Adaptive Control for a Piezoelectric Positioning Platform Based on Improved Recursive Least Squares

Abstract

High-precision positioning is critical in modern industrial applications, yet the inherent hysteresis of piezoelectric actuators limits their accuracy and control performance. To address this problem, this paper proposes an adaptive control method combining feedforward and feedback control. Hammerstein structure is applied to characterize a piezoelectric actuator, which consists of a Prandtl-Ishlinskii model and a second-order linear model. The pseudo-inverse of the Prandtl-Ishlinskii model is applied as a feedforward controller to compensate for the hysteresis characteristics. As to the feedback control, a recursive least square with adaptive forgetting factor is proposed to estimate system parameters. Based on the estimated parameters, an adaptive self-tuning controller is designed to track the dynamic characteristics and reduce the feedforward compensation error. Finally, the proposed method is validated on a piezoelectric positioning platform. The results show that the feedforward pseudoinverse can compensate the hysteresis nonlinearity and the compensation error is close to 0. Compared to the PID composite control, the mean absolute error and the root mean square error are reduced by more than 12% and 13%, respectively.