TY - JOUR
T1 - Further results on the long-time behavior of a 2D overhead crane with a boundary delay
T2 - Exponential convergence
AU - Ammari, Kaïs
AU - Chentouf, Boumediène
N1 - Funding Information:
This work was supported and funded by Kuwait University, Research Grant no. SM04/17. The authors are grateful to the associate editor and the anonymous referees for the careful reading of the original manuscript and for their valuable suggestions and comments.
Funding Information:
This work was supported and funded by Kuwait University , Research Grant no. SM04/17 . The authors are grateful to the associate editor and the anonymous referees for the careful reading of the original manuscript and for their valuable suggestions and comments.
Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2020/1/15
Y1 - 2020/1/15
N2 - This article is mainly concerned with the exponential convergence of solutions of a 2D overhead crane, which consists of a platform and a flexible cable holding a load mass. While taking into consideration the occurrence of a delay in one boundary condition, the dynamics of the platform and the load mass are taken into consideration. Furthermore, the modulus of the cable is assumed to vary. Besides, the mathematical model of the crane system is assumed to have no displacement term. Then, a distributed (interior) damping feedback law is proposed so that one can exclude any possible negative impact of the delay. Indeed, invoking the frequency domain method, we show that the solutions of the closed-loop system must exponentially converge to a stationary position. This outcome improves the recent result obtained in [3], where the rate of convergence of solutions of the system without the interior damping is at most of polynomial type. The relevance of the theoretical findings is shown through several numerical examples.
AB - This article is mainly concerned with the exponential convergence of solutions of a 2D overhead crane, which consists of a platform and a flexible cable holding a load mass. While taking into consideration the occurrence of a delay in one boundary condition, the dynamics of the platform and the load mass are taken into consideration. Furthermore, the modulus of the cable is assumed to vary. Besides, the mathematical model of the crane system is assumed to have no displacement term. Then, a distributed (interior) damping feedback law is proposed so that one can exclude any possible negative impact of the delay. Indeed, invoking the frequency domain method, we show that the solutions of the closed-loop system must exponentially converge to a stationary position. This outcome improves the recent result obtained in [3], where the rate of convergence of solutions of the system without the interior damping is at most of polynomial type. The relevance of the theoretical findings is shown through several numerical examples.
KW - Asymptotic behavior
KW - Damping control
KW - Exponential convergence
KW - Overhead crane
KW - Time-delay
UR - http://www.scopus.com/inward/record.url?scp=85072247260&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85072247260&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2019.124698
DO - 10.1016/j.amc.2019.124698
M3 - Article
AN - SCOPUS:85072247260
SN - 0096-3003
VL - 365
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
M1 - 124698
ER -