Output-based optimal placement of actuators and sensors for active vibration and structural acoustic control

A novel method for optimal sensor and actuator placement for active vibration control (AVC) and active structural acoustic control (ASAC) is presented which will use the concept of an output controllability grammian (OCG). The OCG is based on minimum energy principles from linear systems theory in a similar manner to the well known controllability and observability grammians. This provides a means of qualitatively gauging the controllability of outputs to determine the optimality of actuator and sensor arrangements. This is in contrast to using the state response which has been well explored in the structural control community.;The proposed output controllability grammian based placement method will be shown to be more effective than other state based methods in a least squares based LQR feedback control system when applied to vibration suppression problems. Distributed parameter systems are used as examples utilizing point force and distributed moment actuation and accelerometers as structural sensors. Considerations are also given to actuation dynamics when using a proof mass actuator (PMA) to provide the closed loop control force. Studies are performed which show that the placement results from OCG are relatively insensitive to variations in PMA damping and stiffness properties.;Experimentally, an aluminum space-frame is used as a test bed for the optimal actuator and sensor locations found using the OCG. Two AVC problems are investigated. First an active strut is used in a collocated actuator/sensor arrangement using direct velocity feedback (DVFB). Next a small piezoelectric PMA is used with acceleration feedback to attenuate the structures motion when subjected to broad-band noise from an electromagnetic shaker.;The OCG is also used for placement of a PMA for an ASAC application. Two different types of problems are examined, (1) sound minimization at a point, and (2) global reduction of acoustic pressure within a rigid walled container. A study of the placement sensitivity to changes in actuator properties show that the optimal locations are relatively insensitive to actuator dynamics. However the closed loop performance is more sensitive to changes in the actuator dynamics.