Discrete-Time Repetitive Control with a Range-Based Filter for Dual-Stage Systems

This paper describes a closed-loop implementation of a range-based filter (RBF) augmented by repetitive control (RC) for tracking periodic trajectories in dual-stage nano-positioning devices. Building on the authors' previous work, which focused on design and development of the RBF, this paper seeks to improve tracking performance by adding RC to the closed-loop control structure. The RBF is designed with the goal of allocating control effort to the individual actuators based on desired motion range. Assuming the reference trajectory is periodic, residual tracking error will persist in each cycle of the trajectory. RC has the ability to reduce the residual error with each operating cycle. The control algorithm is presented and experiments are carried out on a custom serial dual-stage nanopositioner in order to verify the proposed RC-RBF control method. Results show that the root-mean-square (RMS) tracking error can be improved with the addition of RC by up to 40% when compared to the RBF alone.