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Stabilization Problem (stabilization + problem)

Distribution by Scientific Domains
Engineering94%

Kinds of Stabilization Problem

  • robust stabilization problem
    		•

    Selected Abstracts

    Delay-dependent robust control for singular discrete-time Markovian jump systems with time-varying delay

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 10 2010
    Wuneng Zhou
    Abstract The problem of delay-dependent robust stabilization for uncertain singular discrete-time systems with Markovian jumping parameters and time-varying delay is investigated. In terms of free-weighting-matrix approach and linear matrix inequalities, a delay-dependent condition is presented to ensure a singular discrete-time system to be regular, causal and stochastically stable based on which the stability analysis and robust stabilization problem are studied. An explicit expression for the desired state-feedback controller is also given. Some numerical examples are provided to demonstrate the effectiveness of the proposed approach. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Static output feedback sliding mode control for time-varying delay systems with time-delayed nonlinear disturbances

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 7 2010
    X. G. Yan
    Abstract In this paper, a robust stabilization problem for a class of linear time-varying delay systems with disturbances is studied using sliding mode techniques. Both matched and mismatched disturbances, involving time-varying delay, are considered. The disturbances are nonlinear and have nonlinear bounds which are employed for the control design. A sliding surface is designed and the stability of the corresponding sliding motion is analysed based on the Razumikhin Theorem. Then a static output feedback sliding mode control with time delay is synthesized to drive the system to the sliding surface in finite time. Conservatism is reduced by using features of sliding mode control and systems structure. Simulation results show the effectiveness of the proposed approach. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Stabilization of complex cascade systems using boundedness information in finite time

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 10 2009
    Huawen Ye
    Abstract In this paper, the stabilization problem of several classes of complex cascade systems is investigated from a new point of view. If the closed-loop system is proven to have no finite escape time, the boundedness information in finite time, which is obtained from robust stable subsystems or recursive analysis procedures, is then sufficiently employed to deal with crucial nonlinear terms. The proposed method does not rely on complicated Lyapunov functions, and in some cases it can avoid strong growth conditions and complicated small gain analysis. In addition, simple saturated control laws are explicitly constructed in an almost unified way. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    An augmented system approach to static output-feedback stabilization with ,, performance for continuous-time plants

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 7 2009
    Zhan Shu
    Abstract This paper revisits the static output-feedback stabilization problem of continuous-time linear systems from a novel perspective. The closed-loop system is represented in an augmented form, which facilitates the parametrization of the controller matrix. Then, new equivalent characterizations on stability and ,, performance of the closed-loop system are established in terms of matrix inequalities. On the basis of these characterizations, a necessary and sufficient condition with slack matrices for output-feedback stabilizability is proposed, and an iteration algorithm is given to solve the condition. An extension to output-feedback ,, control is provided as well. The effectiveness and merits of the proposed approach are shown through several examples. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Passivity-based control of a magnetically levitated flexible beam

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 6 2009
    T. 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]

    Explicit constructions of global stabilization and nonlinear H, control laws for a class of nonminimum phase nonlinear multivariable systems

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 12 2008
    Weiyao Lan
    Abstract This paper investigates a global stabilization problem and a nonlinear H, control problem for a class of nonminimum phase nonlinear multivariable systems. To avoid the complicated recursive design procedure, an asymptotic time-scale and eigenstructure assignment method is adopted to construct the control laws for the stabilization problem and the nonlinear H, control problem. A sufficient solvability condition is established onthe unstable zero dynamics of the system for global stabilization problem and nonlinear H, control problem, respectively. Moreover, based on the sufficient solvability condition, an upper bound of the achievable L2 -gain is estimated for the nonlinear H, control problem. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    On an output-feedback stabilization problem with uncertainty in the relative degree

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 7 2008
    Giorgio Bartolini
    Abstract This paper deals with an output-feedback finite-time control problem for a class of nonlinear uncertain systems whose relative degree is affected by an uncertain system parameter and is therefore unknown at the stage of control design. We show that an existing second-order sliding mode control algorithm can address successfully the control task of a finite-time output-feedback stabilization when the uncertain relative degree is equal to 1 or 2. We derive constructive tuning rules for the control parameters and show its effectiveness by using computer simulations. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Robust stabilizers for an implicit dynamical delay system of the neutral type

