Fuzzy sliding mode control for a class of piezoelectric system with a sliding mode state estimator

A new fuzzy sliding mode hysteresis compensating control strategy for a kind of typical piezoelectric system (PES) is proposed in this paper. Firstly, a typical nonlinear dynamic model of the PES is introduced. In order to compensate the hysteresis of the PES, an ideal linear hysteretic model is introduced by analyzing the characteristic of dynamic hysteretic model. Then, the ideal hysteretic model is transformed into an expected linear model by multiplying a slope conversion factor which can be obtained by experiment. Further, the sliding mode control principle is constructed to calculate the hysteretic compensating control law, which can guarantee the practical hysteretic characteristic to reach the expected linear output feature. Consider the unmeasured hysteresis output of the PES, we further design a sliding mode estimator to estimate the hysteretic part’s output. Finally, we derive the adaptive law of the fuzzy sliding mode controller, and demonstrate its stability through Lyapunov stability theory. The simulation results show the validity of the sliding mode compensator for this kind of nonlinear dynamic model of PES.