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Journal of Control Science and Engineering
Volume 2019, Article ID 9640814, 8 pages
Research Article

Vibration Suppression Control of a Flexible Gantry Crane System with Varying Rope Length

1Hanoi University of Science and Technology, Vietnam
2Thai Nguyen University of Technology, Vietnam

Correspondence should be addressed to Tung Lam Nguyen; nv.ude.tsuh@gnutneyugn.mal

Received 4 October 2018; Revised 3 December 2018; Accepted 12 December 2018; Published 11 February 2019

Guest Editor: Quang Hieu Ngo

Copyright © 2019 Tung Lam Nguyen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The paper presents a control approach to a flexible gantry crane system. From Hamilton’s extended principle the equations of motion that characterized coupled transverse-transverse motions with varying rope length of the gantry is obtained. The equations of motion consist of a system of ordinary and partial differential equations. Lyapunov’s direct method is used to derive the control located at the trolley end that can precisely position the gantry payload and minimize vibrations. The designed control is verified through extensive numerical simulations.