Adaptive Iterative Learning Control for Tracking Trajectories With Non-Equal Trail Lengths and Initial Errors

Mingxuan Sun,Yizhao Zhan,Shengxiang Zou,Xiongxiong He

doi:10.1109/access.2021.3073458

Abstract

Both non-equal trail lengths and non-zero initial errors are practical challenges to learning control of robotic and mechatronic systems. Iterative learning to update input is still desired, because of the repetitive motion nature of the controlled objects. This paper concerns with the adaptive iterative learning control method for performing non-identical tasks. The time scaling technique is applied to normalize non-equal trail lengths, while the error-tracking approach is adopted for coping with initial errors. Theoretical results for performance analysis are presented in detail. The uniform convergence of the tracking error is examined, while boundedness of the variables in the closed-loop is characterized. It is shown that the fully-saturated learning algorithm plays an important role in assuring uniform boundedness of the control input. The proposed control design method does not require the magnitude transformation, and removes the assumption of identical initial conditions. The time scaling technique is verified to be effective in assuring the expected performance, for tracking tasks with non-equal trail lengths and initial errors.

Highlights

Iterative learning control (ILC) is to make full use of repetition of tasks, and by virtue of learning, the control performance is able to be improved effectively
We focus our attention on the time scaling technique for Adaptive ILC (AILC) control designs for tracking tasks with non-equal trial lengths, where the error-tracking approach is adopted in order to cope with initial errors
In this paper, the adaptive iterative learning control design method is presented for systems performing tasks with non-equal trial lengths and initial errors

Summary

INTRODUCTION

Iterative learning control (ILC) is to make full use of repetition of tasks, and by virtue of learning, the control performance is able to be improved effectively. Conventional AILC designs allow iteration-varying tasks with equal lengths. An iteration-average operator was introduced for the ILC controller design in [30] such that control information of previous trials can be useful for performance improvement of current trial The convergence both in almost sure and mean square senses was established in [31], as long as the probability of full-length iteration is not zero. By Lyapunov synthesis, it was shown that the adaptive ILC scheme is effective for parametric nonlinear systems in which the operation lengths vary randomly, under identical initial conditions. We focus our attention on the time scaling technique for AILC control designs for tracking tasks with non-equal trial lengths, where the error-tracking approach is adopted in order to cope with initial errors.

PROBLEM FORMULATION

AILC DESIGN AND ANALYSIS

NUMERICAL SIMULATION

CONCLUSION