Simultaneous optimization of actuators' configuration and vibration control in ultra-precision motion systems with a time-varying performance location

Abstract

Demands for both high accuracy and throughput levels of ultra-precision motion systems lead to a lightweight and flexible design, which makes the vibration control indispensable. Simultaneous optimization of vibration controllers and actuators' configuration (sizes and locations) could result in better vibration control performance. However, linear time-invariant vibration controllers that are mostly adopted in the optimization may not be adequate for motion systems with a time-varying performance location, while advanced vibration controllers are too complicated to be integrated into the simultaneous optimization. In this paper, a simple and effective vibration control method is proposed for ultra-precision motion systems with a time-varying performance location based on over-actuation and modal assumption principles, then the controller parameter and actuators' configuration are simultaneously optimized to minimize the H2 norm of vibration magnitudes across all performance locations for optimal global vibration control performance, meanwhile satisfying other mechanical requirements such as accelerations and currents constraints. R-functions and level-set functions are utilized to translate the complicated nonoverlapping constraints of actuators into a simple integral equality. The genetic algorithm is adopted for optimization solving. The proposed method is verified on a simplified fine stage in the wafer stage and the numerical results proved its effectiveness.