Optimized decentralized filtered-x least mean square algorithm for over-determined systems with periodic disturbances

Although decentralized control has great potential to facilitate multi-channel active noise/vibration control (ANC/AVC) systems, the practical implementations are greatly restricted by its inherent risk of system instability. In this paper, an optimized decentralized filtered-x least mean square algorithm is proposed for over-determined ANC/AVC systems subject to periodic disturbances. A diagonal parametric matrix is added into the update equations and a set of nonlinear equations is established with respect to the diagonal elements of this parametric matrix. An assumption is made and is verified through simulations that the nonlinear equations are solvable and have multiple solutions. With these solutions, all the eigenvalues of the characteristic matrix corresponding to system stability can be forced close to the point (1,0) in the complex domain. Convergence behaviors of the proposed algorithm are analysed in both frequency-domain and time-domain, through which the existence and characteristics of the convergence ripples are revealed. A criterion function is further established for the diagonal parametric matrix so that the convergence ripples can be restricted in an average sense. Simulations and experiments based on a multi-channel ANC system are carried out to validate the proposed algorithm. Corresponding results demonstrate that, compared with the original decentralized control, the proposed algorithm has advantages of guaranteed stability and accelerated convergence rates over the whole control frequency band without performance degradation as well as extra computational cost.