Segmented iterative learning control for precision positioning of waferstages

This paper presents an application of a segmented iterative learning control (ILC) scheme for precision positioning of wafer stages using linear motors. The process of wafer scanning is repetitive, hence ILC has been used to improve performance from cycle to cycle. However, using uniform learning over the entire cycle results in degraded performance in those areas of the trajectory where nonrepetitive disturbances dominate. The paper proposes and compares implementation and performance of a segmented ILC scheme (a segmented P-type ILC algorithm) vis-a-vis a standard P-type ILC algorithm. Segmentation refers to separating the repetitive process into smaller segments with different learning rates. In this paper, we first consider the simple case of on-off learning, i.e., in certain segments learning is switched on, and in others, no learning is done. A metric is proposed to determine which segments to learn, and sufficient conditions for convergence and stability aspects of an on-off type segmented ILC scheme are presented. Finally, a comparison of the segmented ILC scheme and the standard P-type scheme is provided to illustrate the advantages of segmentation. Experimental validation of the theory developed is provided by implementation of these ILC schemes on a one-DOF prototype wafer stage.