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A Nonlinear Programming Approach For The Swing-Up Control Problem

Year 2008, Volume: 21 Issue: 2, 109 - 124, 31.12.2008

Ahmet Yazıcı Abdurrahman Karamancıoğlu

Abstract

A nonlinear programming approach for the inverted pendulum swing-up control is presented. Even though it is an energy-based method, it uses fundamentally different mathematical tools to achieve the swing-up goal. The control problem translated into nonlinear programming model with appropriate objective function and constraints. While the objective function provides energy increase in the system, physical restrictions of the system are handled in the constraints of the nonlinear programming model. It is also shown that this model is intrinsically suitable for embedding any nonlinear system constraints. Simulation results for illustrative cases are included to validate the design method.


Keywords

Swing-up control problem Inverted pendulum Underactuated systems Nonlinear Programming Energy based methods.

References

  • [1] K.J. Astrom and K. Furuta, “Brief Paper Swinging up a pendulum by energy control”, Automatica, vol.36, pp. 287-295, 2000.
  • [2] A.S. Shiriaev, O. Egeland, H. Ludvigsen, and A.L. Fradkov, “VSS-version of energy-based control for swinging up a pendulum”, Systems and Control Letters, vol. 44, pp. 45-56, 2001.
  • [3] K. Yoshida, “Swing-up control of an inverted pendulum by energy-based Methods”, Proceedings of American Control Conference, pp. 4045-4047, 1999.
  • [4] D. Chatterjee, A. Patra, and H. K. Joglekar, “Swing-up and stabilization of a cartpendulum system under restricted cart track length", Systems and Control Letters, vol. 47, pp. 355-364, 2002.
  • [5] N. Muskinja, and B. Tovornik, “Swinging up and stabilization of a real inverted pendulum”, IEEE Transactions on Industrial Electronics, vol. 53, pp. 631-639, 2006.
  • [6] R. Lozano, I. Fantoni, and D. J. Block, “Stabilization of the inverted pendulum around its homoclinic orbit", Systems and Control Letters, vol. 40, pp.197-204, 2000.
  • [7] J. Yi, N. Yubazaki, and K. Hirota, “Upswing and stabilization control of inverted pendulum system based on the SIRMs dynamically connected fuzzy inference model”, Fuzzy Sets and Systems, vol. 122, pp. 139-152, 2001.
  • [8] K. Ogata, Modern Control Engineering, Prentice-Hall Inc, 1990.
  • [9] M. S. Bazaraa, H. D. Sherali, and C. M. Shetty, “Nonlinear Programming: Theory and Algoritms”, John Wiley and Sons, 1993.

A Nonlinear Programming Approach For The Swing-Up Control Problem

Year 2008, Volume: 21 Issue: 2, 109 - 124, 31.12.2008

Ahmet Yazıcı Abdurrahman Karamancıoğlu

Abstract

A nonlinear programming approach for the inverted pendulum swing-up control is presented. Even though it is an energy-based method, it uses fundamentally different mathematical tools to achieve the swing-up goal. The control problem translated into nonlinear programming model with appropriate objective function and constraints. While the objective function provides energy increase in the system, physical restrictions of the system are handled in the constraints of the nonlinear programming model. It is also shown that this model is intrinsically suitable for embedding any nonlinear system constraints. Simulation results for illustrative cases are included to validate the design method.

Keywords

Swing-up control problem Inverted pendulum Underactuated systems Nonlinear Programming Energy based methods

References

  • [1] K.J. Astrom and K. Furuta, “Brief Paper Swinging up a pendulum by energy control”, Automatica, vol.36, pp. 287-295, 2000.
  • [2] A.S. Shiriaev, O. Egeland, H. Ludvigsen, and A.L. Fradkov, “VSS-version of energy-based control for swinging up a pendulum”, Systems and Control Letters, vol. 44, pp. 45-56, 2001.
  • [3] K. Yoshida, “Swing-up control of an inverted pendulum by energy-based Methods”, Proceedings of American Control Conference, pp. 4045-4047, 1999.
  • [4] D. Chatterjee, A. Patra, and H. K. Joglekar, “Swing-up and stabilization of a cartpendulum system under restricted cart track length", Systems and Control Letters, vol. 47, pp. 355-364, 2002.
  • [5] N. Muskinja, and B. Tovornik, “Swinging up and stabilization of a real inverted pendulum”, IEEE Transactions on Industrial Electronics, vol. 53, pp. 631-639, 2006.
  • [6] R. Lozano, I. Fantoni, and D. J. Block, “Stabilization of the inverted pendulum around its homoclinic orbit", Systems and Control Letters, vol. 40, pp.197-204, 2000.
  • [7] J. Yi, N. Yubazaki, and K. Hirota, “Upswing and stabilization control of inverted pendulum system based on the SIRMs dynamically connected fuzzy inference model”, Fuzzy Sets and Systems, vol. 122, pp. 139-152, 2001.
  • [8] K. Ogata, Modern Control Engineering, Prentice-Hall Inc, 1990.
  • [9] M. S. Bazaraa, H. D. Sherali, and C. M. Shetty, “Nonlinear Programming: Theory and Algoritms”, John Wiley and Sons, 1993.
There are 9 citations in total.

Details

Subjects Computer Software
Journal Section Research Articles
Authors

Ahmet Yazıcı

Abdurrahman Karamancıoğlu

Publication Date December 31, 2008
Acceptance Date November 4, 2008
Published in Issue Year 2008 Volume: 21 Issue: 2

Cite

APA Yazıcı, A., & Karamancıoğlu, A. (2008). A Nonlinear Programming Approach For The Swing-Up Control Problem. Eskişehir Osmangazi Üniversitesi Mühendislik Ve Mimarlık Fakültesi Dergisi, 21(2), 109-124.
AMA Yazıcı A, Karamancıoğlu A. A Nonlinear Programming Approach For The Swing-Up Control Problem. ESOGÜ Müh Mim Fak Derg. December 2008;21(2):109-124.
Chicago Yazıcı, Ahmet, and Abdurrahman Karamancıoğlu. “A Nonlinear Programming Approach For The Swing-Up Control Problem”. Eskişehir Osmangazi Üniversitesi Mühendislik Ve Mimarlık Fakültesi Dergisi 21, no. 2 (December 2008): 109-24.
EndNote Yazıcı A, Karamancıoğlu A (December 1, 2008) A Nonlinear Programming Approach For The Swing-Up Control Problem. Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi 21 2 109–124.
IEEE A. Yazıcı and A. Karamancıoğlu, “A Nonlinear Programming Approach For The Swing-Up Control Problem”, ESOGÜ Müh Mim Fak Derg, vol. 21, no. 2, pp. 109–124, 2008.
ISNAD Yazıcı, Ahmet - Karamancıoğlu, Abdurrahman. “A Nonlinear Programming Approach For The Swing-Up Control Problem”. Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi 21/2 (December 2008), 109-124.
JAMA Yazıcı A, Karamancıoğlu A. A Nonlinear Programming Approach For The Swing-Up Control Problem. ESOGÜ Müh Mim Fak Derg. 2008;21:109–124.
MLA Yazıcı, Ahmet and Abdurrahman Karamancıoğlu. “A Nonlinear Programming Approach For The Swing-Up Control Problem”. Eskişehir Osmangazi Üniversitesi Mühendislik Ve Mimarlık Fakültesi Dergisi, vol. 21, no. 2, 2008, pp. 109-24.
Vancouver Yazıcı A, Karamancıoğlu A. A Nonlinear Programming Approach For The Swing-Up Control Problem. ESOGÜ Müh Mim Fak Derg. 2008;21(2):109-24.
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