Shape control of piezoelectric bimorph by piezo response function and global optimization algorithms: a comparative study

Abstract

In this paper shape control optimization of piezoelectric bimorph is done by piezo response function (PRF) and global optimization technique. PRF is used to formulate the optimization problem and global optimization algorithm is used to minimize the error between the target and the achieved shape. The performance of four global optimization techniques, simulated annealing (SA), genetic algorithm, particle swarm optimization and teacher learning based optimization are compared for the shape control of piezoelectric bimorph. 28 piezoelectric actuators are used in the piezoelectric bimorph to generate the sinusoidal profile, elliptical profile and arbitrary deformation profile by the external load. PRF is calculated by solving finite element model of piezoelectric bimorph and, optimization of electric potential with safety limit is done to achieve the target profiles by using all the aforementioned optimization techniques. SA gives best value of the objective function. At optimum electrode potential, the target and, achieved sinusoidal, elliptical and arbitrary deformation profiles obtained by SA at 5 × 107 computation, matches closely with root mean square (RMS) errors of 0.72, 12.18 and 28.86 nm, respectively. Subsequently, a robust and fully reproducible method for the shape control of piezo actuated deformable mirrors and smart structures is developed.