Precise trajectory tracking of a piezoactuator-driven stage using an adaptive backstepping control scheme

In this paper, an adaptive backstepping control scheme is proposed for precise trajectory tracking of a piezoactuator-driven stage. Differential equations consisting of dynamics of a linear motion system and a hysteresis function are investigated first for describing the dynamics of motion of the piezoactuator-driven stage with hysteresis behavior. Then, to identify the uncertain parameters designed in the differential equations, the Powell method of a numerical optimization technique is used. From the differential equations identified, an equivalent state-space model is developed, then a linear state-space model through a state transformation is established. In the linear state-space model, the hysteresis function is approximated by the first three terms of a Taylor series expansion. Based on the linear state-space model, we developed an adaptive backstepping control for the trajectory tracking. By using the proposed control approach to trajectory tracking of the piezoactuator-driven stage, improvements in the tracking performance, steady-state error, and robustness to disturbance can be obtained. To validate the proposed control scheme, a computer-controlled, single-axis piezoactuator-driven stage with a laser displacement interferometer was set up. Experimental results illustrate the feasibility of the proposed control for practical applications in trajectory tracking