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Mathematical Problems in Engineering
Volume 2013, Article ID 523251, 7 pages
http://dx.doi.org/10.1155/2013/523251
Research Article

Study on the Nonsingular Problem of Fractional-Order Terminal Sliding Mode Control

State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China

Received 9 June 2013; Accepted 7 July 2013

Academic Editor: G. Rega

Copyright © 2013 Kening Li 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. I. Petrás, Fractional-Order Nonlinear Systems, vol. 1 of Nonlinear Physical Science, Springer, Berlin, Germany, 2011.
  2. R. E. Gutierrez, J. M. Rosario, and M. J. Tenreiro, “Fractional order calculus: basic concepts and engineering applications,” Mathematical Problems in Engineering, vol. 2010, Article ID 375858, 19 pages, 2010. View at Publisher · View at Google Scholar
  3. M. S. Tavazoei, M. Haeri, S. Jafari, S. Bolouki, and M. Siami, “Some applications of fractional calculus in suppression of chaotic oscillations,” IEEE Transactions on Industrial Electronics, vol. 55, no. 11, pp. 4094–4101, 2008. View at Publisher · View at Google Scholar · View at Scopus
  4. M. S. Couceiro, N. M. Fonseca Ferreira, and J. A. Tenreiro Machado, “Application of fractional algorithms in the control of a robotic bird,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 4, pp. 895–910, 2010. View at Publisher · View at Google Scholar · View at Scopus
  5. S. Victor, P. Melchior, and A. Oustaloup, “Robust path tracking using flatness for fractional linear MIMO systems: a thermal application,” Computers & Mathematics with Applications, vol. 59, no. 5, pp. 1667–1678, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  6. A. Oustaloup, “From fractality to non-integer derivation through recursively, a property common to these two concepts: a fundamental idea from a new process control strategy,” in Proceedings of the 12th IMACS World Conference, pp. 203–208, Paris, France, 1988.
  7. A. Oustaloup, X. Moreau, and M. Nouillant, “The CRONE suspension,” Control Engineering Practice, vol. 4, no. 8, pp. 1101–1108, 1996. View at Publisher · View at Google Scholar · View at Scopus
  8. A. Oustaloup, J. Sabatier, and P. Lanusse, “From fractal robustness to the CRONE control,” Fractional Calculus & Applied Analysis, vol. 2, no. 1, pp. 1–30, 1999. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. B. Vinagre, I. Podlubny, L. Dorcak, and V. Felin, “On fractional PID controllers: a frequency domain approach,” in Proceedings of the IFAC WorkShop on Digital Control, Past, Present, and Future of PID Control, pp. 53–58, Terrasa, Spain, 2000.
  10. D. Valério and J. Sá da Costa, “Variable order fractional controllers,” Asian Journal of Control, vol. 15, no. 3, pp. 648–657, 2013. View at Google Scholar
  11. F. Padula and A. Visioli, “Set-point weight tuning rules for fractional-order PID controllers,” Asian Journal of Control, vol. 15, no. 6, pp. 678–690, 2013. View at Google Scholar
  12. S. Domek, “Switched state model predictive control of fractional-order nonlinear discrete-time systems,” Asian Journal of Control, vol. 15, no. 3, pp. 658–668, 2013. View at Google Scholar
  13. Y. Luo, Y. Chen, and Y. Pi, “Fractional order adaptive feed-forward cancellation for periodic disturbances,” Asian Journal of Control, vol. 15, no. 3, pp. 751–763, 2013. View at Google Scholar
  14. R. Caponetto, G. Dongola, F. Pappalardo, and V. Tomasello, “Auto-tuning and fractional order controller implementation on hardware in the loop system,” Journal of Optimization Theory and Applications, vol. 156, no. 1, pp. 141–152, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. J. A. Tenreiro Machado, “The effect of fractional order in variable structure control,” Computers & Mathematics with Applications, vol. 64, no. 10, pp. 3340–3350, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  16. C. Tricaud and Y. Chen, “An approximate method for numerically solving fractional order optimal control problems of general form,” Computers & Mathematics with Applications, vol. 59, no. 5, pp. 1644–1655, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. J. J. E. Slotine and W. Li, Applied Nonlinear Control, vol. 1, Prentice Hall, New Jersey, NJ, USA, 1991.
  18. D. Zhao, S. Li, and F. Gao, “A new terminal sliding mode control for robotic manipulators,” International Journal of Control, vol. 82, no. 10, pp. 1804–1813, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. W. Q. Tang and Y. L. Cai, “High-order sliding mode control design based on adaptive terminal sliding mode,” International Journal of Robust and Nonlinear Control, vol. 23, no. 2, pp. 149–166, 2013. View at Publisher · View at Google Scholar · View at Scopus
  20. S. Dadras and H. R. Momeni, “Fractional terminal sliding mode control design for a class of dynamical systems with uncertainty,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 1, pp. 367–377, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet