Feedback control of decoupled bending and torsional vibrations of flexible beams

In this article, we consider a flexible beam with a rigid body, of which the bending vibration and the torsional vibration are decoupled. Therefore we need two control motors to suppress the vibrations. Each set of dynamic equations is treated in the form of an appropriate Hilbert space. A stabilizing feedback control law of each rotation motor will be established on the basis of modal analysis. A set of experiments has been carried out, and the results demonstrate the effectiveness of the dynamic model and the proposed control law.