2015-01-01
The analytic general solutions for the complex field envelopes are derived using Weierstrass elliptic functions for two and three mode systems of differential equations coupled via quadratic $\\chi_2$ type nonlinearity as well as two mode systems coupled via cubic $\\chi_3$ type nonlinearity. For the first time, a compact form of the solutions is given involving simple ratios of Weierstrass sigma functions (or equivalently Jacobi theta functions). A Fourier series is also given. All possible launch states are considered. The models describe sum and difference frequency generation, polarization dynamics, parity-time dynamics and optical processing applications.
New adaptive quasi-sliding mode control for nonlinear discrete-time systems
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
A new adaptive quasi-sliding mode control algorithm is developed for a class of nonlinear diecrete-time systems,which is especially useful for nonlinear systems with vaguely known dynamics.This design is model-free,and is based directly on pseudo-partial-derivatives derived on-line from the input and output information of the system using an improved recursive projection type of identification algorithm.The theoretical analysis and simulation results show that the adaptive quasi-sliding mode control system is stable and convergent.
Nonlinear interaction of two trapped-mode resonances in a bilayer "fish-scale" metamaterial
Tuz, Vladimir R; Mladyonov, Pavel L; Prosvirnin, Sergey L; Novitsky, Andrey V
2014-01-01
We report on a bistable light transmission through a bilayer "fish-scale" (meander-line) metamaterial. It is demonstrated that an all-optical switching may be achieved nearly the frequency of the high-quality-factor Fano-shaped trapped-mode resonance excitation. The nonlinear interaction of two closely spaced trapped-mode resonances in the bilayer structure composed with a Kerr-type nonlinear dielectric slab is analyzed in both frequency and time domains. It is demonstrated that these two resonances react differently on the applied intense light which leads to destination of a multistable transmission.
Free chattering hybrid sliding mode control for a class of non-linear systems
DEFF Research Database (Denmark)
Khooban, Mohammad-Hassan; Niknam, Taher; Blaabjerg, Frede
2016-01-01
In current study, in order to find the control of general uncertain nonlinear systems, a new optimal hybrid control approach called Optimal General Type II Fuzzy Sliding Mode (OGT2FSM) is presented. In order to estimate unknown nonlinear activities in monitoring dynamic uncertainties, the benefits...... on the same topic, which are an Adaptive Interval Type-2 Fuzzy Logic Controller (AGT2FLC) and Conventional Sliding Mode Controller (CSMC), to assess the efficiency of the suggested controller. The suggested control scheme is finally used to the Electric Vehicles type as a case study. Results of simulation...
Differential rotation of the unstable nonlinear r -modes
Friedman, John L.; Lindblom, Lee; Lockitch, Keith H.
2016-01-01
At second order in perturbation theory, the r -modes of uniformly rotating stars include an axisymmetric part that can be identified with differential rotation of the background star. If one does not include radiation reaction, the differential rotation is constant in time and has been computed by Sá. It has a gauge dependence associated with the family of time-independent perturbations that add differential rotation to the unperturbed equilibrium star: For stars with a barotropic equation of state, one can add to the time-independent second-order solution arbitrary differential rotation that is stratified on cylinders (that is a function of distance ϖ to the axis of rotation). We show here that the gravitational radiation-reaction force that drives the r -mode instability removes this gauge freedom; the exponentially growing differential rotation of the unstable second-order r -mode is unique. We derive a general expression for this rotation law for Newtonian models and evaluate it explicitly for slowly rotating models with polytropic equations of state.
Differential rotation of the unstable nonlinear r-modes
Friedman, John L; Lockitch, Keith H
2016-01-01
At second order in perturbation theory, the $r$-modes of uniformly rotating stars include an axisymmetric part that can be identified with differential rotation of the background star. If one does not include radiation-reaction, the differential rotation is constant in time and has been computed by S\\'a. It has a gauge dependence associated with the family of time-independent perturbations that add differential rotation to the unperturbed equilibrium star: For stars with a barotropic equation of state, one can add to the time-independent second-order solution arbitrary differential rotation that is stratified on cylinders (that is a function of distance $\\varpi$ to the axis of rotation). We show here that the gravitational radiation-reaction force that drives the $r$-mode instability removes this gauge freedom: The expontially growing differential rotation of the unstable second-order $r$-mode is unique. We derive a general expression for this rotation law for Newtonian models and evaluate it explicitly for s...
Directory of Open Access Journals (Sweden)
Wameedh Riyadh Abdul-Adheem
2016-12-01
Full Text Available This paper presents a new strategy for the active disturbance rejection control (ADRC of a general uncertain system with unknown bounded disturbance based on a nonlinear sliding mode extended state observer (SMESO. Firstly, a nonlinear extended state observer is synthesized using sliding mode technique for a general uncertain system assuming asymptotic stability. Then the convergence characteristics of the estimation error are analyzed by Lyapunov strategy. It revealed that the proposed SMESO is asymptotically stable and accurately estimates the states of the system in addition to estimating the total disturbance. Then, an ADRC is implemented by using a nonlinear state error feedback (NLSEF controller; that is suggested by J. Han and the proposed SMESO to control and actively reject the total disturbance of a permanent magnet DC (PMDC motor. These disturbances caused by the unknown exogenous disturbances and the matched uncertainties of the controlled model. The proposed SMESO is compared with the linear extended state observer (LESO. Through digital simulations using MATLAB / SIMULINK, the chattering phenomenon has been reduced dramatically on the control input channel compared to LESO. Finally, the closed-loop system exhibits a high immunity to torque disturbance and quite robustness to matched uncertainties in the system.
The role of pressure flattening in calculating tearing mode stability
Ham, C. J.; Connor, J. W.; Cowley, S. C.; Hastie, R. J.; Hender, T. C.; Liu, Y. Q.
2013-12-01
Calculations of tearing mode stability in tokamaks split conveniently into one in an external region, where marginally stable ideal magnetohydrodynamics (MHD) is applicable, and one in a resonant layer around the rational surface where sophisticated kinetic physics is needed. These two regions are coupled by the stability parameter Δ‧. Axisymmetric pressure and current perturbations localized around the rational surface significantly alter Δ‧. Equations governing the changes in the external solution and Δ‧ are derived for arbitrary perturbations in axisymmetric toroidal geometry. These equations can be used in two ways: (i) the Δ‧ can be calculated for a physically occurring perturbation to the pressure or current; (ii) alternatively we can use these equations to calculate Δ‧ for profiles with a pressure gradient at the rational surface in terms of the value when the perturbation removes this gradient. It is the second application we focus on here since resistive magnetohydrodynamics (MHD) codes do not contain the appropriate layer physics and therefore cannot predict stability for realistic hot plasma directly. They can, however, be used to calculate Δ‧. Existing methods (Ham et al 2012 Plasma Phys. Control. Fusion 54 025009) for extracting Δ‧ from resistive codes are unsatisfactory when there is a finite pressure gradient at the rational surface and favourable average curvature because of the Glasser stabilizing effect (Glasser et al 1975 Phys. Fluids 18 875). To overcome this difficulty we introduce a specific artificial pressure flattening function that allows the earlier approach to be used. The technique is first tested numerically in cylindrical geometry with an artificial favourable curvature. Its application to toroidal geometry is then demonstrated using the toroidal tokamak tearing mode stability code T7 (Fitzpatrick et al 1993 Nucl. Fusion 33 1533) which employs an approximate analytic equilibrium. The prospects for applying this
Flow stabilization of the ideal MHD resistive wall mode^1
Smith, S. P.; Jardin, S. C.; Freidberg, J. P.; Guazzotto, L.
2009-05-01
We demonstrate for the first time in a numerical calculation that for a typical circular cylindrical equilibrium, the ideal MHD resistive wall mode (RWM) can be completely stabilized by bulk equilibrium plasma flow, V, for a window of wall locations without introducing additional dissipation into the system. The stabilization is due to a resonance between the RWM and the Doppler shifted ideal MHD sound continuum. Our numerical approach introduces^2 u=φξ+ iV .∇ξ and the perturbed wall current^3 as variables, such that the eigenvalue, φ, only appears linearly in the linearized stability equations, which allows for the use of standard eigenvalue solvers. The wall current is related to the plasma displacement at the boundary by a Green's function. With the introduction of the resistive wall, we find that it is essential that the finite element grid be highly localized around the resonance radius where the parallel displacement, ξ, becomes singular. We present numerical convergence studies demonstrating that this singular behavior can be approached in a limiting sense. We also report on progress toward extending this calculation to an axisymmetric toroidal geometry. ^1Work supported by a DOE FES fellowship through ORISE and ORAU. ^2L.Guazzotto, J.P Freidberg, and R. Betti, Phys.Plasmas 15, 072503 (2008). ^3S.P. Smith and S. C. Jardin, Phys. Plasmas 15, 080701 (2008).
ON THE PARTIAL EQUIASYMPTOTIC STABILITY OF NONLINEAR TIME-VARYING DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
JianJigui; JiangMinghui; ShenYanjun
2005-01-01
In this paper, the problem of partial equiasymptotic stability for nonlinear time-varying differential equations are analyzed. A sufficient condition of partial stability and a set of sufficient conditions of partial equiasymptotic stability are given. Some of these conditions allow the derivative of Lyapunov function to be positive. Finally, several numerical examples are also given to illustrate the main results.
Directory of Open Access Journals (Sweden)
Meng-Meng Jiang
2016-01-01
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.
Walasik, Wiktor; Renversez, Gilles
2014-01-01
We study the nonlinear waves propagating in metal slot waveguides with a Kerr-type dielectric core. We develop two independent semi-analytical models to describe the properties of such waveguides. Using those models we compute the dispersion curves for the first ten modes of a nonlinear slot waveguide. For symmetric waveguides we find symmetric, antisymmetric, and asymmetric modes which are grouped in two families. In addition, we study the influence of the slot width on the first symmetric and asymmetric modes, and we show that the dispersion curve of the first asymmetric mode is invariant with respect to the slot width for high propagation constant values and we provide analytical approximations of this curve.
Control of nonlinear systems using terminal sliding modes
Venkataraman, S. T.; Gulati, S.
1992-01-01
The development of an approach to control synthesis for robust robot operations in unstructured environments is discussed. To enhance control performance with full model information, the authors introduce the notion of terminal convergence and develop control laws based on a class of sliding modes, denoted as terminal sliders. They demonstrate that terminal sliders provide robustness to parametric uncertainty without having to resort to high-frequency control switching, as in the case of conventional sliders. It is shown that the proposed method leads to greater guaranteed precision in all control cases discussed.
Institute of Scientific and Technical Information of China (English)
Shu-jun Liu; Ji-feng Zhang; Zhong-ping Jiang
2008-01-01
In this paper, the property of practical input-to-state stability and its application to stability of cascaded nonlinear systems are investigated in the stochastic framework. Firstly, the notion of (practical)stochastic input-to-state stability with respect to a stochastic input is introduced, and then by the method of changing supply functions, (a) an (practical) SISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for cascaded (practical) SISS subsystems.
Non-linear Spectroscopy of Sr Atoms in an Optical Cavity for Laser Stabilization
Christensen, Bjarke T R; Schäffer, Stefan A; Westergaard, Philip G; Ye, Jun; Holland, Murray; Thomsen, Jan W
2015-01-01
We study the non-linear interaction of a cold sample of strontium-88 atoms coupled to a single mode of a low finesse optical cavity in the so-called bad cavity limit and investigate the implications for applications to laser stabilization. The atoms are probed on the weak inter-combination line $\\lvert 5s^{2} \\, ^1 \\textrm{S}_0 \\rangle \\,-\\, \\lvert 5s5p \\, ^3 \\textrm{P}_1 \\rangle$ at 689 nm in a strongly saturated regime. Our measured observables include the atomic induced phase shift and absorption of the light field transmitted through the cavity represented by the complex cavity transmission coefficient. We demonstrate high signal-to-noise-ratio measurements of both quadratures - the cavity transmitted phase and absorption - by employing FM spectroscopy (NICE-OHMS). We also show that when FM spectroscopy is employed in connection with a cavity locked to the probe light, observables are substantially modified compared to the free space situation where no cavity is present. Furthermore, the non-linear dynami...
NONLINEAR BOUNDARY STABILIZATION OF WAVE EQUATIONS WITH VARIABLE C OEFFICIENTS
Institute of Scientific and Technical Information of China (English)
冯绍继; 冯德兴
2003-01-01
The wave equation with variable coefficients with a nonlinear dissipative boundary feedbackis studied. By the Riemannian geometry method and the multiplier technique, it is shown thatthe closed loop system decays exponentially or asymptotically, and hence the relation betweenthe decay rate of the system energy and the nonlinearity behavior of the feedback function isestablished.
Directory of Open Access Journals (Sweden)
Qiang Yang
2016-01-01
Full Text Available Based on adaptive nonlinear damping, a novel decentralized robust adaptive output feedback stabilization comprising a decentralized robust adaptive output feedback controller and a decentralized robust adaptive observer is proposed for a large-scale interconnected nonlinear system with general uncertainties, such as unknown nonlinear parameters, bounded disturbances, unknown nonlinearities, unmodeled dynamics, and unknown interconnections, which are nonlinear function of not only states and outputs but also unmodeled dynamics coming from other subsystems. In each subsystem, the proposed stabilization only has two adaptive parameters, and it is not needed to generate an additional dynamic signal or estimate the unknown parameters. Under certain assumptions, the proposed scheme guarantees that all the dynamic signals in the interconnected nonlinear system are bounded. Furthermore, the system states and estimate errors can approach arbitrarily small values by choosing the design parameters appropriately large. Finally, simulation results illustrated the effectiveness of the proposed scheme.
Nonlinear breathing modes at a defect site in DNA.
Duduială, Ciprian-Ionuţ; Wattis, Jonathan A D; Dryden, Ian L; Laughton, Charles A
2009-12-01
Molecular-dynamics simulations of a normal DNA duplex show that breathing events typically occur on the microsecond time scale. This paper analyzes a 12 base pairs DNA duplex containing the "rogue" base difluorotoluene (F) in place of a thymine base (T), for which the breathing events occur on the nanosecond time scale. Starting from a nonlinear Klein-Gordon lattice model and adding noise and damping, we obtain a mesoscopic model of the DNA duplex close to that observed in experiments and all-atom molecular dynamics simulations. The mesoscopic model is calibrated to data from the all-atom molecular dynamics package AMBER for a variety of twist angles of the DNA duplex. Defects are considered in the interchain interactions as well as in the along-chain interactions. This paper also discusses the role of the fluctuation-dissipation relations in the derivation of reduced (mesoscopic) models, the differences between the potential of mean force and the potential energies used in Klein-Gordon lattices, and how breathing can be viewed as competition between the along-chain elastic energy and the interchain binding energy.
