Integrated optimal design of vibration control system for smart beams using genetic algorithms

In this paper, the parameters of vibration control system of smart beams, including the placement and size of piezoelectric sensors and actuators (S/As) bonded on smart beams and the feedback control gains of the control system, have been simultaneously optimized for vibration suppression of beam structures. Since the sizes of the S/As are selected from a prescribed patch pool provided by the manufactures, the size design variable is then discrete, but the locations and feedback gains are continuous. Thus, the resulting optimization problem has discrete-continuous design variables which is difficult for the conventional optimization methods to solve. An integer-real-encoded genetic algorithm has thus been developed to search for the optimal placement and size of the piezoelectric patches as well as the optimal feedback control gains. The criterion based on the maximization of energy dissipation was adopted for the optimization of the control system. The optimal distributions of the piezoelectric patches based on specific controlled vibration modes have also been addressed. The results showed that the control effect could be significantly enhanced with appropriate distribution of piezoelectric patches and selection of feedback control gains, and meaningful observations have been obtained for practical design.