Orientation and stabilization of a flexible beam attached to a rigid body: planar motion

The author considers a flexible structure modeled as a rigid body which rotates in inertial space; a light flexible beam is clamped to the rigid body at one end and free one is clamped at the other. It is assumed that the flexible beam performs only planar motion. The equations of motion are obtained by using free body diagrams. Two control problems are posed, namely the orientation and stabilization of the system. It is shown that suitable boundary controls applied to the free end of the beam and suitable control torques applied to the rigid body solve the problems posed above. The proofs are obtained by using the energy of the system as a Lyapunov functional.<
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