Optimal placement of piezoelectric actuators and sensors on a smart beam and a smart plate using multi-objective genetic algorithm

In this paper a method of finding optimal positions for piezoelectric actuators and sensors on different structures is presented. The genetic algorithm and multi-objective genetic algorithm are selected for optimization and H norm is defined as a cost function for the optimization process. To optimize the placement concerning the selected modes simultaneously, the multi-objective genetic algorithm is used. The optimization is investigated for two different structures: a cantilever beam and a simply supported plate. Vibrating structures are controlled in a closed loop with feedback gains, which are obtained using optimal LQ control strategy. Finally, output of a structure with optimized placement is compared with the output of the structure with an arbitrary, non-optimal placement of piezoelectric patches.