Trajectory tracking of piezoelectric positioning stages using a dynamic sliding-mode control.

Trajectory tracking performance of a piezoelectric positioning stage almost depends on whether the tracking controller can effectively compensate the inherent hysteresis phenomenon. In this paper, a dynamic sliding-mode control (DSMC) with backstepping is proposed for the trajectory tracking of the piezoelectric positioning stage, which is suitable for a component of scanning microscopes. An equivalent model developed from a linear motion dynamics with addition of the hysteresis nonlinearity and strain-dependent function first is proposed to approximately represent the dynamics of motion of a one-dimensional piezoelectric positioning stage. Then, based on the equivalent model, the DSMC with an asymptotical sliding surface is proposed for the trajectory tracking control of the piezoelectric positioning stage. Moreover, the analysis of stability can be completed by mathematics, and the convergence rate of the tracking error can be governed by the choice of the control parameter values. Using the DSMC to trajectory tracking control, the piezoelectric positioning stage becomes more suitable for practical applications, especially with the need of various trajectories tracking in microscopy. To validate the proposed control scheme, a computer-based controller and a piezoelectric positioning stage with a capacitive displacement sensor are implemented. Experimental results illustrate the feasibility of the proposed controller for trajectory tracking applications.