Linear Structure Control by Modal Force Technique

Abstract

This investigation presents a way of modeling complex structures by the modal force technique (MFT) and its application for structure control. A structure can be divided into substructures and the frequency response function (FRF) of the original structure can be obtained from the FRFs of its substructures by applying this technique. The synthesized FRF is transferred through the process of realization to the state space equation for designing an active vibration controller. The optimal control theory (LQG) is employed to design an active vibration controller with piezoelectric film (PVF₂) as the distributed-parameter actuator. At the same time, a Kalman filter is also designed. The exact solution for the modal parameters of an L-shaped cantilever beam structure is obtained by using MFT. The L-shaped cantilever beam structure is used to illustrate the application of the method proposed to vibration control. Numerical simulations reveal that the active vibration controller provides appropriate damping to suppress the tip point vibration when the structure is under random excitation. The Kalman filter can estimate accurately the states of the system and reduce the effects of disturbance and noise.