Sun, Limin; Chen, Lin
2017-10-01
Residual mode correction is found crucial in calibrating linear resonant absorbers for flexible structures. The classic modal representation augmented with stiffness and inertia correction terms accounting for non-resonant modes improves the calibration accuracy and meanwhile avoids complex modal analysis of the full system. This paper explores the augmented modal representation in calibrating control devices with nonlinearity, by studying a taut cable attached with a general viscous damper and its Equivalent Dynamic Systems (EDSs), i.e. the augmented modal representations connected to the same damper. As nonlinearity is concerned, Frequency Response Functions (FRFs) of the EDSs are investigated in detail for parameter calibration, using the harmonic balance method in combination with numerical continuation. The FRFs of the EDSs and corresponding calibration results are then compared with those of the full system documented in the literature for varied structural modes, damper locations and nonlinearity. General agreement is found and in particular the EDS with both stiffness and inertia corrections (quasi-dynamic correction) performs best among available approximate methods. This indicates that the augmented modal representation although derived from linear cases is applicable to a relatively wide range of damper nonlinearity. Calibration of nonlinear devices by this means still requires numerical analysis while the efficiency is largely improved owing to the system order reduction.
Theory and analysis of nonlinear dynamics and stability in storage rings: A working group summary
Energy Technology Data Exchange (ETDEWEB)
Chattopadhyay, S.; Audy, P.; Courant, E.D.; Forest, E.; Guignard, G.; Hagel, J.; Heifets, S.; Keil, E.; Kheifets, S.; Mais, H.; Moshammer, H.; Pellegrini, C.; Pilat, F.; Suzuki, T.; Turchetti, G.; Warnock, R.L.
1988-07-01
A summary and commentary of the available theoretical and analytical tools and recent advances in the nonlinear dynamics, stability and aperture issues in storage rings are presented. 11 refs., 4 figs.
ON THE BOUNDEDNESS AND THE STABILITY OF SOLUTION TO THIRD ORDER NON-LINEAR DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
In this paper we investigate the global asymptotic stability,boundedness as well as the ultimate boundedness of solutions to a general third order nonlinear differential equation,using complete Lyapunov function.
Large Optical Nonlinearity of Surface Plasmon Modes on Thin Gold Films
DEFF Research Database (Denmark)
Huck, Alexander; Witthaut, Dirk; Kumar, Shailesh
2013-01-01
We investigate the optical nonlinear effects of a long-range surface plasmon polariton mode propagating on a thin gold film. These effects may play a key role in the design of future nanophotonic circuits as they allow for the realization of active plasmonic elements. We demonstrate a significant...
On Landau damping of dipole modes by non-linear space charge and octupoles
Möhl, D
1995-01-01
The joint effect of space-charge non-linearities and octupole lenses is important for Landau damping of coherent instabilities. The octupole strength required for stabilisation can depend strongly on the sign of the excitation current of the lenses. This note tries to extend results, previously obtained for coasting beams and rigid bunches, to more general head--tail modes.
Global stability of the ballooning mode in a cylindrical model
Mazur, N. G.; Fedorov, E. N.; Pilipenko, V. A.
2013-07-01
Ballooning disturbances in a finite-pressure plasma in a curvilinear magnetic field are described by the system of coupled equations for the Alfvén and slow magnetosonic modes. In contrast to most previous works that locally analyzed the stability of small-scale disturbances using the dispersion relationship, a global analysis outside a WKB approximation but within a simple cylindrical geometry, when magnetic field lines are circles with constant curvature, is performed in the present work. This model is relatively simple; nevertheless, it has the singularities necessary for the formation of the ballooning mode: field curvature and non-uniform thermal plasma pressure. If the disturbance finite radial extent is taken into account, the instability threshold increases as compared to a WKB approximation. The simplified model used in this work made it possible to consider the pattern of unstable disturbances at arbitrary values of the azimuthal wavenumber ( k y ). Azimuthally large-scale disturbances can also be unstable, although the increment increases with decreasing azimuthal scale and reaches saturation when the scales are of the order of the pressure nonuniformity dimension.
Stabilization of nonlinear sandwich systems via state feedback-Discrete-time systems
Wang, Xu; Stoorvogel, Anton A.; Saberi, Ali; Grip, H°avard Fjær; Sannuti, Peddapullaiah
2011-01-01
A recent paper (IEEE Trans. Aut. Contr. 2010; 55(9):2156–2160) considered stabilization of a class of continuous-time nonlinear sandwich systems via state feedback. This paper is a discrete-time counterpart of it. The class of nonlinear sandwich systems consists of saturation elements sandwiched bet
Stabilization of solutions to higher-order nonlinear Schrodinger equation with localized damping
Directory of Open Access Journals (Sweden)
Eleni Bisognin
2007-01-01
Full Text Available We study the stabilization of solutions to higher-order nonlinear Schrodinger equations in a bounded interval under the effect of a localized damping mechanism. We use multiplier techniques to obtain exponential decay in time of the solutions of the linear and nonlinear equations.
Stability of two-dimensional spatial solitons in nonlocal nonlinear media
DEFF Research Database (Denmark)
Skupin, S.; Bang, Ole; Edmundson, D.;
2006-01-01
We discuss the existence and stability of two-dimensional solitons in media with spatially nonlocal nonlinear response. We show that such systems, which include thermal nonlinearity and dipolar Bose-Einstein condensates, may support a variety of stationary localized structures, including rotating...
Institute of Scientific and Technical Information of China (English)
Wan-sheng WANG; Shou-fu LI; Run-sheng YANG
2012-01-01
A series of contractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations (NFDEs) in Banach spaces are obtained,which provide unified theoretical foundation for the contractivity analysis of solutions to nonlinear problems in functional differential equations (FDEs),neutral delay differential equations (NDDEs) and NFDEs of other types which appear in practice.
A novel sliding mode nonlinear proportional-integral control scheme for controlling chaos
Institute of Scientific and Technical Information of China (English)
Yu Dong-Chuan; Wu Ai-Guo; Yang Chao-Ping
2005-01-01
A novel sliding mode nonlinear proportional-integral control (SMNPIC) scheme is proposed for driving a class of time-variant chaotic systems with uncertainty to arbitrarily desired trajectory with high accuracy. The SMNPIC differs from the previous sliding mode techniques in the sense that a nonlinear proportional-integral action of sliding function is involved in control law, so that both the steady-state error and the high-frequency chattering are reduced,and meanwhile, robustness and fastness are guaranteed. In addition, the proposed SMNPIC actually acts as a class of nonlinear proportional-integral-differential (PID) controller, in which the tracking error and its derivatives up to (n-1)thorder as well as the integral of tracking error are considered, so that more useful information than traditional PID can be implemented and better dynamic and static characteristics can obtained. Its good performance for chaotic control is illustrated through a During-Holmes system with uncertainty.
Nonlinear Dual-Mode Control of Variable-Speed Wind Turbines with Doubly Fed Induction Generators
Tang, Choon Yik; Jiang, John N
2010-01-01
This paper presents a feedback/feedforward nonlinear controller for variable-speed wind turbines with doubly fed induction generators. By appropriately adjusting the rotor voltages and the blade pitch angle, the controller simultaneously enables: (a) control of the active power in both the maximum power tracking and power regulation modes, (b) seamless switching between the two modes, and (c) control of the reactive power so that a desirable power factor is maintained. Unlike many existing designs, the controller is developed based on original, nonlinear, electromechanically-coupled models of wind turbines, without attempting approximate linearization. Its development consists of three steps: (i) employ feedback linearization to exactly cancel some of the nonlinearities and perform arbitrary pole placement, (ii) design a speed controller that makes the rotor angular velocity track a desired reference whenever possible, and (iii) introduce a Lyapunov-like function and present a gradient-based approach for mini...
Nazemosadat, Elham
2014-01-01
We explore the practical challenges which should be addressed when designing a multi-core fiber coupler for nonlinear switching or mode-locking applications. The inevitable geometric imperfections formed in these fiber couplers during the fabrication process affect the performance characteristics of the nonlinear switching device. Fabrication uncertainties are tolerable as long as the changes they impose on the propagation constant of the modes are smaller than the linear coupling between the cores. It is possible to reduce the effect of the propagation constant variations by bringing the cores closer to each other, hence, increasing the coupling. However, higher coupling translates into a higher switching power which may not be desirable in some practical situations. Therefore, fabrication errors limit the minimum achievable switching power in nonlinear couplers.
Global stabilization of nonlinear systems based on vector control lyapunov functions
Karafyllis, Iasson
2012-01-01
This paper studies the use of vector Lyapunov functions for the design of globally stabilizing feedback laws for nonlinear systems. Recent results on vector Lyapunov functions are utilized. The main result of the paper shows that the existence of a vector control Lyapunov function is a necessary and sufficient condition for the existence of a smooth globally stabilizing feedback. Applications to nonlinear systems are provided: simple and easily checkable sufficient conditions are proposed to guarantee the existence of a smooth globally stabilizing feedback law. The obtained results are applied to the problem of the stabilization of an equilibrium point of a reaction network taking place in a continuous stirred tank reactor.
Rotation in a reversed field pinch with active feedback stabilization of resistive wall modes
Cecconello, M.; Menmuir, S.; Brunsell, P. R.; Kuldkepp, M.
2006-09-01
Active feedback stabilization of multiple resistive wall modes (RWMs) has been successfully proven in the EXTRAP T2R reversed field pinch. One of the features of plasma discharges operated with active feedback stabilization, in addition to the prolongation of the plasma discharge, is the sustainment of the plasma rotation. Sustained rotation is observed both for the internally resonant tearing modes (TMs) and the intrinsic impurity oxygen ions. Good quantitative agreement between the toroidal rotation velocities of both is found: the toroidal rotation is characterized by an acceleration phase followed, after one wall time, by a deceleration phase that is slower than in standard discharges. The TMs and the impurity ions rotate in the same poloidal direction with also similar velocities. Poloidal and toroidal velocities have comparable amplitudes and a simple model of their radial profile reproduces the main features of the helical angular phase velocity. RWMs feedback does not qualitatively change the TMs behaviour and typical phenomena such as the dynamo and the 'slinky' are still observed. The improved sustainment of the plasma and TMs rotation occurs also when feedback only acts on internally non-resonant RWMs. This may be due to an indirect positive effect, through non-linear coupling between TMs and RWMs, of feedback on the TMs or to a reduced plasma-wall interaction affecting the plasma flow rotation. Electromagnetic torque calculations show that with active feedback stabilization the TMs amplitude remains well below the locking threshold condition for a thick shell. Finally, it is suggested that active feedback stabilization of RWMs and current profile control techniques can be employed simultaneously thus improving both the plasma duration and its confinement properties.
Matsas, V J; Richardson, D J; Newson, T P; Payne, D N
1993-03-01
A full characterization of a self-starting, passively mode-locked soliton ring fiber laser in terms of its various modes of mode-locked operation, cavity length, and type of fiber used is presented. Direct evidence, based on state-of-polarization measurements, that nonlinear polarization evolution is the responsible mode-locking mechanism is also given.
Certifiable higher order sliding mode control: Practical stability margins approach
Panathula, Chandrasekhara Bharath
The Higher Order Sliding Mode (HOSM) controllers are well known for their robustness/insensitivity to bounded perturbations and for handling any given arbitrary relative degree system. The HOSM controller is to be certified for robustness to unmodeled dynamics, before deploying the controller for practical applications. Phase Margin (PM) and Gain Margin ( GM) are the classical characteristics used in linear systems to quantify the linear controller robustness to unmodeled dynamics, and certain values of these margins are required to certify the controller. These conventional margins (PM and GM) are extended to Practical Stability Phase Margin (PSPM) and Practical Stability Gain Margin (PSGM) in this dissertation, and are used to quantify the HOSM control robustness to unmodeled dynamics, presiding the tool to close the gap for HOSM control certification. The proposed robustness metrics ( PSPM and PSGM) are identified by developing tools/algorithms based on Describing Function-Harmonic Balance method. In order for the HOSM controller to achieve the prescribed values on robustness metrics ( PSPM and PSGM), the HOSM controller is cascaded with a linear compensator. A case study of the application of the proposed metrics (PSPM and PSGM) for the certification of F-16 aircraft HOSM attitude control robustness to cascade unmodeled dynamics is presented. In addition, several simulation examples are presented to verify and to validate the proposed methodology.
2011-01-01
International audience; In this paper, stabilizing control design for a class of nonlinear affine systems is presented by using a new generalized Gronwall-Bellman lemma approach. The nonlinear systems under consideration can be non Lipschitz. Two cases are treated for the exponential stabilization~: the static state feedback and the static output feedback. The robustness of the proposed control laws with regards to parameter uncertainties is also studied. A numerical example is given to show ...
P-th moment and almost sure stability of stochastic switched nonlinear systems.
Gu, Haibo; Gao, Caixia
2016-01-01
This paper mainly tends to utilize [Formula: see text]-type function to investigate p-th moment and almost sure stability for a class of stochastic switched nonlinear systems. Based on the multiple Lyapunov functions approach, some sufficient conditions are derived to check the stability criteria of stochastic switched nonlinear systems. One numerical example is provided to demonstrate the effectiveness of the proposed results.
Improved Stability Analysis of Nonlinear Networked Control Systems over Multiple Communication Links
Delavar, Rahim; Tavassoli, Babak; Beheshti, Mohammad Taghi Hamidi
2015-01-01
In this paper, we consider a nonlinear networked control system (NCS) in which controllers, sensors and actuators are connected via several communication links. In each link, networking effects such as the transmission delay, packet loss, sampling jitter and data packet miss-ordering are captured by time-varying delays. Stability analysis is carried out based on the Lyapunov Krasovskii method to obtain a condition for stability of the nonlinear NCS in the form of linear matrix inequality (LMI...
Kartashov, Yaroslav V
2014-01-01
We study specific features of resonant mode conversion in nonlinear waveguides stimulated by the bi-harmonic longitudinal modulation of its parameters, which includes changes of the waveguide depth as well as its bending (in the one-dimensional case) or spiraling (in the two-dimensional case). We demonstrate the possibility of simultaneous excitation of higher-order modes of different parities and topologies with controllable energy weights. The output mode composition is highly sensitive to the variation in the input power and detuning from the resonant modulation frequency.
Miranowicz, A; Miranowicz, Adam; Leonski, Wieslaw
2006-01-01
Schemes for optical-state truncation of two cavity modes are analysed. The systems, referred to as the nonlinear quantum scissors devices, comprise two coupled nonlinear oscillators (Kerr nonlinear coupler) with one or two of them pumped by external classical fields. It is shown that the quantum evolution of the pumped couplers can be closed in a two-qubit Hilbert space spanned by vacuum and single-photon states only. Thus, the pumped couplers can behave as a two-qubit system. Analysis of time evolution of the quantum entanglement shows that Bell states can be generated. A possible implementation of the couplers is suggested in a pumped double-ring cavity with resonantly enhanced Kerr nonlinearities in an electromagnetically-induced transparency scheme. The fragility of the generated states and their entanglement due to the standard dissipation and phase damping are discussed by numerically solving two types of master equations.
Possible Discovery of Nonlinear Tail and Quasinormal Modes in Black Hole Ringdown
Okuzumi, Satoshi; Sakagami, Masa-aki
2008-01-01
We investigate the nonlinear evolution of black hole ringdown in the framework of higher-order metric perturbation theory. By solving the initial-value problem of a simplified nonlinear field model analytically as well as numerically, we find that (i) second-order quasinormal modes (QNMs) are indeed excited at frequencies different from those of first-order QNMs, as predicted recently. We also find serendipitously that (ii) late-time evolution is dominated by a new type of power-law tail. This ``second-order power-law tail'' decays more slowly than any late-time tails known in the first-order (i.e., linear) perturbation theory, and is generated at the wavefront of the first-order perturbation by an essentially nonlinear mechanism. These nonlinear components should be particularly significant for binary black hole coalescences, and could open a new precision science in gravitational wave studies.
