Microvibration isolation by adaptive feedforward control with asymmetric hysteresis compensation

Abstract

Abstract This paper proposes an improved adaptive filtered-x normalized least-mean-square (FxNLMS) algorithm to achieve active microvibration isolation. Physically, microvibration disturbance is attenuated by a custom-developed magnetostrictive-actuated device. Whereas, magnetostrictive materials characterize hysteresis. Particularly, when the amplitude of the input current is large, the hysteresis loop describes strong asymmetry and nonlinearity. To avoid this phenomenon, in some studies, the actuators are limited to move over a small range, and thus the potential range of the isolated microvibration is restrictive. Then Jiles-Atherton model and Bouc-Wen model are utilized to compensate hysteresis, however these models are non-analytical with certain approximation. In order to compensate hysteresis more accurately, Preisach model, a popular operator-based model, is presented. However, due to the double integrals in this model, the hysteresis identification and inversion process is complicated. Therefore, we reduce hysteresis based on a modified Prandtl-Ishlinskii (PI) model which is more simple but effective. This model utilizes the polynomial operators to describe hysteresis asymmetry and nonlinearity. The inverse hysteresis is then applied to compensate the magnetostrictive-induced hysteresis and to alleviate microvibration combining with the conventional FxNLMS algorithm. An experimental setup is fabricated and some experimental investigations are conducted. Experimental results show that the improved FxNLMS algorithm enhances the performance of microvibration isolation effectively—in the presence of single-tone (4 Hz at amplitude of 250 μm) and double tone (2 Hz mixed with 6 Hz at amplitude of 250 μm) excited microvibration, the isolation ratios of the improved FxNLMS controller are 20.79 dB and 15.32 dB respectively, while those of the conventional FxNLMS controller are 13.83 dB and 10.65 dB respectively.