Lp. Heck et al., TRANSDUCER PLACEMENT FOR BROAD-BAND ACTIVE VIBRATION CONTROL USING A NOVEL MULTIDIMENSIONAL QR FACTORIZATION, Journal of vibration and acoustics, 120(3), 1998, pp. 663-670
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.