Piezoelectric Actuators with Uncertainty: Observer-Based Hysteresis Compensation and Joint Stability Analysis

This brief considers sliding mode control of hysteresis in piezoelectric actuators. For modeling of hysteresis, the Bouc–Wen model that is based on differential equations is utilized. One of the states of this model is unmeasurable. Therefore, a state observer is proposed, and the proper selection of observer parameters is discussed. Based on the observed state, a control rule is proposed, and asymptotic stability of the observer-based closed-loop system is proven using the Lyapunov theory. This brief also presents a design method, i.e., sufficient conditions on design parameters for closed-loop stability are derived explicitly. Furthermore, the mass, stiffness, and damping coefficients in the model are assumed unknown. The values of these parameters are estimated using an online adaptation rule, and the control rule is modified based on the estimated parameters. The adaptation rule is extracted so that the asymptotic stability of the whole system is guaranteed. Simulation and experimental results are presented to demonstrate the effectiveness of the proposed scenarios.