Multi-objective H∞ control applied to a wafer stage model

This paper considers several practical aspects of designing multi-objective H_∞ controllers. As a starting point, the LMI approach for designing multi-objective H_∞ controllers, as well as for computing lower bounds on the achievable performance, is summarized. Both techniques are based on the Youla parameterization. Subsequently, two important aspects are to choose the initial observer-based controller used to construct the Youla parameterization and the poles of the Youla parameter itself. In this paper, a specific synthesis technique is suggested for designing H_∞ controllers with an observer structure on which to base the Youla parameterization. Furthermore, a heuristic choice of the poles of the Youla parameter is presented. The results are illustrated in an academic example. Finally, the benefits of a multi-objective approach are demonstrated by applying the techniques to a model of a wafer stage; a mechanical positioning system used in IC manufacturing.