Asymptotic behavior of a 2D overhead crane with input delays in the boundary control

Fadhel Al-Musallam, Kaïs Ammari, Boumediène Chentouf*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

Abstract

The paper investigates the asymptotic behavior of a 2D overhead crane with input delays in the boundary control. A linear boundary control is proposed. The main feature of such a control lies in the fact that it solely depends on the velocity but under the presence of time-delays. We end-up with a closed-loop system where no displacement term is involved. It is shown that the problem is well-posed in the sense of semigroups theory. LaSalle's invariance principle is invoked in order to establish the asymptotic convergence for the solutions of the system to a stationary position which depends on the initial data. Using a resolvent method, it is proved that the convergence is indeed of polynomial type as long as the delay term satisfies a smallness condition. Lastly, non-convergence results are put forward in the case when such a condition on the delay term is not fulfilled.

Original languageEnglish
Pages (from-to)1103-1122
Number of pages20
JournalZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Volume98
Issue number7
DOIs
Publication statusPublished - Jul 2018
Externally publishedYes

Keywords

  • asymptotic behavior
  • boundary velocity control
  • overhead crane
  • polynomial convergence
  • time-delay

ASJC Scopus subject areas

  • Computational Mechanics
  • Applied Mathematics

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