Model-reference Control For Linear Systerms Using Dynamic Compensators

Model-reference tracking control is one of the most important issues in the theory of control system design.A vast amount of systems is mainly controlled by model-reference tracking and related methods.This problem has been widely studied since Whitaker and his collaborators propose the theory of model-reference tracking control in the 1950 s.In this paper,we study the model-reference tracking control problem for linear systems using dynamic compensator.The main results can be summarized as follows:Firstly,a sufficient condition for the existence of the model tracking controller is given and the model tracking controller is established.This controller is composed of two parts: one is a feedback stabilizing controller and the other is a compensator.Based on a result on output feedback eigenstructure assignment,parametric expression for the feedback stabilizing controller is proposed;based on a parametric solution to a class of Sylvester matrix equations,parametric expression for the compensator is presented.On this basis,a parametric algorithm for solving the model-reference tracking control problem is given.The algorithm involves only the selection of design parameters and simple algebraic operations.This design approach provides all the design degrees of freedom and allows us to further consider other performance indexes,such as robustness.A numerical example illustrates the application process of the algorithm,which shows that the algorithm is simple and effective.Secondly,based on the proposed model tracking controller,the robust model-reference tracking control problem for linear systems subject to parameter perturbations is considered.It is shown that the problem can be decomposed into two sub-problems: one is robust feedback stabilization problem and the other is a robust tracking compensation problem.The main task is to solve the robust tracking compensation problem.Based on the criterion of minimum error of tracking compensation condition,an objective function on robust model-reference tracking is established.Based on the obtained parametric solution to the model-reference tracking controller,the robust tracking compensation problem can be turned to a minimization problem of the objective function.On this basis,an algorithm for solving the robust model-reference tracking control problem is given.A numerical example demonstrates the application process of the algorithm,which proves that the algorithm is simple and effective.