Robust State Feedback Controller Research Articles

Robust control for a nonlinear servomechanism problem

This paper deals with the design of output feedback control to achieve asymptotic tracking and disturbance rejection for a class of nonlinear systems when the exogenous signals are generated by a known linear exosystem. The system under consideration is single-input single-output, input-output linearizable, minimum phase, and modelled by an input-output model of the form of an nth-order differential equation. We assume that, at steady state, the nonlinearities of the system can only introduce a finite number of harmonics of the original exosystem modes. This assumption enables us to identify a linear servo-compensator which is augmented with the original system. Moreover, we augment a series of m integrators at the input side, where m is the highest derivative of the input, and then represent the augmented system by a state model. The augmented system is stabilized via a separation approach in which a robust state feedback controller is designed first to ensure boundedness of all state variables and tracking error convergence; then, a high gain observer and control saturation are used to recover the asymptotic properties achieved under state feedback.

On a state-space approach in robust control for singularly perturbed systems

A direct state-space approach for an estimate of the graph metric of singularly perturbed systems (SPS) is proposed. Based on a new version of the Tikhonov Theorem on uniform convergence of the slow variables in a stable SPS over the L unit ball of inputs in, an estimate of the first order to the small parameter for a 2 graph metric between SPS and its 'state decoupled form' is obtained for both time varying and time invariant cases. Moreover, a similar estimate of a graph metric between SPS and its slow system when the fast system satisfies some additional H conditions is given. Furthermore, the robust state feedback control for SPS is also considered in an analogous manner. An advantage there is that infinitely many composite feedback controls are obtained directly, bypassing the traditional arguments used in SPS theory such as approximation of solutions of Riccati equations and the Implicit function theorem.

Robust control of sampled-data uncertain systems using digitally redesigned observer-based controllers

This paper presents a new digital redesign method for robust control of a sampleddata uncertain system using an observer-based digital controller. The multiplesegment trapezoidal rule together with interval arithmetic is utilized to find a digital interval model of the original continuous-time uncertain system. A dual concept of the digital interval modelling, which captures the intersample states of the original continuous-time uncertain system is used to discretize a predesigned continuous-time state-feedback robust controller so that the states of the digitally controlled continuous-time uncertain system closely match those of the original analogously controlled continuous-time uncertain system. A discrete-time observer is constructed from the original continuous-time observer such that the estimated states of the redesigned discrete-time observer match those of the original continuous-time observer at the sampling instants. Using the newly digitally redesigned observerbased controllers, the resulting dynamic states of the digitally controlled sampleddata uncertain systems are able to match closely those of the original analogously controlled continuous-time uncertain systems.

A new robust control for a class of uncertain discrete-time systems

A new linear robust state-feedback controller that guarantees uniform boundedness for a class of discrete-time uncertain systems with multi-inputs is presented, based on the second method of Lyapunov. Furthermore, an upper bound of the uncertainties has been derived in order to make the closed-loop system stable.

Robust memoryless H∞ controller design for linear time-delay systems with norm-bounded time-varying uncertainty

We consider the robust H∞ control problem for linear time-delay systems with norm-bounded time-varying uncertainty. Based on the Riccati-equation approach, we present a method for designing a robust memoryless linear time-invariant state feedback control law, which stabilizes the system and reduces the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties.

Robust controller design for uncertain linear systems with circular pole constraints

In this paper, the problem of robust controller design for uncertain linear continuous-and discrete-time systems with circular pole constraints is considered. The problem we address is the design of robust state feedback controllers such that all poles of the closed-loop systems are placed within a prescribed circular region. Sufficient conditions for the existence of the desired controllers are given based on the generalized inverse theory. The analytical expression of the set of desired controllers is also presented. It is emphasized that, when the uncertainties are absent, the results include the characterization of all state-feedback controllers achieving the specified circular pole constraints. An illustrative example is given to show the applicability of the proposed design procedure. Accepted in final revised form 7 February 1996. Communicated by Professor H. Kimura.

Robust Control for Linear Systems with Markovian Jumping Parameters

This paper investigates the problem of robust control for a class of systems with both Markovian jumping parameters and parametric uncertainty. The jumping parameters considered here form a continuous-time discrete-state homogeneous Markov process, and the parameter uncertainty is real time-varying norm-bounded. A methodology is proposed for the design of robust state feedback controllers. We show that the problem of robust control for linear systems with Markovian jumping parameters can be solved in terms of the solutions to a set of either int ercoupled Riccati differential equations, or algebraic Riccati equations.

Robust control via state feedback for a class of uncertain bilinear systems

This paper is concerned with the problem of designing a satabilizing controller for a class of uncertain bilinear systems. The uncertainties in the systems must satisfy matching condition and their bounds should be known. The so-called improved approach for stability analysis of nonlinear systems is used. Under some suitable assumptions a linear robust state feedback controller can be designed. At last an illustrative example is demonstrated.

Quadratic guaranteed cost control with robust pole placement in a disk

The paper is concerned with the design of robust state feedback controllers for a class of uncertain systems with norm bounded uncertainty, where uncertainty enters in both the state and input matrices. The controller is designed to place the closed loop poles of the uncertain system in a specified disk and guarantees an upper bound on a quadratic cost function. A procedure is given for the construction of a controller which minimises a bound on an integral quadratic performance index.

Reducing the computation required to solve a standard minimax problem

Minimax optimization problems have a long and rich history in the area of control. We show how the computation required to find the solution of a popular and widely applicable minimax problem can be significantly reduced. This reduction in computation results from an observation concerning the inner level (finite) maximization. In particular, we show that the number of parameter combinations that must be considered may be significantly reduced. We next indicate how this optimization problem can be used to synthesize a robust state feedback control for a system with parameter uncertainty. We conclude with an example robust control design problem that has 15 independent uncertain parameters and would not be practical were it not for the reduced computational requirement.

