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Lyapunov Function (lyapunov + function)
Kinds of Lyapunov Function Terms modified by Lyapunov Function Selected AbstractsConstruction of Lyapunov function for power system based on solving linear matrix inequalityELECTRICAL ENGINEERING IN JAPAN, Issue 4 2007Atsushi Ishigame Abstract This paper presents construction of Lyapunov functions for power systems based on solving the Linear Matrix Inequality (LMI) derived from the Lyapunov stability theorem considering the dynamics of load characteristic and AVR control system. The proposed Lyapunov function is constructed as a quadratic form of state variables and an integral term which satisfies the curl equation and the sector condition. An induction machine and a synchronous machine are considered as load characteristics. One-machine one-load infinite bus system is considered taking into account the flux decay effects and AVR with one time constant of the generator. To verify the proposed Lyapunov function, the transient stability assessment is shown. The critical clearing times given by the proposed Lyapunov function are compared with those obtained by the numerical integration method, and they are shown to be practical. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 158(4): 42, 50, 2007; Published online in Wiley InterScience (www.interscience. wiley.com). DOI 10.1002/eej.20328 [source] Experiments on stabilizing receding horizon control of a direct drive manipulatorELECTRONICS & COMMUNICATIONS IN JAPAN, Issue 5 2008Yasunori Kawai Abstract In this paper, the application of receding horizon control to a two-link direct drive robot arm is demonstrated. Instead of terminal constraints, a terminal cost on receding horizon control is used to guarantee stability, because of the computational demand. The key idea of this paper is to apply receding horizon control with a terminal cost derived from the energy function of the robot system. The energy function is defined as the control Lyapunov function by considering inverse optimality. In experimental results, stability and performance are compared with respect to the horizon length by applying receding horizon control and inverse optimal control to the robot arm. © 2008 Wiley Periodicals, Inc. Electron Comm Jpn, 91(5): 33,40, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecj.10113 [source] Design of adaptive variable structure controllers for T,S fuzzy time-delay systemsINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 2 2010Tai-Zu Wu Abstract In this paper, the adaptive variable structure control problem is presented for Takagi,Sugeno (T,S) fuzzy time-delay systems with uncertainties and external disturbances. The fuzzy sliding surfaces for the T,S fuzzy time-delay system are proposed by using a Lyapunov function, and we design the adaptive variable structure controllers such that the global T,S fuzzy time-delay system confined on the fuzzy sliding surfaces is asymptotically stable. One example is given to illustrate the effectiveness of our proposed methods. Copyright © 2009 John Wiley & Sons, Ltd. [source] Robust diagnosis and fault-tolerant control of distributed processes over communication networksINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 8 2009Sathyendra Ghantasala Abstract This paper develops a robust fault detection and isolation (FDI) and fault-tolerant control (FTC) structure for distributed processes modeled by nonlinear parabolic partial differential equations (PDEs) with control constraints, time-varying uncertain variables, and a finite number of sensors that transmit their data over a communication network. The network imposes limitations on the accuracy of the output measurements used for diagnosis and control purposes that need to be accounted for in the design methodology. To facilitate the controller synthesis and fault diagnosis tasks, a finite-dimensional system that captures the dominant dynamic modes of the PDE is initially derived and transformed into a form where each dominant mode is excited directly by only one actuator. A robustly stabilizing bounded output feedback controller is then designed for each dominant mode by combining a bounded Lyapunov-based robust state feedback controller with a state estimation scheme that relies on the available output measurements to provide estimates of the dominant modes. The controller synthesis procedure facilitates the derivation of: (1) an explicit characterization of the fault-free behavior of each mode in terms of a time-varying bound on the dissipation rate of the corresponding Lyapunov function, which accounts for the uncertainty and network-induced measurement errors and (2) an explicit characterization of the robust stability region where constraint satisfaction and robustness with respect to uncertainty and measurement errors are guaranteed. Using the fault-free Lyapunov dissipation bounds as thresholds for FDI, the detection and isolation of faults in a given actuator are accomplished by monitoring the evolution of the dominant modes within the stability region and declaring a fault when the threshold is breached. The effects of network-induced measurement errors are mitigated by confining the FDI region to an appropriate subset of the stability region and enlarging the FDI residual thresholds appropriately. It is shown that these safeguards can be tightened or relaxed by proper selection of the sensor