Reduction of structural weight, costs and complexity of a control system in the active vibration reduction of flexible structures

This paper concerns the active vibration reduction of a flexible structure with discrete piezoelectric sensors and actuators in collocated pairs bonded to its surface. In this study, a new fitness and objective function is proposed to determine the optimal number of actuators, based on variations in the average closed loop dB gain margin reduction for all of the optimal piezoelectric pairs and on the modes that are required to be attenuated using the optimal linear quadratic control scheme. The aim of this study is to find the minimum number of optimally located sensor/actuator pairs, which can achieve the same vibration reduction as a greater number, in order to reduce the cost, complexity and power requirement of the control system. This optimization was done using a genetic algorithm. The technique may be applied to any lightly damped structure, and is demonstrated here by attenuating the first six vibration modes of a flat cantilever plate. It is shown that two sensor/actuator pairs, located and controlled optimally, give almost the same vibration reduction as ten pairs. These results are validated by comparing the open and closed loop time responses and actuator feedback voltages for various numbers of piezoelectric pairs using the ANSYS finite element package and a proportional differential control scheme.