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

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.