Gang, Zhou
2008-01-01
Nonlinear Schrodinger / Gross-Pitaevskii equations play a central role in the understanding of nonlinear optical and macroscopic quantum systems. The large time dynamics of such systems is governed by interactions of the nonlinear ground state manifold, discrete neutral modes (``excited states'') and dispersive radiation. Systems with symmetry, in spatial dimensions larger than one, typically have degenerate neutral modes. Thus, we study the large time dynamics of systems with degenerate neutral modes. This requires a new normal form (nonlinear matrix Fermi Golden Rule) governing the system's large time asymptotic relaxation to the ground state (soliton) manifold.
Stabilization and Control Models of Systems With Hysteresis Nonlinearities
Directory of Open Access Journals (Sweden)
Mihail E. Semenov
2012-05-01
Full Text Available Mechanical and economic systems with hysteresis nonlinearities are studied in article. Dissipativity condition of inverted pendulum under the hysteresis control is obtained. The solution of the optimal production strategy problem was found where price has hysteresis behaviour.
Robust adaptive dynamic programming and feedback stabilization of nonlinear systems.
Jiang, Yu; Jiang, Zhong-Ping
2014-05-01
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.
Nonlinear terahertz spectroscopy of Higgs mode in s-wave superconductors
Matsunaga, Ryusuke; Shimano, Ryo
2017-02-01
We review our recent experiments of ultrafast dynamics in s-wave superconductors Nb1-x Ti x N by using nonlinear terahertz (THz) spectroscopy. The free oscillation of the Higgs mode, i.e. the amplitude mode of the superconducting order parameter, is observed after instantaneous injection of quasiparticles at the superconducting gap edge by an intense monocycle THz pulse. The ultrafast nonequilibrium dynamics of the order parameter under the strong AC driving field with the photon energy tuned below the superconducting gap is also investigated. A resonant nonlinear interaction between the Higgs mode and the electromagnetic field is revealed, as manifested by an efficient THz third-harmonic generation from the superconductor.
Strozzi, Matteo; Smirnov, Valeri V.; Manevitch, Leonid I.; Milani, Massimo; Pellicano, Francesco
2016-10-01
In this paper, the nonlinear vibrations and energy exchange of single-walled carbon nanotubes (SWNTs) are studied. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration. The SWNT deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported, clamped and free boundary conditions are considered. The circumferential flexural modes (CFMs) are investigated. Two different approaches based on numerical and analytical models are compared. In the numerical model, an energy method based on the Lagrange equations is used to reduce the nonlinear partial differential equations of motion to a set of nonlinear ordinary differential equations, which is solved by using the implicit Runge-Kutta numerical method. In the analytical model, a reduced form of the Sanders-Koiter theory assuming small circumferential and tangential shear deformations is used to get the nonlinear ordinary differential equations of motion, which are solved by using the multiple scales analytical method. The transition from energy beating to energy localization in the nonlinear field is studied. The effect of the aspect ratio on the analytical and numerical values of the nonlinear energy localization threshold for different boundary conditions is investigated. Time evolution of the total energy distribution along the axis of a simply supported SWNT
Stability for a class of nonlinear time-delay systems via Hamiltonian functional method
Institute of Scientific and Technical Information of China (English)
YANG RenMing; WANG YuZhen
2012-01-01
This paper investigates the stability of a class of nonlinear time-delay systems via Hamiltonian functional method,and proposes a number of new results on generalized Hamiltonian realization (GHR) and stability analysis for this class of systems.Firstly,the concept of GHR of general nonlinear time-delay systems is proposed,and several new GHR methods are given.Then,based on the new GHR methods obtained,the stability of time-delay systems is investigated,and several delay-dependent sufficient conditions in term of matrix inequalities are derived for the stability analysis by constructing suitable Lyapunov-Krasovskii (L-K) functionals.Finally,an illustrative example shows that the results obtained in this paper have less conservatism,and work very well in the stability analysis of some nonlinear time-delay Hamiltonian systems.
Olivier, Michel; Gagnon, Marc-Daniel; Habel, Joé
2016-02-28
When a laser is mode-locked, it emits a train of ultra-short pulses at a repetition rate determined by the laser cavity length. This article outlines a new and inexpensive procedure to force mode locking in a pre-adjusted nonlinear polarization rotation fiber laser. This procedure is based on the detection of a sudden change in the output polarization state when mode locking occurs. This change is used to command the alignment of the intra-cavity polarization controller in order to find mode-locking conditions. More specifically, the value of the first Stokes parameter varies when the angle of the polarization controller is swept and, moreover, it undergoes an abrupt variation when the laser enters the mode-locked state. Monitoring this abrupt variation provides a practical easy-to-detect signal that can be used to command the alignment of the polarization controller and drive the laser towards mode locking. This monitoring is achieved by feeding a small portion of the signal to a polarization analyzer measuring the first Stokes parameter. A sudden change in the read out of this parameter from the analyzer will occur when the laser enters the mode-locked state. At this moment, the required angle of the polarization controller is kept fixed. The alignment is completed. This procedure provides an alternate way to existing automating procedures that use equipment such as an optical spectrum analyzer, an RF spectrum analyzer, a photodiode connected to an electronic pulse-counter or a nonlinear detecting scheme based on two-photon absorption or second harmonic generation. It is suitable for lasers mode locked by nonlinear polarization rotation. It is relatively easy to implement, it requires inexpensive means, especially at a wavelength of 1550 nm, and it lowers the production and operation costs incurred in comparison to the above-mentioned techniques.
Energy Technology Data Exchange (ETDEWEB)
M.H. Redi; C.L. Fiore; W. Dorland; D.R. Mikkelsen; G. Rewoldt; P.T. Bonoli; D.R. Ernst; J.E. Rice; S.J. Wukitch
2003-11-20
Recent H-mode experiments on Alcator C-Mod [I.H. Hutchinson, et al., Phys. Plasmas 1 (1994) 1511] which exhibit an internal transport barrier (ITB), have been examined with flux tube geometry gyrokinetic simulations, using the massively parallel code GS2 [M. Kotschenreuther, G. Rewoldt, and W.M. Tang, Comput. Phys. Commun. 88 (1995) 128]. The simulations support the picture of ion/electron temperature gradient (ITG/ETG) microturbulence driving high xi/ xe and that suppressed ITG causes reduced particle transport and improved ci on C-Mod. Nonlinear calculations for C-Mod confirm initial linear simulations, which predicted ITG stability in the barrier region just before ITB formation, without invoking E x B shear suppression of turbulence. Nonlinear fluxes are compared to experiment, which both show low heat transport in the ITB and higher transport within and outside of the barrier region.
Static feedback stabilization of nonlinear systems with single sensor and single actuator.
Wang, Jiqiang; Hu, Zhongzhi; Ye, Zhifeng
2014-01-01
This paper considers a single sensor and single actuator approach to the static feedback stabilization of nonlinear systems. This is essentially a remote control problem that is present in many engineering applications. The proposed method solves this problem that is less expensive to implement and more reliable in practice. Significant results are obtained on the design of controllers for stabilizing the nonlinear systems. Important issues on control implementation are also discussed. The proposed design method is validated through its application to nonlinear control of aircraft engines.
Directory of Open Access Journals (Sweden)
Mingzhu Song
2016-01-01
Full Text Available We address the problem of globally asymptotic stability for a class of stochastic nonlinear systems with time-varying delays. By the backstepping method and Lyapunov theory, we design a linear output feedback controller recursively based on the observable linearization for a class of stochastic nonlinear systems with time-varying delays to guarantee that the closed-loop system is globally asymptotically stable in probability. In particular, we extend the deterministic nonlinear system to stochastic nonlinear systems with time-varying delays. Finally, an example and its simulations are given to illustrate the theoretical results.
Frequency domain stability analysis of nonlinear active disturbance rejection control system.
Li, Jie; Qi, Xiaohui; Xia, Yuanqing; Pu, Fan; Chang, Kai
2015-05-01
This paper applies three methods (i.e., root locus analysis, describing function method and extended circle criterion) to approach the frequency domain stability analysis of the fast tool servo system using nonlinear active disturbance rejection control (ADRC) algorithm. Root locus qualitative analysis shows that limit cycle is generated because the gain of the nonlinear function used in ADRC varies with its input. The parameters in the nonlinear function are adjustable to suppress limit cycle. In the process of root locus analysis, the nonlinear function is transformed based on the concept of equivalent gain. Then, frequency domain description of the nonlinear function via describing function is presented and limit cycle quantitative analysis including estimating prediction error is presented, which virtually and theoretically demonstrates that the describing function method cannot guarantee enough precision in this case. Furthermore, absolute stability analysis based on extended circle criterion is investigated as a complement.
Nonlinear mode coupling and internal resonances in MoS2 nanoelectromechanical system
Samanta, C.; Yasasvi Gangavarapu, P. R.; Naik, A. K.
2015-10-01
Atomically thin two dimensional (2D) layered materials have emerged as a new class of material for nanoelectromechanical systems (NEMS) due to their extraordinary mechanical properties and ultralow mass density. Among them, graphene has been the material of choice for nanomechanical resonator. However, recent interest in 2D chalcogenide compounds has also spurred research in using materials such as MoS2 for the NEMS applications. As the dimensions of devices fabricated using these materials shrink down to atomically thin membrane, strain and nonlinear effects have become important. A clear understanding of the nonlinear effects and the ability to manipulate them is essential for next generation sensors. Here, we report on all electrical actuation and detection of few-layer MoS2 resonator. The ability to electrically detect multiple modes and actuate the modes deep into the nonlinear regime enables us to probe the nonlinear coupling between various vibrational modes. The modal coupling in our device is strong enough to detect three distinct internal resonances.
Stability analysis of nonlinear systems by multiple time scaling. [using perturbation methods
Morino, L.
1974-01-01
The asymptotic solution for the transient analysis of a general nonlinear system in the neighborhood of the stability boundary was obtained by using the multiple-time-scaling asymptotic-expansion method. The nonlinearities are assumed to be of algebraic nature. Terms of order epsilon to the 3rd power (where epsilon is the order of amplitude of the unknown) are included in the solution. The solution indicates that there is always a limit cycle which is stable (unstable) and exists above (below) the stability boundary if the nonlinear terms are stabilizing (destabilizing). Extension of the solution to include fifth order nonlinear terms is also presented. Comparisons with harmonic balance and with multiple-time-scaling solution of panel flutter equations are also included.
Studying Climate Response to Forcing by the Nonlinear Dynamical Mode Decomposition
Mukhin, Dmitry; Gavrilov, Andrey; Loskutov, Evgeny; Feigin, Alexander
2017-04-01
An analysis of global climate response to external forcing, both anthropogenic (mainly, CO2 and aerosol) and natural (solar and volcanic), is needed for adequate predictions of global climate change. Being complex dynamical system, the climate reacts to external perturbations exciting feedbacks (both positive and negative) making the response non-trivial and poorly predictable. Thus an extraction of internal modes of climate system, investigation of their interaction with external forcings and further modeling and forecast of their dynamics, are all the problems providing the success of climate modeling. In the report the new method for principal mode extraction from climate data is presented. The method is based on the Nonlinear Dynamical Mode (NDM) expansion [1,2], but takes into account a number of external forcings applied to the system. Each NDM is represented by hidden time series governing the observed variability, which, together with external forcing time series, are mapped onto data space. While forcing time series are considered to be known, the hidden unknown signals underlying the internal climate dynamics are extracted from observed data by the suggested method. In particular, it gives us an opportunity to study the evolution of principal system's mode structure in changing external conditions and separate the internal climate variability from trends forced by external perturbations. Furthermore, the modes so obtained can be extrapolated beyond the observational time series, and long-term prognosis of modes' structure including characteristics of interconnections and responses to external perturbations, can be carried out. In this work the method is used for reconstructing and studying the principal modes of climate variability on inter-annual and decadal time scales accounting the external forcings such as anthropogenic emissions, variations of the solar activity and volcanic activity. The structure of the obtained modes as well as their response to
Directory of Open Access Journals (Sweden)
Xiaomin Tian
2014-02-01
Full Text Available In this paper, the problem of stabilizing a class of fractional-order chaotic systems with sector and dead-zone nonlinear inputs is investigated. The effects of model uncertainties and external disturbances are fully taken into account. Moreover, the bounds of both model uncertainties and external disturbances are assumed to be unknown in advance. To deal with the system’s nonlinear items and unknown bounded uncertainties, an adaptive fractional-order sliding mode (AFSM controller is designed. Then, Lyapunov’s stability theory is used to prove the stability of the designed control scheme. Finally, two simulation examples are given to verify the effectiveness and robustness of the proposed control approach.
Nonlinear r-modes in a spherical shell issues of principle
Levin, Y; Levin, Yuri; Ushomirsky, Greg
1999-01-01
We use a simple physical model to study the nonlinear behaviour of the r-mode instability. We assume that r-modes (Rossby waves) are excited in a thin spherical shell of rotating incompressible fluid. For this case, exact Rossby wave solutions of arbitrary amplitude are known. We find that: (a) These nonlinear Rossby waves carry ZERO physical angular momentum and positive physical energy, which is contrary to the folklore belief that the r-mode angular momentum and energy are negative. (b) Within our model, we confirm the differential drift reported by Rezzolla, Lamb and Shapiro (1999). Radiation reaction is introduced into the model by assuming that the fluid is electrically charged; r-modes are coupled to electromagnetic radiation through current (magnetic) multipole moments. We find that: (c) To linear order in the mode amplitude, r-modes are subject to the CFS instability, as expected. (d) Radiation reaction decreases the angular velocity of the shell and causes differential rotation (which is distinct fr...
Stupishin, L.; Nikitin, K.; Kolesnikov, A.
2017-05-01
A methodology for shell stability research and determining buckling load, based on the mixed finite element method are proposed. Axisymmetric geometrically nonlinear shallow shells made of orthotropic material are considered. The results of numerical research of stability by changing the shape of shells, ratio of elastic modulus of the material and parameters of the support contour are presented.
Results on stabilization of nonlinear systems under finite data-rate constraints
Persis, Claudio De
2004-01-01
We discuss in this paper a result concerning the stabilization problem of nonlinear systems under data-rate constraints using output feedback. To put the result in a broader context, we shall first review a number of recent contributions on the stabilization problem under data-rate constraints when
RESEARCH OF THE PERIODIC MOTION AND STABILITY OF TWO-DEGREE-OF-FREEDOM NONLINEAR OSCILLATING SYSTEMS
Institute of Scientific and Technical Information of China (English)
刘俊
2002-01-01
The periodic motion and stability for a class of two-degree-of freedom nonlinear oscillating systems are studied by using the method of Liapunov function.The sufficient conditions which guarantee the existence, uniqueness and asymptotic stability of the periodic solutions are obtained.
Non-smooth finite-time stabilization for a class of nonlinear systems
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, global finite-time stabilization problem for a large class of nonlinear control systems is considered. An iterative design approach is given based on Lyapunov function. The finite time stabilizing control laws are constructed in the form of continuous but non-smooth time-invariant feedback.
