The tracking performance of piezoelectric nanopositioning stages is vital in many applications, such as scanning probe microscopes (SPMs). Although modified repetitive control (MRC) can improve tracking performance for commonly used periodic reference input, it is sensitive to unexpected disturbances that deteriorate tracking precision, especially for high-speed motion. In order to achieve high-speed and precision motion, in this paper, a new composite control scheme by integrating MRC with disturbance observer (DOB) is developed. To simplify controller implementation, the hysteresis nonlinearity is treated as external disturbance and the proposed method is designed in frequency domain. The stability and robust stability are analyzed, and an optimization procedure to calculate the controller parameters is employed to enhance the performance to the maximum extent. To validate the effectiveness of the proposed method, comparative experiments are performed on a piezoelectric nanopositioning stage. Experimental results indicate that the hysteresis is suppressed effectively and the proposed method achieves high-speed and precision tracking with triangular waves references up to 25 Hz and improves the disturbance rejection ability with disturbances under different frequencies and robustness to model uncertainty through comparing with feedback controllers and MRC, respectively.
Disturbance observer-based predictive repetitive control with constraints
