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

Abstract

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.

Keywords:

• High-order repetitive control
• model reference control
• time-varying references
• uncertain disturbances

Data availability statement

The data that support the findings of this study are available from the corresponding author, [E. Kurniawan], upon reasonable request.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Kementerian Riset dan Teknologi/Badan Riset dan Inovasi Nasional [grant number INSINAS2021].