TRANSDUCER PLACEMENT FOR BROAD-BAND ACTIVE VIBRATION CONTROL USING A NOVEL MULTIDIMENSIONAL QR FACTORIZATION

This paper advances the state of the art in the selection of minimal c onfigurations of sensors and actuators for active vibration control wi th smart structures. The method extends previous transducer selection work by (1) presenting a unified treatment of the selection and placem ent of large numbers of both sensors and actuators in a smart structur e, (2) developing computationally efficient techniques to select the b est sensor-actuator pairs for multiple unknown force disturbances exci ting the structure, (3) selecting the best sensors and actuators over multiple frequencies, and (4) providing bounds on the performance of t he transducer selection algorithms. The approach is based on a novel, multidimensional extension of the Householder QR factorization algorit hm applied to the frequency response matrices that define the vibratio n control problem. The key features of the algorithm are its very low computational complexity, and a computable bound that can be used to p redict whether the transducer selection algorithm will yield an optima l configuration before completing the search. Optimal configurations w ill result from the selection method when the bound is tight, which is the case for many practical vibration control problems. This paper pr esents the development of the method, as well as its application in ac tive vibration control of a plate.