Journal of Applied Mathematics
Volume 2004 (2004), Issue 2, Pages 107-126
doi:10.1155/S1110757X04312027
Dynamic boundary controls of a rotating body-beam system with time-varying angular velocity
Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Al-Khod 123, Oman
Received 7 December 2003; Revised 24 February 2004
Copyright © 2004 Boumediène Chentouf. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
This paper deals with feedback stabilization of a flexible beam
clamped at a rigid body and free at the other end. We assume that
there is no damping and the rigid body rotates with a
nonconstant angular velocity. To stabilize this system,
we propose a feedback law which consists of a control torque
applied on the rigid body and either a dynamic boundary
control moment or a dynamic boundary control force or
both of them applied at the free end of the beam. Then it is
shown that the closed loop system is well posed and exponentially
stable provided that the actuators, which generate the boundary
controls, satisfy some classical assumptions and the angular
velocity is smaller than a critical one.