Robust Guaranteed-Cost Preview Repetitive Control for Polytopic Uncertain Discrete-Time Systems

Abstract

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, the 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 the guaranteed cost control problem for the augmented dynamic system. For given performance index, the sufficient condition of asymptotic stability for the closed-loop system is derived by combining parameter-dependent Lyapunov function method with linear matrix inequality (LMI) techniques. By 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.

Preview repetitive control for linear discrete‐time periodic systems

“…where 𝛥A(k) and 𝛥B(k) represent time-varying N 1 -periodic uncertain matrices. The proposed design methods in this article were extended to uncertain periodic systems (37); but, these results are not presented in this article.…”

“…Comparison of the output response of the periodic system with PRC and RC for signal (37) F I G U R E 2 Tracking error of the periodic system with PRC and RC for signal (37) F I G U R E 3 Output response of system (1) with PRC and RC for signal (38) F I G U R E 4 Tracking error of the periodic system with PRC and RC for signal (38) F I G U R E 5 Output response of the periodic system with PPC, PC, and RC F I G U R E 6 Tracking error of the periodic system with PRC, PC, and RC Example 2. To present the effectiveness of the proposed methods in the output-feedback setting, a numerical example is expressed as follows:…”

“…We adopt N = 20, N 1 = 2, and 𝛽 = 0.7, matrices S(k) = 1.5C Z (k)(k = 1, 2), and preview length M R = 6 and M R = 1. According to Theorem 2, we used LMI toolbox of MATLAB to solve matrix variables L(k), U(k), Y 2 (k), and X 2 (k) in LMIs (35).…”

“…To our knowledge, PRC problems for discrete-time periodic systems have not been considered and have been rarely studied in literature. [35][36][37] The proposed PRC design method can be used in certain applications [35][36][37] when N 1 = 1. This study focused on the design of periodic preview repetitive (PPR) controller for discrete-time periodic systems, under the assumption that periodic reference signals are previewable.…”

Optimal preview repetitive control for impulse-free continuous-time descriptor systems

“…The design method of discretetime sliding mode preview repetitive servo systems was introduced [36,37]. Very recently, an LMI-based robust guaranteed-cost preview RC for uncertain discrete-time systems was proposed [38].…”