Asymptotic stability for a class of boundary control systems with non-linear damping
Zwart, Heiko J.; Ramirez, Hector; Le Gorrec, Yann
2016-01-01
The asymptotic stability of boundary controlled port-Hamiltonian systems defined on a 1D spatial domain interconnected to a class of non-linear boundary damping is addressed. It is shown that if the port-Hamiltonian system is approximately observable, then any boundary damping which behaves linear for small velocities asymptotically stabilizes the system.
THE EXISTENCE, UNIQUENESS AND STABILITY OF ALMOST PERIODIC SOLUTION FOR A CLASS OF NONLINEAR SYSTEM
Institute of Scientific and Technical Information of China (English)
方聪娜; 王全义
2004-01-01
In this paper, we study the problems on the existence, uniqueness and stability of almost periodic solution for a class of nonlinear system. Using fixed point theorem and Lyapunov functional, the sufficient conditions are given which guarantee the existence, uniqueness and stability of almost periodic solution for the system.
Nonlinear behaviour and stability of thin-walled shells
Obodan, Natalia I; Gromov, Vasilii A
2013-01-01
This book focuses on the nonlinear behaviour of thin-wall shells (single- and multilayered with delamination areas) under various uniform and non-uniform loadings. The dependence of critical (buckling) load upon load variability is revealed to be highly non-monotonous, showing minima when load variability is close to the eigenmode variabilities of solution branching points of the respective nonlinear boundary problem. A novel numerical approach is employed to analyze branching points and to build primary, secondary, and tertiary bifurcation paths of the nonlinear boundary problem for the case of uniform loading. The load levels of singular points belonging to the paths are considered to be critical load estimates for the case of non-uniform loadings.
Directory of Open Access Journals (Sweden)
Takeshi Yoshida
2015-11-01
Full Text Available Nonlinear ultrashort pulse propagation in a mode-locked Yb:YAG laser with a highly nonlinear intra-cavity medium is analyzed using a nonlinear Schrodinger equation. The output spectra are extended by the increased laser intensity, and spectral bandwidths wider than those of the gain medium are achieved. Moreover, pulse widths are shortened by increased laser intensity to considerably less than those of the gain medium. The simulation results qualitatively agree with the experimental results.
Oblique non-neutral solitary Alfven modes in weakly nonlinear pair plasmas
Energy Technology Data Exchange (ETDEWEB)
Verheest, Frank [Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281, B-9000 Gent (Belgium); School of Physics, Howard College Campus, University of KwaZulu-Natal, Durban 4041 (South Africa); Lakhina, G S [Indian Institute of Geomagnetism, New Panvel, Navi Mumbai 410218 (India); Research Institute for Sustainable Humanosphere, Kyoto University, Gokasho, Uji, Kyoto 611-0011 (Japan)
2005-04-01
The equal charge-to-mass ratio for both species in pair plasmas induces a decoupling of the linear eigenmodes between waves that are charge neutral or non-neutral, also at oblique propagation with respect to a static magnetic field. While the charge-neutral linear modes have been studied in greater detail, including their weakly and strongly nonlinear counterparts, the non-neutral mode has received less attention. Here the nonlinear evolution of a solitary non-neutral mode at oblique propagation is investigated in an electron-positron plasma. Employing the framework of reductive perturbation analysis, a modified Korteweg-de Vries equation (with cubic nonlinearity) for the lowest-order wave magnetic field is obtained. In the linear approximation, the non-neutral mode has its magnetic component orthogonal to the plane spanned by the directions of wave propagation and of the static magnetic field. The linear polarization is not maintained at higher orders. The results may be relevant to the microstructure in pulsar radiation or to the subpulses.
Three-Dimensional Single-Mode Nonlinear Ablative Rayleigh-Taylor Instability
Yan, R.; Betti, R.; Sanz, J.; Liu, B.; Frank, A.
2015-11-01
The nonlinear evolution of the ablative Rayleigh-Taylor (ART) instability is studied in three dimensions for conditions relevant to inertial confinement fusion targets. The simulations are performed using our newly developed code ART3D and an astrophysical code AstroBEAR. The laser ablation can suppress the growth of the short-wavelength modes in the linear phase but may enhance their growth in the nonlinear phase because of the vortex-acceleration mechanism. As the mode wavelength approaches the cutoff of the linear spectrum (short-wavelength modes), it is found that the bubble velocity grows faster than predicted in the classical 3-D theory. When compared to 2-D results, 3-D short-wavelength bubbles grow faster and do not reach saturation. The unbounded 3-D bubble acceleration is driven by the unbounded accumulation of vorticity inside the bubble. The vorticity is transferred by mass ablation from the Rayleigh-Taylor spikes into the ablated plasma filling the bubble volume. A density plateau is observed inside a nonlinear ART bubble and the plateau density is higher for shorter-wavelength modes. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0001944.
Institute of Scientific and Technical Information of China (English)
SUN LiYing; WANG YuZhen
2009-01-01
This paper studies simultaneous stabilization of a class of nonlinear descriptor systems via the Hamiltonlan function method.Firstly,based on the Hamiltonian realization of the nonlinear descriptor systems and a suitable output feedback,two nonlinear descriptor systems are equivalently transformed into two nonlinear Hamiltonian differential-algebraic systems by a nonsingular transformation,and a sufficient condition for two closed-loop systems to be impulse-free is given.The two systems are then combined to generate an augmented dissipative Hamiltonian differential-algebraic system by using the system-augmentation technique,based on which a simultaneous stabilization controller and a robust simultaneous stabilization controller are designed for the two systems.Secondly,the case of more than two nonlinear descriptor systems is investigated,and two new results are proposed for the simultaneous stabilization and robust simultaneous stabilization,respectively.Finally,an illustrative example is studied by using the results proposed in this paper,and simulations show that the simultaneous stabilization controllers obtained in this paper work very well.
Modeling and stability analysis of the nonlinear reactive sputtering process
Directory of Open Access Journals (Sweden)
György Katalin
2011-12-01
Full Text Available The model of the reactive sputtering process has been determined from the dynamic equilibrium of the reactive gas inside the chamber and the dynamic equilibrium of the sputtered metal atoms which form the compound with the reactive gas atoms on the surface of the substrate. The analytically obtained dynamical model is a system of nonlinear differential equations which can result in a histeresis-type input/output nonlinearity. The reactive sputtering process has been simulated by integrating these differential equations. Linearization has been applied for classical analysis of the sputtering process and control system design.
Yan, Zhiguo; Song, Yunxia; Park, Ju H
2017-05-01
This paper is concerned with the problems of finite-time stability and stabilization for stochastic Markov systems with mode-dependent time-delays. In order to reduce conservatism, a mode-dependent approach is utilized. Based on the derived stability conditions, state-feedback controller and observer-based controller are designed, respectively. A new N-mode algorithm is given to obtain the maximum value of time-delay. Finally, an example is used to show the merit of the proposed results. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Feedback diagonal canonical form and its application to stabilization of nonlinear systems
Institute of Scientific and Technical Information of China (English)
CHENG Daizhan; HU Qingxi; QIN Huashu
2005-01-01
This paper considers the problem of stabilization of a class of nonlinear systems, which are possibly of non-minimum phase. A new feedback-equivalent canonical form, called diagonal normal form, of linear control systems is proposed. Using it, the corresponding normal form of affine nonlinear control systems is obtained. Based on this new normal form and the design technique of center manifold, a new constructing method for stabilizing control is presented. Certain examples are included to demonstrate the design strategy of stabilizers.
DEFF Research Database (Denmark)
Fuhrmann, David R.; Bingham, Harry B.; Madsen, Per A.;
2004-01-01
This paper considers a method of lines stability analysis for finite difference discretizations of a recently published Boussinesq method for the study of highly nonlinear and extremely dispersive water waves. The analysis demonstrates the near-equivalence of classical linear Fourier (von Neumann......) techniques with matrix-based methods for formulations in both one and two horizontal dimensions. The matrix-based method is also extended to show the local de-stabilizing effects of the nonlinear terms, as well as the stabilizing effects of numerical dissipation. A comparison of the relative stability...... moderately non-normal, suggesting that the eigenvalues are likely suitable for analysis purposes. Numerical experiments demonstrate excellent agreement with the linear analysis, and good qualitative agreement with the local nonlinear analysis. The various methods of analysis combine to provide significant...
Spectral and modulational stability of periodic wavetrains for the nonlinear Klein-Gordon equation
Jones, Christopher K. R. T.; Marangell, Robert; Miller, Peter D.; Plaza, Ramón G.
2014-12-01
This paper is a detailed and self-contained study of the stability properties of periodic traveling wave solutions of the nonlinear Klein-Gordon equation utt-uxx+V‧(u)=0, where u is a scalar-valued function of x and t, and the potential V(u) is of class C2 and periodic. Stability is considered both from the point of view of spectral analysis of the linearized problem (spectral stability analysis) and from the point of view of wave modulation theory (the strongly nonlinear theory due to Whitham as well as the weakly nonlinear theory of wave packets). The aim is to develop and present new spectral stability results for periodic traveling waves, and to make a solid connection between these results and predictions of the (formal) modulation theory, which has been developed by others but which we review for completeness.
Yang, Jianke
2012-01-01
Linear stability of both sign-definite (positive) and sign-indefinite solitary waves near pitchfork bifurcations is analyzed for the generalized nonlinear Schroedinger equations with arbitrary forms of nonlinearity and external potentials in arbitrary spatial dimensions. Bifurcations of linear-stability eigenvalues associated with pitchfork bifurcations are analytically calculated. It is shown that the smooth solution branch switches stability at the bifurcation point. In addition, the two bifurcated solution branches and the smooth branch have the opposite (same) stability when their power slopes have the same (opposite) sign. One unusual feature on the stability of these pitchfork bifurcations is that the smooth and bifurcated solution branches can be both stable or both unstable, which contrasts such bifurcations in finite-dimensional dynamical systems where the smooth and bifurcated branches generally have opposite stability. For the special case of positive solitary waves, stronger and more explicit stab...
STABILITY OF INNOVATION DIFFUSION MODEL WITH NONLINEAR ACCEPTANCE
Institute of Scientific and Technical Information of China (English)
Yu Yumei; Wang Wendi
2007-01-01
In this article, an innovation diffusion model with the nonlinear acceptance is proposed to describe the dynamics of three competing products in a market. It is proved that the model admits a unique positive equilibrium, which is globally stable by excluding the existence of periodic solutions and by using the theory of three dimensional competition systems.
Stability of planar diffusion wave for nonlinear evolution equation
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
It is known that the one-dimensional nonlinear heat equation ut = f(u)x1x1,f'(u) 0,u(±∞,t) = u±,u+ = u_ has a unique self-similar solution u(x1/1+t).In multi-dimensional space,u(x1/1+t) is called a planar diffusion wave.In the first part of the present paper,it is shown that under some smallness conditions,such a planar diffusion wave is nonlinearly stable for the nonlinear heat equation:ut-△f(u) = 0,x ∈ Rn.The optimal time decay rate is obtained.In the second part of this paper,it is further shown that this planar diffusion wave is still nonlinearly stable for the quasilinear wave equation with damping:utt + utt+ △f(u) = 0,x ∈ Rn.The time decay rate is also obtained.The proofs are given by an elementary energy method.
STABILITY OF NONLINEAR NEUTRAL DIFFERENTIAL EQUATION VIA FIXED POINT
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
In this paper,a nonlinear neutral differential equation is considered.By a fixed point theory,we give some conditions to ensure that the zero solution to the equation is asymptotically stable.Some existing results are improved and generalized.
Robust Stability Analysis of Nonlinear Switched Systems with Filippov Solutions
DEFF Research Database (Denmark)
Ahmadi, Mohamadreza; Mojallali, Hamed; Wisniewski, Rafal
2012-01-01
. Based on the theory of differential inclusions, a Lyapunov stability theorem is brought forward. These results are also extended to autonomous switched systems subject to polytopic uncertainty. Furthermore, the proposed stability theorems are reformulated using the sum of squares decomposition method...... which provides sufficient means to construct the corresponding Lyapunov functions via available semi-definite programming techniques....
Tilt stability in nonlinear programming under Mangasarian-Fromovitz constraint qualification
Mordukhovich, B. S.; Outrata, J. (Jiří)
2013-01-01
The paper concerns the study of tilt stability of local minimizers in standard problems of nonlinear programming. This notion plays an important role in both theoretical and numerical aspects of optimization and has drawn a lot of attention in optimization theory and its applications, especially in recent years. Under the classical Mangasarian–Fromovitz Constraint Qualification, we establish relationships between tilt stability and some other stability notions in constrained optimization. I...
Energy Technology Data Exchange (ETDEWEB)
Prill, Dennis; Class, Andreas G. [Karlsruhe Institute of Technology (KIT), Eggenstein-Leopoldshafen (Germany). AREVA Nuclear Professional School (ANPS)
2013-07-01
Unexpected non-linear boiling water reactor (BWR) instability events in various plants, e.g. LaSalle II in 1988 and Oskarshamn II in 1990 amongst others, emphasize the major safety relevance and the existence of parameter regions with unstable behavior. A detailed description of the complete dynamical non-linear behavior is of paramount importance for BWR operation. An extension of state-of-the-art methodology towards a more general stability description, also applicable in the non-linear region, could lead to a deeper understanding of non-linear BWR stability phenomena. With the intention of a full non-linear stability analysis of the two-phase BWR system, the present paper aims at a general non-linear methodology capable to achieve reliable and numerical stable reduced order models (ROMs), representing the dynamical behavior of an original system based on a small number of transients. Model-specific options and aspects of the proposed methodology are focused on and illustrated by means of a strongly non-linear dynamical system showing complex oscillating behavior. Prediction capability of the proposed methodology is also addressed. (orig.)
Mei, Chuh; Shen, Mo-How
1987-01-01
Multiple-mode nonlinear forced vibration of a beam was analyzed by the finite element method. Inplane (longitudinal) displacement and inertia (IDI) are considered in the formulation. By combining the finite element method and nonlinear theory, more realistic models of structural response are obtained more easily and faster.
PARTIAL STABILIZATION OF A CLASS OF CONTINUOUS NONLINEAR CONTROL SYSTEMS WITH SEPARATED VARIABLES
Institute of Scientific and Technical Information of China (English)
Jigui JIAN; Xiaoxin LIAO
2005-01-01
In this paper, the partial stabilization problem for a class of nonlinear continuous control systems with separated variables is investigated. Several stabilizing controllers are constructed based on the partial stability theory of Lyapunov and the property of M-matrix, and some of these stabilizing controllers are only related to partial state variables. The controllers constructed here are shown to guarantee partial asymptotic stability of the closed-loop systems and these sufficient conditions may give some instructions to actual engineering application. A example is also given to illustrate the design method.
Generalized exponential input-to-state stability of nonlinear systems with time delay
Sun, Fenglan; Gao, Lingxia; Zhu, Wei; Liu, Feng
2017-03-01
This paper studies the general input-to-state stability problem of the nonlinear delay systems. By employing Lypaunov-Razumikhin technique, several general input-to-state stability concepts, that is generalized globally exponential integral input-to-state stability (GGE-iISS), generalized globally integral exponential integral input-to-state stability (GGIE-iISS), and eλt-weighted generalized globally integral exponential integral input-to-state stability (eλt-weighted GGIE-iISS) are studied. An example is given to illustrate the correctness of the obtained theoretical results.
