Abstract
In this paper, a robust guaranteed-cost preview repetitive controller is proposed for a class of polytopic uncertain discrete-time systems. In order to improve the tracking performance, a repetitive controller, combined with preview compensator, is inserted in the forward channel. By using the L-order forward difference operator, an augmented dynamic system is constructed. Then, the guaranteed-cost preview repetitive control problem is transformed into a guaranteed-cost control problem for the augmented dynamic system. For a given performance index, the sufficient condition of asymptotic stability for the closed-loop system is derived by using a parameter-dependent Lyapunov function method and linear matrix inequality (LMI) techniques. Incorporating the controller obtained into the original system, the guaranteed-cost preview repetitive controller is derived. A numerical example is also included, to show the effectiveness of the proposed method.
Highlights
In some control systems, it is hoped that the output can track the reference signal without steady-state error, even in the presence of uncertainty and/or exogenous disturbances
Preview control [1,2] is one of the many ways to solve this kind of control problem
As a typical regulator method, the linear quadratic regulator optimal control is a powerful technique for designing preview controllers [8,9,10]
Summary
It is hoped that the output can track the reference signal without steady-state error, even in the presence of uncertainty and/or exogenous disturbances. In [8], a preview-based linear quadratic design method was investigated for reference-tracking motion control. For a class of polytopic uncertain discrete systems, by combining parameter-dependent Lyapunov function method with LMI techniques, a static output feedback preview tracking controller was presented in [18]. Based on two-dimensional system theory, the problem of designing discrete-time repetitive-control systems was studied in [26,27]. The observer-based repetitive controller design method for discrete-time systems with uncertainties was presented in [28]. For a class of uncertain discrete-time systems, a guaranteed-cost preview controller was proposed in [19]. For discrete-time linear systems with uncertainties, a method of designing a guaranteed-cost robust discrete repetitive controller based on two-dimensional model was proposed in [34]. The notation X > 0 (< 0) means that matrix X is positive (negative) definite
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