Open-Closed-Loop Iterative Learning Control for Linear Systems With Iteratively Variable Trail Lengths

Yun-Shan Wei,Kai Wan,Xuejing Lan

doi:10.1109/access.2019.2941276

Abstract

This paper addresses the open-closed-loop iterative learning control (ILC) issue for linear systems with iteratively variable trail lengths. Due to the varying trail lengths in iteration domain, some tracking information would be lost at the previous iterations. To compensate the absent information, an open-closed-loop ILC scheme composing of a feed-forward ILC part and a feedback control part is designed. The convergence of ILC tracking error in mathematical expectation sense is guaranteed by the feed-forward part. The tracking information of the current iteration is employed by feedback control part to compensate the missing tracking information at the previous iterations. To deal with the iteratively variable trail lengths, a modified tracking error at desired trail length is adopted in the designed ILC scheme. It is shown that the mathematical expectation of tracking error is convergent to zero. Two illustrative examples are carried out to show the effectiveness of the proposed ILC schemes.

Highlights

Iterative learning control (ILC) is especially suited for the dynamical systems with repetitive operation characteristics in a fixed time interval
The proposed open-closed-loop ILC law can be improved for linear discrete-time systems with higher relative degree
This paper has contributions relative to the related works in three main aspects as follows: (i) unlike the existing ILC schemes for dynamical systems with iteratively variable trail lengths [8]–[23], feedback control part is introduced in modified tracking error based P-type ILC such that the tracking information of the current iteration can be used to compensate the missing tracking information at the previous iterations. (ii) the developed open-closed-loop ILC method guarantees the asymptotic convergence of tracking errors in mathematical expectation sense, and speeds up the convergence process. (iii) the linear discrete-time systems with higher relative degree and initial state vibration with fixed mathematical expectation are considered

Summary

INTRODUCTION

Iterative learning control (ILC) is especially suited for the dynamical systems with repetitive operation characteristics in a fixed time interval. Since the order of ILC law designed in [15]–[20] is limited, the tracking information at the employed iterations might still be missing at some time points To cope with this situation, in this paper, an open-closedloop ILC scheme including feed-forward and feedback control parts is developed for linear discrete-time systems with iteratively variable trail lengths. This paper has contributions relative to the related works in three main aspects as follows: (i) unlike the existing ILC schemes for dynamical systems with iteratively variable trail lengths [8]–[23], feedback control part is introduced in modified tracking error based P-type ILC such that the tracking information of the current iteration can be used to compensate the missing tracking information at the previous iterations.

PROBLEM FORMULATION

ILLUSTRATIVE EXAMPLES

CONCLUSION