Synthesis of robust multivariable iterative learning controllers with application to a wafer stage motion system

Iterative Learning Control (ILC) is a powerful control concept 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-infinity mathematical framework. However, so far only performance and robustness analysis of ILC schemes has been performed for a given (heuristically designed) 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-infinity (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, process uncertainty can be included explicitly in the 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 mu-synthesis problem. The practical usefulness of the scheme is verified on a wafer stage experimental set-up.