Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 179724, 11 pages
http://dx.doi.org/10.1155/2009/179724
Research Article

PD Control for Vibration Attenuation in a Physical Pendulum with Moving Mass

1Centro de Investigación en Computación del IPN, Apartado Postal 75-476, 07700 México, DF, Mexico
2Departamento de Control Automático, Centro de Investigación y de Estudios Avanzados del IPN, Apartado Postal 14-740, 07300 México, DF, Mexico

Received 8 December 2008; Accepted 22 May 2009

Academic Editor: John Burns

Copyright © 2009 Oscar Octavio Gutiérrez-Frias 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. S. Behrens, “Potential system efficiencies for MEMS vibration energy harvesting,” in Smart Structures, Devices, and Systems III, S. F. Al-Sarawi, Ed., vol. 6414 of Proceedings of SPIE, 2007. View at Publisher · View at Google Scholar
  2. D. Inman, Engineering Vibration, Prentice-Hall, New York, NY, USA, 1994.
  3. H. Matsuhisa, R. Gu, Y. Wang, O. Nishihara, and S. Sato, “Vibration control of a ropeway carrier by passive dynamic vibration absorbers,” JSME International Journal, Series C, vol. 38, no. 4, pp. 657–662, 1995. View at Google Scholar
  4. P. Dong, H. Benaroya, and T. Wei, “Integrating experiments into an energy-based reduced-order model for vortex-induced-vibrations of a cylinder mounted as an inverted pendulum,” Journal of Sound and Vibration, vol. 276, no. 1-2, pp. 45–63, 2004. View at Publisher · View at Google Scholar
  5. H. Sira-Ramírez and O. Llanes-Santiago, “Sliding mode control of nonlinear mechanical vibrations,” Journal of Dynamic Systems, Measurement and Control, vol. 122, no. 4, pp. 674–678, 2000. View at Publisher · View at Google Scholar
  6. C. Aguilar-Ibanez and S. Sira-Ramirez, “PD control for active vibration damping in an underactuated nonlinear system,” Asian Journal of Control, vol. 4, no. 4, pp. 502–508, 2002. View at Google Scholar
  7. C. Aguilar-Ibañez and R. Lozano, “The ball and beam acting on the ball,” in Non-Linear Control for Underactuated Mechanical Systems, A. Isidori, J. H. Van Schuppen, E.D. Sontag, and M. Thoma, Eds., chapter 10, pp. 143–151, Springer, London, UK, 2002. View at Google Scholar
  8. C. F. Aguilar-Ibañez, F. Guzmán-Aguilar, R. Lozano, and J. C. Chimal-E., “A control energy approach for the stabilization of the rigid beam balanced by the cart,” International Journal of Robust and Nonlinear Control, vol. 19, no. 11, pp. 1278–1289, 2008. View at Publisher · View at Google Scholar
  9. C. Aguilar-Ibáñez and H. Sira-Ramírez, “A linear differential flatness approach to controlling the Furuta pendulum,” IMA Journal of Mathematical Control and Information, vol. 24, no. 1, pp. 31–45, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. W. T. Thomson, Theory of Vibrations with Applications, Allen and Unwin, London, UK, 1981.
  11. C. Fuller, S. J. Elliot, and P. A. Nelson, Active Control of Vibration, Academic Press, San Diego, Calif, USA, 1996.
  12. R. Ortega, A. Loria, P. J. Nicklasson, and H. Sira-Ramirez, Passivity-Based Control of Euler—Lagrange Systems, Springer, Berlin, Germany, 1998.
  13. C. A. Ibáñez and J. H. Sossa Azuela, “Stabilization of the Furuta pendulum based on a Lyapunov function,” Nonlinear Dynamics, vol. 49, no. 1-2, pp. 1–8, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  14. V. Utkin, Sliding Modes Control in Electromechanical Systems, Taylor & Francis, London, UK, 1999.
  15. A. Isidori, Nonlinear Control Systems, Communications and Control Engineering Series, Springer, Berlin, Germany, 3rd edition, 1995. View at MathSciNet
  16. D. S. D. Stilling, Vibration attenuation by mass redistribution, Ph.D. thesis, University of Saskatchewan, Saskatoon, Canada, 2000.
  17. D. S. D. Stilling and W. Szyszkowski, “Controlling angular oscillations through mass reconfiguration: a variable length pendulum case,” International Journal of Non-Linear Mechanics, vol. 37, no. 1, pp. 89–99, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. W. Szyszkowski and D. S. D. Stilling, “On damping properties of a frictionless physical pendulum with a moving mass,” International Journal of Non-Linear Mechanics, vol. 40, no. 5, pp. 669–681, 2005. View at Publisher · View at Google Scholar
  19. K. Yoshida, K. Kawanishi, and H. Kawabe, “Stabilizing control for a single pendulum by moving the center of gravity: theory and experiment,” in Proceedings of the American Control Conference (ACC '97), Alburquerque, NM, USA, June 1997.
  20. H. K. Khalil, Non-Linear Systems, Prentice-Hall, Upper Saddle River, NJ, USA, 3rd edition, 2002.
  21. S. Lefschetz and J. P. La Salle, Stability By Liapunov's Direct Method with Applications, Academic Press, San Diego, Calif, USA, 1964.