High-order repetitive model reference control for linear systems with uncertain periodic references and disturbances

• Published in: International journal of systems science Vol. 53; no. 7; pp. 1456 - 1468
• Main Authors: Kurniawan, Edi, Harno, Hendra G., Adinanta, Hendra
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis 19.05.2022; Taylor & Francis Ltd
• Subjects: Control methods; Control systems design; Controllers; Discrete time systems; Disturbances; Feedback control; High-order repetitive control; Linear systems; Mathematical models; Model reference adaptive control; model reference control; Repetitive control; Stability analysis; time-varying references; Transient response; uncertain disturbances
• ISSN: 0020-7721; 1464-5319
• DOI: 10.1080/00207721.2021.2008545

This paper presents a systematic method to design a high-order repetitive model reference controller (HO-RMRC) for a discrete-time linear system that is subject to uncertain periodic references and disturbances. The controller design method we propose is established by combining two controller design schemes: high-order repetitive control (HORC) and model reference control (MRC). Here, the HORC is used to suppress uncertain periodic disturbances significantly and the MRC is used to track time-varying references without introducing new transient responses. The stability analysis of the resulting closed-loop system is provided and describes how admissible learning gains are determined to achieve stability and a desirable convergence rate. The efficacy of the proposed control method is demonstrated via numerical simulations where the performance of the resulting HO-RMRC is compared with those of the HORC and the MRC as standalone controllers. It is evident that the HO-RMRC outperforms the HORC and the MRC in simultaneously achieving perfect reference tracking and disturbance cancellation/attenuation.