Quasinormal modes of nonlinear electromagnetic black holes from unstable null geodesics
Breton, N
2016-01-01
The expressions for the quasinormal modes (QNMs) of black holes with nonlinear electrodynamics, calculated in the eikonal approximation, are presented. In the eikonal limit QNMs of black holes are determined by the parameters of the circular null geodesics. The unstable circular null orbits are derived from the effective metric that is the one obeyed by light rays under the influence of a nonlinear electromagnetic field. As an illustration we calculate the QNMs of four nonlinear electromagnetic black holes, two singular and two regular, namely from Euler-Heisenberg and Born-Infeld theories, for singular, and the magnetic Bardeen black hole and the one derived by Bronnikov for regular ones. Comparison is shown with the QNMs of the linear electromagnetic counterpart, their Reissner-Nordstr\\"{o}m black hole.
Quasinormal modes of nonlinear electromagnetic black holes from unstable null geodesics
Bretón, Nora; López, L. A.
2016-11-01
The expressions for the quasinormal modes (QNM) of black holes with nonlinear electrodynamics, calculated in the eikonal approximation, are presented. In the eikonal limit QNM of black holes are determined by the parameters of the circular null geodesics. The unstable circular null orbits are derived from the effective metric that is the one obeyed by light rays under the influence of a nonlinear electromagnetic field. As an illustration we calculate the QNM of four nonlinear electromagnetic black holes, two singular and two regular, namely, from Euler-Heisenberg and Born-Infeld theories, for singular ones, and the magnetic Bardeen black hole and the one derived by Bronnikov for regular ones. Comparing with the QNM of the linear electromagnetic counterpart, their Reissner-Nordström black hole is done.
Nonlinear and Perturbative Evolution of Distorted Black Holes; 2, Odd-parity Modes
Baker, J; Campanelli, M; Loustó, C O; Seidel, E; Takahashi, R
2000-01-01
We compare the fully nonlinear and perturbative evolution of nonrotating black holes with odd-parity distortions utilizing the perturbative results to interpret the nonlinear results. This introduction of the second polarization (odd-parity) mode of the system, and the systematic use of combined techniques brings us closer to the goal of studying more complicated systems like distorted, rotating black holes, such as those formed in the final inspiral stage of two black holes. The nonlinear evolutions are performed with the 3D parallel code for Numerical Relativity, {Cactus}, and an independent axisymmetric code, {Magor}. The linearized calculation is performed in two ways: (a) We treat the system as a metric perturbation on Schwarzschild, using the Regge-Wheeler equation to obtain the waveforms produced. (b) We treat the system as a curvature perturbation of a Kerr black hole (but here restricted to the case of vanishing rotation parameter a) and evolve it with the Teukolsky equation The comparisons of the wa...
Orain, François; Bécoulet, M.; Morales, J.; Huijsmans, G. T. A.; Dif-Pradalier, G.; Hoelzl, M.; Garbet, X.; Pamela, S.; Nardon, E.; Passeron, C.; Latu, G.; Fil, A.; Cahyna, P.
2015-01-01
The dynamics of a multi-edge localized mode (ELM) cycle as well as the ELM mitigation by resonant magnetic perturbations (RMPs) are modeled in realistic tokamak X-point geometry with the non-linear reduced MHD code JOREK. The diamagnetic rotation is found to be a key parameter enabling us to reproduce the cyclical dynamics of the plasma relaxations and to model the near-symmetric ELM power deposition on the inner and outer divertor target plates consistently with experimental measurements. Moreover, the non-linear coupling of the RMPs with unstable modes are found to modify the edge magnetic topology and induce a continuous MHD activity in place of a large ELM crash, resulting in the mitigation of the ELMs. At larger diamagnetic rotation, a bifurcation from unmitigated ELMs—at low RMP current—towards fully suppressed ELMs—at large RMP current—is obtained.
Directory of Open Access Journals (Sweden)
Mostafa H. Ali, Ahmed E. Elsamahy, Maher A. Farhoud and Taymour A. Hamdalla
2012-10-01
Full Text Available Near field distribution, propagation constant and dispersion characteristics of nonlinear single-mode optical fibers have been investigated. Shooting-method technique is used and implemented into a computer code for both profiles of step-index and graded-index fibers. An error function is defined to estimate the discrepancy between the expected electric-field radial derivative at the core-cladding interface and that obtained by numerically integrating the wave equation through the use of Runge-Kutta method. All of the above calculations done under the ocean depth in which the depth will affect the refractive index that have a direct effect on all the optical fiber parameters.KeyWords: Nonlinear refractive index, Normalized propagation constant, Mode delay factor, Material dispersion, Waveguide dispersion.
Variable structure control with sliding mode prediction for discrete-time nonlinear systems
Institute of Scientific and Technical Information of China (English)
Lingfei XIAO; Hongye SU; Xiaoyu ZHANG; Jian CHU
2006-01-01
A new variable structure control algorithm based on sliding mode prediction for a class of discrete-time nonlinear systems is presented. By employing a special model to predict future sliding mode value, and combining feedback correction and receding horizon optimization methods which are extensively applied on predictive control strategy, a discrete-time variable structure control law is constructed. The closed-loop systems are proved to have robustness to uncertainties with unspecified boundaries. Numerical simulation and pendulum experiment results illustrate that the closed-loop systems possess desired performance, such as strong robustness, fast convergence and chattering elimination.
Kong, Lingjie; Xiao, Xiaosheng; Yang, Changxi
2011-09-12
We numerically studied the polarization dynamics in dissipative soliton lasers mode-locked by nonlinear polarization rotation (NPR). It was found that the polarization states of the intracavity dissipative soliton vary with time across the pulse. Depending on output coupling ratios, the polarization states of the pulse peak before the polarizer can be either nearly circular or nearly linear polarizations. The polarization dependent component in NPR is found to play a role of spectral filter under high and medium output coupling. However, NPR may work as a weak optical limiter under low output coupling, when additional spectral filtering is necessary to maintain steady mode-locking state.
Stabilization and utilization of nonlinear phenomena based on bifurcation control for slow dynamics
Yabuno, Hiroshi
2008-08-01
Mechanical systems may experience undesirable and unexpected behavior and instability due to the effects of nonlinearity of the systems. Many kinds of control methods to decrease or eliminate the effects have been studied. In particular, bifurcation control to stabilize or utilize nonlinear phenomena is currently an active topic in the field of nonlinear dynamics. This article presents some types of bifurcation control methods with the aim of realizing vibration control and motion control for mechanical systems. It is also indicated through every control method that slowly varying components in the dynamics play important roles for the control and the utilizations of nonlinear phenomena. In the first part, we deal with stabilization control methods for nonlinear resonance which is the 1/3-order subharmonic resonance in a nonlinear spring-mass-damper system and the self-excited oscillation (hunting motion) in a railway vehicle wheelset. The second part deals with positive utilizations of nonlinear phenomena by the generation and the modification of bifurcation phenomena. We propose the amplitude control method of the cantilever probe of an atomic force microscope (AFM) by increasing the nonlinearity in the system. Also, the motion control of a two link underactuated manipulator with a free link and an active link is considered by actuating the bifurcations produced under high-frequency excitation. This article is a discussion on the bifurcation control methods presented by the author and co-researchers by focusing on the actuation of the slowly varying components included in the original dynamics.
Calini, A.; Schober, C. M.
2013-09-01
In this article we present the results of a broad numerical investigation on the stability of breather-type solutions of the nonlinear Schrödinger (NLS) equation, specifically the one- and two-mode breathers for an unstable plane wave, which are frequently used to model rogue waves. The numerical experiments involve large ensembles of perturbed initial data for six typical random perturbations. Ensemble estimates of the "closeness", Calligraphy">A(t), of the perturbed solution to an element of the respective unperturbed family indicate that the only neutrally stable breathers are the ones of maximal dimension, that is: given an unstable background with N unstable modes, the only neutrally stable breathers are the N-dimensional ones (obtained as a superimposition of N simple breathers via iterated Backlund transformations). Conversely, breathers which are not fully saturated are sensitive to noisy environments and are unstable. Interestingly, Calligraphy">A(t) is smallest for the coalesced two-mode breather indicating the coalesced case may be the most robust two-mode breather in a laboratory setting. The numerical simulations confirm and provide a realistic realization of the stability behavior established analytically by the authors.
Energy Technology Data Exchange (ETDEWEB)
Bai, Xiao-Dong; Ai, Qing; Zhang, Mei; Xiong, Jun, E-mail: junxiong@bnu.edu.cn; Yang, Guo-Jian; Deng, Fu-Guo
2015-09-15
We investigate the stability and phase transition of localized modes in Bose–Einstein Condensates (BECs) in an optical lattice with the discrete nonlinear Schrödinger model by considering both two- and three-body interactions. We find that there are three types of localized modes, bright discrete breather (DB), discrete kink (DK), and multi-breather (MUB). Moreover, both two- and three-body on-site repulsive interactions can stabilize DB, while on-site attractive three-body interactions destabilize it. There is a critical value for the three-body interaction with which both DK and MUB become the most stable ones. We give analytically the energy thresholds for the destabilization of localized states and find that they are unstable (stable) when the total energy of the system is higher (lower) than the thresholds. The stability and dynamics characters of DB and MUB are general for extended lattice systems. Our result is useful for the blocking, filtering, and transfer of the norm in nonlinear lattices for BECs with both two- and three-body interactions.
Circuits and systems based on delta modulation linear, nonlinear and mixed mode processing
Zrilic, Djuro G
2005-01-01
This book is intended for students and professionals who are interested in the field of digital signal processing of delta-sigma modulated sequences. The overall focus is on the development of algorithms and circuits for linear, non-linear, and mixed mode processing of delta-sigma modulated pulse streams. The material presented here is directly relevant to applications in digital communication, DSP, instrumentation, and control.
Dynamic Sliding Mode Control Design Based on an Integral Manifold for Nonlinear Uncertain Systems
Qudrat Khan; Aamer Iqbal Bhatti; Antonella Ferrara
2014-01-01
An output feedback sliding mode control law design relying on an integral manifold is proposed in this work. The considered class of nonlinear systems is assumed to be affected by both matched and unmatched uncertainties. The use of the integral sliding manifold allows one to subdivide the control design procedure into two steps. First a linear control component is designed by pole placement and then a discontinuous control component is added so as to cope with the uncertainty presence. In c...
Preservation of stability and synchronization in nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
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: guillermo.fernandez@uia.mx; 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: job.flores@uia.mx; 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: rfemat@ipicyt.edu.mx; 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: jjar@xanum.uam.mx
2007-11-12
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.
Stabilization and Stochastic Control of a Class of Nonlinear Systems.
1980-10-01
0 is infinite. Thus it is not sufficient that our composite control be only a stabilizing control . To qualify as a candidate for near-optimality uc...completes the proof. 8. Near Optimality The question can now be posed whether uc, being a stabilizing control which produces a bounded cost, is also...procedure when jjc is a small but unknown parameter. For u to be a meaningful feedback control of the system (2.1), it c must first of all be a stabilizing
Han, Yaozhen; Liu, Xiangjie
2016-05-01
This paper presents a continuous higher-order sliding mode (HOSM) control scheme with time-varying gain for a class of uncertain nonlinear systems. The proposed controller is derived from the concept of geometric homogeneity and super-twisting algorithm, and includes two parts, the first part of which achieves smooth finite time stabilization of pure integrator chains. The second part conquers the twice differentiable uncertainty and realizes system robustness by employing super-twisting algorithm. Particularly, time-varying switching control gain is constructed to reduce the switching control action magnitude to the minimum possible value while keeping the property of finite time convergence. Examples concerning the perturbed triple integrator chains and excitation control for single-machine infinite bus power system are simulated respectively to demonstrate the effectiveness and applicability of the proposed approach.
Directory of Open Access Journals (Sweden)
Guo Haigang
2012-01-01
Full Text Available Combining adaptive fuzzy sliding mode control with fuzzy or variable universe fuzzy switching technique, this study develops two novel direct adaptive schemes for a class of MIMO nonlinear systems with uncertainties and external disturbances. The proposed control schemes consist of fuzzy equivalent control terms, fuzzy switching control terms (in scheme one or variable universe fuzzy switching control terms (in scheme two, and compensation control terms. The compensation control terms are used to relax the assumption on fuzzy approximation error. Based on Lyapunov stability theory, the parameters update laws are adaptively tuned online and the global asymptotic stability of the closed-loop system can be guaranteed. The major contribution of this study is to develop a novel framework for designing direct adaptive fuzzy sliding mode control scheme facing model uncertainties and external disturbances. The derived schemes can effectively solve the chattering problem and the equivalent control calculation in that environment. Simulation results performed on a two-link robotic manipulator demonstrate the feasibility of the proposed control schemes.
Directory of Open Access Journals (Sweden)
Zhenxin He
2014-01-01
Full Text Available A continuous nonsingular fast terminal sliding mode (NFTSM control scheme with the extended state observer (ESO and the tracking differentiator (TD is proposed for second-order uncertain SISO nonlinear systems. The system’s disturbances and states can be estimated by introducing the ESO, then the disturbances are compensated effectively, and the ideal transient process of the system can be arranged based on TD to provide the target tracking signal and its high-order derivatives. The proposed controller obtains finite-time convergence property and keeps good robustness of sliding mode control (SMC for disturbances. Moreover, compared with conventional SMC, the proposed control law is continuous and no chattering phenomenon exists. The property of system stability is guaranteed by Lyapunov stability theory. The simulation results show that the proposed method can be employed to shorten the system reaching time, improve the system tracking precision, and suppress the system chattering and the input noise. The proposed control method is finally applied for the rotating control problem of theodolite servo system.
Stability Analysis of Nonlinear Vibrations of a Deploying Flexible Beam
Institute of Scientific and Technical Information of China (English)
JunfengLI; ZhaolinWANG
1996-01-01
Consider a rigid-flexible coupled system which consists of a central rigid body deploying a flexible appendage,The appendage is modeled as a finite deflection beam having linear constitutive equations.By taking the energy integral as Lyapunov function,it is proved that nonlinear transverse vibrations of the beam undergoing uniform extension or retrieval are stable when there are not controlling moment in the central rigid body and driving force on the beam,according to the partial stablity theorem.
Hou, Huazhou; Zhang, Qingling
2016-11-01
In this paper we investigate the finite-time synchronization for second-order multi-agent system via pinning exponent sliding mode control. Firstly, for the nonlinear multi-agent system, differential mean value theorem is employed to transfer the nonlinear system into linear system, then, by pinning only one node in the system with novel exponent sliding mode control, we can achieve synchronization in finite time. Secondly, considering the 3-DOF helicopter system with nonlinear dynamics and disturbances, the novel exponent sliding mode control protocol is applied to only one node to achieve the synchronization. Finally, the simulation results show the effectiveness and the advantages of the proposed method.
Nazemosadat, Elham; Mafi, Arash
2014-08-15
We propose an all-fiber mode-locking device, which operates based on nonlinear switching in a novel two-concentric-core fiber structure. The design is particularly attractive given the ease of fabrication and coupling to other components in a mode-locked fiber laser cavity. The nonlinear switching in this coupler is studied, and the relative power transmission is obtained. The analysis shows that this nonlinear switch is practical for mode-locking fiber lasers and is forgiving to fabrication errors.
