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 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 feasibility of the 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.