Discrete composite control for piezoelectric actuator systems

This paper considers the precise control of piezoelectric actuator systems with hysteresis nonlinearity. First, the piezoelectric nonlinearity model is described by a quasi-static hysteresis which is cascaded a non-hysteretic dynamics. Next, A discrete Preisach model represents the quasi-static hysteresis and a composite controller is proposed which consists of inverse model-based control (IMC) and discrete sliding mode control (DSMC) for piezoelectric actuator systems. In order to reduce the chattering, a hyperbolic tangent function replace signum function in DSMC. Moreover, a selector is proposed to select the appropriate input between the output of IMC and DSMC for the quasi-static hysteresis to promote the accuracy of the control strategy and the response speed. Finally, the stability of this piezoelectric system is guaranteed by a Lyapunov-based approach and the numerical simulation demonstrates the effectiveness of the proposed control strategy.