Mathematical Problems in Engineering 
Volume 2007 (2007), Article ID 57238, 19 pages
doi:10.1155/2007/57238
Research Article

Stabilization and Observability of a Rotating Timoshenko Beam Model

Alexander Zuyev1 and Oliver Sawodny2

 1Institute of Applied Mathematics & Mechanics, National Academy of Sciences of Ukraine, R. Luxembourg 74, Donetsk 83114, Ukraine
2Institute for System Dynamics, Universität Stuttgart, Pfaffenwaldring 9, Stuttgart 70569, Germany
Received 30 September 2006; Revised 12 February 2007; Accepted 13 May 2007

Recommended by José Manoel Balthazar

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.