spatial configuration. Finally, the implementation of the networked FDI,FTC architecture on the infinite-dimensional system is discussed and the proposed methodology is demonstrated using a diffusion,reaction process example. Copyright © 2008 John Wiley & Sons, Ltd. [source] Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a finite number of stable second order linear time-invariant systemsINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 10 2002Robert N. Shorten In this paper, necessary and sufficient conditions are derived for the existence of a common quadra-tic Lyapunov function for a finite number of stable second order linear time-invariant systems. Copyright © 2002 John Wiley & Sons, Ltd. [source] On the existence of common quadratic Lyapunov functions for second-order linear time-invariant discrete-time systemsINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 10 2002Mehmet Akar Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function (CQLF) are given for two second-order linear time-invariant discrete-time systems. These conditions are later extended to an arbitrary number of systems. The conditions are readily verifiable both analytically and graphically. The paper also provides a constructive procedure for computing a CQLF when it exists. Copyright © 2002 John Wiley & Sons, Ltd. [source] Modelling and simulation of a double-star induction machine vector control using copper-losses minimization and parameters estimationINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 9 2002M.F. Mimouni Abstract This paper shows that it is possible to extend the principle of field-oriented control (FOC) approach to a double-star induction motor (DSIM). In the first stage, a robust variable structure current controller based on space phasor voltages PWM scheme is established. In this current controller design, only the stator currents and rotor speed sensors are used. In the second stage, the FOC method developed for DSIM is motivated by the minimization of the copper losses. The developed approach uses a loss model controller (LMC) and an adaptive rotor flux observer to compute the adequate rotor flux value minimizing the copper losses. The control variables are the stator currents or the machine input power. Compared to the constant rotor flux approach, it is proved that higher performances are achieved. However, the sensitivity of the FOC to parameter error of the machine still remains a problem. To guarantee the performance of the vector control, the stator and rotor resistances are adapted on-line, based on the Lyapunov theory. An appropriate choice of the reference model allows building a Lyapunov function by means of which the updating law can be found. The simulation results show the satisfactory behaviour of the proposed identification algorithm. Copyright © 2002 John Wiley & Sons, Ltd. [source] Generalized forgetting functions for on-line least-squares identification of time-varying systemsINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 4 2001R. E. Mahony The problem of on-line identification of a parametric model for continuous-time, time-varying systems is considered via the minimization of a least-squares criterion with a forgetting function. The proposed forgetting function depends on two time-varying parameters which play crucial roles in the stability analysis of the method. The analysis leads to the consideration of a Lyapunov function for the identification algorithm that incorporates both prediction error and parameter convergence measures. A theorem is proved showing finite time convergence of the Lyapunov function to a neighbourhood of zero, the size of which depends on the evolution of the time-varying error terms in the parametric model representation. Copyright © 2001 John Wiley & Sons, Ltd. [source] Some new algebraic criteria for chaos synchronization of Chua's circuits by linear state error feedback controlINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 3 2006Xiaofeng Wu Abstract The research on the sufficient criterion for chaos synchronization of the master,slave Chua's circuits by linear state error feedback control has received much attention and some synchronization criteria for special control matrix were proposed. In this paper, the above synchronization issue is investigated in the situation of general linear state error feedback controller with propagation delay of control signals from the master Chua's circuit. First of all, a master,slave synchronization scheme for Chua's circuits with propagation delay is given and the relevant error system is derived. Using a quadratic Lyapunov function and frequency domain method, three new algebraic synchronization criteria for the synchronization scheme with general control matrix are proven. They are applied to derive the synchronization criteria for simple control matrices. Some examples are given to show the sharpness of these new criteria compared with the known criteria. Copyright © 2006 John Wiley & Sons, Ltd. [source] H, fuzzy control design of discrete-time nonlinear active fault-tolerant control systemsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 10 2009Huai-Ning Wu Abstract This paper is concerned with the problem of H, fuzzy controller synthesis for a class of discrete-time nonlinear active fault-tolerant control systems (AFTCSs) in a stochastic setting. The Takagi and Sugeno (T,S) fuzzy model is employed to exactly