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Boundary feedback stabilization of a rotating body-beam system. (English) Zbl 0847.93026

The purpose of this paper is to study a question concerning the 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 dynamic equation of the rigid body. The main result is the following: In any case, the system is stabilizable using a local boundary feedback law. For any regular velocity smaller than some constant which is determined only by the physical parameters of the system, a local boundary feedback law which exponentially stabilizes the system so that the beam vibrations are suppressed and the whole structure rotates about the axis with the given angular velocity, is proposed.

MSC:

93C20 Control/observation systems governed by partial differential equations
93D15 Stabilization of systems by feedback
93C85 Automated systems (robots, etc.) in control theory
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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