Beyond decentralized wafer/reticle stage control design: a double-Youla approach for enhancing synchronized motion

Industrial wafer scanners often consists of multiple subsystems. Traditionally, these systems-of-systems are divided into manageable subproblems at the expense of the overall performance, that is determined by the synchronicity of the motions of the subsystems. The aim of this paper is to enhance overall system performance by posterior coupling of the controlled subsystems. A framework that relates to the Youla parameterization is developed that connects the additional control elements affinely to the overall system performance criterion. The resulting framework parametrizes all stabilizing bidirectional coupling controllers, and enables improved performance. Robust stability is subsequentially addressed through a double-Youla approach. Application to a wafer scanner confirms superior performance of the joint wafer stage and reticle stage performance, while maintaining full system robust stability.