Summary

Many industrial/construction sites (e.g., nuclear waste-handling facilities, shipyards, airports, automobile plants, new buildings, etc.) use overhead cranes to transport large, heavy payloads. During transit, the payload swings freely making accurate positioning difficult, especially in work sites congested with equipment and personnel. Crane operators often move payloads slowly to minimize the induced swing, reducing overall site efficiency.

This paper develops implementable stabilizing controllers for a distributed model of a gantry crane system. The governing partial differential equations of a horizontally-translating gantry, flexible cable, and payload are derived. A control law, based on Lyapunov theory, is developed to dampen the vibrations of the payload using the gantry motor, gantry position and velocity sensors, and a cable departure angle sensor. An exact modal analysis of the closed loop system without damping is performed. A Galerkin approach incorporates damping. The control gains are designed using the root locus approach. A distributed Invariance Principle proves asymptotic stability. The theory is successfully tested on an experimental mockup of the gantry crane system. The controller significantly reduces the time required for the payload oscillations to damp out.

Collaborators
 
Darren Dawson, Clemson University

Publications

Baicu, C. F., Rahn, C. D., and Nibali, B. D., “Active Boundary Control of Elastic Cables:  Theory and Experiment,” Journal of Sound and Vibration, Vol 198, No. 1, pp. 17-26, 1996.

Canbolat, H., Dawson, D., Rahn, C., and Nagarkatti, S., “Adaptive Boundary Control of Out-of-Plane Cable Vibration,” ASME Journal of Applied Mechanics, Vol. 65, pp. 963-969, December 1998.

Baicu, C., Rahn, C. D., and Dawson, D., “Exponentially Stabilizing Boundary Control of String-Mass Systems,” Journal of Vibration and Control, Vol. 5, No. 3, pp. 491-502, May 1999.

Rahn, C., Zhang, F., Joshi, S., and Dawson, D., “Asymptotically Stabilizing Angle Feedback for a Flexible Cable Gantry Crane,” ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 121, No. 3, pp. 563-656, September 1999.

Sponsor

National Science Foundation

Root Locus Design

For further information:  cdrahn@psu.edu. 

Copyright © 2001 Mechatronics Research Laboratory