Observer-based sliding mode control with adaptive perturbation estimation for micropositioning actuators

Control of piezoelectric actuators is under the effects of hysteresis that could affect actuators micropositioning accuracy. In this paper a modified Prandtl-Ishlinskii (PI) operator and its inverse is utilized for both identification and real time compensation of the hysteresis effect. As a result, the actuator dynamic model would be transformed to the second order linear dynamic model. Considering the parametric uncertainties, PI estimation error and probably unmodeled dynamics, a variable structure controller coupled with adaptive perturbation estimation is proposed for trajectory tracking of the piezoelectric position. Considering the very noisy output of the actuator, a high-gain observer would estimate full states from the only measurable position trajectory. The stability of the controller in the presence of the estimated state is demonstrated with the Lyapunov criterion. Comparing to the widely used proportional-integral controller, the experimental results depicts that the proposed approach is greatly achieved in precisely tracking of multiple frequency trajectories.