Modeling and compensation of hysteresis in piezoelectric actuators

Piezoelectric actuator has the advantages of high rigidity, wide bandwidth, fast response and high resolution. Therefore, they are widely used in many micro and nano positioning applications. However, the hysteresis characteristic in the piezoelectric actuator (PEA) seriously affects its positioning accuracy and even causes instability. In this paper, a modified Prandtl-Ishlinskii (MPI) model, which can describe the rate asymmetric hysteresis of piezoelectric actuator, is studied. The hysteresis compensation is realized by using the rate dependent Prandtl-Iishlinskii model based on the improved Prandtl-Iishlinskii hysteresis model and the hysteresis characteristics of the driver measured in the laboratory under the frequency input of up to 100 Hz. In order to further reduce the error of feedforward compensation, a sliding mode controller is designed. The stability of the control system is proved by Lyapunov theory. The experimental results show that the linear error of the system is reduced from 10% to less than 1%, and the tracking error can also be reduced by 90%.