Multi-Objective Optimization of Piezoelectric Actuator Placement for Shape Control of Plate Using Genetic Algorithms

Shape control of adaptive structures using piezoelectric actuators has found a wide range of applications in recent years. In this paper, the problem of finding optimal distribution of piezoelectric actuators and corresponding actuation voltages for static shape control of a plate is formulated as a multi objective optimization problem. Two conflicting objectives: minimization of input control energy and minimization of mean square deviation between the desired and actuated shapes are considered with constraints on maximum number of actuators and maximum induced stresses. A shear lag model of the smart plate structure is created and the optimization problem is solved using an evolutionary multi-objective optimization (EMO) algorithm NSGA-II. Pareto-optimal solutions are obtained for different case studies. Further, the obtained solutions are verified by comparing with single-objective optimization solutions.