Vibration control of beams with piezoelectric sensors and actuators using particle swarm optimization

Abstract

This paper presents the design of a vibration control mechanism for a beam with bonded piezoelectric sensors and actuators. The mechanical modeling of the structure and the subsequent finite element approximation are based on the classical equations of motion, as they are derived from Hamilton’s principle, in connection with simplified modeling of the piezoelectric sensors and actuators. One nature-inspired intelligence method, the Particle Swarm Optimization, is used for the vibration control of the beam. Three different variants of the Particle Swarm Optimization were tested, namely, the simple Particle Swarm Optimization, the inertia Particle Swarm Optimization and the Constriction Particle Swarm Optimization. A linear feedback control law and a quadratic cost function are used, so that the results are comparable with the classical linear quadratic regulator approach. The same problem has been solved with two other stochastic based optimization algorithms, namely a Genetic Algorithm and a Differential Evolution and the results are used for comparison. The numerical simulation shows that sufficient vibration suppression can be achieved by means of this method.