Fractional-order control for nano-positioning of piezoelectric actuators

Piezoelectric actuators are widely used in the field of high-precision positioning control. However, due to the inherent hysteresis nonlinearity of piezoelectric actuators, it can seriously affect their accuracy in tracking and positioning systems, and even cause system instability. In order to suppress the hysteresis characteristics of piezoelectric, based on the analysis of piezoelectric characteristics and the characteristics of classical Bouc- Wen model, a Bouc-Wen model is adopted to describe the hysteresis characteristics of piezoelectric actuators, an artificial bee colony (ABC) algorithm is used to identify Bouc-Wen. The maximum error of the model is 2.49%. According to the established hysteresis model, its inverse model is obtained as the feedforward controller, and the inverse model compensation method is used to realize the open-loop control of the system. Since the feedforward controller based on the inverse model cannot eliminate the modeling errors and external disturbances of the inverse model, a fractional-order controller is designed on the basis of inverse compensation, and a compound control method combining feedforward control and feedback control is adopted. Experiments show that the fractional-order control system has fast response speed, small steady-state error and simple structure compared with other nonlinear controllers, positioning error is about 3%.