Optimal Actuator Placement and Active Vibration Control of Over-Actuated Motion System in the Wafer Stage

Abstract

The null space of the 6-DOF gain decoupling matrix of actuators and a modified velocity feedback controller are adopted to suppress the vibration of the wafer stage during exposure. To deal with varying flexibilities at different performance locations, the vibration controller is designed to be a time-variant linear quadratic regulator, using the conventional gain scheduling method, which could provide good vibration control for each field under exposure. This control method can guarantee the stability of the closed-loop system and will not deteriorate the rigid modes control of the wafer stage. To minimize the control spillover caused by the higher uncontrolled modes, actuator placement is optimized to minimize their controllability grammians in modal coordinates. An unconstrained rectangular plate is used to represent the fine stage of the wafer stage. Effectiveness of the proposed method is verified on the plate through a closed-loop simulation.

Keywords

ultra-precision motion stage / vibration control / time-variant performance location