Reweighted adaptive bilinear filters for an active noise control system with a nonlinear secondary path

The nonlinearities of active control systems are the main factors that deteriorate noise-reduction performance. To improve the performance of a control system with a nonlinear secondary path, a filtered-x least mean square algorithm using reweighted bilinear filters is proposed in this paper and a generalized filter to model different nonlinear secondary paths is explored. Within the controller of an adaptive feedforward control system, the proposed algorithm uses trigonometric expansions to achieve high-order nonlinearities and combines the cross terms between the controller output, sine and cosine functions of the input with the reference signal. As a result, satisfactory control performance can be achieved with a shorter memory length of the controller compared to certain control algorithms. It is also found that the introduction of a reweighting factor in the weight-updating process can effectively reduce the interference produced by the small coefficients of the control filter and accelerate the convergence rate. The computational complexity of the proposed algorithm is analyzed and its control performance is verified through simulation experiments with different nonlinear secondary paths and input noises. Simulation results show that the proposed algorithm outperforms four other widely accepted algorithms in terms of convergence rate and residual error.