represent a nonlinear AFTCS. For this AFTCS, two random processes with Markovian transition characteristics are introduced to model the failure process of system components and the fault detection and isolation (FDI) decision process used to reconfigure the control law, respectively. The random behavior of the FDI process is conditioned on the state of the failure process. A non-parallel distributed compensation (non-PDC) scheme is adopted for the design of the fault-tolerant control laws. The resulting closed-loop fuzzy system is the one with two Markovian jump parameters. Based on a stochastic fuzzy Lyapunov function (FLF), sufficient conditions for the stochastic stability and H, disturbance attenuation of the closed-loop fuzzy system are first derived. A linear matrix inequality (LMI) approach to the fuzzy control design is then developed. Moreover, a suboptimal fault-tolerant H, fuzzy controller is given in the sense of minimizing the level of disturbance attenuation. Finally, a simulation example is presented to illustrate the effectiveness of the proposed design method. Copyright © 2008 John Wiley & Sons, Ltd. [source] Strongly absolute stability of Lur'e descriptor systems: Popov-type criteriaINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 7 2009Chunyu Yang Abstract In this paper, we consider the strongly absolute stability problem of Lur'e descriptor systems (LDSs). First, we define a generalized Lur'e Lyapunov function (GLLF) and show that the negative-definite property of the derivative of the GLLF guarantees strongly absolute stability of LDSs. As a result, the existing Popov-type criteria are reduced to sufficient conditions for the existence of the GLLF. Then, we propose a necessary and sufficient condition for the existence of the GLLF to guarantee the strongly absolute stability of LDSs. This criterion is shown to be less conservative than the existing ones. Finally, we discuss the computational issues and present two numerical examples to illustrate the effectiveness of the obtained results. Copyright © 2008 John Wiley & Sons, Ltd. [source] Exponential H, filtering for uncertain discrete-time switched linear systems with average dwell time: A µ-dependent approachINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 11 2008Lixian Zhang Abstract In this paper, the problem of exponential H, filter problem for a class of discrete-time polytopic uncertain switched linear systems with average dwell time switching is investigated. The exponential stability result of the general discrete-time switched systems using a discontinuous piecewise Lyapunov function approach is first explored. Then, a new µ- dependent approach is proposed, which means the analysis or synthesis of the underlying systems is dependent on the increase degree µ of the piecewise Lyapunov function at the switching instants. A mode-dependent full-order filter is designed such that the developed filter error system is robustly exponentially stable and achieves an exponential H, performance. Sufficient existence conditions for the desired filter are derived and formulated in terms of a set of linear matrix inequalities, and consequently the minimal average dwell time and the corresponding filter are obtained from such conditions for a given system decay degree. A numerical example is presented to demonstrate the potential and effectiveness of the developed theoretical results. Copyright © 2007 John Wiley & Sons, Ltd. [source] Predictor-based repetitive learning control for a class of remote control nonlinear systemsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 16 2007Ya-Jun Pan Abstract In this paper, a repetitive learning control (RLC) approach is proposed for a class of remote control nonlinear systems satisfying the global Lipschitz condition. The proposed approach is to deal with the remote tracking control problem when the environment is periodic or repeatable over infinite time domain. Since there exist time delays in the two transmission channels: from the controller to the actuator and from the sensor to the controller, tracking a desired trajectory through a remote controller is not an easy task. In order to solve the problem caused by time delays, a predictor is designed on the controller side to predict the future state of the nonlinear system based on the delayed measurements from the sensor. The convergence of the estimation error of the predictor is ensured. The gain design of the predictor applies linear matrix inequality (LMI) techniques developed by Lyapunov Kravoskii method for time delay systems. The RLC law is constructed based on the feedback error from the predicted state. The overall tracking error tends to zero asymptotically over iterations. The proof of the stability is based on a constructed Lyapunov function related to the Lyapunov Kravoskii functional used for the proof of the predictor's convergence. By well incorporating the predictor and the RLC controller, the system state tracks the desired trajectory independent of the influence of time delays. A numerical simulation example is shown to verify the effectiveness of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd. [source] Lur'e Lyapunov functions and absolute stability criteria for Lur'e systems with multiple nonlinearitiesINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 9 2007Chunyu Yang Abstract In this paper, the absolute stability problem of Lur'e systems with