Experimental Study on Feedback Control of Coupled Bending and Torsional Vibrations of Flexible Beams

Abstract

Modeling and control of flexible beams has received a great deal of attention in recent years. When a tip-body of a flexible beam is a rigid body, not only bending vibration but also torsional vibration will occur. In this paper, we model the coupled bending and torsional vibrations as a set of decoupled partial differential equations with a set of coupled boundary conditions. The whole set of dynamic equations will be rewritten together as an evolution equation in a properly defined Hilbert space. It will be proven that a differential operator governing the system is selfadjoint and has a compact inverse. A stabilizing feedback control law of a rotation motor will be established on the basis of modal analysis. Experimental methods are discussed in detail, and the results demonstrate the effectiveness of the dynamic model and the proposed control law.