Robust Repetitive Learning Control for a Class of Nonlinear Systems

This paper proposes a framework for designing a repetitive learning controller (RLC) to track a periodic reference signal for a class of nonlinear systems in the presence of periodic uncertainties. The design process consists of several decoupled steps. First, a tracking controller is presented to track the reference without considering the uncertainties. Second, a robust controller is developed for linearized model around the equilibrium to handle uncertainties without taking into account the tracking performance. Third, by using a complementary robust control structure, a tuning parameter is introduced to balance the tracking performance and robustness. If the optimal parameter exists, by tuning this parameter with a data-driven optimization technique over repetition, the optimal performance can be obtained. Under the RLC setting, the existence of the optimal parameter makes this framework directly applicable to RLC. In this work, a well-known nonlinear output regulation is selected to track the periodic reference signal, while $\mathcal{H}_{\infty}$ is selected as the robust controller, and extremum seeking is picked as a data-driven optimization, to demonstrate our idea. The effectiveness and performance of our proposed control framework are analyzed and verified via the Furuta inverted pendulum system.

1 Introduction

Repetitive learning control (RLC) is an advanced control methodology designed for tracking a periodic reference or rejecting periodic uncertainties using the tracking performance observed in the last periods [1]–[3]. Different from feedback control, in which the measured error is fed back at the current period, the information of previous periods stored in the memory is used to enhance the tracking performance over the periods. Such a method has found successful applications in various engineering fields such as three-phase constant-voltage constant-frequency pulse width modulation inverters [4], permanent magnet synchronous motor servo systems [5], and lower limb rehabilitation exoskeleton [6]. More detailed information can refer to survey papers [7], [8].