Robust control design for a piezoelectric actuator system with dominant hysteresis

In this paper, a robust controller for a piezoelectric actuator system with dominant hysteresis is developed. First, the external part of a transformed piezoelectric actuator via a feedback linearizing control evokes a linear dynamic system with uncertainties. The uncertainty is not necessarily to satisfy the matching condition. A reference model with the desired amplitude and phase properties for the time-varying trajectory is given to obtain an error model. Then, an equivalent control using the known part of system dynamics is designed to achieve the desired control behavior. Furthermore, the uncertainties are tackled by the switching control. In summary, the proposed control contains a feedback linearizing control with a reference model and a sliding-mode control including an equivalent control and a switching control. Finally, the stability of the overall system is verified by the Lyapunov theory so that the ultimately bounded tracking is accomplished. Simulations of piezoelectric actuator are presented to verify the usefulness of the proposed control.