New IIR filter-based adaptive algorithm in active noise control applications: Commutation error-introduced LMS algorithm and associated convergence assessment by a deterministic approach

In this study, commutation error (CE) is defined in adaptive infinite impulse response (IIR) filter-based ANC systems. CE is subsequently introduced into a new residual error to develop a new LMS-based ANC algorithm in an aim to liberate the restriction of slow adaptation posed on traditional ANC algorithms. A new deterministic analysis based on a linear time-varying system is performed to investigate convergence properties of the developed algorithm: (1) An optimal step size for the fastest convergence rate can be derived. (2) Given a persistent excitation condition and a step-size constraint, we find that the algorithm is uniformly asymptotically stable. Computer simulations indeed demonstrate a greatly improved convergence rate and efficient ANC performance for the developed algorithm as compared with that using the conventional algorithms. Experimental results verify the enhanced ANC performance in real applications. These together support the new IIR filter-based adaptive algorithm that includes CE for superior ANC performance with respect to the convergence rate and noise reduction level.