A New Variable Forgetting-Factor and Variable Step-Size FxLMS Algorithm for Active Vibration Control

The step-size in the Filtered-x Least Mean Square (FxLMS) algorithm significantly impacts the algorithm's convergence speed and steady-state error. To enable the control algorithm to balance the relationship between convergence speed and steady-state error, the hyperbolic secant function is introduced to update the step-size factor, leading to the proposal of the variable step-size FxLMS algorithm based on the hyperbolic secant function. To reduce the parameter tuning workload for the forgetting factor in the step-size update formula of the proposed algorithm, a normalized update formula for the forgetting factor is designed, the variable forgetting-factor and variable step-size FxLMS algorithm is proposed. The proposed algorithms ensure that when the error is large, the step-size factor is also large, allowing for rapid convergence. As the error decreases, the step-size factor reduces while maintaining a small steady-state error. This paper summarizes two variable step-size FxLMS algorithms and two proposed improved algorithms, and validates their effectiveness using a joint simulation platform constructed by ADAMS and Simulink.