Integrated optimization of 3D structural topology and actuator configuration for vibration control in ultra-precision motion systems

Ever-increasing demands for precision and efficiency in ultra-precision motion systems will result in a lightweight and flexible motion system with complex dynamics. In this paper, integrated optimization of 3D structural topology and actuator configuration is investigated to achieve better vibration control performance in ultra-precision motion systems. A material interpolation model with high accuracy is proposed for the integrated optimization; a simple integral equation utilizing R-functions and level-set functions is established to represent non-overlapping constraints of actuators. Over-actuation degrees are utilized to actively control the dominant flexible modes. The objective function is the weighted sum of natural frequencies of the selected flexible modes. Controllability of the controlled flexible modes is guaranteed, and controllability of residual (uncontrolled) flexible modes is restricted in optimization. Mechanical requirements on thrust to mass ratios and currents in actuators are also considered as design constraints. A two-loop solving strategy combining the genetic algorithm and the modified optimal criteria method is adopted for optimization solving. The proposed method is verified by designing a simplified fine stage in the wafer stage; the optimized result proved its effectiveness.