Variable–structure repetitive control for discrete–time linear systems with multiple–period exogenous signals

• Published in: International journal of applied mathematics and computer science 2020-06, Vol.30 (2), p.207-218
• Main Authors: Kurniawan, Edi, Harno, Hendra G., Wijonarko, Sensus, Widiyatmoko, Bambang, Bayuwati, Dwi, Purwowibowo, Purwowibowo, Maftukhah, Tatik
• Format: Article
• Language: English
• Subjects: Control systems; fast transient response; Feedback control; Linear systems; multiple-period signals; Parameter robustness; Repetitive control; Resonant frequencies; Robustness; Stability analysis; Transient response; variable-structure control
• ISSN: 1641-876X; 2083-8492
• DOI: 10.34768/amcs-2020-0016

A new method to construct a discrete-time variable-structure repetitive controller for a class of linear systems perturbed by multiple-period exogenous signals is presented. The proposed control scheme combines the features of the discrete-time multiple-period repetitive control (MP-RC) and variable-structure control (VSC) techniques. The MP-RC part is assigned to simultaneously track and reject periodic signals consisting of multiple uncorrelated fundamental frequencies. The VSC part is then integrated to provide a fast transient response and robustness against plant parameter variations. Stability and robustness analyses are also elaborated to ensure that the resulting closed-loop system satisfies the desired control objectives. Moreover, it is shown through an example that the repetitive control system constructed using the proposed control method can effectively track a sinusoidal reference signal despite the presence of a multiple-period disturbance.