On eigenvalue shaping for two-channel decentralized active noise control systems

Recent works show that two-channel decentralized active noise control (DANC) systems are able to achieve optimal noise reduction performance with guaranteed convergence by proper matrix eigenvalue shaping for each frequency. In this paper, we study the impact of three eigenvalue shaping approaches on the performance of a time-domain two-channel DANC system, where the first two approaches are from the literature and the third one is newly proposed as an extension of one of the two approaches. By theoretical analysis and experimental investigation of the three approaches, it is found that the eigenvalues of the 2 × 2 so-called characteristic matrices in the frequency-domain should be shaped by considering two aspects. Firstly, the two eigenvalues for each matrix need to be pushed towards the positive real axis to ensure stability. Secondly, the eigenvalues inherently affect the two auxiliary filters in the time-domain. They should be shaped so that the two filters have roughly the same magnitudes to facilitate implementation. Simulation results using the measured acoustic paths demonstrate the efficacy of the proposed eigenvalue shaping approach and the adaptive filtering technique for controlling sinusoidal noise, multitone noise, white noise and traffic noise. Experimental result shows the efficacy of the proposed approach for controlling white noise in three dimensional space.