Optimal placement of piezoelectric sensors/actuators in vibration control of a flexible beam

A method of finding the optimal locations of piezoelectric sensors and actuators for the control a of flexible structure is presented. The basic equations of the flexible structure bonded with piezoelectric sensors/actuators are derived. The method is based on the orthogonal projection of structural modes into the intersection subspace of the controllable and observable subspaces corresponding to the actuators/sensors. The controllability and observability grammians are then used to weight the projections to reflect the degrees of controllability and observability. This method produces the optimal locations of actuators/sensors. The simulation results show that the vibration of a flexible structure can be suppressed efficiently by using optimized actuators/sensors.