Vibration control of plates using discretely distributed piezoelectric quasi-modal actuators/sensors

A novel approach is presented for vibration control of smart plates using d iscretely distributed piezoelectric actuators and sensors. The new method c onsists of techniques for designing quasi-modal sensors and quasi-modal act uators. The modal coordinates and the modal velocities are obtained approxi mately from the outputs of the discretely distributed piezoelectric sensor elements, whereas the modal actuators are implemented by applying proper vo ltages on each actuator element. The observation error of the modal sensor is analyzed, and an upper bound for the observation error is determined. Th e control spillover of the modal actuator is also estimated, and an upper b ound of the control spillover is also found. The criteria are developed for finding the optimal locations and sizes of both piezoelectric sensor and a ctuator elements. In the optimality criteria the optimal locations and size s of the sensor elements can be found by minimizing the observation error o f the modal sensor, and those of the actuator elements can be obtained by m inimizing both the control energy and the control spillover. The results ob tained using the present optimal criteria show that they do not depend on t he initial condition of vibration of the structures, nor do they depend on the control gains.