Note: Precision control of nano-positioning stage: An iterative learning-based model predictive control approach.

Due to mechanical vibration and nonlinearities such as hysteresis and creep effect, it is difficult to achieve precise control of nano-positioning stages for high-speed/bandwidth trajectory tracking. In this paper, we propose an iterative learning-based model predictive control (IL-MPC) approach to achieve this goal. IL-MPC strategically combines both model predictive control (MPC) and iterative learning control (ILC) tools: the MPC is applied to ensure that the tracking error is limited through all iterations and the ILC is applied to the system consisting of the MPC and the stage to guarantee high precision trajectory tracking with the existence of MPC modeling uncertainty and system nonlinearity. For experimental validation, IL-MPC was implemented to control a nano-piezo actuator to track both repetitive high-speed/broadband trajectories and trajectories with varying amplitude, phase, and frequency, respectively.