Prescribed Performance Sliding-mode Control for Piezoelectric Micro-Positioning Stage

In order to further improve the positioning accuracy of piezoelectric micro-positioning stages, a discrete-time sliding mode controller with a prescribed performance function is designed based on the Hammerstein model. First, this paper proposes a new prescribed performance function, which can set the time at which the system reaches the steady state arbitrarily. Then, the error with constraint range is transformed into an unconstrained form by using the error transformation method, and a discrete sliding mode controller is designed. Finally, the control simulation is carried out using sine wave and triangle wave, and compared with the conventional discrete sliding mode controller. The simulation results show that the error of the piezoelectric micro-positioning stages can converge in the prescribed region, and the error of the proposed method is less than that of the discrete sliding mode control.