On the modeling, and open loop control of a rotating thin flexible beam
Abstract
A set of governing differential equations is derived for the inplane motion of a rotating thin flexible beam. The beam is assumed to be linearly elastic and is connected to a rigid hub driven by a torque motor. Both flexural and extensional effects are included in the derivation. This coupling due to flexure and extension is usually neglected in studies dealing with the control of such a system. Models for typical control studies are often derived by utilizing an assumed mode approach where the mode shapes are obtained by solving the EulerBernoulli beam equation for flexural vibrations, with clampedfree or pinnedfree boundary conditions. The coupled equations developed in this paper are used to demonstrate that typical models in control studies give satisfactory results up to a critical rotational speed. For the case where these coupled equations are specialized to simple flexure only, valid for low angular speeds, a unique feedforward control strategy can be derived. This is an open loop control strategy that enables total elimination of an a priori specified vibratory mode from the gross motion in a finite critical time.
 Publication:

ASME
 Pub Date:
 December 1989
 Bibcode:
 1989asme.meetQ....C
 Keywords:

 Beams (Supports);
 Control Theory;
 Equations Of Motion;
 Feedforward Control;
 Flexible Bodies;
 Rotating Bodies;
 Angular Velocity;
 Vibration Damping;
 Vibration Mode;
 Engineering (General)