Journal of Applied Nonlinear Dynamics 10(2) (2021) 339--350 | DOI:10.5890/JAND.2021.06.012

Robert Vrabel

Slovak University of Technology in Bratislava, Faculty of Materials Science and Technology, Institute of Applied Informatics, Automation and Mechatronics, Bottova~25, 917 01 Trnava, Slovakia

Abstract

The problem of feed-forward control of overhead crane system is discussed. By combining the Kalman's controllability theory and Hartman-Grobman theorem from the dynamical system theory, a linear, continuous state feedback-based feed-forward controller that stabilizes the crane system at the desired end position of payload is designed. The efficacy of proposed controller is demonstrated by comparing the simulation experiment results for overhead crane with/without time-varying length of hoisting/lowering rope.

References

1. [1]	Park, H., Chwa, D., and Hong, K.-S. (2007), A feedback linearization control of container cranes: varying rope length, International Journal of Control, Automation, and Systems, 5(4), 379-387.

2. [2]	Tagawa, Y., Mori, Y., Wada, M., Kawajiri, E., and Nouzuka, K. (2016), Development of sensorless easy-to-use overhead crane system via simulation-based control, Journal of Physics: Conference Series 744(012017).

3. [3]	Tagawa, Y., Hashizume, Y., and Shimono K. (2014), Simulation based control and its application to a crane system, ASME 2013 Dynamic Systems and Control Conference, October 21-23, 2013, Palo Alto, California, USA, DSCC2013-4031, 10 pages.

4. [4]	Yang, J.H. and Yang, K.S. (2007), Adaptive coupling control for overhead crane systems, Mechatronics, 17(2-3), 143-152.

5. [5]	Tuan, L.A. (2016), Design of sliding mode controller for the 2D motion of an overhead crane with varying cable length, Journal of Automation and Control Engineering, 4(3), 181-188.

6. [6]	Tomczyk, J., Cink, J., and Kosucki, A. (2014), Dynamics of an overhead crane under a wind disturbance condition, Automation in Construction, 42, 100-111.

7. [7]	Sorensen, K.L., Singhose, W., and Dickerson, S. (2007), A controller enabling precise positioning and sway reduction in bridge and gantry cranes, Control Engineering Practice, 15, 825-837.

8. [8]	Zhang, M., Ma, X., Rong, X., Tian, X., and Li, Y. (2017), Error tracking control for underactuated overhead cranes against arbitrary initial payload swing angles, Mechanical Systems and Signal Processing, 84, 268-285.

9. [9]	Slotine, J.J.E., and Li, W. (1991), Applied Nonlinear Control, Prentice Hall Englewood Cliffs, New Jersey.

10. [10]	Li, X., Peng, X., and Geng, Z. (2019), Anti-swing control for 2-D under-actuated cranes with load hoisting/lowering: A coupling-based approach, ISA Transactions, 95, 372-378.

11. [11]	Antsaklis, P.J. and Michel, A.N. (2006), Linear Systems, Birkhauser Boston, 2nd Corrected Printing. Originally published by McGraw-Hill, Englewood Cliffs, NJ, 1997.

12. [12]	Perko, L. (2001), Differential Equations and Dynamical Systems (3rd Ed.). Texts in Applied Mathematics 7, New York: Springer-Verlag.

13. [13]	Barbashin, E.A. (1970), Introduction to the theory of stability, Wolters-Noordhoff, Groningen.

14. [14]	Horn, R.A. and Johnson, C.R. (1990), Matrix analysis, Cambridge University Press, New York, NY.

15. [15]	Zhang, M., Ma, X., Rong, X., Tian, X., and Li, Y. (2016), Adaptive tracking control for double-pendulum overhead cranes subject to tracking error limitation, parametric uncertainties and external disturbances, Mechanical Systems and Signal Processing, 76-77, 15-32.

16. [16]	Zhang, M., Ma, X., Chai, H., Rong, X., Tian, X., and Li Y. (2016), A novel online motion planning method for double-pendulum overhead cranes, Nonlinear Dynamics 85(2), 1079-1090.

17. [17]	Sun, N., Wu, Y., Fang, Y., and Chen, H. (2018), Nonlinear antiswing control for crane systems with double-pendulum swing effects and uncertain parameters: Design and experiments, IEEE Transactions on Automation Science and Engineering, 15(3), 1413-1422.

18. [18]	Kautsky, J., Nichols, N.K., and Van Dooren, P. (1985), Robust pole assignment in linear state feedback, International Journal of Control, 41, 1129-1155.