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 4 2006
    D. P. GoodallArticle first published online: 28 DEC 200
    Abstract A feedback stabilization problem is investigated for a class of imperfectly known implicit systems with discrete and distributed delays. The imperfections acting on the systems, which may be time-, state-, delayed state-, and/or input-dependent, are modelled as additive nonlinear perturbations influencing a known set of nonlinear functional differential equations of the neutral type. Sufficient conditions, which include a delay-dependent matrix inequality and a delay-dependent stability criterion involving some bounding parameters for the uncertainty in the system, are presented and a class of robust feedback stabilizers, including both memoryless and those with memory, are designed to guarantee a prescribed stability property for the class of implicit systems. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    Linear PI control of batch exothermic reactors with temperature measurement

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 3 2006
    Jose Alvarez-Ramirez
    Abstract A wide variety of speciality materials and fine chemicals such as plastics, pharmaceutical and microelectronics components are produced in batch reactors. The nonlinear, transient and finite-time features of the batch reactors give rise to complex process and control design problems. In particular, the safe operation of exothermic reactors depends on the adequate functioning of a temperature tracking controller, and to a good extent, the same is true for the attainment of a suitable compromise between productivity and product quality attributes. While the stabilization problem of continuous exothermic chemical reactors has been recently addressed with rigorous asymptotic-stability methods, the same kind of studies have not yet been performed for the finite-time batch reactor case. In this paper, the problem of designing a temperature tracking controller for an exothermic batch reactor, with n species and m reactions, is addressed under the following premises: (i) only the reactor temperature is measured, (ii) the (typically uncertain) reaction rate and heat exchange nonlinear functions are unknown, (iii) the controller must be linear and easy to tune, and (iv) the closed-loop reactor motion must be stable in a suitable sense. The combination of industrial-oriented inventory control concepts in conjunction with singular perturbation results yields a linear controller with a combined feedforward-PI feedback structure, antireset windup scheme, and conventional-like tuning rules. The controller: (i) tracks, arbitrarily fast and close, a prescribed temperature trajectory, with admissibly deviated concentration motions, and (ii) quickly recovers the behaviour of an exact model-based nonlinear I/O linearizing controller. The proposed design is put in perspective with the geometric and IMC nonlinear control approaches. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    Robust output regulation for discrete-time nonlinear systems

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 2 2005
    Weiyao Lan
    Abstract In this paper, we will establish a framework that can convert the robust output regulation problem for discrete-time nonlinear systems into a robust stabilization problem for an appropriately augmented system consisting of the given plant and a specific dynamic system called internal model. We then apply this framework to solve the local robust output regulation problem for a general class of discrete-time nonlinear systems. The results of this paper gives a discrete-time counterpart of the recent results on the continuous-time robust output regulation problem. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    Global robust stabilization of nonlinear systems subject to input constraints

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 14 2002
    Rodolfo 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 10 are also considered. Working along the line of Artstein,Sontag's approach, we construct an explicit formula for a one-parameterized family of continuous feedback controls taking values in ,rm(p) that globally asymptotically stabilize an affine system, provided an appropriate control Lyapunov function is known. The designed family of controls is suboptimal with respect to the robust stability margin for uncertain systems. The problem of achieving disturbance attenuation for persistent disturbances is also considered. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Adaptive robust stabilization of dynamic nonholonomic chained systems

    JOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 3 2001
    S. S. Ge
    In this article, the stabilization problem is investigated for dynamic nonholonomic systems with unknown inertia parameters and disturbances. First, to facilitate control system design, the nonholonomic kinematic subsystem is transformed into a skew-symmetric form and the properties of the overall systems are discussed. Then, a robust adaptive controller is presented in which adaptive control techniques are used to compensate for the parametric uncertainties and sliding mode control is used to suppress the bounded disturbances. The controller guarantees the outputs of the dynamic subsystem (the inputs to the kinematic subsystem) to track some bounded auxiliary signals which subsequently drive the kinematic subsystem to the origin. In addition, it can also be shown all the signals in the closed loop are bounded. Simulation studies on the control of a unicycle wheeled mobile robot are used to show the effectiveness of the proposed scheme. © 2001 John Wiley & Sons, Inc. [source]

    Polynomial and analytic stabilization of a wave equation coupled with an Euler,Bernoulli beam

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 5 2009
    Kaďs Ammari
    Abstract We consider a stabilization problem for a model arising in the control of noise. We prove that in the case where the control zone does not satisfy the geometric control condition, B.L.R. (see Bardos et al. SIAM J. Control Optim. 1992; 30:1024,1065), we have a polynomial stability result for all regular initial data. Moreover, we give a precise estimate on the analyticity of reachable functions where we have an exponential stability. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Stabilization for a class of complex interlaced systems using asymptotical gain,