multiple nonlinearities is investigated. Popov-type absolute stability criteria are surveyed and classified by distinguishing the Lur'e Lyapunov function upon which the criteria are based. A modified Lur'e Lyapunov function is presented. Some necessary and sufficient conditions for the existence of the Lyapynov function to guarantee the absolute stability of Lur'e systems are derived. By these conditions, LMI-based stability criteria are presented. The obtained criteria are expected to be less conservative than the existing ones. Finally, numerical examples are given to illustrate the advantages and effectiveness of our results. Copyright © 2006 John Wiley & Sons, Ltd. [source] ,2 -Stabilization of continuous-time linear systems with saturating actuatorsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 18 2006E. B. Castelan Abstract This paper addresses the problem of controlling a linear system subject to actuator saturations and to ,2 -bounded disturbances. Linear matrix inequality (LMI) conditions are proposed to design a state feedback gain in order to satisfy the closed-loop input-to-state stability (ISS) and the closed-loop finite gain ,2 stability. By considering a quadratic candidate Lyapunov function, two particular tools are used to derive the LMI conditions: a modified sector condition, which encompasses the classical sector-nonlinearity condition considered in some previous works, and Finsler's Lemma, which allows to derive stabilization conditions which are adapted to treat multiple objective control optimization problems in a potentially less conservative framework. Copyright © 2006 John Wiley & Sons, Ltd. [source] Further constructive results on interconnection and damping assignment control of mechanical systems: the Acrobot exampleINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 14 2006Arun D. Mahindrakar Abstract Interconnection and damping assignment passivity-based control is a controller design methodology that achieves (asymptotic) stabilization of mechanical systems endowing the closed-loop system with a Hamiltonian structure with a desired energy function,that qualifies as Lyapunov function for the desired equilibrium. The assignable energy functions are characterized by a set of partial differential equations that must be solved to determine the control law. A class of underactuation degree one systems for which the partial differential equations can be explicitly solved,making the procedure truly constructive,was recently reported by the authors. In this brief note, largely motivated by the interesting Acrobot example, we pursue this investigation for two degrees-of-freedom systems where a constant inertia matrix can be assigned. We concentrate then our attention on potential energy shaping and give conditions under which an explicit solution of the associated partial differential equation can be obtained. Using these results we show that it is possible to swing-up the Acrobot from some configuration positions in the lower half plane, provided some conditions on the robot parameters are satisfied. Copyright © 2006 John Wiley & Sons, Ltd. [source] LMI-based computation of optimal quadratic Lyapunov functions for odd polynomial systemsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 1 2005G. Chesi Abstract The problem of estimating the domain of attraction (DA) of equilibria is considered for odd polynomial systems. Specifically, the computation of the optimal quadratic Lyapunov function (OQLF), i.e. the quadratic Lyapunov function (QLF) which maximizes the volume of the largest estimate of the DA (LEDA), is addressed. In order to tackle this double non-convex optimization problem, a relaxation approach based on homogeneous polynomial forms is proposed. The first contribution of the paper shows that a lower bound of the LEDA for a fixed QLF can be obtained via linear matrix inequalities (LMIs) based procedures. Also, condition for checking tightness of the lower bound are provided. The second contribution is a strategy for selecting a good starting point for the OQLF search, which is based on the volume maximization of the region where the time derivative of the QLFs is negative and is given in terms of LMIs. Several application examples are presented to illustrate the numerical behaviour of the proposed approach. Copyright © 2005 John Wiley & Sons, Ltd. [source] A complete parameterization of clf-based input-to-state stabilizing control lawsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 17 2004J. W. Curtis Abstract Sontag's formula proves constructively that the existence of a control Lyapunov function implies asymptotic stabilizability. A similar result can be obtained for systems subject to unknown disturbances via input-to-state stabilizing control Lyapunov functions (ISS-clfs) and the input-to-state analogue of Sontag's formula. The present paper provides a generalization of the ISS version of Sontag's formula by completely parameterizing all continuous ISS control laws that can be generated by a known ISS-clf. When a simple inner-product constraint is satisfied, this parameterization also conveniently describes a large family of ISS controls that solve the inverse-optimal gain assignment problem, and it is proved that these controls possess Kalman-type gain margins. Copyright © 2004 John Wiley & Sons, Ltd. [source] Model predictive control for constrained systems with uncertain