Boundary feedback stabilization of a rotating body-beam system

This paper deals with boundary feedback stabilization of a flexible beam clamped to a rigid body and free at the other end. The system is governed by the beam equation nonlinearly coupled with the dynamical equation of the rigid body. We propose a stabilizing boundary feedback law which suppresses the beam vibrations so that the whole structure rotates about a fixed axis with any given small constant angular velocity. The stabilizing feedback law is composed of control torque applied on the rigid body and either boundary control moment or boundary control force (or both of them) at the free end of the beam. It is shown that in any case the beam vibrations are forced to decay exponentially to zero