An Adaptive Approximator-Based Backstepping Control Approach for Piezoactuator-Driven Stages

This paper investigates precise trajectory tracking of a piezoactuator-driven stage with hysteresis behavior by using an approximator-based adaptive tracking control approach. Differential equations consisting of the dynamics of a linear motion system and a hysteresis function are first studied for describing the dynamics of motion of the piezoactuator-driven stage with hysteresis behavior. Then, a numerical optimization method is taken to identify the values of the parameters adopted in the differential equations. From the differential equations, an equivalent state-space model with an augmented integral input and with a defined hysteresis variable is established. Moreover, to approximate the unavailable hysteresis variable, an adaptive approximator that comprises a Gaussian radial-basis function network is adopted. Furthermore, from the state-space model, an adaptive approximator-based backstepping trajectory-tracking control is developed. Using the proposed control approach to trajectory tracking of the piezoactuator-driven stage, an improvement in transient performance and tracking errors, and robustness to the disturbance load, can be provided. Last, to show the validity of the proposed control approach, an implementation of the control algorithm on the computer-controlled single-axis piezoactuator-driven stage was developed. From the experimental results, the feasibility of the proposed control for practical applications can be confirmed.