Simultaneous optimization in ultra-precision motion systems

In ultra-precision motion systems, vibration has non-negligible influence on motion performance, especially when these systems are getting more lightweight and more flexible. Research on simultaneous optimization of structural and controller design has been conducted to achieve effective vibration control. However, these methods will not have an adequate performance when used in ultra-precision motion systems with a time-varying performance location. In this paper, structural sizes, actuators configuration, and controller parameters are simultaneously optimized. To realize global vibration control and facilitate simultaneous optimization, a new vibration controller with position-dependent control gains is proposed, in which the worst-case vibration magnitude across all considered performance locations is set to be the objective function. To achieve high modeling accuracy, mass and stiffness distribution of actuators is also included into structural dynamics since it plays a large role in structural dynamics. The genetic algorithm is adopted to search for a global optimum. To increase efficiency, R-functions and level-set functions are introduced to translate the complicated over-lapping constraints into a simple integral equality. Neural fitting models instead of the finite element analysis method are used to derive eigenvalues and eigenvectors of the plant. The proposed method is verified on a simplified fine stage in the wafer stage. The numerical results prove its effectiveness.