Vibration Control of Plates Using Discretely Distributed Piezoelectric Quasi-Modal Actuators/Sensors

A novel approach is presented for vibration control of smart plates using discretely distributed piezoelectric actuators and sensors. The new method consists of techniques for designing quasi-modal sensors and quasi-modal actuators. The modal coordinates and the modal velocities are obtained approximately from the outputs of the discretely distributed piezoelectric sensor elements, whereas the modal actuators are implemented by applying proper voltages on each actuator element. The observation error of the modal sensor is analyzed, and an upper bound for the observation error is determined. The control spillover of the modal actuator is also estimated, and an upper bound of the control spillover is also found. The criteria are developed for finding the optimal locations and sizes of both piezoelectric sensor and actuator elements. In the optimality criteria the optimal locations and sizes of the sensor elements can be found by minimizing the observation error of the modal sensor, and those of the actuator elements can be obtained by minimizing both the control energy and the control spillover. The results obtained using the present optimal criteria show that they do not depend on the initial condition of vibration of the structures, nor do they depend on the control gains.

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