Robust Disturbance Rejection Problem Research Articles

Robust Disturbance Rejection in Uncertain Singular Systems Using Equivalent-Input-Disturbance Method Based on Output Feedback Control

A robust disturbance-rejection problem for an uncertain singular system is considered in this paper. An equivalent-input-disturbance (EID) method is applied to improve disturbance-rejection performance. At first, the disturbance estimation is obtained by the EID method; Then, the disturbance estimation is compensation to the control input channel to offset the adverse effect of external disturbance and uncertainties on the system. Two sufficient and necessary conditions using linear matrix inequality are obtained, which can guarantee the admissibility (regularity, non-impulsiveness, and stability) for the closed-loop control system. In addition, output-feedback control laws (static, dynamic) and observer gain are obtained using the singular value decomposition method. A numerical example and simulation studies prove the validity and feasibility of the presented method.

Time-Varying Optimal Disturbance Minimization in Presence of Plant Uncertainty

The optimal robust disturbance rejection problem plays an important role in feedback control theory. Here, its time-varying version is solved explicitly in terms of duality and operator theory. In particular, the optimum is shown to satisfy a time-varying allpass property. Moreover, optimal performance is given in terms of the norm of a bilinear form. The latter depends on a lower triangular projection and a multiplication operator defined on special versions of spaces of compact operators.

Robust output feedback control against disturbance filter uncertainty described by dynamic integral quadratic constraints

AbstractMotivated by a robust disturbance rejection problem, in which disturbances are described by an uncertain filter at the plant input, a convex solution is presented for the robust output feedback controller synthesis problem for a particularly structured plant. The uncertainties are characterized by an integral quadratic constraint (IQC) with general frequency‐dependent multipliers. By exploiting the structure of the generalized plant, linear matrix inequality (LMI)‐synthesis conditions are derived in order to guarantee a specified ℒ︁2‐gain or ℋ︁2‐norm performance level, provided that the IQC multipliers are described by LMI constraints. Moreover, it is shown that part of the controller variables can be eliminated. Finally, the rejection of non‐stationary sinusoidal disturbance signals is considered. In a numerical example, it is shown that specifying a bound on the rate‐of‐variation of the time‐varying frequency can improve the performance if compared with the static IQC multipliers. Copyright © 2009 John Wiley & Sons, Ltd.

Robust disturbance rejection via P-D state feedback Example for lane keeping of highway vehicles

The problem of robust disturbance rejection (RDR) using a Proportional plus Derivative (P-D) state feedback controller is studied for the case of single-input single output (SISO) linear systems with nonlinear uncertain structure. The linear systems are considered to be subjected to nonmeasurable disturbances. Sufficient conditions for the problem to have a solution are established. A family of P-D feedback controllers solving the problem is analytically determined. Sufficient conditions for the solution of the RDR problem with simultaneous robust stability are also established. Furthermore, the latter problem together with normality and asymptotic command matching is solved. The problem of lane keeping of highway vehicles was the motive for the derivation of all the above results. In particular, the problem of zeroing the relative lateral position of a vehicle travelling along a highway is formulated here as an RDR problem. The curvature of the road plays the role of the unknown disturbance. The problem of rejecting robustly the influence of the road curvature to the lateral position is proved to be always solvable, using a P-D feedback controller. The controller is analytically determined using a finite step algorithm. Furthermore, the free responses of the vehicle’s relative lateral position and lateral velocity are proved to be expressed only in terms of arbitrary modes. The general set of P-D feedback controllers solving the problem is proved also to guarantee robust stability of the closed-loop system. Using the infinity norm, the good performance of the rest of the vehicle’s variables, namely the yaw angle, the yaw rate and the front steering angle, is proved. Simulation results illustrate the good performance of the RDR over a wide range of system uncertainties and measurement errors.

Control design for the nonlinear benchmark problem via the output regulation method

The problem of designing a feedback controller to achieve asymptotic disturbance rejection / attenuation while maintaining good transient response in the RTAC system is known as a benchmark nonlinear control problem, which has been an intensive research subject since 1995. In this paper, we will further investigate the solvability of the robust disturbance rejection problem of the RTAC system by the measurement output feedback control based on the robust output regulation method. We have obtained a design by overcoming two major obstacles: find a closed-form solution of the regulator equations; and devise a nonlinear internal model to account for non-polynomial nonlinearities.

Simultaneous (C, A, B)-pairs for Infinite-Dimensional Systems

In this paper, the infinite-dimensional version of the simultaneous (C,A,B)-pair is introduced and its properties are investigated. And robust disturbance-rejection problem with dynamic compensator is formulated and then its solvability conditions are presented.

Robust Disturbance Rejection for Left-Invertible Linear Systems With Nonlinear-Uncertain Structure

The problem of robust disturbance rejection for left invertible linear systems, with nonlinear uncertain structure and with measurable and nonmeasurable disturbances, is solved via an independent from the uncertainties static measurement output feedback law. The necessary and sufficient conditions for the problem to have a solution are established. The general explicit expression of the measurement output feedback matrix and the measurement disturbances feedback matrix are derived. The feedback invariant poles are determined. Sufficient conditions for robust disturbance rejection with simultaneous robust stability are also established. The rejection of the influence of the rotary gust disturbing the vertical velocity of the longitudinal motion of an aircraft is achieved.

Robust disturbance-rejection problems for linear ω-periodic discrete-time systems

Two robust disturbance-rejection problems with state feedback and with incomplete-state feedback for linear /spl omega/-periodic discrete-time systems are studied in the framework of the so-called geometric approach. Also, some necessary conditions and/or sufficient conditions for the problems to be solvable are presented.

A note on robust disturbance-rejection problems for infinite-dimensional systems

In this paper, for infinite-dimensional systems characterized by unknown and unbounded system operators, some sufficient conditions for robust disturbance-rejection problems to be solvable are studied in the framework of the so-called geometric approach.

Robust Disturbance Rejection with Simultaneous Robust Input-Output Decoupling

The problem of robust disturbance rejection with simultaneous robust input-output decoupling of linear systems with nonlinear uncertain structure is solved. The controller is static and independent of the uncertainties. The necessary and sufficient conditions for the problem to have a solution via state feedback are established. The general analytical expressions of the feedback matrices and the decoupled closed-loop system are derived. The closed-loop system structural properties of pole assignment and stabilizability are studied. © 1997 Elsevier Science Ltd.