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Author:

Chen, G. (Chen, G..) | Vazquez, R. (Vazquez, R..) | Krstic, M. (Krstic, M..)

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EI Scopus SCIE

Abstract:

In this article, we present rapid boundary stabilization of a Timoshenko beam with antidamping and antistiffness at the uncontrolled boundary, by using infinite-dimensional backstepping. We introduce a Riemann transformation to map the Timoshenko beam states into a set of coordinates that verify a 1-D hyperbolic PIDE-ODE system. Then backstepping is applied to obtain a control law guaranteeing closed-loop stability of the origin in the L{2} sense. Arbitrarily rapid stabilization can be achieved by adjusting control parameters, and has not been achieved in previous results. Finally, a numerical simulation shows the effectiveness of the proposed controller. This result extends a previous work which considered a slender Timoshenko beam with Kelvin-Voigt damping, by allowing destabilizing boundary conditions at the uncontrolled boundary and attaining an arbitrarily rapid convergence rate.  © 1963-2012 IEEE.

Keyword:

Timoshenko beam Boundary control PDE backstepping distributed parameter systems hyperbolic systems

Author Community:

  • [ 1 ] [Chen G.]Beijing University of Technology, Faculty of Information Technology, Beijing, 100124, China
  • [ 2 ] [Vazquez R.]Camino de Los Descubrimiento S.n., Departamento de Ingenieria Aeroespacial y Mecanica de Fluidos, Universidad de Sevilla, Sevilla, 41092, Spain
  • [ 3 ] [Krstic M.]University of California, Department of Mechanical Aerospace Engineering, San Diego, 92093, CA, United States

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Source :

IEEE Transactions on Automatic Control

ISSN: 0018-9286

Year: 2024

Issue: 2

Volume: 69

Page: 1141-1148

6 . 8 0 0

JCR@2022

Cited Count:

WoS CC Cited Count: 0

SCOPUS Cited Count: 4

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 3

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