Multi-Period Repetitive Control for Nonparametric Uncertain Systems

Qiuzhen Yan,Zengfang Li,Jianping Cai,Qiyao Yang

doi:10.1109/access.2019.2946103

Abstract

This paper addresses the period-signal tracking problem for a class of nonparametric uncertain systems with several periodic time-varying disturbances, where there is no common multiple among the period lengths of reference signal and disturbances, or the common multiple is difficult to be obtained even if it exists. A multi-period repetitive control scheme is proposed by using Lyapunov approach, with robust technique and unsaturated multi-period repetitive learning technique being integratedly used to compensate uncertainties and periodic disturbances. As the repetitive cycle increases, the system output can track its reference signal perfectly over its full period. Through rigorous analysis, we prove that the estimations themselves are bounded, which is better than the boundedness in the sense of $L_{2}$ norm obtained in many existing unsaturated learning results. In the end, an illustrative examples is provided to demonstrate the efficacy of the proposed multi-period repetitive control scheme.

Highlights

In the real industrial process, there exist many periodic control tasks that need be accomplished over an infinite time intervals, such as tracking periodic trajectory and rejecting periodic disturbances
Yan et al.: Multi-Period Repetitive Control for Nonparametric Uncertain Systems repetitive learning method is adopted for compensating periodic uncertainties in nonlinear discrete-time systems
Motivated by the above discussions, this work focus on the tracking problem for a class of nonparametric uncertain systems with a number of periodic time-varying disturbances, where there is no common multiple among the period lengths of reference signal and disturbances, or the common multiple is difficult to be obtained even if it exists

Summary

INTRODUCTION

In the real industrial process, there exist many periodic control tasks that need be accomplished over an infinite time intervals, such as tracking periodic trajectory and rejecting periodic disturbances. In [24], Yang et al proposed a continuous universal repetitive learning control scheme to solve the periodic trajectory tracking problem for a class of nonlinear dynamical systems with nonparametric uncertainty and unknown state-dependent control direction matrix. Q. Yan et al.: Multi-Period Repetitive Control for Nonparametric Uncertain Systems repetitive learning method is adopted for compensating periodic uncertainties in nonlinear discrete-time systems. Motivated by the above discussions, this work focus on the tracking problem for a class of nonparametric uncertain systems with a number of periodic time-varying disturbances, where there is no common multiple among the period lengths of reference signal and disturbances, or the common multiple is difficult to be obtained even if it exists. In order to overcome this difficulty, this work proposes a novel multi-period repetitive control scheme, with multiperiod learning control and robust control combinedly used to handle nonparametric uncertainties and periodic disturbances. To demonstrate the effectiveness of the proposed multi-period repetitive control scheme, an illustrated example is shown in Section 5, followed by Section 6 which concludes this work

PROBLEM FORMULATION

CONVERGENCE ANALYSIS

ILLUSTRATIVE EXAMPLE

CONCLUSION