Stabilization of nonlinear system using uniform eigenvalue assignment in linear model
Siahaan, Sahat P.; Pangaribuan, Timbang
2017-09-01
Some plant in control system has nonlinear dynamic, so it is not easy to do in analysis to see its behavior using eigenstructure assignment. From many observations which have been made, some literature give methods to design nonlinear control system. The modern control theory uses state-space method to explain the behaviour on stability of a plant. To improve the stability of the closed-loop system, designer commonly use the state feedback control law. For the case inverted pendulum plant with the nonlinear dynamics, its need to perform the nonlinear control law with the concepts of modern control theory to satisfy the closed-loop system characteristic, and all the behaviour of the closed-loop system only determined from the given linear pole specifications.
Stabilization of nonlinear systems with parametric uncertainty using variable structure techniques
Energy Technology Data Exchange (ETDEWEB)
Schoenwald, D.A. [Oak Ridge National Lab., TN (United States); Oezguener, Ue. [Ohio State Univ., Columbus, OH (United States). Dept. of Electrical Engineering
1995-07-01
The authors present a result on the robust stabilization of a class of nonlinear systems exhibiting parametric uncertainty. They consider feedback linearizable nonlinear systems with a vector of unknown constant parameters perturbed about a known value. A Taylor series of the system about the nominal parameter vector coupled with a feedback linearizing control law yields a linear system plus nonlinear perturbations. Via a structure matching condition, a variable structure control law is shown to exponentially stabilize the full system. The novelty of the result is that the linearizing coordinates are completely known since they are defined about the nominal parameter vector, and fewer restrictions are imposed on the nonlinear perturbations than elsewhere in the literature.
Explicit finite-difference time domain for nonlinear analysis of waveguide modes
Barakat, N. M.; Shabat, M. M.; El-Azab, S.; Jaeger, Dieter
2003-07-01
The Finite Difference Time Domain Technique is at present the most widely used tool employed in the study of light propagation in various photonic waveguide structure. In this paper we derived an explicit finite-difference time-domain (FDTD) method for solving the wave equation in a four optical waveguiding rectangular structure. We derive the stability condition to achieve the stability in nonlinear media region, we also check that the wave equation used is consistence and convergent with the approximate finite difference equation. Our method is tested against some previous problems and we find a high degree of accuracy, moreover it is easy for programming. Numerical results are illustrated for a rectangular waveguide with four layers, where one of these layers is a nonlinear medium.
Numerical {Delta}` studies of the nonlinear finite-{beta} tearing mode
Energy Technology Data Exchange (ETDEWEB)
Pletzer, A. [Ecole Polytechnique Federale, Lausanne (Switzerland). Centre de Recherche en Physique des Plasma (CRPP)
1996-09-01
Tearing modes have recently attracted attention following theoretical successes in predicting the presence of magnetic island with moderate poloidal m = 3,4 and toroidal n = 2,3 mode numbers during TFTR (Tokamak Fusion Test Reactor) supershots. Classical linear resistive mode theory predicts instability when the asymptotic matching index {Delta}` defined as the jump of logarithmic derivative of the radial magnetic perturbation across the rational surface is positive. Recently, it was suggested that tearing modes could also persist when {Delta}`<0 provided bootstrap current effects are taken into account. In all the above theories, the crucial parameter which determines the stability from both the geometry and equilibrium profiles is {Delta}`. It is shown in the present study that the {Delta}` of the (m=2, n=1) mode computed with the PEST-3 code is virtually always positive. Saturation can nevertheless be achieved provided the symmetry breaking term of a current gradient is included in the resistive layer. (author) 3 figs., 11 refs.
Davijani, Nafiseh Zare; Jahanfarnia, Gholamreza; Abharian, Amir Esmaeili
2017-01-01
One of the most important issues with respect to nuclear reactors is power control. In this study, we designed a fractional-order sliding mode controller based on a nonlinear fractional-order model of the reactor system in order to track the reference power trajectory and overcome uncertainties and external disturbances. Since not all of the variables in an operating reactor are measurable or specified in the control law, we propose a reduced-order fractional neutron point kinetic (ROFNPK) model based on measurable variables. In the design, we assume the differences between the approximated model and the real system is limited. We use the obtained model in the controller design process and use the Lyapunov method to perform a stability analysis of the closed-loop system. We simulate the proposed reduced-order fractional-order sliding mode controller (ROFOSMC) using Matlab/Simulink, and its performance is compared with that of a reduced order integer-order sliding mode controller (ROIOSMC). Our simulation results indicate an acceptable performance of the proposed approach in tracking the reference power trajectory with respect to ROIOSMC because of faster response of control effort signal and the smaller tracking error. Moreover, the results illustrate the capability of the controller in rejection of the disturbance and the noise signals and the robustness of controller against uncertainty.
Frequency Stabilization of a Single Mode Terahertz Quantum Cascade Laser to the Kilohertz Level
2009-04-27
Frequency stabilization of a single mode terahertz quantum cascade laser to the kilohertz level 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT...primarily in a single-longitudinal mode (SLM) up to a bias voltage of 3.7 V and a multi-lodgitudinal mode ( MLM ) at higher voltages. It was mounted in a
Indian Academy of Sciences (India)
P A Subha; C P Jisha; V C Kuriakose
2007-08-01
The nonlinear Schrödinger equation which governs the dynamics of two-dimensional spatial solitons in Kerr media with periodically varying diffraction and nonlinearity has been analyzed in this paper using variational approach and numerical studies. Analytical expressions for soliton parameters have been derived using variational analysis. Variational equations and partial differential equation have been simulated numerically. Analytical and numerical studies have shown that nonlinearity management and diffraction management stabilize the pulse against decay or collapse providing undisturbed propagation even for larger energies of the incident beam.
Institute of Scientific and Technical Information of China (English)
周少波; 薛明皋
2014-01-01
The paper develops exponential stability of the analytic solution and convergence in probability of the numerical method for highly nonlinear hybrid stochastic pantograph equation. The classical linear growth condition is replaced by polynomial growth conditions, under which there exists a unique global solution and the solution is almost surely exponen-tially stable. On the basis of a series of lemmas, the paper establishes a new criterion on convergence in probability of the Euler-Maruyama approximate solution. The criterion is very general so that many highly nonlinear stochastic pantograph equations can obey these conditions. A highly nonlinear example is provided to illustrate the main theory.
Mode Coupling and Nonlinear Resonances of MEMS Arch Resonators for Bandpass Filters
Hajjaj, Amal Z.
2017-01-30
We experimentally demonstrate an exploitation of the nonlinear softening, hardening, and veering phenomena (near crossing), where the frequencies of two vibration modes get close to each other, to realize a bandpass filter of sharp roll off from the passband to the stopband. The concept is demonstrated based on an electrothermally tuned and electrostatically driven MEMS arch resonator operated in air. The in-plane resonator is fabricated from a silicon-on-insulator wafer with a deliberate curvature to form an arch shape. A DC current is applied through the resonator to induce heat and modulate its stiffness, and hence its resonance frequencies. We show that the first resonance frequency increases up to twice of the initial value while the third resonance frequency decreases until getting very close to the first resonance frequency. This leads to the phenomenon of veering, where both modes get coupled and exchange energy. We demonstrate that by driving both modes nonlinearly and electrostatically near the veering regime, such that the first and third modes exhibit softening and hardening behavior, respectively, sharp roll off from the passband to the stopband is achievable. We show a flat, wide, and tunable bandwidth and center frequency by controlling the electrothermal actuation voltage.
Distributed mode filtering rod fiber amplifier delivering 292W with improved mode stability
DEFF Research Database (Denmark)
Laurila, Marko; Jørgensen, Mette Marie; Hansen, Kristian Rymann
2012-01-01
We demonstrate a high power fiber (85μm core) amplifier delivering up to 292Watts of average output power using a mode-locked 30ps source at 1032nm. Utilizing a single mode distributed mode filter bandgap rod fiber, we demonstrate 44% power improvement before the threshold-like onset of mode...
Characterization of the shape stability for nonlinear elliptic problems
Bucur, Dorin
We characterize all geometric perturbations of an open set, for which the solution of a nonlinear elliptic PDE of p-Laplacian type with Dirichlet boundary condition is stable in the L-norm. The necessary and sufficient conditions are jointly expressed by a geometric property associated to the γ-convergence. If the dimension N of the space satisfies N-1
Xiao, Jianyuan; Qin, Hong; Yu, Zhi; Xiang, Nong
2015-01-01
In this paper, the nonlinear mode conversion of extraordinary waves in nonuniform magnetized plasmas is studied using the variational symplectic particle-in-cell simulation. The accuracy of the nonlinear simulation is guaranteed by the long-term accuracy and conservativeness of the symplectic algorithm. The spectra of the electromagnetic wave, the evolution of the wave reflectivity, the energy deposition profile, and the parameter-dependent properties of radio-frequency waves during the nonlinear mode conversion are investigated. It is illustrated that nonlinear effects significantly modify the physics of the radio-frequency injection in magnetized plasmas. The evolutions of the radio-frequency wave reflectivity and the energy deposition are observed, as well as the self-interaction of the Bernstein waves and mode excitations. Even for waves with small magnitude, nonlinear effects can also become important after continuous wave injections, which are common in the realistic radio-frequency wave heating and cur...
Song, Yong-Won; Yamashita, Shinji; Goh, Chee S.; Set, Sze Y.
2007-01-01
We demonstrate a novel passive mode-locking scheme for pulsed lasers enhanced by the interaction of carbon nanotubes (CNTs) with the evanescent field of propagating light in a D-shaped optical fiber. The scheme features all-fiber operation as well as a long lateral interaction length, which guarantees a strong nonlinear effect from the nanotubes. Mode locking is achieved with less than 30% of the CNTs compared with the amount of nanotubes used for conventional schemes. Our method also ensures the preservation of the original morphology of the individual CNTs. The demonstrated pulsed laser with our CNT mode locker has a repetition rate of 5.88 MHz and a temporal pulse width of 470 fs.
Song, Yong-Won; Yamashita, Shinji; Goh, Chee S; Set, Sze Y
2007-01-15
We demonstrate a novel passive mode-locking scheme for pulsed lasers enhanced by the interaction of carbon nanotubes (CNTs) with the evanescent field of propagating light in a D-shaped optical fiber. The scheme features all-fiber operation as well as a long lateral interaction length, which guarantees a strong nonlinear effect from the nanotubes. Mode locking is achieved with less than 30% of the CNTs compared with the amount of nanotubes used for conventional schemes. Our method also ensures the preservation of the original morphology of the individual CNTs. The demonstrated pulsed laser with our CNT mode locker has a repetition rate of 5.88 MHz and a temporal pulse width of 470 fs.
Electronic control of nonlinear-polarization-rotation mode locking in Yb-doped fiber lasers.
Shen, Xuling; Li, Wenxue; Yan, Ming; Zeng, Heping
2012-08-15
We demonstrate a convenient approach to precisely tune the polarization state of a nonlinear-polarization-rotation mode-locked Yb-doped fiber laser by using an electronic polarization controller. It is shown to benefit self-starting of mode-locking states, with precise tuning of the spectral profile, pulse width, and carrier-envelope offset frequency. The pulse width changed linearly by 0.78 ps in the time domain, and the carrier-envelope offset frequency shifted ~77.5 MHz in the frequency domain with a slight change of the driving voltage of 30.7 mV applied on the controller, corresponding to a polarization rotation of 0.0135π. This facilitated precise and automatic regeneration of a particular mode-locking state by setting an accurate voltage at the polarization controller with a programmed microprocessor control unit.
Stability of Gain Scheduling Control for Aircraft with Highly Nonlinear Behavior
Directory of Open Access Journals (Sweden)
Fany Mendez-Vergara
2014-01-01
Full Text Available The main goal of this work is to study the stability properties of an aircraft with nonlinear behavior, controlled using a gain scheduled approach. An output feedback is proposed which is able to guarantee asymptotical stability of the task-coordinates origin and safety of the operation in the entire flight envelope. The results are derived using theory of hybrid and singular perturbed systems. It is demonstrated that both body velocity and orientation asymptotic tracking can be obtained in spite of nonlinearities and uncertainty. The results are illustrated using numerical simulations in F16 jet.
Stability analysis of a general family of nonlinear positive discrete time-delay systems
Nam, P. T.; Phat, V. N.; Pathirana, P. N.; Trinh, H.
2016-07-01
In this paper, we propose a new approach to analyse the stability of a general family of nonlinear positive discrete time-delay systems. First, we introduce a new class of nonlinear positive discrete time-delay systems, which generalises some existing discrete time-delay systems. Second, through a new technique that relies on the comparison and mathematical induction method, we establish explicit criteria for stability and instability of the systems. Three numerical examples are given to illustrate the feasibility of the obtained results.
On Robust Stability of a Class of Uncertain Nonlinear Systems with Time-Varying Delay
Institute of Scientific and Technical Information of China (English)
NIAN Xiao-hong
2002-01-01
The problem of robust stability of a class of uncertain nonlinear dynamical systems with time-delay is considered. Based on the assumption that the nominal system is stable, some sufficient conditions onrobust stability of uncertain nonlinear dynamical systems with time-delay are derived. Some analytical methods and a type of Lyapunov functional are used to investigate such sufficient conditions. The results obtained in this paper are applicable to perturbed time-delay systems with unbounded time-varying delay.Some previous results are improved and a numerical example is given to demonstrate the validity of our results.
Nonlinear model predictive control with guaraneed stability based on pesudolinear neural networks
Institute of Scientific and Technical Information of China (English)
WANG Yongji; WANG Hong
2004-01-01
A nonlinear model predictive control problem based on pseudo-linear neural network (PNN) is discussed, in which the second order on-line optimization method is adopted. The recursive computation of Jacobian matrix is investigated. The stability of the closed loop model predictive control system is analyzed based on Lyapunov theory to obtain the sufficient condition for the asymptotical stability of the neural predictive control system. A simulation was carried out for an exothermic first-order reaction in a continuous stirred tank reactor. It is demonstrated that the proposed control strategy is applicable to some of nonlinear systems.
STABILITY AND BIFURCATION BEHAVIORS ANALYSIS IN A NONLINEAR HARMFUL ALGAL DYNAMICAL MODEL
Institute of Scientific and Technical Information of China (English)
WANG Hong-li; FENG Jian-feng; SHEN Fei; SUN Jing
2005-01-01
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.
Finite-time stabilization for a class of stochastic nonlinear systems via output feedback.
Zha, Wenting; Zhai, Junyong; Fei, Shumin; Wang, Yunji
2014-05-01
This paper investigates the problem of global finite-time stabilization in probability for a class of stochastic nonlinear systems. The drift and diffusion terms satisfy lower-triangular or upper-triangular homogeneous growth conditions. By adding one power integrator technique, an output feedback controller is first designed for the nominal system without perturbing nonlinearities. Based on homogeneous domination approach and stochastic finite-time stability theorem, it is proved that the solution of the closed-loop system will converge to the origin in finite time and stay at the origin thereafter with probability one. Two simulation examples are presented to illustrate the effectiveness of the proposed design procedure.
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The nonlinear dynamical behaviors of artificial neural network (ANN) and their application to science and engineering were summarized. The mechanism of two kinds of dynamical processes, i.e. weight dynamics and activation dynamics in neural networks, and the stability of computing in structural analysis and design were stated briefly. It was successfully applied to nonlinear neural network to evaluate the stability of underground stope structure in a gold mine. With the application of BP network, it is proven that the neuro-computing is a practical and advanced tool for solving large-scale underground rock engineering problems.
