Transducer placement for broadband active vibration control using a novel multidimensional QR factorization

This paper advances the state of the art in the selection of minimal configurations of sensors and actuators for active vibration control with smart structures. The method extends previous transducer selection work by (1) presenting a unified treatment of the selection and placement of large numbers of both 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 extension of the Householder QR factorization algorithm applied to the frequency response matrices that define the vibration control problem. The key features of the algorithm are its very low computational complexity, and a computable bound that can be used to predict whether the transducer selection algorithm will yield an optimal configuration before completing the search. Optimal configurations will result from the selection method when the bound is tight, which is the case for many practical vibration control problems. This paper presents the development of the method, as well as its application in active vibration control of a plate.