An Energy Function Based Fuzzy Variable Step Size FxLMS Algorithm for Active Noise Control

This paper describes real-time implementation of a Lyapunov energy function based fuzzy adaptive step size filtered-x-LMS (FxLMS) algorithm for active control of noise in a single channel duct. The proposed method uses a Lyapunov energy function of the error for step size adjustment in the filtered-x-LMS (FxLMS) algorithm. The energy function and its rate of change are taken as the principal signals to generate the step size through a Fuzzy Inference System (FIS). Experimental results of the algorithm are compared with a recently proposed variable step size algorithm as well as the fixed step size FxLMS algorithm. The paper also reports a new method of implementation of the FIS by generating a nonlinear mapping through a feed-forward neural network to reduce the computational complexity. The CPU time of this method has been compared with the other existing methods to establish the feasibility of implementation with a 10 kHz sampling.