Analysis Of Linear Iterative Learning Control Schemes Using Repetitive Process Theory

Abstract

ABSTRACTThe purposes of this paper are (i) to critically review existing results on the use of the systems theory for repetitive processes in the analysis of a wide class of linear iterative control laws, and (ii) to present some new results on controller design using this general approach. This paper first presents results on the stability and convergence properties of a general class of iterative learning control schemes using, in the main, theory first developed for the subclass of so‐called differential and discrete linear repetitive processes. A general learning law that uses information from the current and a finite number of previous trials is considered and the results are interpreted in terms of basic systems theoretic concepts such as the relative degree and minimum phase characteristics. It is also shown that a number of other approaches reported in the literature are, in fact, special cases of the results obtained in the repetitive process setting. In the second part of the paper, new results on controller design are given based on 2D transfer function matrices together with new results on the robustness of norm optimal iterative learning control schemes.