Robust optimal pole-clustering in a vertical strip and disturbance rejection for uncertain Lagrange's systems

This paper presents an approach to design a state-feedback robust control law for uncertain Lagrange's systems such that the designed closed-loop systems have the properties of robust pole-clustering within a vertical strip and disturbance rejection with anH∞-norm constraint. This approach is based on solving an algebraic Riccati equation with the adjustable scalars and prespecified parameters. The uncertainties considered include both unstructured and structured uncertainties in the system and the input matrices. Also, a constraint is established to verify that the proposed robust LQRs preserveH2 optimality with respect to a specific quadratic cost function.

Comments on ‘Robust stabilization of uncertain linear dynamical systems’

Based on the stabilizability of a nominal system, by making use of the Lyapunov stability criterion and combining with the algebraic Riccati equation, Wu and Mizukami (1993) present a new approach to designing a robust linear state feedback controller for uncertain linear dynamical systems. The robust stabilization conditions given by Wu and Mizukami (1993), however, seem to be conservative and can be easily improved upon. In this note we design another robust linear feedback controller to render the uncertain system asymptotically stable. An example is presented to demonstrate our new control law and to compare it with the existing one.

Robust servomechanism output feedback controllers for feedback linearizable systems

We consider a single-input-single-output nonlinear system which has a uniform relative degree equal to the dimension of the state vector. The system can be transformed into a normal form with no zero dynamics. We allow the system's equation to depend on bounded uncertain parameters which do not change the relative degree. Disturbances are assumed to satisfy a strict-feedback condition which allows us to use a time-varying, disturbance-dependent transformation to transform the system into an error space where disturbances and uncertainties satisfy the matching condition. The nonlinear functions in the error space are used to choose an internal model which is augmented with the system, and a robust state feedback control is designed to drive the error to a positively invariant set that contains the origin. We then show the existence of a zero-error manifold inside this set which attracts all trajectories inside the set. To implement this control using output feedback, we saturate the state feedback control outside a compact set of interest and estimate the state using a high-gain observer. The output feedback controller recovers the robustness and asymptotic tracking properties of the state feedback controller.

Optimal guaranteed cost control and filtering for uncertain linear systems

The paper presents results on the design of robust state feedback controllers and steady-state robust state estimators for a class of uncertain linear systems with norm bounded uncertainty. The state feedback results extend the linear quadratic regulator to the case in which the underlying system is dependent on uncertain parameters. The state estimation results extend the steady-state Kalman filter to the case in which the underlying system is also uncertain.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Maximally robust state-feedback controllers for stabilization of plants with normalized right coprime factor uncertainty

It is shown that a maximally robust state-feedback controller for a plant with normalized right coprime factor uncertainty is given by the solution to a standard linear quadratic regulator problem.

Robust stabilization of uncertain linear dynamical systems

Abstract Based on the stabilizability of a nominal system (i.e. a system in the absence of uncertainty), by making use of the Lyapunov stability criterion and combining with the algebraic Riccati equation, a new approach for designing a robust linear state feedback controller for uncertain linear dynamical systems is presented. Using this approach, the BIBO stability of uncertain linear dynamical systems is also discussed, Some analytical methods and the Bellman-Gronwall inequality are employed to investigate the robust stabilization conditions on the feedback controller. The main features of this approach are that no matching condition about uncertainty is needed and the uncertain systems can be asymptotically stabilized. An example is given to demonstrate the validity of our results.

Discrete time robust control via state feedback for single input systems

A nonlinear robust state feedback controller for discrete-time uncertain systems is proposed. The uncertainties in the system must satisfy the matching condition, but only their bounds need to be known. The controller is designed via the second method of Lyapunov. The detailed derivation of the controller for single-input systems is given. The system response remains in the neighborhood of the zero state if uncertainties are small. The uncertainty bound for the stability condition is derived. >

Robust stabilization of linear constrained uncertain time delay systems

The sufficient conditions for the robust stability of constrained uncertain time delay systems are presented in the time domain. The properties of the matrix measure and comparison theorem are used in the formulation. Then, a method is proposed for the design of a robust state feedback controller to satisfy the robustness requirement. Examples are given to illustrate the proposed method.

Robust stability for linear time-delay systems with linear parameter perturbations

Abstract A new robust state feedback controller design in the time domain is developed for parametrically perturbed linear systems with time delay. The properties of the matrix measure and comparison theorem are employed to investigate the robust stability conditions of systems with linear structured or unstructured perturbations. A method is proposed to design the robust state feedback controller to satisfy the robustness requirement. Examples are given to illustrate the proposed method.

A COMPUTATIONAL PROCEDURE FOR MULTIVARIABLE STATE FEEDBACK ROBUST CONTROLLER DESIGN

This paper describes a procedure for multivariable state feedback robust controller design. The plant in state space is given by the operational point description or in terms of a vector of slow varying physical parameters. Through solution of the Sylvester matrix equation, a nonunique static feedback controller, which assigns the prespecified closed-loop spectrum, is calculated. In addition, all the remaining feedback degrees of freedom are utilized to optimize a multiobjective function that reflects further design properties. The robust feedback gains is calculated through a three-phase computational algorithm. Numerical examples show that under the robust state feedback control, the closed-loop systems can both achieve satisfied transient characteristics and greatly reduce state trajectory sensitivity to small or large parameter variations in the plant. The pro-posed procedure is still applied to a VTOL aircraft model.