Improvement in performance of active structural vibration controller using updated finite element model

Abstract

Effect of correctness of mathematical model of a mechanical structure on performance of Active Vibration Control (AVC) scheme is investigated in this thesis. Vibrations of a smart plate instrumented with PZT sensor and actuator are suppressed using a negative velocity feedback controller. The AVC controllers are designed and compared for two cases. In first case it is assumed that there is a mismatch between the analytical model and the actual structure. In the second case the mismatch in analytical model and actual structure is compensated using direct method of model updating. Numerical simulations carried out in MATLAB software for these two cases demonstrate the improvement in performance of the AVC controller when updation is carried out. Finite element (FE) model of the smart cantilevered is created using Hamilton s principle. Rotational degrees of freedom (dofs) of the FE model are eliminated using system equivalent reduction expansion process (SEREP). Experimental mode shapes and natural frequencies are extracted from the structure using high speed cameras and digital image correlation (DIC) technique. Initial FE model is updated using experimental mode shapes and natural frequencies by well-known Berman and Nagy approach. Updated FE model thus derived is further reduced to first three modes using orthonormal modal reduction technique. Modal model of the smart plate is then used to derive state space model of the smart plate. Two Kalman observers are constructed: one using initial FE model and other using updated FE model. Active vibration control experiments are conducted on the cantilevered using these two Kalman observers in the control law. It is observed that much better vibration suppression occurs when Kalman observer based on updated FE model is used in the control law. Strategy suggested in this work to implement a typical active vibration control scheme on a structure is simple and yet very effective. newline