Stabilization and Observability of a Rotating Timoshenko Beam Model

Zuyev, Alexander; Sawodny, Oliver

doi:https://doi.org/10.1155/2007/57238

Mathematical Problems in Engineering

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Dynamics and Control in Sciences and Engineering

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Research Article | Open Access

Volume 2007 | Article ID 057238 | https://doi.org/10.1155/2007/57238

Stabilization and Observability of a Rotating Timoshenko Beam Model

Alexander Zuyev¹and Oliver Sawodny²

Academic Editor: José Manoel Balthazar

Received30 Sept 2006

Revised12 Feb 2007

Accepted13 May 2007

Published02 Aug 2007

Abstract

A control system describing the dynamics of a rotating Timoshenko beam is considered. We assume that the beam is driven by a control torque at one of its ends, and the other end carries a rigid body as a load. The model considered takes into account the longitudinal, vertical, and shear motions of the beam. For this distributed parameter system, we construct a family of Galerkin approximations based on solutions of the homogeneous Timoshenko beam equation. We derive sufficient conditions for stabilizability of such finite dimensional system. In addition, the equilibrium of the Galerkin approximation considered is proved to be stabilizable by an observer-based feedback law, and an explicit control design is proposed.

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Copyright

Copyright © 2007 Alexander Zuyev and Oliver Sawodny. 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.

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