Sliding-Mode Control for Piezoelectric Actuators Based on Hysteresis Observer

A sliding-mode control (SMC) scheme based on hysteresis observer is designed in this paper for precision trajectory tracking of piezoelectric actuators. A mathematical model considering the dynamics of a mass-spring-damper trio and the hysteresis friction force describing the parameters of bristle stiffness, damping and viscous is proposed. A lumped uncertain function composed of the mechanical parameters, displacement and its deriviation, hysteresis friction force and external load force is estimated by a hysteresis observer. An asymptotically stable sliding surface is defined. Lyapunov stability theory is applied to guarantee the asymptotical stability for the trajectory tracking error. Experiments are conducted to validate the effectiveness of the proposed method. Results show that a satisfied tracking response to a sinusoidal trajectory is achieved, and the positioning errors under a triangle scanning contour are dramatically reduced compared with the traditional SMC.

Hysteresis Observer Design of Sliding Mode Control for Piezoelectric Actuators

Piezoelectric actuators (PEAs) have been widely used in micro fabrication. But the hysteresis inherited in PEAs leads to a severe inaccuracy and deteriorated tracking performance. In this paper, a hysteresis observer is designed for PEAs to estimate the hysteresis, mechanical parameter varieties, positioning error and external disturbance. A Bouc-Wen model is associated with a linear second-order mass-damping-spring trio to model the dynamics. An asymptotic sliding surface is selected. Lyapunov stability theory is applied to guarantee the asymptotical stability for the trajectory tracking error. Experiments are conducted to validate the effectiveness of the proposed method. Results show that a satisfied tracking response to a sinusoidal trajectory is achieved, and the positioning errors under a triangle scanning contour are dramatically reduced compared with the traditional SMC.