Acceleration feedback of tracking control based on real time Fourier series

Acceleration feedback can be very useful in improving the performance of the closed-loop system, as indicated by many researchers. However, the difficulty in obtaining a good acceleration signal limits its applications. Acceleration estimation through numerical differentiation is noisy and direct measurement using an accelerometer may not be possible due to the cost or the availability. We propose a method of estimating the acceleration signal using real time shifting digital Fourier series (FS) transformation (RSDFT) and use this estimated acceleration as a feedback signal. Since the acceleration obtained through RSDFT is expressed in FS with finite terms, the high frequency noise and the resonant frequency of the system can be easily removed from the feedback signals. Therefore, high gain can be used to improve the performance of the closed-loop system. An experiment on a positioning table shows that this new method is effective in tracking control both in performance and implementation.