Abstract: In order to optimize the control performances of an ultra-precision position stage with varying dynamics, a systematic procedure for discrete loop shaping controller optimization is proposed, which minimizes the conservativeness of the controller and eliminates the discretization approximating error of the commonly used continuous design-discretization approach. With the mapping between the z-plane and the w-plane established by w transformation, the design of discrete controllers in the z-plane is converted to the design of continuous controllers, and then accomplished by continuous loop shaping method. Besides the design criteria of loop shaping, structure singular value(μ) analysis is introduced as a non-conservative constraint for robustness, and a completed framework for discrete controller optimization is constructed with the objective of maximizing the control bandwidth and disturbance rejection. Then the genetic algorithm is applied to solve the optimization problem and obtain the optimal discrete controller. Analysis shows that the proposed method evade the influence of discretization approximating error, and the optimized discrete controller significantly improve the control performance of the ultra-precision positioning stage in experiments, which demonstrates the effectiveness of the proposed method.

Key words: Discrete controller, Genetic algorithm, Loop shaping, Robust control, Ultra-precision stage