    ASIAN JOURNAL OF CONTROL, Issue 2 2010
    Huawen Ye
    Abstract This paper addresses the stabilization problem of a class of interlaced systems that are not in a strict-feedforward form and contain some severe nonlinear terms. Bounded control laws in a fractional form are explicitly constructed. The feature of stability analysis allows the closed-loop system, when it is proven to have no finite escape time, to employ the asymptotical gain, which is obtained from an input-to-state stable (ISS) subsystem, to calculate the severe nonlinear terms, and the related estimate in turn guides the assignment of small controls. Together with the use of the passivity theory and the ISS-based stability criterion, the proposed method requires no small gain analysis although the asymptotical gain is used, and differs from the state-dependent saturation scheme since the controls do not include saturation functions. As an application, a new stabilizing control law is presented for the well-known friction ball-and-beam system. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

    Stabilization of uncertain chained nonholonomic systems using adaptive output feedback,

    ASIAN JOURNAL OF CONTROL, Issue 6 2009
    Z. P. Yuan
    Abstract In this paper, adaptive output feedback control is presented to solve the stabilization problem of nonholonomic systems in chained form with strong nonlinear drifts and uncertain parameters using output signals only. The objective is to design adaptive nonlinear output feedback laws which can steer the closed-loop systems to globally converge to the origin, while the estimated parameters remain bounded. The proposed systematic strategy combines input-state scaling with backstepping technique. Motivated from a special case, adaptive output feedback controllers are proposed for a class of uncertain chained systems. The simulation results demonstrate the effectiveness of the proposed controllers. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

    ROBUST STABILITY AND STABILIZATION OF A CLASS OF SINGULAR SYSTEMS WITH MULTIPLE TIME-VARYING DELAYS

    ASIAN JOURNAL OF CONTROL, Issue 1 2006
    S. M. Saadni
    ABSTRACT This paper deals with the problem of robust stability and robust stabilization for uncertain continuous singular systems with multiple time-varying delays. The parametric uncertainty is assumed to be norm bounded. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties. The purpose of the robust stabilization problem is to design a feedback control law such that the resulting closed-loop system is robustly stable. This problem is solved via generalized quadratic stability approach. A strict linear matrix inequality (LMI) design approach is developed. Finally, a numerical example is provided to demonstrate the application of the proposed method. [source]

    GENERALIZED QUADRATIC STABILIZATION FOR DISCRETE-TIME SINGULAR SYSTEMS WITH TIME-DELAY AND NONLINEAR PERTURBATION

    ASIAN JOURNAL OF CONTROL, Issue 3 2005
    Guoping Lu
    ABSTRACT This paper discusses a generalized quadratic stabilization problem for a class of discrete-time singular systems with time-delay and nonlinear perturbation (DSSDP), which the satisfies Lipschitz condition. By means of the S-procedure approach, necessary and sufficient conditions are presented via a matrix inequality such that the control system is generalized quadratically stabilizable. An explicit expression of the static state feedback controllers is obtained via some free choices of parameters. It is shown in this paper that generalized quadratic stability also implies exponential stability for linear discrete-time singular systems or more generally, DSSDP. In addition, this new approach for discrete singular systems (DSS) is developed in order to cast the problem as a convex optimization involving linear matrix inequalities (LMIs), such that the controller can stabilize the overall system. This approach provides generalized quadratic stabilization for uncertain DSS and also extends the existing robust stabilization results for non-singular discrete systems with perturbation. The approach is illustrated here by means of numerical examples. [source]

    Semi-global stabilization of discrete-time systems subject to non-right invertible constraints

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 11 2010
    Xu Wang
    Abstract This paper investigates time-invariant linear systems subject to input and state constraints. We study discrete-time systems with full or partial constraints on both input and state. It has been shown earlier that the solvability conditions of stabilization problems are closely related to important concepts such as the right invertibility or non-right invertibility of the constraints, the location of constraint invariant zeros, and the order of constraint infinite zeros. In this paper, for general time-invariant linear systems with non-right invertible constraints, necessary and sufficient conditions are developed under which semi-global stabilization in the admissible set can be achieved by state feedback. Sufficient conditions are also developed for such a stabilization in the case where measurement feedback is used. Such sufficient conditions are almost necessary. Controllers for both state feedback and measurement feedback are constructed as well. Copyright © 2009 John Wiley & Sons, Ltd. [source]