Adaptive control for the systems with Prandtl-Ishlinskii hysteresis

Hysteresis hinders the effectiveness of smart materials in sensors and actuators. It is a challenging task to control the systems with hysteresis. This paper discusses the robust control for the discrete time linear systems preceded with hysteresis described by Prandtl-Ishlinskii model. The unknown parameters of the system together with the density function of the hysteresis are adaptively estimated simultaneously. The robust sliding mode tracking controller is synthesized by using the estimated parameters of the system and the density function of the hysteresis. The output tracking error can be controlled to be as small as required by using the proposed controller. Simulation results show the effectiveness of the proposed algorithm.