Hysteretic non‐linearity observer design and robust control for piezoelectric actuators

Abstract

The problem of tracking control for piezoelectric actuator (PEA) is investigated in this article. In consideration of that, the control precision of PEA is being restricted due to the hysteretic effect. For the purpose of improving the tracking performance, two issues are, respectively, taken into account – the compensation of the hysteretic effect and the controller design for the PEA system. To solve these problems, first, a new hysteresis observer based on sliding mode control theory is established. The design of the observer has considered the uncertainty in PEA modelling and the exogenous disturbance. Besides, according to Lyapunov theory, the hysteresis observer can asymptotically estimate the hysteretic character with H ∞ performance. Second, a fault-tolerant controller based on robust backstepping control theory is presented to make the PEA system to track the desire input. At last, numerical examples are given to verify the effectiveness of the proposed methods.