Stabilization and Observability of a Rotating Timoshenko Beam Model | Zendy

Alexander Zuyev | Zendy; Oliver Sawodny | Zendy

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Stabilization and Observability of a Rotating Timoshenko Beam Model

Author(s) -

Alexander Zuyev,

Oliver Sawodny

Publication year - 2007

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2007/57238

Subject(s) - observability , timoshenko beam theory , galerkin method , beam (structure) , mathematics , observer (physics) , control theory (sociology) , distributed parameter system , mathematical analysis , finite element method , physics , control (management) , computer science , partial differential equation , quantum mechanics , artificial intelligence , optics , thermodynamics

A control system describing the dynamics of a rotating Timoshenkobeam is considered. We assume that the beam is driven by a controltorque at one of its ends, and the other end carries a rigid body asa load. The model considered takes into account the longitudinal,vertical, and shear motions of the beam. For this distributedparameter system, we construct a family of Galerkin approximationsbased on solutions of the homogeneous Timoshenko beam equation. Wederive sufficient conditions for stabilizability of such finitedimensional system. In addition, the equilibrium of the Galerkinapproximation considered is proved to be stabilizable by anobserver-based feedback law, and an explicit control design isproposed.

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