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Stability Theory (stability + theory)
Kinds of Stability Theory Selected AbstractsStability and identification for rational approximation of frequency response function of unbounded soilEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 2 2010Xiuli Du Abstract Exact representation of unbounded soil contains the single output,single input relationship between force and displacement in the physical or transformed space. This relationship is a global convolution integral in the time domain. Rational approximation to its frequency response function (frequency-domain convolution kernel) in the frequency domain, which is then realized into the time domain as a lumped-parameter model or recursive formula, is an effective method to obtain the temporally local representation of unbounded soil. Stability and identification for the rational approximation are studied in this paper. A necessary and sufficient stability condition is presented based on the stability theory of linear system. A parameter identification method is further developed by directly solving a nonlinear least-squares fitting problem using the hybrid genetic-simplex optimization algorithm, in which the proposed stability condition as constraint is enforced by the penalty function method. The stability is thus guaranteed a priori. The infrequent and undesirable resonance phenomenon in stable system is also discussed. The proposed stability condition and identification method are verified by several dynamic soil,structure-interaction examples. Copyright © 2009 John Wiley & Sons, Ltd. [source] Energy functions analysis in voltage collapseEUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 4 2001F. Jurado Time-domain approach examines the behaviour of the system, one determines whether stability has been maintained or lost. In contrast to the time-domain approach, direct methods determine system stability based on energy functions. The basis of direct methods for the stability assessment of a system is knowledge of the stability region. During the last decade, many researches have thoroughly analysed the use of energy functions for the direct stability assessment of networks. Energy function analysis offers a different geometric view of voltage collapse. The Transient Energy Function, a technique based on Lyapunov stability theory and originally developed for direct stability analysis of power systems, has been successfully used as a voltage stability index for collapse studies. In this paper the simulation results are on the IEEE 173-bus test system. [source] Linear stability analysis of flow in a periodically grooved channelINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2003T. Adachi1 Abstract We have conducted the linear stability analysis of flow in a channel with periodically grooved parts by using the spectral element method. The channel is composed of parallel plates with rectangular grooves on one side in a streamwise direction. The flow field is assumed to be two-dimensional and fully developed. At a relatively small Reynolds number, the flow is in a steady-state, whereas a self-sustained oscillatory flow occurs at a critical Reynolds number as a result of Hopf bifurcation due to an oscillatory instability mode. In order to evaluate the critical Reynolds number, the linear stability theory is applied to the complex laminar flow in the periodically grooved channel by constituting the generalized eigenvalue problem of matrix form using a penalty-function method. The critical Reynolds number can be determined by the sign of a linear growth rate of the eigenvalues. It is found that the bifurcation occurs due to the oscillatory instability mode which has a period two times as long as the channel period. Copyright © 2003 John Wiley & Sons, Ltd. [source] Robust speed estimation and control of an induction motor drive based on artificial neural networksINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 5 2008Oscar Barambones Abstract In this paper, a speed estimation and control scheme of an induction motor drive based on an indirect field-oriented control is presented. On one hand, a rotor speed estimator based on an artificial neural network is proposed, and on the other hand, a control strategy based on the sliding-mode controller type is proposed. The stability analysis of the presented control scheme under parameter uncertainties and load disturbances is provided using the Lyapunov stability theory. Finally, simulated results show that the presented controller with the proposed observer provides high-performance dynamic characteristics and that this scheme is robust with respect to plant parameter variations and external load disturbances. Copyright © 2007 John Wiley & Sons, Ltd. [source] Improved exponential stability for stochastic Markovian jump systems with nonlinearity and time-varying delayINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 1 2010Yong He Abstract This paper is concerned with delay-dependent exponential stability for stochastic Markovian jump systems with nonlinearity and time-varying