Adaptive Sliding Mode Control of Piezoelectric Tube Actuator With Hysteresis, Creep and Coupling Effect

The piezoelectric tube actuator of Atomic Force Microscope (AFM) realizes rapid scanning in nano-scale. However, hysteresis, creep and coupling effect of piezoelectric tube actuator significantly limit the precision of AFM. In this paper, an adaptive sliding mode controller is proposed to minimize the tracking error due to the adverse effects. The piezoelectric tube actuator is characterized as a multiple-input-multiple-output (MIMO) nonlinear time-varying system because of hysteresis and creep. The controller is designed based on the reduced order nonlinear finite element (FE) model. Hysteresis is divided into a linear part and a bounded time-varying unknown part to reduce the bound of the uncertainties. The latter part together with creep and electrode dislocation is considered as bounded uncertainty. The controller gains of the equivalent control part are estimated through adaptive laws. The sliding mode observer is designed based on Walcott Zak observer for estimating the unmeasurable states. Lyapunov criterion is stated to guarantee the stability of the closed loop system. The simulation of the piezoelectric tube actuator with the adaptive sliding mode controller is performed under scanning operation. The result shows that the tracking errors are bounded in small values. Finally, the performance of the adaptive sliding mode controller is compared with the output feedback controller and the proportional-integral (PI) controller which is commonly adopted in AFM.