Modeling and Control of a Variable Length Flexible Cable Overhead Crane Using the Modified Galerkin Method

Authors

Kamal A.F. Moustafa, United Arab Emirates UniversityFollow
Mohamed Trabia, University of Nevada, Las VegasFollow
Mohamed I.S. Ismail, Department of Design and Production Engineering, Zagazig University

Document Type

Conference Proceeding

Publication Date

11-11-2008

Publication Title

ASME International Mechanical Engineering Congress and Exposition, Proceedings

Publisher

ASME

Volume

9 PART C

First page number:

1783

Last page number:

1794

Abstract

A mathematical model that accurately represents an overhead crane with flexible cable and load hoisting/lowering is developed. The analysis includes the transverse vibrations of the flexible cable and the trolley motion as well as the load hoisting/lowering motions. A set of highly non-linear partial differential equations and ordinary differential equations that govern the motion of the crane system within time-varying spatial domain is derived via calculus of variation and Hamilton’s principle. Variable-time modified Galerkin method has been used to discretize the non-linear system. State space transformation is then used to get a set of first order ordinary differential equation. A proportional derivative control scheme is applied to derive the underlying crane so that the cable and payload swing are damped out. Numerical simulations for the control performance of the considered system are presented for various operating conditions.

Keywords

Cables; Control modeling; Galerkin methods; Gantry cranes; Live loads; Mathematical models

Disciplines

Acoustics, Dynamics, and Controls | Applied Mechanics | Electro-Mechanical Systems | Mechanical Engineering | Numerical Analysis and Computation

Language

English

Comments

Conference held: Seattle, Washington, USA, November 11–15, 2007

Permissions

Use Find in Your Library, contact the author, or interlibrary loan to garner a copy of the item. Publisher policy does not allow archiving the final published version. If a post-print (author's peer-reviewed manuscript) is allowed and available, or publisher policy changes, the item will be deposited.

Repository Citation

Moustafa, K. A., Trabia, M., Ismail, M. I. (2008). Modeling and Control of a Variable Length Flexible Cable Overhead Crane Using the Modified Galerkin Method. ASME International Mechanical Engineering Congress and Exposition, Proceedings, 9 PART C 1783-1794. ASME.