Time optimal swing-up control of single pendulum

Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME

Volumn 123, Issue 3, 2001, Pages 518-527

  Xu, Yongcai ^a   Iwase, Masami ^b   Furuta, Katsuhisa ^b  

^a ESS Technology   (United States)

^b TOKYO DENKI UNIVERSITY   (Japan)

Author keywords

Inverted pendulum; Nonlinear optimization; Nonlinear systems; Time Optimal Control

Indexed keywords

EID: 0038596392     PISSN: 00220434     EISSN: 15289028     Source Type: Journal    
DOI: 10.1115/1.1383027     Document Type: Article

References (26)

1. Mori, S., Nishihara, H., and Furuta, K., 1976, Control Of Unstable Mechanical Control Of Pendulum, Int. J. Control, 23, No. 5, pp. 673-692.
2. Furuta, K., Yamakita, M., and Kobayashi, S., 1992, Swing-up Control of Inverted Pendulum Using Pseudo-state Feedback, Proc. of Institute of Mechanical Engineers, Vol. 206, pp. 263-269.
3. Shiriaev, A. S., Ludvigsen, H., Egeland, O., and Fradkov, A. L., 1999, Swinging up of Simplified Furuta Pendulum, Proc. of ECC’99.
4. Astrom, K. J., and Furuta, K., 1996, Swing Up a Pendulum by Energy Control, IFAC 13th Triennial World Congress, San Francisco.
5. Yamakita, M., Iwashiro, M., Sugahara, Y., and Furuta, K., 1996, Robust Swing Up Control of Double Pendulum, Proceedings of the American Control Conference, Seattle, Washington.
6. Yurkovich, S., and Widjaja, M., 1996, Fuzzy Controller Synthesis for an Inverted Pendulum System, Control Engineering Practice, 4, No. 4, pp. 455-469.
7. Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., and Mischenko, E. F., 1962, The Mathematical Theory of Optimal Processes, Interscience Publishers.
8. Kirk, D. E., 1970, Optimal Control Theory, Prentice-Hall, Englewood, NJ.
9. Polak, E., 1971, Computational Methods in Optimization: A Unified Approach, Academic Press, New York.
10. Canon, M. D., Cullum, C. D., and Polak, E., 1970, Theory of Optimal Control and Mathematical Programming, McGraw-Hill, New York.
11. Lee, Y. D., Kim, B. H., and Gyoo, H., 1999, Evolutionary Approach for Time Optimal Trajectory Planning of a Robotic Manipulator, Information Sciences, 113, No. 3-4, pp. 245-260.
12. Melikyan, A. A., 1994, Necessary Optimality Conditions for a Singular Surface in the Form of Synthesis, J. Optim. Theory Appl., 82, No. 2, pp. 203-217.
13. Meier, E. B., and Bryson, A. E., Jr., 1990, Efficient Algorithm for TimeOptimal Control of a Two-Link Manipulator, Journal of Guidance, 13, No. 5.
14. Van Willigenburg, L. G., and Loop, R. P. H., 1991, Computation of Timeoptimal Controls Applied to Rigid Manipulators With Friction, Int. J. Control, 54, No. 5, pp. 1097-1117.
15. Gafert, M., Svensson, J., and Astrom, K. A., Friction and Friction Compensation in the Furuta Pendulum, Proc. of ECC’99.
16. Arczewski, K., and Blajer, W., 1996, A Unified Approach to the Modelling of Holonomic and Nonholonomic Mechanical Systems, Mathematical Modelling of Systems, 2, No. 3, pp. 157-174.
17. Furuta, K., and Xu, Y., 1999, Project of Super-Mechano Systems—Study on Single Pendulum, Proc. of SMC’99, Tokyo Japan, Vol. 3, pp. 123-128.
18. Gabasov, R., and Kirillova, F. M., 1999, Numerical Methods of Open-loop and Closed-loop Optimization of Linear Control Systems, Report.
19. Lewis, F. L., 1986, Optimal Control, Wiley, New York.
20. Wu, C. J., 1995, Minimum-time Control for an Inverted Pendulum Under Force Constraints, Journal of Intelligent &Robotic Systems, 12, No. 2, pp. 127-143.
21. Czogala, E. M., and Pawlak, Z. A., 1995, Idea of a Rough Fuzzy Controller and its Application to the Stabilization of a Pendulum-car System, Fuzzy Sets Syst., 72, No. 1, pp. 61-73.
22. Gregory, J., and Lin, C., 1992, Constrained Optimization in the Calculus of Variations and Optimal Control Theory, Van Nostrand Reinhold.
23. Eltohamy, K. G., and Kuo, C. Y., 1998, Nonlinear Optimal Control of a Triple Link Inverted Pendulum With Single Control Input, Int. J. Control, 69, No. 2, pp. 239-256.
24. Huang, S. J., and Huang, C. L., 1996, Control of a Sliding Inverted Pendulum Using a Neural Network, International Journal of Computer Application, 9, No. 2-3, pp. 67-75.
25. Liu, Y., and Kojima, H., 1994, Optimal Design Method of Nonlinear Stabilizing Control System of Inverted Pendulum by Genetic Algorithm, Nippon Kikai Gakkai Ronbunshu, C Hen, Vol. 60, No. 577, pp. 3124-3129.
26. Lin, Z., Saberi, A., Gutmann, M., and Shamash, Y., 1996, Linear Controller of an Inverted Pendulum having Restricted Travel: a High-and-low Gain Approach, Automatica, 32, No. 6, pp. 933-937.