Control of Torsional Vibrations By Piezoelectric Sensors and Actuators

This paper concerns the control of torsional vibrations of laminated rods with solid cross-sections by piezoelectric sensors and actuators. Exemplarily, a rod clamped at one end and subjected to a torque at the other end is considered. Utilizing the direct piezoelectric ef-fect, a piezoelectric layer can be used as a sensor. Measuring either the electrical potential or the charge of the electrodes on a piezoelectric layer, the torsional angle can be identified. On the other hand, the converse piezoelectric effect can be utilized for piezoelectric actuation. Prescribing an electric potential at the electrodes yields an actuating torsional moment. Based on a refinement of Saint Venant's theory of torsion, which considers the influence of piezoelectric strains on the cross-sectional warping, the sensor and actuator equations are formulated. The results are verified by means of three-dimensional Finite Element computa-tion showing good coincidence with rod theory. Two control strategies are investigated. In the first step, a feed-forward shape control solution is presented: Assuming that the external excitation is known, the actuating moment is computed in order to completely compensate the torsional vibrations. In the second step, it is assumed that the time-response of the tip torque is not known. Using a piezoelectric layer as a sensor to measure the torsional angle, a feed-back control algorithm is implemented. Numerical simulations show that a significant reduc-tion of torsional vibrations can be achieved by the proposed control strategy.