Optimization of design parameters for active control of smart piezoelectric structures

Abstract

The objective of this work is to design an optimal controller for plate structures to control their response under the influence of external excitation. The finite element method based on the Mindlin–Reissner plate theory has been extended to incorporate the piezoelectric effects. A genetic algorithm is applied to find the optimal placement of piezoelectric actuators and input voltages for static shape control. The objective function is the error in transverse displacements between the desired and the achieved shape. In addition, the optimal placement of actuators and sensors for vibration control of laminated plates is studied. The objective taken into consideration is the controllability index, which is the singular value decomposition of a control matrix as can be found at the bibliography. The index measures the input energy required to achieve the desired structural control using piezoelectric actuators. Finally, the linear quadratic regulator (LQR) closed loop control is applied to study the control effectiveness. A comparison is made between the optimal locations of piezoactuators obtained through controllability index and a nonoptimal case.