Abstract
Boundary feedback controllers are designed to stabilize Timoshenko beams with large translational and rotational motions in space under external disturbances. The exact nonlinear partial differential equations governing motion of the beams are derived and used in the control design. The designed controllers guarantee globally practically asymptotically (and locally practically exponentially) stability of the beam motions at the reference state. The control design, well-posedness and stability analysis are based on various relationships between the earth-fixed and body-fixed coordinates, Sobolev embeddings, and a Lyapunov-type theorem developed to study well-posedness and stability for a class of evolution systems in Hilbert space. Simulation results are included to illustrate the effectiveness of the proposed control design.
Highlights
Timoshenko beams are widely used in practical structures such as poles, bars, columns, and robot arms
In modeling and control of Timoshenko beams, shear deformation and rotational bending effects need to be considered as opposed to neglection of shearing in Bernoulli beams
Control of Timoshenko beams is different from that of (Bernoulli) slender beams due to the fact that slender beams are usually supported by tension, which providing structural stiffness, in addition to boundary control forces and moments
Summary
Timoshenko beams are widely used in practical structures such as poles, bars, columns, and robot arms. In modeling and control of Timoshenko beams, shear deformation and rotational bending effects need to be considered as opposed to neglection of shearing in Bernoulli beams. These effects result in nonlinear couplings between translational and rotational motions of the beams. Timoshenko beams work in a wide range of operations, under which the beams deform with a large magnitude of both translational and rotational motions. An exact nonlinear model of Timoshenko beams, of which motions are restricted in two-dimensional space, and their boundary control design are addressed in [14]. The above discussion motivates the writing of this paper on modelling, boundary control design, and stability analysis of Timoshenko beams in space under external loads.
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