Optimal Vibration Control and Innovization for Rectangular Plate

Vibration control of flexible structures has always been one of the most important issues and Among variant available control methods, active vibration control using piezoelectric sensors and actuators has become popular due to its high efficiency and flexibility for designing a control system. The main concern in designing a control system with piezoelectric patches is finding best position for patches. On the other hand, number of used sensors and actuators is another important issue which affects the costs of the project as well as the performance. The main goal of the present study is to control oscillation of a rectangular plate using minimum number of piezoelectric sensors and actuators (i.e., objective one) and finding their optimum placement to get the maximum possible performance (i.e., objective two); the mentioned two objectives are in conflict. The plate have been mathematically modeled using the Kirchhoff-Love theory. By considering the piezoelectric sensor-actuators effects, the control equation of the cantilever plate has been obtained. In order to find the optimum number and placement of the sensors and actuators, the multi-objective genetic algorithm (GA) has been used and the objective functions have been defined based on maximization of observability and countability indexes of the cantilever plate. After conducting the optimization process, a few thumb rules have been extracted using the innovization technique. The results have been verified by implementing the designed controller using the optimum solution found by optimization method. The importance of the rules found by innovization technique have been illustrated in the numerical discussion.