Practical stabilization of a class of uncertain time-varying nonlinear delay systems
Institute of Scientific and Technical Information of China (English)
Bassem Ben HAMED; Mohamed Ali HAMMAMI
2009-01-01
In this paper we deal with a class of uncertain time-varying nonlinear systems with a state delay. Under some assumptions, we construct some stabilizing continuous feedback, i.e. linear and nonlinear in the state, which can guarantee global uniform exponential stability and global uniform practical convergence of the considered system. The quadratic Lyapunov function for the nominal stable system is used as a Lyapunov candidate function for the global system. The results developed in this note are applicable to a class of dynamical systems with uncertain time-delay. Our result is illustrated by a numerical example.
ROBUST STABILITY WITH GUARANTEEING COST FOR DISCRETE TIME-DELAY SYSTEMS WITH NONLINEAR PERTURBATION
Institute of Scientific and Technical Information of China (English)
JIA Xinchun; ZHENG Nanning; LIU Yuehu
2005-01-01
The problems of robust stability and robust stability with a guaranteeing cost for discrete time-delay systems with nonlinear perturbation are discussed. A sufficient criterion for robust stability is established in an LMI framework and a linear convex optimization problem with LMI constraints for computing maximal perturbation bound is proposed. Meanwhile, a sufficient criterion for robust stability with a guaranteeing cost for such systems is obtained, and an optimal procedure for decreasing the value of guaranteeing cost is put forward. Two examples are used to illustrate the efficiency of the results.
Nonlinear Image Restoration in Confocal Microscopy : Stability under Noise
Roerdink, J.B.T.M.
1995-01-01
In this paper we study the noise stability of iterative algorithms developed for attenuation correction in Fluorescence Confocal Microscopy using FT methods. In each iteration the convolution of the previous estimate is computed. It turns out that the estimators are robust to noise perturbation.
Nonlinear Image Restoration in Confocal Microscopy : Stability under Noise
Roerdink, J.B.T.M.
1995-01-01
In this paper we study the noise stability of iterative algorithms developed for attenuation correction in Fluorescence Confocal Microscopy using FT methods. In each iteration the convolution of the previous estimate is computed. It turns out that the estimators are robust to noise perturbation.
Non-Linear Stability of an Electrified Plane Interface in Porous Media
El-Dib, Yusry O.; Moatimid, Galal M.
2004-03-01
The non-linear electrohydrodynamic stability of capillary-gravity waves on the interface between two semi-infinite dielectric fluids is investigated. The system is stressed by a vertical electric field in the presence of surface charges. The work examines a few representative porous media configurations. The analysis includes Rayleigh-Taylor and Kelvin-Helmholtz instabilities. The boundary - value problem leads to a non-linear equation governing the surface evolution. Taylor theory is adopted to expand this equation, in the light of multiple scales, in order to obtain a non-linear Schr¨odinger equation describing the behavior of the perturbed interface. The latter equation, representing the amplitude of the quasi-monochromatic traveling wave, is used to describe the stability criteria. These criteria are discussed both analytically and numerically. In order to identifiy regions of stability and instability, the electric field intensity is plotted versus the wave number. Through a linear stability approach it is found that Darcy's coefficients have a destabilizing influence, while in the non-linear scope these coefficients as well as the electric field intensity play a dual role on the stability.
Institute of Scientific and Technical Information of China (English)
Liu Yang; Tang Yi
2008-01-01
By means of the Glauber's coherent state method combined with multiple-scale method,this paper investigates the localized modes in a quantum one-dimensional Klein-Gordon chain and finds that the equation of motion of annihilation operator is reduced to the nonlinear Schr(o)dinger equation.Interestingly,the model can support both bright and dark small amplitude travelling and non-travelling nonlinear localized modes in different parameter spaces.
Non-linear Dynamics in ETG Mode Saturation and Beam-Plasma Instabilities
Tokluoglu, Erinc K.
Non-linear mechanisms arise frequently in plasmas and beam-plasma systems resulting in dynamics not predicted by linear theory. The non-linear mechanisms can influence the time evolution of plasma instabilities and can be used to describe their saturation. Furthermore time and space averaged non-linear fields generated by instabilities can lead to collisionless transport and plasma heating. In the case of beam-plasma systems counter-intuitive beam defocusing and scaling behavior which are interesting areas of study for both Low-Temperature and High Energy Density physics. The non-linear mode interactions in form of phase coupling can describe energy transfer to other modes and can be used to describe the saturation of plasma instabilities. In the first part of this thesis, a theoretical model was formulated to explain the saturation mechanism of Slab Electron Temperature Gradient (ETG) mode observed in the Columbia Linear Machine (CLM), based on experimental time-series data collected through probe diagnostics [1]. ETG modes are considered to be a major player in the unexplained high levels of electron transport observed in tokamak fusion experiments and the saturation mechanism of these modes is still an active area of investigation. The data in the frequency space indicated phase coupling between 3 modes, through a higher order spectral correlation coefficient known as bicoherence. The resulting model is similar to [2], which was a treatment for ITG modes observed in the CLM and correctly predicts the observed saturation level of the ETG turbulence. The scenario is further supported by the fact that the observed mode frequencies are in close alignment with those predicted theoretical dispersion relations. Non-linear effects arise frequently in beam-plasma systems and can be important for both low temperature plasma devices commonly used for material processing as well as High Energy Density applications relevant to inertial fusion. The non-linear time averaged
Brown, Gerald V.; Kascak, Albert F.; Jansen, Ralph H.; Dever, Timothy P.; Duffy, Kirsten P.
2006-01-01
For magnetic-bearing-supported high-speed rotating machines with significant gyroscopic effects, it is necessary to stabilize forward and backward tilt whirling modes. Instability or low damping of these modes can prevent the attainment of desired shaft speed. We show analytically that both modes can be stabilized by using cross-axis proportional gains and high- and low-pass filters in the magnetic bearing controller. Furthermore, at high shaft speeds, where system phase lags degrade the stability of the forward-whirl mode, a phasor advance of the control signal can partially counteract the phase lag. In some range of high shaft speed, the derivative gain for the tilt modes (essential for stability for slowly rotating shafts) can be removed entirely. We show analytically how the tilt eigenvalues depend on shaft speed and on various controller feedback parameters.
Xu, Zhouxiang; Huang, Kaikai; Jiang, Yunfeng; Lu, Xuanhui
2011-12-01
We have realized a long-term frequency stabilization system for external cavity diode laser (ECDL) based on mode boundary detection method. In this system, the saturated absorption spectroscopy was used. The current and the grating of the ECDL were controlled by a computer-based feedback control system. By checking if there are mode boundaries in the spectrum, the control system determined how to adjust current to avoid mode hopping. This procedure was executed periodically to ensure the long-term stabilization of ECDL in the absence of mode hops. This diode laser system with non-antireflection coating had operated in the condition of long-term mode-hop-free stabilization for almost 400 h, which is a significant improvement of ECDL frequency stabilization system.
Modulating toroidal flow stabilization of edge localized modes with plasma density
Cheng, Shikui; Banerjee, Debabrata
2016-01-01
Recent EAST experiments have demonstrated mitigation and suppression of edge localized modes (ELMs) with toroidal rotation flow in higher collisionality regime, suggesting potential roles of plasma density. In this work, the effects of plasma density on the toroidal flow stabilization of the high-$n$ edge localized modes have been extensively studied in linear calculations for a circular-shaped limiter H-mode tokamak, using the extended MHD code NIMROD. In the single MHD model, toroidal flow has a weak stabilizing effects on the high-$n$ modes. Such a stabilization, however, can be significantly enhanced with the increase in plasma density. Furthermore, our calculations show that the enhanced stabilization of high-$n$ modes from toroidal flow with higher edge plasma density persists in the 2-fluid MHD model. These findings may explain the ELM mitigation and suppression by toroidal rotation in higher collisionality regime due to the enhancement of plasma density obtained in recent EAST experiments.
STABILITY, BIFURCATIONS AND CHAOS IN UNEMPLOYMENT NON-LINEAR DYNAMICS
Directory of Open Access Journals (Sweden)
Pagliari Carmen
2013-07-01
Full Text Available The traditional analysis of unemployment in relation to real output dynamics is based on some empirical evidences deducted from Okun’s studies. In particular the so called Okun’s Law is expressed in a linear mathematical formulation, which cannot explain the fluctuation of the variables involved. Linearity is an heavy limit for macroeconomic analysis and especially for every economic growth study which would consider the unemployment rate among the endogenous variables. This paper deals with an introductive study about the role of non-linearity in the investigation of unemployment dynamics. The main idea is the existence of a non-linear relation between the unemployment rate and the gap of GDP growth rate from its trend. The macroeconomic motivation of this idea moves from the consideration of two concatenate effects caused by a variation of the unemployment rate on the real output growth rate. These two effects are concatenate because there is a first effect that generates a secondary one on the same variable. When the unemployment rate changes, the first effect is the variation in the level of production in consequence of the variation in the level of such an important factor as labour force; the secondary effect is a consecutive variation in the level of production caused by the variation in the aggregate demand in consequence of the change of the individual disposal income originated by the previous variation of production itself. In this paper the analysis of unemployment dynamics is carried out by the use of the logistic map and the conditions for the existence of bifurcations (cycles are determined. The study also allows to find the range of variability of some characteristic parameters that might be avoided for not having an absolute unpredictability of unemployment dynamics (deterministic chaos: unpredictability is equivalent to uncontrollability because of the total absence of information about the future value of the variable to
Global asymptotic stability of a class of nonlinear systems with parametric uncertainty
Institute of Scientific and Technical Information of China (English)
Cai Xiushan; Lǜ Ganyun; Zhang Changfiang; He Xiuhui
2009-01-01
Stability of a class of nonlinear systems with parametric uncertainty is dealt with. This kind of systems can be viewed as feedback interconnection systems. By constructing the Lyapunov function for one of the feedback interconnection systems, the Lyapunov function for this kind of systems is obtained. Sufficient conditions of global asymptotic stability for this class of systems axe deduced. The simulation shows the effectiveness of the method.
A NEW APPROACH TO THE NONLINEAR STABILITY OF PARALLEL SHEAR FLOWS
Institute of Scientific and Technical Information of China (English)
XU Lan-xi; HUANG Yong-nian
2005-01-01
Lyapunov's second method was used to study the nonlinear stability of parallel shear flows for stress-free boundaries. By introducing an energy functional, it was shown that the plane Couette and plane Poiseuille flows are conditionally and asymptotically stable for all Reynolds numbers. In particular, to two-dimensional perturbations, by defining new energy functionals the unconditional stability of the basic flows was proved.
Adaptive Stabilization for a Class of Dynamical Systems with Nonlinear Delayed State Perturbations
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
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.
Inductive intrinsic localized modes in a one-dimensional nonlinear electric transmission line
Sato, M.; Mukaide, T.; Nakaguchi, T.; Sievers, A. J.
2016-07-01
The experimental properties of intrinsic localized modes (ILMs) have long been compared with theoretical dynamical lattice models that make use of nonlinear onsite and/or nearest-neighbor intersite potentials. Here it is shown for a one-dimensional lumped electrical transmission line that a nonlinear inductive component in an otherwise linear parallel capacitor lattice makes possible a new kind of ILM outside the plane wave spectrum. To simplify the analysis, the nonlinear inductive current equations are transformed to flux transmission line equations with analog onsite hard potential nonlinearities. Approximate analytic results compare favorably with those obtained from a driven damped lattice model and with eigenvalue simulations. For this mono-element lattice, ILMs above the top of the plane wave spectrum are the result. We find that the current ILM is spatially compressed relative to the corresponding flux ILM. Finally, this study makes the connection between the dynamics of mass and force constant defects in the harmonic lattice and ILMs in a strongly anharmonic lattice.
Frequency-domain L2-stability conditions for time-varying linear and nonlinear MIMO systems
Institute of Scientific and Technical Information of China (English)
Zhihong HUANG; Y. V. VENKATESH; Cheng XIANG; Tong Heng LEE
2014-01-01
The paper deals with the L2-stability analysis of multi-input-multi-output (MIMO) systems, governed by integral equations, with a matrix of periodic/aperiodic time-varying gains and a vector of monotone, non-monotone and quasi-monotone nonlin-earities. For nonlinear MIMO systems that are described by differential equations, most of the literature on stability is based on an application of quadratic forms as Lyapunov-function candidates. In contrast, a non-Lyapunov framework is employed here to derive new and more general L2-stability conditions in the frequency domain. These conditions have the following features:i) They are expressed in terms of the positive definiteness of the real part of matrices involving the transfer function of the linear time-invariant block and a matrix multiplier function that incorporates the minimax properties of the time-varying linear/nonlinear block. ii) For certain cases of the periodic time-varying gain, they contain, depending on the multiplier function chosen, no restrictions on the normalized rate of variation of the time-varying gain, but, for other periodic/aperiodic time-varying gains, they do. Overall, even when specialized to periodic-coefficient linear and nonlinear MIMO systems, the stability conditions are distinct from and less restrictive than recent results in the literature. No comparable results exist in the literature for aperiodic time-varying gains. Furthermore, some new stability results concerning the dwell-time problem and time-varying gain switching in linear and nonlinear MIMO systems with periodic/aperiodic matrix gains are also presented. Examples are given to illustrate a few of the stability theorems.
Effects of nonlinear strength parameters on stability of 3D soil slopes
Institute of Scientific and Technical Information of China (English)
高玉峰; 吴迪; 张飞; 秦红玉; 朱德胜
2016-01-01
Actual slope stability problems have three-dimensional (3D) characteristics and the soils of slopes have curved failure envelopes. This incorporates a power-law nonlinear failure criterion into the kinematic approach of limit analysis to conduct the evaluation of the stability of 3D slopes. A tangential technique is adopted to simplify the nonlinear failure criterion in the form of equivalent Mohr-Coulomb strength parameters. A class of 3D admissible rotational failure mechanisms is selected for soil slopes including three types of failure mechanisms: face failure, base failure, and toe failure. The upper-bound solutions and corresponding critical slip surfaces can be obtained by an efficient optimization method. The results indicate that the nonlinear parameters have significant influences on the assessment of slope stability, especially on the type of failure mechanism. The effects of nonlinear parameters appear to be pronounced for gentle slopes constrained to a narrow width. Compared with the solutions derived from plane-strain analysis, the 3D solutions are more sensitive to the values of nonlinear parameters.
Directory of Open Access Journals (Sweden)
Taochang Li
2014-01-01
Full Text Available Automatic steering control is the key factor and essential condition in the realization of the automatic navigation control of agricultural vehicles. In order to get satisfactory steering control performance, an adaptive sliding mode control method based on a nonlinear integral sliding surface is proposed in this paper for agricultural vehicle steering control. First, the vehicle steering system is modeled as a second-order mathematic model; the system uncertainties and unmodeled dynamics as well as the external disturbances are regarded as the equivalent disturbances satisfying a certain boundary. Second, a transient process of the desired system response is constructed in each navigation control period. Based on the transient process, a nonlinear integral sliding surface is designed. Then the corresponding sliding mode control law is proposed to guarantee the fast response characteristics with no overshoot in the closed-loop steering control system. Meanwhile, the switching gain of sliding mode control is adaptively adjusted to alleviate the control input chattering by using the fuzzy control method. Finally, the effectiveness and the superiority of the proposed method are verified by a series of simulation and actual steering control experiments.
