Theoretical convergence analysis of the FXLMS-based feedforward hybrid active noise control system

Abstract

Real noise typically includes both broadband and narrowband components, such as noise generated by rotating machines. The feedforward hybrid active noise control (FFHANC) system reduces both components separately by arranging broadband and narrowband controllers in parallel. Although considerable efforts have been made to improve the FFHANC system, a theoretical analysis of its performance is still lacking. Consequently, the application of the FFHANC system lacks a solid foundation. Furthermore, the stability bounds of step sizes that guarantee convergence are not available in the literature. To address these problems, a convergence analysis of the FFHANC system based on the filtered-x least-mean-square algorithm is proposed. The analysis of the mean and mean-square convergence behaviors of the weight errors theoretically illustrates the advantages of the FFHANC system in terms of fast convergence and high reduction. The mutual coupling of parallel controllers in the mean-square sense is derived and discussed. By predicting the steady-state mean-square error and stability bounds, the proposed model can also guide the choice of step sizes. Our analysis lays the theoretical foundation for the practical application of the FFHANC system. Extensive simulations are performed to demonstrate the validity of the proposed theoretical theory.