A novel approach for improved noise reduction performance in feed-forward active noise control systems with (loudspeaker) saturation non-linearity in the secondary path

In active noise control systems, the performance of the most celebrated filtered-x-least mean square (FxLMS) adaptive algorithm is degraded in the presence of non-linearity in the secondary path. In this article, we propose a novel approach to improve the performance of FxLMS algorithm in the presence of saturation type non-linearity in the secondary path. In the proposed method, the weights of the controller are adapted by minimizing a cost function consisting of two terms. The first term is the squared instantaneous residual error while the second term is the weighted square of the difference between input and output of (estimated) saturation non-linearity. Consequently, in case the saturation has occurred, the resultant adaptive algorithm minimizes the residual error while keeping the controller output close to its saturation limit. This avoids unnecessary fluctuation of the (controller) weights due to large variation (or windup) of the controller output after the saturation has occurred. Numerical simulations are provided to verify the superiority of the reported approach as compared to existing methods under different conditions.