A Principal Component Algorithm for Feedforward Active Noise and Vibration Control

Abstract

A principal component least mean square (PC-LMS) adaptive algorithm is described that has considerable benefits for large control systems used to implement feedforward control of single frequency disturbances. The algorithm is a transform domain version of the multichannel filtered-x LMS algorithm. The transformation corresponds to the principal components (PCs) of the transfer function matrix between the sensors and actuators in a control system at a single frequency. The method is similar to other transform domain LMS algorithms because the transformation can be used to accelerate convergence when the control system is ill-conditioned. This ill-conditioning is due to actuator and sensor placement on a continuous structure. The principal component transformation rotates the control filter coefficient axes to a more convenient coordinate system where (1) independent convergence factors can be used on each coordinate to accelerate convergence, (2) insignificant control coordinates can be eliminated from the controller, and (3) coordinates that require excessive control effort can be eliminated from the controller. The resulting transform domain algorithm has lower computational requirements than the filtered-x LMS algorithm. The formulation of the algorithm given here applies only to single frequency control problems, and computation of the decoupling transforms requires an estimate of the transfer function matrix between control actuators and error sensors at the frequency of interest. The robustness of the PC-LMS algorithm to modeling errors is shown to be identical to the filtered-x LMS algorithm, and the statistical properties of the principal components are used to select a subset of the PCs to control, depending on the control application. The variation of the PCs with frequency is investigated, and an online identification procedure is described to compute the transfer function matrix while the controller is operating. The feasibility of the PC-LMS method was demonstrated in real-time noise control experiments involving 48 microphones and 12 control actuators mounted on a closed cylindrical shell. Convergence of the PC-LMS algorithm was more stable than the filtered-x LMS algorithm. In addition, the PC-LMS controller produced more noise reduction with less control effort than the filtered-x LMS controller in several tests.

Controle ativo de ruído e vibrações mecânicas utilizando um algoritmo de controle tipo deadbeat

“…Por exemplo, a estrutura física de controle por reduzir ruído no interior de aeronaves não é igual à estrutura física necessária para reduzir a transmissão de ruído num tubo de condução de ar ou num sistema para isolamento de vibrações em um microscópio eletrônico. Da mesma forma, o controlador eletrônico para um sistema de controle ativo tipo feedforward (Cabell et al, 1999) não será igual a aquele controlador eletrônico para um sistema tipo realimentação de saída. Porém, os princípios básicos de projeto eficiente para cada aplicação serão os mesmos, Hansen (1996).…”

Robust Design and Robust Stability Analysis of Active Noise Control Systems

“…This e!ect could be taken into account by replacing equation (39) by the following stability condition [5,6,18] (for "xed ):…”

Optimizing Sensor and Actuator Arrays for ASAC Noise Control

“…This algorithm is a transform domain version of the multi-channel filtered-x LMS algorithm [8,12], and is described in detail elsewhere [13]. In PC-LMS the controller parameters (filter weights) are adapted in the transformed coordinate system of (18), that decouples the feedforward control system at a single frequency.…”