Adaptive Filtered-x Least Mean Mixed-Norm Algorithm via Convex Combination for Active-Passive Hybrid Vibration Isolation

Micro vibration poses a significant challenge to the accuracy and reliability of the ultraprecision instruments. Among various vibration suppression methods, active-passive hybrid vibration isolation (APHVI) is a credible method that can isolate the external vibration and guarantee the effectiveness of the instruments. Typically, the vibration suppression algorithm of active vibration isolation (AVI) unit has an essential influence on the vibration isolation performance of the APHVI system. In this study, a convex combination based on two different normalized feedback filtered-x least mean mixed-norm (C-NFxLMMN) algorithms is established. The proposed C-NFxLMMN algorithm can mitigate the necessity of measurable external vibration and avoid the influence of external vibration on system stability by incorporating the feedback reconstruction of reference vibration signal and introduction of the normalized step size. Furthermore, the proposed algorithm can address the compromise between convergence rate and steady-state error by designing two adaptive filters grounded in different cost functions. To ensure the effectiveness of the proposed algorithm, its stability and computational complexity are also analyzed. Ultimately, the vibration isolation performance of the APHVI system employing the proposed algorithm is validated through a series of experiments.