Synthesis of a robust iterative learning controller using an H∞ approach

Iterative learning control (ILC) is a powerful feedback methodology that iteratively improves the transient behaviour of processes that are repetitive in nature. Although most of the published ILC schemes are heuristic in nature, some initial research has been performed on the formulation of the ILC problem in the H_∞ mathematical framework. However, so far only the performance and robustness analysis of the ILC schemes has been performed for a given learning controller. In this paper it is shown how the synthesis of an iterative learning controller can be generalized to the synthesis of an H_∞ (sub)optimal controller. It is shown how a general learning control problem can be reformulated in the so-called `standard plant´ format, by choosing an appropriate weighting function for learning performance. Moreover, the process uncertainty can be included explicitly in the ILC design, by choosing appropriate weighting functions related to this uncertainty. It turns out that convergence and learning performance of this ILC scheme can be obtained for all systems in the uncertainty set, by solving a μ-synthesis problem. The practical usefulness of the scheme is verified on a wafer stage experimental setup