state-delaysINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 17 2004Xiao-Bing Hu Abstract This paper presents a model predictive control (MPC) algorithm for a class of constrained linear systems with uncertain state-delays. Based on a novel artificial Lyapunov function, a new stabilizing condition dependent of the upper bound of uncertain state-delays is presented in an LMI (linear matrix inequality) form. The proposed MPC algorithm is developed by following the fashion of stability-enforced scheme. The new algorithm is then extended to linear time varying (LTV) systems with multiple uncertain state-delays. Numerical examples illustrate the effectiveness of the new algorithm. Copyright © 2004 John Wiley & Sons, Ltd. [source] Robust trajectory tracking for a scale model autonomous helicopterINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 12 2004Robert Mahony Abstract This paper considers the question of obtaining an a priori bound on the tracking performance, for an arbitrary trajectory, of closed-loop control of an idealized model of a scale model autonomous helicopter. The problem is difficult due to the presence of small body forces that cannot be directly incorporated into the control design. A control Lyapunov function is derived for an approximate model (in which the small body forces are neglected) using backstepping techniques. The Lyapunov function derived is used to analyse the closed-loop performance of the full system. A theorem is proved that provides a priori bounds on initial error and the trajectory parameters (linear acceleration and its derivatives) that guarantees acceptable tracking performance of the system. The analysis is expected to be of use in verification of trajectory planning procedures. Copyright © 2004 John Wiley & Sons, Ltd. [source] Stability analysis and guaranteed domain of attraction for a class of hybrid systems: an LMI approachINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 5 2003S. Palomino Bean Abstract This paper presents sufficient conditions for the regional stability problem for switched piecewise affine systems, a special class of Hybrid Systems. This class of systems are described by an affine differential equation of the type x,=A(,)x+b(,), where x denotes the continuous state vector and , is a vector of logical variables that modifies the local model of the system in accordance with the continuous dynamics. Using a Lyapunov function of the type v(x)=x,P(x)x, we present LMI conditions that, when feasible, guarantee local stability of the origin of the switched system. Examples of switched affine systems are used to illustrate the results. Copyright © 2003 John Wiley & Sons, Ltd. [source] A new absolute stability test for systems with state-dependent perturbationsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 14 2002M. C. de Oliveira Abstract In this paper, a new test for the absolute stability of nonlinear systems with state-dependent nonlinearities is developed. Scalar nonlinearities are assumed to lie in sectors. Using a Lur'e function as a Lyapunov function, a linear matrix inequalities (LMI) stability condition is derived. The new condition lets one go from a pure integral (Persidskii) to a pure quadratic Lyapunov function in an unified framework. Several results available in the literature are generated as particular cases of the new test. An example shows that the proposed condition can be much less conservative than available diagonal stability and passivity based methods, as the circle and Popov criteria. Tests for infinite as well as finite nonlinearity sectors can be easily generated, since the parameters of the nonlinearity sectors appear in the LMI condition in a very convenient way. This feature can also provide optimization of the absolute stability sector through convex programming techniques. Copyright © 2002 John Wiley & Sons, Ltd. [source] Global robust stabilization of nonlinear systems subject to input constraintsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 14 2002Rodolfo Suárez Abstract Our main purpose in this paper is to further address the global stabilization problem for affine systems by means of bounded feedback control functions, taking into account a large class of control value sets: p,r -weighted balls ,mr(p), with 1 Linear, parameter-varying control and its application to a turbofan engineINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 9 2002Gary J. BalasArticle first published online: 15 JUL 200 This paper describes application of parameter-dependent control design methods to a turbofan engine. Parameter-dependent systems are linear systems, whose state-space descriptions are known functions of time-varying parameters. The time variation of each of the parameters is not known in advance, but is assumed to be measurable in real-time. Three linear, parameter-varying (LPV) approaches to control design are discussed. The first method is based on linear fractional transformations which relies on the small gain theorem for bounds on performance and robustness. The other methods make use of either a single (SQLF) or parameter-dependent (PDQLF) quadratic Lyapunov function to bound the achievable level of performance. The latter two techniques are used to synthesize controllers for a high-performance turbofan engine. A LPV model of the turbofan engine is constructed from Jacobian linearizations at fixed power codes for control design. The control problem