High precision tracking of a piezoelectric positioner using a discrete-time sliding mode control

This paper proposes a new comprehensive control strategy to precisely control a piezoelectric positioner by combining discrete-time sliding mode control (DSMC) with the Prandtl-Ishlinskii hysteresis model. In order to obtain precision tracking control, a direct inverse hysteresis compensation method is firstly adopted to compensate for the asymmetric hysteresis nonlinearity. Due to the existence of hysteresis modeling error, the dynamics behavior of the piezoelectric positioner with hysteresis compensation can be treated as a linear second order plant plus an unknown lumped disturbance term. Then a discrete-time sliding mode controller with a disturbance observer is designed to stabilize the position error and improve the position accuracy. The stability of DSMC and the convergence of the disturbance observer are both carried out. It is shown that the tracking performances are robust to the parametric uncertainties and unknown disturbances. Eventually, different trajectory-tracking experiments are performed, and the comparative experimental results are presented to confirm the significantly better performance of the proposed control strategy.