Assessment of stability of distributed FxLMS active noise control systems

Abstract

This paper addresses the assessment of the stability of distributed active noise control (ANC) systems, which are designed to cancel acoustic noise at given points in space. These systems distribute the control task across several simple acoustic nodes that generate the control signals by filtering a noise reference signal. The coefficients of each node filter are iteratively calculated by the filtered-X LMS algorithm. The nodes remain stable when the adaptive filters computed in each node converge to finite values. However, the acoustic coupling among nodes can cause instability (i.e., divergence). Collaboration among nodes is required to avoid this phenomenon. It is shown that the properties of the system are summarized in a system matrix and that the system remains stable when the real parts of all of the eigenvalues of this system matrix are positive. However, computation of all of the eigenvalues is computationally expensive. In this paper, we propose a fast method for checking the positiveness of the real parts of the system matrix eigenvalues. It is shown that the proposed method is faster than the direct calculation of eigenvalues and it assesses the stability/instability of the ANC systems without any false stability outcomes and more accurately than existing alternatives.