Weighted arrays for modal isolation and active control of complex structures

Abstract

Arrays of sensors and actuators are designed to provide modal isolation and robust broadband feedback control on complex structures with high performance and limited modeling. The weighted array technique proposed here enables the design of reduced-order controllers for complex structures and offers the potential to improve closed-loop robustness and to broaden the region of good performance even as the plant changes. The weighted summation of the transducer signals senses the modes that are relevant to performance while rejecting the remaining modes; therefore reducing the required complexity of the controller. These weights are obtained from the minimization of a cost function and, under certain assumptions, it can be shown that a single optimum solution exists. The use of weighted arrays is motivated by the need to control the vibration response of aircraft. A representative fuselage test-bed was designed to retain the essential structural-acoustic dynamics of aircraft on a reduced size structure. Sensing and actuation plies of piezoelectric transducers were bonded to the fuselage test-bed and to other representative cylinder sections. Array weights were computed and successfully applied to isolate the targeted modes. The modal isolation allowed the implementation of simple control algorithms on the complex structures. Different methods of computing the weights are implemented and compared. The deleterious effects of spatial aliasing, the performance as a function of the array size, the sensitivity to random perturbations, and the effects of transducer failure are explored.