Realistic determination of the optimal size and location of piezoelectric actuator/sensors

We address the problem of obtaining the optimal size and location of piezoelectric actuator/sensors. An optimization problem is formulated for a general beam which can be subject to any boundary and may have as many piezoelectric patches as needed. The proposed optimization criterion is based on the beam modal cost and modal controllability. By adding a penalty term to the criterion, the size of the actuator/sensor can be reduced to a practical and reasonable size. Thus there is no need to pre-select the size of the actuator/sensor. The optimal size and location for beams with various boundary conditions are determined for a single pair and for two pairs of piezoelectric patches. The results in this paper are in very good agreement with those reported by other investigators. A comparison is also made between the performance of two pairs of actuators and the performance of a single pair. It has been shown that the two pair actuators can control the bending vibration more efficiently than a single pair.