Stability Guaranteed Active Noise Control: Algorithms and Applications

Stability of the controller, robust stability of the active noise control (ANC) system, and limited output power of the hardware control board or actuators are crucial issues for ANC applications. Violation of these requirements results in output saturation, and hence nonlinear distortion by overloading the actuators. As a consequence, noise reduction performance of an ANC system will be dramatically degraded. A novel frequency-weighted leaky filtered-x least-mean-square (FxLMS) algorithm is developed in this article to fulfill these requirements. The proposed algorithm is an improvement of the traditional leaky FxLMS algorithm, where a frequency-weighted matrix is designed to replace the corresponding scalar weight. The frequency-weighted matrix, which is achieved by solving a constrained optimization problem, consists of $\it N$ frequency-weighted factors. By the frequency-weighted factors, the frequency response of the control filter is only suppressed at specific frequencies where the requirements on stability and/or limited output power are violated. Thus, the proposed control algorithm achieves better noise reduction performance than the traditional leaky FxLMS algorithm, which unnecessarily suppresses the control filter at all the frequencies. Simulations and experiments are carried out in a duct ANC system to verify the effectiveness of the proposed algorithm for both the feedforward and feedback ANC systems.