Active control of smart structures with optimal actuator and sensor locations

Sensors and actuators used in active control of smart structures have to be located appropriately in order to ensure maximum control and measurement effectiveness. Many placement techniques are based on the structure itself and overlook the effects of the applied control law. The optimal locations determined from open-loop system can not guarantee the best performance of the closed-loop system because the performance is closely related with the design requirements and applied controller. In this paper, we presented a method of obtaining the optimal locations of actuators/sensors by combining the open-loop and closed-loop optimal criterions. First, for open-loop system, location indices of the controlled modes are calculated on the basis of modal controllability and observability. The controlled modes are weighted based on the controller design requirements. To reduce the "spill-over" effect of uncontrolled modes, the location index values of uncontrolled modes are added as penalty terms. Locations with high index values are chosen as candidate locations of actuator/sensor for the next determining step on the closed-loop system. Three control techniques, optimal H₂, H_∞ norms and optimal pole-placement, are utilized for two different control objectives, disturbance rejection and damping property enhancement. Linear matrix inequality (LMI) techniques are utilized to formulate the control problems and synthesize the controllers. For each candidate location of actuator/sensor, a controller is designed and the obtained performance is taken as location index. By solving the location problem in two steps, we reduced the computational burden and ensured good control performance of the closed-loop system. The proposed method is tested on a clamped plate with piezoelectric actuators and sensors.