Modelling and control of overhead cranes with flexible variable-length cable by finite element method

Abstract

This work considers the modelling problem of the dynamics of overhead cranes with flexible cable and load hoisting or lowering during crane travel. The analysis includes the transverse vibrations of the flexible cable and trolley motion. A set of nonlinear ordinary differential equations governing the motion of the crane system with time-varying spatial domain is derived via the calculus of variation and Hamilton’s principle. A variable-domain finite element method is used to discretize the nonlinear system. A proportional -derivative controller is suggested to drive the crane to a desired destination. Numerical simulations are provided to show the effectiveness of the developed model and to illustrate the results.

Keywords

control finite element flexible cable modelling overhead cranes variable-length cable

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References

Abrate, S. 1992: Vibration of belts and belt drives. Mechanism and Machine Theory 27, 645-659.

Al-Garni, A. Z. , Moustafa, K. A. F. and Javeed Nizami, S. S. A. K. 1995: Time optimal control of overhead cranes with hoisting of the load. Control Engineering Practice 3, 1277-1284.

Ali, H. and Singh, T. 1998: Passive control of overhead cranes. Proceedings of the 1998 IEEE International Conference on Control Applications, Trieste, Italy, 1046-1050.

Cheng, C.-C. and Chen, C.-Y. 1996: Controller design for an overhead crane system with uncertainty. Control Engineering Practice 4, 645-653.

Chien, C. G. , Fung, R. F. and Tsal, C. L. 1999: Non linear vibration analysis of the coupled textile/rotor system by finite element method. Journal of Sound and Vibration 221, 67-84.

D’Andrea-Novel, B. and Coron, J. M. 2000: Experimental stabilization of an overhead crane with flexible cable via a back-stopping approach. Automatica 36, 587-593.

Joshi, S. and Rahn, C. D. 1996: Position control of a flexible cable gantry crane: theory and experiment. Proceedings of the American Control Conference (ACC), Seattle, WA, 2820-2824.

Meirovich, L. 1967: Analytical methods in vibration. London: Macmillan.

Moustafa, K. A. F. 1994: Feedback control of overhead cranes swing with variable rope length. Proceeding of the 1994 American Control Conference (ACC), Baltimore, MD: 691-691.

10.

Moustafa, K. A. F. and Abo-El-Yazid, T., G. 1996: Load sway control of overhead cranes with load hoisting via stability analysis. International Journal of Japanese Society of Mechanical Engineering (JSME), Series C 39, 34-41.

11.

Moustafa, K. A. F. and Ebied, A. M. 1988: Nonlinear modeling and control of overhead cranes load sway. Journal of Dynamic System Measurement and Control 110, 266-271.

12.

Nalley, M. and Trabia, M. 2000: Control of overhead cranes using fuzzy logic controllers. Journal of Intelligent & Fuzzy Systems 8, 1-18.

13.

Stylianou, M. and Tabarrok, B. 1994: Finite element analysis of an axially moving beam, part 1: time integration. Journal of Sound and Vibration 178, 433-453.

14.

Vikkunen, J. , Marttinen, A. , Rintanen, K. , Salminen, R. and Seitsonen, J. 1990: Computer control of overhead and gantry cranes. Proceedings, 11th IFAC Triennial World Congress Tallinn, Estonia, 401-405.

15.

Wang, P. H. , Fung, R. F. and Lee, M. J. 1998: Finite element analysis of a three-dimensional under water cable with time-dependent length. Journal of Sound and Vibration 209, 223-249.

16.

Yao, C. M. , Fung, R. F. and Tseng, C. R. 1999: Non linear vibration analysis of a traveling string with time-dependent length by new hybrid Laplace transform/finite element method. Journal of Sound and Vibration 219, 323-337.