Repetitive control with Prandtl-Ishlinskii hysteresis inverse for piezo-based nanopositioning

Repetitive control (RC) is a feedback-based approach useful for tracking periodic reference trajectories, for example in scanning applications. The major challenges with RC include closed-loop stability, robustness, and minimizing the steady-state tracking error. In piezo-based nanopositioning systems, the hysteresis effect can limit the performance of RC designed based on a linear dynamics model. An enhanced discrete-time repetitive controller is combined with an inverse-hysteresis compensator based on the Prandtl-Ishlinskii (P-I) model for hysteresis. The feasibility of the inverse model and the performance of the RC system with the inverse compensator are investigated experimentally. Measured results from a flexure-guided nano-positioner show that hysteresis compensation leads to improvement in the stability margin and rate of convergence of the tracking error for the closed-loop RC system. For scanning at 25 Hz, the maximum tracking error is 1.72%.