Multi-input sliding mode control of nonlinear uncertain affine systems
Bartolini, Giorgio; Punta, Elisabetta; Zolezzi, Tullio
2011-05-01
In the extension to multi-input nonlinear uncertain systems of the sliding mode methodology, a crucial role is played by the matrix pre-multiplying the control in the dynamic equation of the sliding output. If this matrix is perfectly known and invertible, it is possible to transform a multi-input sliding mode control problem in an almost decoupled set of single-input problems. If this matrix is uncertain then nothing can be done in general, and the investigation is oriented to find conditions ensuring the feasibility of control strategies in a progressively more general set of uncertain matrices. In the case of uncertain and constant matrices, it is possible, in principle, to manage the case in which the matrix in question is invertible. The corresponding adaptive or switching strategy suffers from the curse of dimensionality of the so-called unmixing set. In this article the case of time- and state-varying uncertain matrix is dealt with. A more general class of such a matrices for which there is, at least locally, a solution of the problem is found. The introduction of artificial integrators in the output channel (the integral sliding mode control methodology) allows the practical implementation of the control law without requiring the a priori knowledge of parameters featured by the solution of a relevant nonlinear Lyapunov equation.
Directory of Open Access Journals (Sweden)
Changchuan Xie
2016-01-01
Full Text Available VFAs (very flexible aircraft have begun to attract significant attention because of their good flight performances and significant application potentials; however, they also bring some challenges to researchers due to their unusual lightweight designs and large elastic deformations. A framework for the geometrically nonlinear aeroelastic stability analysis of very flexible wings is constructed in this paper to illustrate the unique aeroelastic characteristics and convenient use of these designs in engineering analysis. The nonlinear aeroelastic analysis model includes the geometrically nonlinear structure finite elements and steady and unsteady nonplanar aerodynamic computations (i.e., the nonplanar vortex lattice method and nonplanar doublet-lattice method. Fully nonlinear methods are used to analyse static aeroelastic features, and linearized structural dynamic equations are established at the structural nonlinear equilibrium state to estimate the stability of the system through the quasimode of the stressed and deformed structure. The exact flutter boundary is searched via an iterative procedure. A wind tunnel test is conducted to validate this theoretical analysis framework, and reasonable agreement is obtained. Both the analysis and test results indicate that the geometric nonlinearity of very flexible wings presents significantly different aeroelastic characteristics under different load cases with large deformations.
Nonlinear stability of cylindrical shells subjected to axial flow: Theory and experiments
Karagiozis, K. N.; Païdoussis, M. P.; Amabili, M.; Misra, A. K.
2008-01-01
This paper, is concerned with the nonlinear dynamics and stability of thin circular cylindrical shells clamped at both ends and subjected to axial fluid flow. In particular, it describes the development of a nonlinear theoretical model and presents theoretical results displaying the nonlinear behaviour of the clamped shell subjected to flowing fluid. The theoretical model employs the Donnell nonlinear shallow shell equations to describe the geometrically nonlinear structure. The clamped beam eigenfunctions are used to describe the axial variations of the shell deformation, automatically satisfying the boundary conditions and the circumferential continuity condition exactly. The fluid is assumed to be incompressible and inviscid, and the fluid-structure interaction is described by linear potential flow theory. The partial differential equation of motion is discretized using the Galerkin method and the final set of ordinary differential equations are integrated numerically using a pseudo-arclength continuation and collocation techniques and the Gear backward differentiation formula. A theoretical model for shells with simply supported ends is presented as well. Experiments are also described for (i) elastomer shells subjected to annular (external) air-flow and (ii) aluminium and plastic shells with internal water flow. The experimental results along with the theoretical ones indicate loss of stability by divergence with a subcritical nonlinear behaviour. Finally, theory and experiments are compared, showing good qualitative and reasonable quantitative agreement.
Microwave emission by nonlinear crystals irradiated with a high-intensity, mode-locked laser
Borghesani, A F; Guarise, M
2016-01-01
We report on the experimental investigation of the efficiency of some nonlinear crystals to generate microwave (RF) radiation as a result of optical rectification (OR) when irradiated with intense pulse trains delivered by a mode-locked laser at $1064\\,$nm. We have investigated lithium triborate (LBO), lithium niobate (LiNbO$_3$), zinc selenide (ZnSe), and also potassium titanyl orthophosphate (KTP) for comparison with previous measurements. The results are in good agreement with the theoretical predictions based on the form of the second-order nonlinear susceptibility tensor. For some crystals we investigated also the second harmonic generation (SHG) to cross check the theoretical model. We confirm the theoretical prediction that OR leads to the production of higher order RF harmonics that are overtones of the laser repetition rate.
On Nonlinear Self-interaction of Geodesic Acoustic Mode Driven By Energetic Particles
Energy Technology Data Exchange (ETDEWEB)
G.Y. Fu
2010-10-01
It is shown that nonlinear self-interaction of energetic particle-driven Geodesic Acoustic Mode does not generate a second harmonic in radial electric field using the fluid model. However, kinetic effects of energetic particles can induce a second harmonic in the radial electric field. A formula for the second order plasma density perturbation is derived. It is shown that a second harmonic of plasma density perturbation is generated by the convective nonlinearity of both thermal plasma and energetic particles. Near the midplane of a tokamak, the second order plasma density perturbation (the sum of second harmonic and zero frequency sideband) is negative on the low field side with its size comparable to the main harmonic at low fluctuation level. These analytic predictions are consistent with the recent experimental observation in DIII-D.
On Nonlinear Self-interaction of Geodesic Acoustic Mode Driven by Energetic Particles
Energy Technology Data Exchange (ETDEWEB)
G. Y. Fu
2010-06-04
It is shown that nonlinear self-interaction of energetic particle-driven Geodesic Acoustic Mode does not generate a second harmonic in radial electric field using the fluid model. However, kinetic effects of energetic particles can induce a second harmonic in the radial electric field. A formula for the second order plasma density perturbation is derived. It is shown that a second harmonic of plasma density perturbation is generated by the convective nonlinearity of both thermal plasma and energetic particles. Near the midplane of a tokamak, the second order plasma density perturbation (the sum of second harmonic and zero frequency sideband) is negative on the low field side with its size comparable to the main harmonic at low uctuation level. These analytic predictions are consistent with the recent experimental observation in DIII-D.
Villanueva, Guillermo E; Jakubinek, Michael B; Simard, Benoit; Oton, Claudio J; Matres, Joaquín; Shao, Li-Yang; Pérez-Millán, Pere; Albert, Jacques
2011-06-01
Single-wall carbon nanotube deposition on the cladding of optical fibers has been carried out to fabricate an all-fiber nonlinear device. Two different nanotube deposition techniques were studied. The first consisted of repeatedly immersing the optical fiber into a nanotube supension, increasing the thickness of the coating in each step. The second deposition involved wrapping a thin film of nanotubes around the optical fiber. For both cases, interaction of transmitted light through the fiber core with the external coating was assisted by the cladding mode resonances of a tilted fiber Bragg grating. Ultrafast nonlinear effects of the nanotube-coated fiber were measured by means of a pump-probe pulses experiment. © 2011 Optical Society of America
Influence of toroidal effects on the stability of the internal kink mode
Energy Technology Data Exchange (ETDEWEB)
Galvao, R.M.O.; Sakanaka, P.H.; Shigueoka, H.
1978-09-25
Using the sigma-stability technique, we study the stability of the internal kink mode in toroidal geometry. We show that there are two unstable regions separated by a stable on in a ..beta..-q/sub c/ stability diagram. In one of these regions toroidal effects are stabilizing and in the other they are destabilizing. Discrepant results of previous analytical theories and experimental results are explained.
Sliding mode H∞ control for a class of uncertain nonlinear state-delayed systems
Institute of Scientific and Technical Information of China (English)
Wu Ligang; Wang Changhong; Gao Huijun; Zhang Lixian
2006-01-01
A new proportional-integral (PI) sliding surface is designed for a class of uncertain nonlinear state-delayed systems. Based on this, an adaptive sliding mode controller (ASMC) is synthesized, which guarantees the occurrence of sliding mode even when the system is undergoing parameter uncertainties and external disturbance. The resulting sliding mode has the same order as the original system, so that it becomes easy to solve the H∞ control problem by designing a memoryless H∞ state feedback controller. A delay-dependent sufficient condition is proposed in terms of linear matrix inequalities (LMIs), which guarantees the sliding mode robust asymptotically stable and has a noise attenuation level γ in an H∞ sense. The admissible state feedback controller can be found by solving a sequential minimization problem subject to LMI constraints by applying the cone complementary linearization method. This design scheme combines the strong robustness of the sliding mode control with the H∞ norm performance. A numerical example is given to illustrate the effectiveness of the proposed scheme.
Spin Evolution of Accreting Neutron Stars: Nonlinear Development of the R-mode Instability
Bondarescu, Ruxandra; Wasserman, Ira
2007-01-01
The nonlinear saturation of the r-mode instability and its effects on the spin evolution of Low Mass X-ray Binaries (LMXBs) are modeled using the triplet of modes at the lowest parametric instability threshold. We solve numerically the coupled equations for the three mode amplitudes in conjunction with the spin and temperature evolution equations. We observe that very quickly the mode amplitudes settle into quasi-stationary states. Once these states are reached, the mode amplitudes can be found algebraically and the system of equations is reduced from eight to two equations: spin and temperature evolution. Eventually, the system may reach thermal equilibrium and either (1) undergo a cyclic evolution with a frequency change of at most 10%, (2) evolve toward a full equilibrium state in which the accretion torque balances the gravitational radiation emission, or (3) enter a thermogravitational runaway on a very long timescale of about $10^6$ years. Alternatively, a faster thermal runaway (timescale of about 100 ...
Indian Academy of Sciences (India)
P K Karmakar
2007-04-01
Application of inertia-induced acoustic excitation theory offers a new resonant excitation source channel of acoustic turbulence in the transonic domain of plasma flow. In bi-ion plasmas like colloidal plasma, two well-defined transonic points exist corresponding to the parent ion and the dust grain-associated acoustic modes. As usual, the modified ion acoustic mode (also known as dust ion-acoustic (DIA) wave) dynamics associated with parent ion inertia is excitable for both nanoscale- and micronscale-sized dust grains. It is found that the so-called (ion) acoustic mode (also known as dust-acoustic (DA) wave) associated with nanoscale dust grain inertia is indeed resonantly excitable through the active role of weak but finite parent ion inertia. It is interestingly conjectured that the same excitation physics, as in the case of normal plasma sound mode, operates through the active inertial role of plasma thermal species. Details of the nonlinear acoustic mode analyses of current interest in transonic domains of such impure plasmas in hydrodynamic flow are presented.
Nonlinear normal modes of a two degree of freedom oscillator with a bilateral elastic stop
Moussi, El Hadi; Cochelin, Bruno; Nistor, I
2013-01-01
A study of the non linear modes of a two degree of freedom mechanical system with bilateral elastic stop is considered. The issue related to the non-smoothness of the impact force is handled through a regularization technique. In order to obtain the Nonlinear Normal Mode (NNM), the harmonic balance method with a large number of harmonics, combined with the asymptotic numerical method, is used to solve the regularized problem. These methods are present in the software "package" MANLAB. The results are validated from periodic orbits obtained analytically in the time domain by direct integration of the non regular problem. The two NNMs starting respectively from the two linear normal modes of the associated underlying linear system are discussed. The energy-frequency plot is used to present a global vision of the behavior of the modes. The dynamics of the modes are also analyzed comparing each periodic orbits and modal lines. The first NNM shows an elaborate dynamics with the occurrence of multiple impacts per p...
Barker, Blake; Noble, Pascal; Rodrigues, L Miguel; Zumbrun, Kevin
2012-01-01
In this paper we consider the spectral and nonlinear stability of periodic traveling wave solutions of a generalized Kuramoto-Sivashinsky equation. In particular, we resolve the long-standing question of nonlinear modulational stability by demonstrating that spectrally stable waves are nonlinearly stable when subject to small localized (integrable) perturbations. Our analysis is based upon detailed estimates of the linearized solution operator, which are complicated by the fact that the (necessarily essential) spectrum of the associated linearization intersects the imaginary axis at the origin. We carry out a numerical Evans function study of the spectral problem and find bands of spectrally stable periodic traveling waves, in close agreement with previous numerical studies of Frisch-She-Thual, Bar-Nepomnyashchy, Chang-Demekhin-Kopelevich, and others carried out by other techniques. We also compare predictions of the associated Whitham modulation equations, which formally describe the dynamics of weak large s...
Directory of Open Access Journals (Sweden)
Wen-Jer Chang
2014-01-01
Full Text Available For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.
Rodríguez, Hugo; Schaft, Arjan J. van der; Ortega, Romeo
2001-01-01
Energy-shaping techniques have been successfully used for stabilization of nonlinear finite dimensional systems for 20 years now. In particular, for systems described by Port-Controlled Hamiltonian (PCH) models, the “control by interconnection” method provides a simple and elegant procedure for stab
Rodríguez, Hugo; Schaft, van der Arjan J.; Ortega, Romeo
2001-01-01
Energy-shaping techniques have been successfully used for stabilization of nonlinear finite dimensional systems for 20 years now. In particular, for systems described by Port-Controlled Hamiltonian (PCH) models, the "control by interconnection" method provides a simple and elegant procedure for stab
Explicit Conditions for Stability of Nonlinear Scalar Delay Impulsive Difference Equation
Directory of Open Access Journals (Sweden)
Bo Zheng
2010-01-01
Full Text Available Sufficient conditions are obtained for the uniform stability and global attractivity of the zero solution of nonlinear scalar delay impulsive difference equation, which extend and improve the known results in the literature. An example is also worked out to verify that the global attractivity condition is a sharp condition.
Bonito, Andrea
2013-10-03
We establish the L2-stability of an entropy viscosity technique applied to nonlinear scalar conservation equations. First-and second-order explicit time-stepping techniques using continuous finite elements in space are considered. The method is shown to be stable independently of the polynomial degree of the space approximation under the standard CFL condition. © 2013 American Mathematical Society.
DEFF Research Database (Denmark)
Fuhrmann, David R.; Bingham, Harry B.; Madsen, Per A.
2004-01-01
This paper considers a method of lines stability analysis for finite difference discretizations of a recently published Boussinesq method for the study of highly nonlinear and extremely dispersive water waves. The analysis demonstrates the near-equivalence of classical linear Fourier (von Neumann...
Minimal data rate stabilization of nonlinear systems over networks with large delays
Persis, Claudio De
2007-01-01
We consider the problem of designing encoders, decoders and controllers which stabilize feedforward nonlinear systems over a communication network with finite bandwidth and large delay. The control scheme guarantees minimal data-rate semi-global asymptotic and local exponential stabilizatioln of the
A Nonlinear Observer for Estimating Transverse Stability Parameters of Marine Surface Vessels
DEFF Research Database (Denmark)
Galeazzi, Roberto; Perez, Tristan
2011-01-01
This paper presents a nonlinear observer for estimating parameters associated with the restoring term of a roll motion model of a marine vessel in longitudinal waves. Changes in restoring, also referred to as transverse stability, can be the result of changes in the vessel’s centre of gravity due...