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TECHNICAL PAPERS

A Gantry Crane Problem Solved

[+] Author and Article Information
William J. O’Connor

Lecturer in Dynamics and Control at University College Dublin, National University of Ireland, Department of Mechanical Engineering, University College Dublin, Belfield, Dublin 4, Ireland e-mail: william.oconnor@ucd.ie

J. Dyn. Sys., Meas., Control 125(4), 569-576 (Jan 29, 2004) (8 pages) doi:10.1115/1.1636198 History: Received August 29, 2002; Revised July 08, 2003; Online January 29, 2004
Copyright © 2003 by ASME
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References

Book,  W. J., 1993, “Controlled Motion in an Elastic World,” ASME J. Dyn. Syst., Meas., Control, 115, pp. 252–261.
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Jayasuriya,  S., and Choura,  S., 1991, “On the Finite Settling Time and Residual Vibration Control of Flexible Structures,” Journal of Sound and Vibration,148(1), pp. 117–136.
Yamada,  I., and Nakagawa,  M., 1985, “Reduction of Residual Vibration in Position Control Mechanisms,” ASME J. Vib., Acoust., Stress, Reliab. Des., 107, pp. 47–52.
Preumont, A., 1997, “Vibration Control of Active Structures,” Kluwer Academic Publishers, Netherlands.
Feliu,  J. J., Feliu,  V., and Cerrada,  C., 1999, “Load Adaptive Control of Single-Link Flexible Arms Based on a New Modelling Technique,” IEEE Trans. Rob. Autom., 15(5), pp. 793–804.
Singh,  T., and Heppler,  G. R., 1993, “Shaped Input Control of a System With Multiple Modes,” ASME J. Dyn. Syst., Meas., Control, 115, 341–347.
Singhose, W. E., Singer, N. C., and Seering, W. P., 1994, “Design and Implementation of Time-Optimal Negative Input Shapes,” Proceedings of the 1994 International Mechanical Engineering Congress and Exposition, Chicago, IL, USA. ASME Dynamic Systems and Control Division (publication) DSC 55-1, pp. 151–157.
Kamal,  A. F. Moustafa, 2001, “Reference Trajectory Tracking of Overhead Cranes,” ASME J. Dyn. Syst., Meas., Control, 123, pp. 139–141.
Rahn,  C., Zhang,  F., Joshi,  S., and Dawson,  D., 1999, “Asymptotically Stabilizing Angle Feedback for a Flexible Cable Gantry Crane,” ASME J. Dyn. Syst., Meas., Control, 121(3), pp. 563–656.
Baicu,  C. F., Rahn,  C. C., and Nibali,  B. D., 1996, “Active Boundary Control of an Elastic Cable,” Journal of Sound and Vibration,198(1), pp. 17–26.
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Figures

Grahic Jump Location
One way to initialize a virtual cable, when load mass over target
Grahic Jump Location
The gantry crane model with (on right) assumed positive transverse force waves f(x−ct) and g(x+ct), components of −T∂y/∂x, producing, as they pass, transverse velocities v=∂y/∂t in opposite directions. Both waves will exert a positive (rightwards) force on the load mass, and a negative (leftwards) force on the trolley, and will be reflected without inversion on reaching load and trolley respectively.
Grahic Jump Location
A 3-m manoeuvre of a 4-m cable, with asymptotic arrival at target, achieved by constant launch velocity until halfway to target, with continuous wave absorption throughout (during and after this launch). Max trolley speed 1 m/s, L=4 m, ρ=0.1 kg/m, m=2 kg,T=23.54 N,c=15.34 m/s,Z=1.534 Ns/m.
Grahic Jump Location
Trolley velocity maintained at maximum until launch displacement is half target distance (at t=5.27 s). Then returning waves are absorbed until system is stationary. Same parameters as Fig. 3, except larger target distance of 8 m to show load “pendulum” swings during launch phase. The unevenness in load speed is due to force waves up and down the cable.
Grahic Jump Location
Example of an “exact” movement of 3-m with same system parameters as for Fig. 3. In contrast with Figs. 3 and 4, after a single, smooth sweep and rapid deceleration, the load arrives at the target and stops L/c seconds before the trolley has stopped. The trolley velocity at all points is the sum of the launch and absorb velocities (Eq. 8).

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