A Data-Driven Variable-Gain Control Strategy for an Ultra-Precision Wafer Stage With Accelerated Iterative Parameter Tuning

Abstract

Wafer stage is an important mechatronic unit of industrial lithography tool for manufacturing integrated circuits. To overcome the inherent limitations of fix-gain feedback control and improve the servo performance, a performance-oriented variable-gain control strategy with accelerated iterative parameter tuning is proposed for an ultra-precision wafer stage. The variable-gain controller comprises a fix-gain proportional-integral-derivative (PID) controller and add-on variable-gain elements, which are the focus of this paper. Specifically, the add-on variable-gain elements are significantly designed based on the main tracking error sources and error frequency of different reference trajectory phases. A weighted two-norm regarding the performance indexes of wafer stages, i.e., moving average (MA) and moving standard deviation (MSD) of the tracking error, is synthesized as the objective function, and the data-driven Levenberg–Marquardt-based iterative parameter tuning scheme is employed to find the optimal parameter values of the proposed variable-gain controller. Furthermore, to improve the convergence rate, a multiparameter accelerated iterative method is developed based on Aitken’s method. Finally, the proposed variable-gain control strategy is implemented on an ultra-precision wafer stage developed in our laboratory. Comparative experimental results demonstrate that the strategy performs best and achieves excellent improvement on both MA and MSD. During the scanning phase, MA and MSD are less than 1.02 and 2.35 nm, respectively. The proposed variable-gain control strategy is also suitable for other industrial applications.