Kouhi S., Montazeri A., Poshtan J.

The locations of actuators and sensors over a flexible structure determine the effectiveness of the controller in controlling vibrations. The flexible structure considered here is a simply-supported thin plate with laminated piezoelectric sensors and actuators. The aim is to reduce the vibrations caused by disturbances on the plate. If it is desired to control some important modes of the plate, the suitable positions for sensors and actuators are where the controllability and observability of those modes be high enough. Another concern in the placement of sensors and actuators is to reduce the observation spillover. The first step is to consider these important factors by proper definition of a performance index. Here, by the use of spatial norms and definition of modal observability and modal controllability this is achieved. This approach will result in effective average vibration reduction with maximum modal controllability and abservability. Then the resultant nonlinear constraint minimization problem is solved by the proposed genetic algorithm. This optimization is performed over the size, position and number of sensors and actuators. The results are also verified and compared by simulating a feedforward H2 controller.