A multidimensional Householder QR algorithm for transducer placement in active noise control systems

Abstract

This paper advances the state of the art in the selection of minimal configurations of sensors and actuators for active noise control systems. The method extends previous transducer selection work by (1) presenting a unified treatment of the selection and placement of large numbers of sensors and actuators in a smart structure, (2) developing computationally efficient techniques to select the best sensor-actuator pairs for multiple unknown force disturbances exciting the structure, (3) selecting the best sensors and actuators over multiple frequencies, and (4) providing bounds on the performance of the transducer selection algorithms. The approach is based on a novel multidimensional Householder QR factorization algorithm applied to the frequency response matrices that define the noise control problem. This paper presents the theoretical development of the method.