Stabilization and observability of a rotating Timoshenko beam model. (English) Zbl 1149.74042

Zuyev, Alexander; Sawodny, Oliver

Math. Probl. Eng. 2007, Spec. Issue, Article ID 57238, 19 p. (2007).

Summary: 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 takes into account 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 Galerkin approximation considered is proved to be stabilizable by an observer-based feedback law, and an explicit control design is proposed.

MSC:

74M05	Control, switches and devices (“smart materials”) in solid mechanics
74K10	Rods (beams, columns, shafts, arches, rings, etc.)
93B52	Feedback control
93B07	Observability

Keywords:

control torque; Galerkin approximation; observer-based feedback law

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