is formulated as a model matching problem in the ,, and LPV framework. The objective is decoupled command response of the closed-loop system to pressure and rotor speed requests. The performance of linear, ,, point designs are compared with the SQLF and PDQLF controllers. Nonlinear simulations indicate that the controller synthesized using the SQLF approach is slightly more conservative than the PDQLF controller. Nonlinear simulations with the SQLF and PDQLF controllers show very robust designs that achieve all desired performance objectives. Copyright © 2002 John Wiley & Sons, Ltd. [source] A Class of Transpose Jacobian-based NPID Regulators for Robot Manipulators with an Uncertain KinematicsJOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 11 2002C. Q. Huang Transpose Jacobian-based controllers present an attractive approach to robot set-point control in Cartesian space that derive the end-effector posture to a specified desired position and orientation with neither solving the inverse kinematics nor computing the inverse Jacobian. By a Lyapunov function with virtual artificial potential energy, a class of complete transpose Jacobian-based Nonlinear proportional-integral-derivative regulators is proposed in this paper for robot manipulators with uncertain kinematics on the basis of the set of all continuous differentiable increasing functions. It shows globally asymptotic stability for the result closed-loop system on the condition of suitable feedback gains and suitable parameter selection for the corresponding function set as well as artificial potential function, and only upper bound on Jacobian matrix error and Cartesian dynamics parameters are needed. The existing linear PID (LPID) regulators are the special cases of it. Nevertheless, in the case of LPID regulators, only locally asymptotic stability is guaranteed if the corresponding conditions are satisfied. Simulations demonstrate the result and robustness of transpose Jacobian-based NPID regulators. © 2002 Wiley Periodicals, Inc. [source] Perfect position/force tracking of robots with dynamical terminal sliding mode controlJOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 9 2001V. Parra-Vega According to a given performance criteria, perfect tracking is defined as the performance of zero tracking error in finite time. It is evident that robotic systems, in particular those that carry out compliant task, can benefit from this performance since perfect tracking of contact forces endows one or many constrained robot manipulators to interact dexterously with the environment. In this article, a dynamical terminal sliding mode controller that guarantees tracking in finite-time of position and force errors is proposed. The controller renders a dynamic sliding mode for all time and since the equilibrium of the dynamic sliding surface is driven by terminal attractors in the position and force controlled subspaces, robust finite-time convergence for both tracking errors arises. The controller is continuous; thus chattering is not an issue and the sliding mode condition as well the invariance property are explicitly verified. Surprisingly, the structure of the controller is similar with respect to the infinite-time tracking case, i.e., the asymptotic stability case, and the advantage becomes more evident because terminal stability properties are obtained with the same Lyapunov function of the asymptotic stability case by using more elaborate error manifolds instead of a more complicated control structure. A simulation study shows the expected perfect tracking and a discussion is presented. © 2001 John Wiley & Sons, Inc. [source] Enhanced stability regions for model predictive control of nonlinear process systemsAICHE JOURNAL, Issue 6 2008Maaz Mahmood Abstract The problem of predictive control of nonlinear process systems subject to input constraints is considered. The key idea in the proposed approach is to use control-law independent characterization of the process dynamics subject to constraints via model predicative controllers to expand on the set of initial conditions for which closed,loop stability can be achieved. An application of this idea is presented to the case of linear process systems for which characterizations of the null controllable region (the set of initial conditions from where closed,loop stability can be achieved subject to input constraints) are available, but not practically implementable control laws that achieve stability from the entire null controllable region. A predictive controller is designed that achieves closed,loop stability for every initial condition in the null controllable region. For nonlinear process systems, while the characterization of the null controllable region remains an open problem, the set of initial conditions for which a (given) Lyapunov function can be made to decay is analytically computed. Constraints are formulated requiring the process to evolve within the region from where continued decay of the Lyapunov function value is achievable and incorporated in the predictive control design, thereby expanding on the set of initial conditions from where closed,loop stability can be achieved. The proposed method is illustrated using a chemical reactor example, and the robustness with respect to parametric uncertainty and disturbances demonstrated via application to a styrene polymerization process. © 2008 American Institute of Chemical