Accounting for hysteresis in repetitive control design: Nanopositioning example

This paper deals with designing a repetitive controller (RC) for tracking periodic reference trajectories for systems that exhibit hysteresis, such as piezoelectric actuators used in nanopositioning systems. Hysteresis can drastically limit the performance of an RC designed around a linear dynamics model, and thus the effect of hysteresis on the closed-loop stability of RC is analyzed and the allowable size of the hysteresis nonlinearity for a stable RC is quantified. But when the hysteresis effect exceeds the maximum bound, an inverse-hysteresis feedforward controller based on the Prandtl–Ishlinskii hysteresis model is used to compensate for the nonlinearity. The control method is implemented on a custom-designed nanopositioning stage. Experimental results show that by incorporating hysteresis compensation the stability margin and the rate of error reduction improve. Likewise, the maximum tracking error reduces by 71%, from 13.7% (using industry-standard integral control) to 3.9% (using RC with hysteresis compensation), underscoring the benefits of RC with hysteresis compensation.