An Improved FXLMS Algorithm Based on Error Weight for Active Vibration Control of Plates

Purpose: This paper aims to address the limitations of the filtered-x least mean square (FXLMS) control algorithm in terms of significant noise in filtered results and hindered convergence and steady-state error reduction due to fixed-step size iterations. Methods: In this study, a new adaptive filtering algorithm based on error weight is proposed. Multiple moment weight errors are introduced into the objective function, and the error weights are automatically calculated during the iterative process. The step size is optimized to accelerate convergence speed and curtail steady-state error. The state space equation and transfer function expression of the simply supported plate system are calculated, and a hybrid control algorithm for plate vibration control is designed. Results: The proposed algorithm is simulated and compared with various existing variable step size algorithms and gradient-based least-squares (GLS) algorithms using Mathematica software. The simulation results demonstrate that the proposed algorithm achieves a convergence rate at least six iteration steps ahead of other algorithms, with a minimum reduction of 0.00405 in the average absolute error. This indicates the superiority of the proposed algorithm in terms of convergence speed and steady-state error reduction. Conclusion: The proposed algorithm demonstrates clear advantages in enhancing the rate of convergence of the FXLMS control algorithm and reducing steady-state error. Future research can focus on reducing variable step input parameters and minimizing algorithmic computational complexity.