Sliding-mode tracking control of piezo-actuated nanopositioners

In this paper we propose a robust control scheme for a piezo-actuated nanopositioner to track arbitrary references. The positioner is represented as a linear system preceded by hysteresis, which is modeled with a Prandtl-Ishlinskii (PI) operator. In order to reduce the hysteresis effect, an approximate operator is used as a feedforward compensator. A sliding mode controller is then used to mitigate the effect of inversion error. In existing work on sliding mode control of piezo-actuated systems, the coefficient of the switching component of the control is typically chosen by trial and error. In contrast, in this work we analytically derive an upper bound on the inversion error using the hysteresis model. This bound is a function of the state and time, which is much less conservative than constant bounds. The stability of the closed-loop system is established by Lyapnuov analysis. Simulation and experimental results are presented to demonstrate the effectiveness of the proposed method.