Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2012, Article ID 810597, 13 pages
http://dx.doi.org/10.1155/2012/810597
Research Article

Stabilization of the Ball on the Beam System by Means of the Inverse Lyapunov Approach

1CIC-IPN, Unidad Profesional Adolfo López Mateos, Avendia Juan de Dios Bátiz S/N, Casi Esquire Miguel Othón de Mendizábal, Colonia Nueva Industrial Vallejo, Delegación Gustavo A. Madero, 07738 Mexico City, DF, Mexico
2ESCOM-IPN, 07738 Mexico City, DF, Mexico
3SEPI-ESIME Azcapotzalco, 02250 Mexico City, DF, Mexico

Received 15 November 2011; Accepted 4 January 2012

Academic Editor: Alexander P. Seyranian

Copyright © 2012 Carlos Aguilar-Ibañez et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Sira-Ramírez, “On the control of the “ball and beam” system: A trajectory planning approach,” in Proceedings of the IEEE Conference on Decision and Control (CDC 00), vol. 4, pp. 4042–4047, 2000.
  2. J. Hauser, S. Sastry, and P. Kokotović, “Nonlinear control via approximate input-output linearization: the ball and beam example,” Institute of Electrical and Electronics Engineers. Transactions on Automatic Control, vol. 37, no. 3, pp. 392–398, 1992. View at Publisher · View at Google Scholar
  3. R. Marino and P. Tomei, Nonlinear Control Design: Geometric, Adaptive and Robust, Prentice Hall, London, UK, 1997.
  4. W.-H. Chen and D. J. Ballance, “On a switching control scheme for nonlinear systems with ill-defined relative degree,” Systems & Control Letters, vol. 47, no. 2, pp. 159–166, 2002. View at Publisher · View at Google Scholar
  5. Y. Guo, D. J. Hill, and Z. P. Jiang, “Global nonlinear control of the ball and beam system,” in Proceedings of the 35th IEEE Conference on Decision and Control, pp. 2355–3592, December 1996. View at Scopus
  6. R. Sepulchre, M. Janković, and P. V. Kokotović, Constructive Nonlinear Control, Communications and Control Engineering Series, Springer, Berlin, Germany, 1997.
  7. D. Auckly, L. Kapitanski, and W. White, “Control of nonlinear underactuated systems,” Communications on Pure and Applied Mathematics, vol. 53, no. 3, pp. 354–369, 2000. View at Publisher · View at Google Scholar
  8. D. Auckly and L. Kapitanski, “On the λ-equations for matching control laws,” SIAM Journal on Control and Optimization, vol. 41, no. 5, pp. 1372–1388, 2002. View at Publisher · View at Google Scholar
  9. F. Andreev, D. Auckly, S. Gosavi, L. Kapitanski, A. Kelkar, and W. White, “Matching linear systems, and the ball and beam,” Automatica, vol. 38, no. 12, pp. 2147–2152, 2002. View at Publisher · View at Google Scholar
  10. J. Hamberg, “General matching conditions in the theory of controlled Lagrangians,” in Proceedings of the 38th IEEE Conference on Decision and Control (CDC '9), pp. 2519–2523, Phoenix, Ariz, USA, December 1999. View at Scopus
  11. R. Ortega, M. W. Spong, F. Gómez-Estern, and G. Blankenstein, “Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment,” Institute of Electrical and Electronics Engineers. Transactions on Automatic Control, vol. 47, no. 8, pp. 1218–1233, 2002. View at Publisher · View at Google Scholar
  12. F. Gómez-Estern and A. J. Van der Schaft, “Physical damping in IDA-PBC controlled underactuated mechanical systems,” European Journal of Control, vol. 10, no. 5, pp. 451–468, 2004. View at Publisher · View at Google Scholar
  13. A. R. Teel, “Semi-global stabilization of the “ball and beam” using “output” feedback,” in Proceedings of the American Control Conference (ACC '93), pp. 2577–2581, San Francisco, Calif, USA, June 1993. View at Scopus
  14. C. Barbu, R. Sepulchre, W. Lin, and Petar V. Kokotovic, “Global asymptotic stabilization of the ball-and-beam system,” in Proceedings of the IEEE Conference on Decision and Control, vol. 3, pp. 2351–2355, San Diego, Calif, USA, 1997.
  15. W. Yu, “Nonlinear PD regulation for ball and beam system,” International Journal of Electrical Engineering Education, vol. 46, no. 1, pp. 59–73, 2009. View at Google Scholar · View at Scopus
  16. C. Woolsey, C. K. Reddy, A. M. Bloch, D. E. Chang, N. E. Leonard, and J. E. Marsden, “Controlled Lagrangian systems with gyroscopic forcing and dissipation,” European Journal of Control, vol. 10, no. 5, pp. 478–496, 2004. View at Publisher · View at Google Scholar
  17. C. K. Reddy, W. W. Whitacre, and C. A. Woolsey, “Controlled lagrangians with gyroscopic forcing: An experimental application,” in Proceedings of the American Control Conference (ACC '04), vol. 1, pp. 511–516, Boston, Mass, USA, 2004.
  18. R. Ortega and E. García-Canseco, “Interconnection and damping assignment passivity-based control: a survey,” European Journal of Control, vol. 10, no. 5, pp. 432–450, 2004. View at Publisher · View at Google Scholar
  19. H. K. Khalil, Non-Linear Systems, Prentice Hall, Upper Saddle River, NJ, USA, 2nd edition, 1996.
  20. I. Fantoni and R. Lozano, Nonlinear Control for Underactuated Mechanical Systems, Springer, London, UK, 2002.