TY - JOUR
T1 - Asymptotic behavior of a 2D overhead crane with input delays in the boundary control
AU - Al-Musallam, Fadhel
AU - Ammari, Kaïs
AU - Chentouf, Boumediène
N1 - Publisher Copyright:
© 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
PY - 2018/7
Y1 - 2018/7
N2 - 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.
AB - 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.
KW - asymptotic behavior
KW - boundary velocity control
KW - overhead crane
KW - polynomial convergence
KW - time-delay
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U2 - 10.1002/zamm.201700208
DO - 10.1002/zamm.201700208
M3 - Article
AN - SCOPUS:85049518932
SN - 0044-2267
VL - 98
SP - 1103
EP - 1122
JO - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
JF - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
IS - 7
ER -