delay. An improved exponential stability criterion for stochastic Markovian jump systems with nonlinearity and time-varying delay is proposed without ignoring any terms by considering the relationship among the time-varying delay, its upper bound and their difference, and using both Itô's differential formula and Lyapunov stability theory. A numerical example is given to illustrate the effectiveness and the benefits of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd. [source] Output feedback control design for station keeping of AUVs under shallow water wave disturbancesINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 13 2009Shuyong Liu Abstract In this paper, we consider the problem of autonomous underwater vehicle (AUV) station keeping (SK) in shallow water area. During SK, an AUV is required to maintain position and orientation with respect to a fixed reference point at the sea floor. When AUV operates in shallow water, high-frequency disturbances due to waves will significantly affect the motion of the AUV. In order to derive wave disturbance information for control purposes, a nonlinear observer is first designed to estimate the shallow water wave velocities and AUV relative velocities by using position and attitude measurement. Using the observer estimates, a nonlinear output feedback controller is subsequently synthesized by applying observer backstepping technique. Global exponential stability (GES) of the proposed nonlinear observer,controller design is proved through Lyapunov stability theory. Simulation studies on a model based on an actual AUV were performed to verify the performance of the proposed nonlinear observer and output feedback controller. Copyright © 2008 John Wiley & Sons, Ltd. [source] Design of finite-time stabilizing controllers for nonlinear dynamical systemsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 8 2009Sergey G. Nersesov Abstract Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. Since finite-time convergence implies nonuniqueness of system solutions in reverse time, such systems possess non-Lipschitzian dynamics. Sufficient conditions for finite-time stability have been developed in the literature using Hölder continuous Lyapunov functions. In this paper, we extend the finite-time stability theory to revisit time-invariant dynamical systems and to address time-varying dynamical systems. Specifically, we develop a Lyapunov-based stability and control design framework for finite-time stability as well as finite-time tracking for time-varying nonlinear dynamical systems. Furthermore, we use the vector Lyapunov function approach to study finite-time stabilization of compact sets for large-scale dynamical systems. Copyright © 2008 John Wiley & Sons, Ltd. [source] Passivity-based control of a magnetically levitated flexible beamINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 6 2009T. Shimizu Abstract This paper solves the asymptotic stabilization problem for a magnetically levitated flexible beam using a nested-loop passivity-based controller design. Passivity analyses reveal that the system can be decomposed into two passive subsystems: a mechanical subsystem that consists of a flexible beam with both ends free and that defines a passive map from external forces to the velocity of the points on the flexible beam at which the external forces act; and an electrical subsystem that consists of a pair of electromagnets and that defines a strictly output-passive map from voltages applied across the electromagnets to magnetic fluxes. The standard method for designing passivity-based controllers leads to a nonlinear feed-forward controller for the electrical subsystem, which enables the electrical subsystem to generate given desired magnetic forces, and an output feedback compensator for the mechanical subsystem, which computes the desired forces required to regulate the position and vibration of the beam. The asymptotic stability of each controller may be proven using Lyapunov's stability theory and LaSalle's invariant set theorem. Numerical simulations confirm the asymptotic stability of the equilibrium configuration of the closed-loop system formed by the magnetically levitated flexible beam together with the proposed controllers. Copyright © 2008 John Wiley & Sons, Ltd. [source] Adaptive sensorless robust control of AC drives based on sliding mode control theoryINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 9 2007O. Barambones Abstract This paper focuses in the design of a new adaptive sensorless robust control to improve the trajectory tracking performance of induction motors. The proposed design employs the so-called vector (or field oriented) control theory for the induction motor drives, being the designed control law based on an integral sliding-mode algorithm that overcomes the system uncertainties. This sliding-mode control law incorporates an adaptive switching gain in order to avoid the need of calculating an upper limit for the system uncertainties. The proposed design also includes a new method in order to estimate the rotor speed. In this method, the rotor speed