Design of an Observer-Based Repetitive Control System to Reject Periodic Disturbance

Abstract

This paper concerns the design of an observer-based repetitive control system (RCS) to improve the periodic disturbance rejection performance. The periodic disturbance is estimated by a repetitive learning based estimator (RLE) and rejected by incorporation of the estimation into a repetitive control (RC) input. Firstly, the configuration of the observer-based RCS with the RLE is described. Then, a continuous–discrete two-dimensional (2D) model is built to describe the RCS. By choosing an appropriate Lyapunov functional, a sufficient condition is proposed to guarantee the stability of the RCS. Finally, a numerical example is given to verify the effectiveness of the proposed method.

Estimation and rejection of periodic disturbance in a preview repetitive control system

“…For most periodic systems, external periodic disturbances are unavoidable. Assumption 3 is the matching condition, often appearing in other literatures, such as [32,[41][42][43].…”

“…On the other hand, when l r = 0 s and H = 1, the RLE-based PRC law degenerates to an RLE-based RC law, which is equivalent to the research method of [32].…”

“…For most periodic systems, external periodic disturbances are unavoidable. Assumption 3 is the matching condition, often appearing in other literatures, such as [32, 41–43]. The matching condition means that the various disturbances and uncertainties enter the system via the same channels as the control inputs, which is necessary for the disturbances and uncertainties to be rejected by the control inputs.…”

“…It is the same way as the method of [37]. On the other hand, when $$$ {l}_r=0 $$$ s and $$$ H=1 $$$, the RLE‐based PRC law degenerates to an RLE‐based RC law, which is equivalent to the research method of [32]. Compared with the RLE‐based RC law, our method uses the future information of previewable reference signal which significantly improve the tracking performance of the closed‐loop system.…”

“…In order to deal with the problem of simultaneous action of disturbances between multiple periodic signals in a system, the design method of multiple repetitive controllers was proposed [31]. In addition, regarding the combination of RC and repetitive learning-based estimator (RLE), Shao and Xiang proposed a structure based on the internal mode principle of repetitive learning estimator combined with an observer to compensate for periodic disturbance at the input channel, which greatly enhances the system robustness [32]. Moreover, RC based on 2D system has been extensively researched by numerous scholars.…”