A variable step-size FxLMS algorithm for active vibration control of cantilever beam

The conventional filtered-x least mean square (FxLMS) algorithm for active vibration control (AVC) is limited by the trade-off between convergence rate and steady-state error and by its sensitivity to abrupt input changes. To address these issues, a nonlinear step-size adjustment mechanism combining a bounded hyperbolic tangent mapping with a normalized variable step-size strategy is developed, based on which a variable step-size FxLMS algorithm, termed VSS-FxtanhLMS, is proposed. The convergence properties of the algorithm are analyzed in the mean and mean-square senses. For AVC of a flexible cantilever beam, the proposed algorithm is evaluated on a co-simulation platform established using ADAMS and Simulink under single-frequency, dual-frequency, and amplitude-step excitations, and is further validated on an experimental AVC platform. Co-simulation results show that VSS-FxtanhLMS achieves the smallest steady-state error, the lowest mean squared error, and the shortest convergence time under both single-frequency and dual-frequency excitations, while remaining convergent under amplitude-step excitation. In experiments, compared with FxasinhLMS, the strongest competing method, VSS-FxtanhLMS reduces the steady-state error by 17.48%, shortens the convergence time by 33.33%, and reduces the power spectral density by 1.72 dB/Hz. These results indicate that VSS-FxtanhLMS achieves improved steady-state accuracy, convergence behavior, and robustness under both simulation and practical conditions.