estimation error is presented as a first-order simple function based on the difference between the real stator currents and the estimated stator currents. The stability analysis of the proposed controller under parameter uncertainties and load disturbances is provided using the Lyapunov stability theory. The simulated results show, on the one hand that the proposed controller with the proposed rotor speed estimator provides high-performance dynamic characteristics, and on the other hand that this scheme is robust with respect to plant parameter variations and external load disturbances. Finally, experimental results show the performance of the proposed control scheme. Copyright © 2006 John Wiley & Sons, Ltd. [source] Intelligent control of DC motor driven mechanical systems: a robust learning control approachINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 1 2003Tae-Yong Kuc Abstract A robust learning controller is presented for DC motor driven mechanical systems with friction. The proposed controller takes advantage of both robust and learning control approaches to learn and compensate periodic and non-periodic uncertain dynamics. In the learning controller, a set of learning rules is implemented in which three types of learnings occur: one is direct learning of desired inverse dynamics input and the other two learning of unknown linear parameters and nonlinear bounding functions in the models of system dynamics and friction. The global asymptotic stability of learning control system is shown by using the Lyapunov stability theory. Experimental data demonstrate the effectiveness of developed learning approach to tracking of DC motor driven mechanical systems. Copyright © 2002 John Wiley & Sons, Ltd. [source] Robust H, control of stochastic time-delay jumping systems with nonlinear disturbancesOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 5 2006Guoliang Wei Abstract This paper deals with the problems of robust stabilization and H, control for a class of uncertain stochastic jumping systems with nonlinear disturbances and time delays. The uncertain parameters are assumed to be norm-bounded and mode dependent, and the time delays enter into the state matrix, the stochastic perturbation term, as well as the state feedback. The stochastic robust stabilization problem addressed in this paper is to design a state feedback controller with input delay such that, for all admissible uncertainties and the nonlinear disturbances, the closed-loop system is robustly, stochastically, exponentially stable in the mean square. Moreover, the purpose of the robust H, control problem is to guarantee a specified H, performance index, while still achieving the mean-square exponential stability requirement for the closed-loop system. By resorting to the Itô's differential formula and the Lyapunov stability theory, sufficient conditions are derived, respectively, for the robust stabilization and the robust H, control problems. It is shown that the addressed problems can be solved if a set of linear matrix inequalities (LMIs) are feasible. A numerical example is employed to illustrate the usefulness of the proposed LMI-based design methods. Copyright © 2006 John Wiley & Sons, Ltd. [source] Extremum-seeking control of retention for a microparticulate systemTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 5 2008Audrey Favache Abstract The operation of a paper machine relies on the close monitoring and control of several integrated units to ensure a high quality paper with the required specifications. In this paper, the retention control system in the wet-end of a paper machine is considered. The control objective is to maximize the retention of fines and fibres in the paper sheet to prevent the accumulation of micro particles in the water system. We present an adaptive extremum-seeking scheme for the optimization and control of retention in the wet-end of a paper machine. An adaptive learning technique is introduced to construct an algorithm that drives the system to the optimal retention value. Lyapunov's stability theory is used in the design of the extremum-seeking controller structure and the development of the parameter learning laws. The performance of the technique is illustrated via simulations based on a first-principles dynamic model developed previously for a micro-particulate system. Le bon fonctionnement d'une machine à papier repose sur le suivi et le contrôle étroits de plusieurs unités intégrées afin d'assurer une haute qualité de papier ayant les spécifications requises. Dans cet article, on considère le système de contrôle de rétention dans la partie humide d'une machine à papier. L'objectif du contrôle est de maximiser la rétention des fines et des fibres dans la feuille de papier afin de prévenir l'accumulation de micro-particules dans le système d'eau. On présente un schéma de recherche adaptatif des extrêmes pour l'optimisation et le contrôle de la rétention dans la partie humide d'une machine à papier. Une technique d'apprentissage adaptative est introduite pour construire un algorithme qui amène le système à une valeur de