Performance evaluation of vibration controller for piezoelectric smart structures in finite element environment

Abstract

This study focuses on performance evaluation of an active vibration controller in a closed loop finite element (FE) environment for piezoelectric smart structures by integrating a reduced-order-model-based controller into the FE model. Based on the first-order shear deformation theory, a coupled piezoelectric-mechanical FE model with electric potential variables is developed for the piezoelectric smart structure to provide a platform for vibration analysis and controller design. A system identification technique known as subspace identification method is employed to obtain a multi-input multi-output state space reduced-order model which can with sufficient accuracy predict the behavior of the piezoelectric smart structure under consideration from the inputs and outputs of FE simulations. A linear-quadratic regulator controller together with a Luenberger observer is designed based on the reduced-order model for the purpose of vibration control. The reduced-order-model-based controller is then integrated into an FE environment by updating the actuator voltages according to the controller at each time instant during the transient analysis of FE simulations. Eventually, the performance robustness characteristics of the proposed vibration controller are evaluated in case of structural parameter variations and taking the sensor or actuator offline in a closed loop FE environment. Numerical examples are presented to demonstrate the efficiency of the proposed scheme for evaluating the vibration controller performance of piezoelectric smart structures in a closed loop FE environment.