Evaluation of FxLMS and FxRLS algorithms in active vibration control using piezoelectric stack actuators for gear transmission

Abstract Control algorithm plays a crucial role in active vibration control (AVC) for gear transmission. This study aims to evaluate the performance of adaptive control algorithms, filtered-x least mean square (FxLMS) and filtered-x recursive least square (FxRLS), in the AVC of gear transmission. A dynamic model incorporating shafts, gear pairs, and bearings is developed. Based on the vibration response of the dynamic model, a AVC system using piezoelectric stack actuators is designed. Theoretical analysis and numerical simulations are conducted to compare the optimal weight search trajectories of the two algorithms under various operating conditions. Results reveal that the FxRLS algorithm is less sensitive to the eigenvalue spread of the correlation matrix than the FxLMS algorithm. Co-simulations and experimental validation confirm the vibration suppression capabilities of the AVC system. While both algorithms effectively reduce vibrations, the FxRLS algorithm demonstrates superior convergence speed and vibration suppression performance.