rétention optimale. La théorie de stabilité de Lyapunov est utilisée dans la conception de la structure des contrôleurs de recherche des extrêmes et l'élaboration de lois d'apprentissage des paramètres. La performance de la technique est illustrée par des simulations basées sur un modèle dynamique fondamental mis au point antérieurement pour un système de micro-particules. [source] Vector control for induction motor drives based on adaptive variable structure control algorithm ,ASIAN JOURNAL OF CONTROL, Issue 5 2010O. Barambones Abstract This paper presents a new adaptive robust control for induction motor drives. The proposed control scheme is based on the so-called field oriented control theory that allows to control the induction motor like a separately excited direct current motor drive, where the field flux (produced by the field current) and the armature flux (produced by the armature current) are decoupled. The robust control law is based on the sliding mode control theory, but unlike the traditional sliding mode control schemes, the proposed design incorporates an adaptive switching gain that avoids the need of calculating an upper limit of the system uncertainties. Moreover the proposed control law is smoothed out in order to avoid the high control activity inherent to the switching control laws. The resulting closed loop system is proven to be stable using the Lyapunov stability theory. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] Design of nonlinear terminal guidance/autopilot controller for missiles with pulse type input devices,ASIAN JOURNAL OF CONTROL, Issue 3 2010Fu-Kuang Yeh Abstract This investigation addresses a nonlinear terminal guidance/autopilot controller with pulse-type control inputs for intercepting a theater ballistic missile in the exoatmospheric region. Appropriate initial conditions on the terminal phase are assumed to apply after the end of the midcourse operation. Accordingly, the terminal controller seeks to minimize the distance between the commanded missile and the target missile to ensure a hit-to-kill interception. In particular, a 3D terminal guidance law is initially developed to eliminate the so-called "sliding velocity, " thus, constraining the relative motion between the missile and the target along the line of sight. Sliding mode control is adopted to design stable pulse-type control systems. Then, a quaternion-based attitude controller is used to orient appropriately the commanded missile, taking into account the fact that the missile is a rigid body, to realize interceptability. The stability of the overall integrated terminal guidance/autopilot system is then analyzed thoroughly, based on Lyapunov stability theory. Finally, extensive simulations are conducted to verify the validity and effectiveness of the integrated controller with the pulse type inputs developed herein. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] Robust Tracking Control For A Wheeled Mobile Manipulator With Dual Arms Using Hybrid Sliding-Mode Neural NetworkASIAN JOURNAL OF CONTROL, Issue 4 2007Ching-Chih Tsai ABSTRACT In this paper, a robust tracking controller is proposed for the trajectory tracking problem of a dual-arm wheeled mobile manipulator subject to some modeling uncertainties and external disturbances. Based on backstepping techniques, the design procedure is divided into two levels. In the kinematic level, the auxiliary velocity commands for each subsystem are first presented. A sliding-mode equivalent controller, composed of neural network control, robust scheme and proportional control, is constructed in the dynamic level to deal with the dynamic effect. To deal with inadequate modeling and parameter uncertainties, the neural network controller is used to mimic the sliding-mode equivalent control law; the robust controller is designed to compensate for the approximation error and to incorporate the system dynamics into the sliding manifold. The proportional controller is added to improve the system's transient performance, which may be degraded by the neural network's random initialization. All the parameter adjustment rules for the proposed controller are derived from the Lyapunov stability theory and e-modification such that uniform ultimate boundedness (UUB) can be assured. A comparative simulation study with different controllers is included to illustrate the effectiveness of the proposed method. [source] Simple Recurrent Neural Network-Based Adaptive Predictive Control for Nonlinear SystemsASIAN JOURNAL OF CONTROL, Issue 2 2002Xiang Li ABSTRACT Making use of the neural network universal approximation ability, a nonlinear predictive control scheme is studied in this paper. On the basis of a uniform structure of simple recurrent neural networks, a one-step neural predictive controller (OSNPC) is designed. The whole closed-loop system's asymptotic stability and passivity are discussed, and stable conditions for the learning rate are determined based on the Lyapunov stability theory for the whole neural system. The effectiveness of OSNPC is verified via exhaustive simulations. [source] | ||||||||||