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Basis Property and Stabilization of a Translating Tensioned Beam Through a Pointwise Control Force

[+] Author Affiliations
Bao-Zhu Guo, Yu Xie

Academy of Mathematics and Systems Sciences, Beijing, P. R. China

Paper No. IMECE2002-33545, pp. 403-410; 8 pages
  • ASME 2002 International Mechanical Engineering Congress and Exposition
  • Dynamic Systems and Control
  • New Orleans, Louisiana, USA, November 17–22, 2002
  • Conference Sponsors: Dynamic Systems and Control Division
  • ISBN: 0-7918-3629-0 | eISBN: 0-7918-1691-5, 0-7918-1692-3, 0-7918-1693-1
  • Copyright © 2002 by ASME


Introducing a recently developed powerful method, Riesz basis method what is so called, and applying to the stabilization of a translating tensioned beam through a pointwise control force are the two purposes of the paper. An asymptotic analysis, which is different from the one in treating the same problem in literature, is used to get a complete asymptotic expansion of the eigenvalues and eigenfunctions for the beam. The controlled system is written as an evolution equation in a state Hilbert space whose energy norm (induced by inner product) is the total energy of the beam. The spectrum-determined growth condition is obtained by showing that there is a set of generalized eigenfunctions of the system, which forms a Riesz basis for the state space. As a consequence, the stability, particularly the exponential stability of the system is developed. The analysis used here can be extended to other distributed systems and the results significantly improve that in [ASME Journal of Dynamic Systems, Measurement, and Control, 122(2000), 322–331].

Copyright © 2002 by ASME
Topics: Force



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