Engineers AIChE J, 2008 [source] Transition from Batch to Continuous Operation in Bio-Reactors: A Model Predictive Control Approach and ApplicationTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 4 2007Prashant Mhaskar Abstract This work considers the problem of determining the transition of ethanol-producing bio-reactors from batch to continuous operation and subsequent control subject to constraints and performance considerations. To this end, a Lyapunov-based non-linear model predictive controller is utilized that stabilizes the bio-reactor under continuous mode of operation. The key idea in the predictive controller is the formulation of appropriate stability constraints that allow an explicit characterization of the set of initial conditions from where feasibility of the optimization problem and hence closed-loop stability is guaranteed. Additional constraints are incorporated in the predictive control design to expand on the set of initial conditions that can be stabilized by control designs that only require the value of the Lyapunov function to decay. Then, the explicit characterization of the set of stabilizable initial conditions is used in determining the appropriate time for which the reactor must be run in batch mode. Specifically, the predictive control approach is utilized in determining the appropriate batch length that achieves stabilizable values of the state variables at the end of the batch. Application of the proposed method to the ethanol production process using Zymomonas mobilis as the ethanol producing micro-organism demonstrates the effectiveness of the proposed model predictive control strategy in stabilizing the bio-reactor. Ce travail porte sur le problème de la détermination de la transition entre le fonctionnement discontinu et continu pour des bioréacteurs produisant de l'éthanol et sur le contrôle subséquent lorsque ceux-ci sont soumis à des contraintes et des considérations de performance. À cette fin, on utilise un contrôleur prédictif par modèles non linéaires de type Lyapunov qui stabilise le bioréacteur lorsqu'il est en mode de fonctionnement continu. L'idée maîtresse dans le contrôleur prédictif est la formulation de contraintes de stabilité appropriées qui permettent une caractérisation explicite du jeu des conditions initiales à partir de laquelle la faisabilité du problème d'optimisation et donc la stabilité en boucle fermée sont garanties. Des contraintes additionnelles sont introduites dans la conception du contrôle prédictif pour étendre le jeu de conditions initiales qui peuvent être stabilisées par la conception du contrôle qui requiert seulement que la valeur de la fonction de Lyapunov diminue. Ensuite, la caractérisation explicite du jeu des conditions initiales stabilisables est utilisée dans la détermination de la durée de fonctionnement adéquate pour laquelle le réacteur doit fonctionner en mode discontinu. Spécifiquement, on utilise la méthode de contrôle prédictif dans la détermination de la longueur discontinue appropriée qui réalise les valeurs stabilisables des variables d'état à la fin du mode discontinu. L'application de la méthode proposée au procédé de production de l'éthanol utilisant Zymomonas mobilis comme microorganisme produisant de l'éthanol, démontre l'efficacité de la stratégie de contrôle prédictif de modèles proposée pour stabiliser le bioréacteur. [source] Poly-quadratic stability of discrete-time nonlinear systems in Takagi-Sugeno's form,ASIAN JOURNAL OF CONTROL, Issue 6 2009Baocang Ding Abstract This paper studies poly-quadratic stability of nonlinear systems represented by a Takagi-Sugeno (T-S) discrete fuzzy model. A system is poly-quadratically stable when its stability can be verified by a parameter dependent Lyapunov function. There are already some results in this area. This paper, however, presents less conservative results by adopting more slack-matrix-variables in the linear matrix inequalities (LMIs). The parallel distributed compensation (PDC) law is utilized in both the analysis and the synthesis problems. The effectiveness of the new results in this paper is validated by a simulation example. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] Stability analysis for discrete-time fuzzy system by utilizing homogeneous polynomial matrix function,ASIAN JOURNAL OF CONTROL, Issue 6 2009Likui Wang Abstract The purpose of this paper is to investigate the stability of nonlinear systems represented by a Takagi-Sugeno discrete-time fuzzy model. The homogeneous polynomial matrix function (HPMF) is developed to obtain new stabilization conditions. Applying the HPMF to the non-parallel distributed compensation (non-PDC) law and non-quadratic Lyapunov function, some new stabilization conditions are obtained by the following two means: (a) utilizing the popular idea of introducing additional variables for some fixed degree of the HPMF; and (b) increasing the degree of the HPMF. It is shown that the conditions obtained with approach (a) are less conservative than some sufficient stability conditions available in the literature to date. It is also shown that as the degree of HPMF increases the conditions obtained under (b) become less conservative. An example is provided to illustrate how the proposed approaches compare with other techniques available in the literature. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]
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