Optimisation of number and placement of piezoelectric sensor / Actuator pairs for active vibration reduction of a flexible plate using the genetic algorithm

This paper is concerned with active vibration reduction of a square isotropic plate, mounted rigidly along one edge to form a cantilever. The number of piezoelectric sensor/actuator pairs, their location and the controller gain are optimised using a genetic algorithm based on linear quadratic index and closed loop dB gain reduction as an objective function. A new method is developed to determine optimal number of actuators based on variations of average closed loop dB gain reduction for all optimal piezoelectric pairs and the required modes to be attenuated using optimal linear quadratic control scheme. The aim of this work was to find the minimum number of discrete sensor/actuator pairs, optimally located, to achieve the same vibration reduction as that achieved with more piezoelectric patches to reduce weight, cost and real time control calculation. The plate, with piezoelectric sensor/actuator pairs bonded to its surfaces, is modelled using the finite element method and Hamilton's principle based on first order shear deformation theory. The first six natural frequencies is compared and validated with the finite element ANSYS package using two dimensional SHELL63, three dimensional SOLID45 elements and experimentally. A MATLAB m-code program was built to incorporate ANSYS results to find optimal placement, gain and minimum number of piezoelectric sensor/actuator pairs taken the effects of the first six modes collectively. Vibration reduction for the cantilever plate bonded with piezoelectric patches in the optimal location was investigated to attenuate vibration and the results validated with ANSYS finite element package. It is shown that four sensor/actuator pairs located in optimal location give almost the same vibration reduction as ten pairs in their optimal locations.