Design and analysis of a sliding mode controller for systems with hysteresis

A sliding mode controller is proposed for a class of systems comprising a hysteresis operator preceding an kth-order linear plant without zero dynamics. The hysteresis operator is modeled with piecewise linear characteristics with uncertainties, and a nominal inverse operator is included to mitigate the hysteresis effect. A bound on the inversion error is used in the design of the sliding mode controller. The stability of the closed-loop system is established, and singular perturbation is exploited to analyze the system behavior within the boundary layer. In particular, analytical insight is gained on the frequency-scaling behavior of the tracking error under a periodic reference. Simulation and experimental results on a piezoelectric actuator-based nanopositioner are presented to illustrate the design and analysis, where the hysteresis nonlinearity is represented by a Prandtal-Ishlinskii operator.