Vibration control with optimized piezoelectric shunt damping system using pole placement

Since 1990, interest in passive vibration control using piezoelectric shunt circuit has grown, but we have not been able to find detailed technical information about it in the open literature. We now present the results of our efforts on exploring such information. Starting from the electric charge balance of the piezoelectric material and voltage balance of the piezoelectric shunt circuit, we derive the mathematical model of the coupled electromechanical system of a cantilever beam with piezoelectric circuit, whose resistor R and inductor L are connected in series. Then the transfer function of the system, which is selected as the objective function, is formulated. Taking the maximum of the decay rate in the motion amplitude of free vibration of the damped beam as the object of optimization, we optimize the parameters in transfer function equation through the pole placement technique. Then the optimal values of resistor and inductor for the piezoelectric shunt circuit are obtained. As an example for verifying the parameter optimization techniques, the vibration control experiment on a cantilever beam with piezoelectric shunt circuit was performed. After the piezoelectric shunt circuit was closed and so was in operation, the decay rate of free vibration increased by about 110% and the amplitude of transfer function, which corresponded to optimal frequency tuning by pole placement criterion, decreased by about 70%. These results validate the effectiveness of parameter optimization techniques in controlling both free vibration and harmonic response.