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Abstract
Although flexible beams for transmitting both translational and rotational large motions are used in practice such as ocean drill pipes, their control has not been considered. This paper develops boundary feedback controllers to stabilise these beams at their reference configurations. Exact nonlinear partial differential equations governing motion of the beams in three-dimensional space are derived and used in the control design. The designed controllers guarantee globally practically asymptotically stability of the beam motions at the reference states (i.e. positions and rotations of a straight beam moving axially with a desired velocity and rotating around its axial axis with a desired velocity). In the control design and analysis of well-posedness and stability, we utilise different transformations between the earth-fixed and body-fixed coordinates, Sobolev embeddings, and a Lyapunov-type theorem developed for a class of evolution systems in Hilbert space. Simulation results are also included to illustrate the effectiveness of the proposed control design.
Disclosure statement
No potential conflict of interest was reported by the authors.
Additional information
Notes on contributors
K. D. Do
K. D. Do received the M.E. and Ph.D. degrees (with Distinction) in mechanical engineering from The University of Wollongong and The University of Western Australia in 1999 and 2003, respectively. Prior to 2012, he was a Research Professor with the School of Mechanical Engineering, The University of Western Australia. He is currently a Professor in the School of Civil and Mechanical Engineering, Curtin University. His research interests include dynamics and control of deterministic and stochastic nonlinear systems, multiple agents, land, air, and ocean vehicles, and systems governed differential equations in infinite dimensions.