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Mathematical Problems in Engineering
Volume 2016, Article ID 3690240, 14 pages
http://dx.doi.org/10.1155/2016/3690240
Research Article

Adaptive Robust Backstepping Control of Permanent Magnet Synchronous Motor Chaotic System with Fully Unknown Parameters and External Disturbances

State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Baoding 071003, China

Received 15 December 2015; Revised 16 March 2016; Accepted 30 March 2016

Academic Editor: Shengjun Wen

Copyright © 2016 Yang Yu 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. N. Hemati, “Strange attractors in brushless DC motors,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 41, no. 1, pp. 40–45, 1994. View at Publisher · View at Google Scholar · View at Scopus
  2. Z. Li, J. B. Park, Y. H. Joo, B. Zhang, and G. Chen, “Bifurcations and chaos in a permanent-magnet synchronous motor,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 49, no. 3, pp. 383–387, 2002. View at Publisher · View at Google Scholar · View at Scopus
  3. Z. Jing, C. Yu, and G. Chen, “Complex dynamics in a permanent-magnet synchronous motor model,” Chaos, Solitons and Fractals, vol. 22, no. 4, pp. 831–848, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  4. C.-L. Li, S.-M. Yu, and X.-S. Luo, “Fractional-order permanent magnet synchronous motor and its adaptive chaotic control,” Chinese Physics B, vol. 21, no. 10, Article ID 100506, 2012. View at Publisher · View at Google Scholar · View at Scopus
  5. Y.-Y. Hou, “Finite-time chaos suppression of permanent magnet synchronous motor systems,” Entropy, vol. 16, no. 4, pp. 2234–2243, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. H. P. Ren and D. Liu, “Nonlinear feedback control of chaos in permanent magnet synchronous motor,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 53, no. 1, pp. 45–50, 2006. View at Publisher · View at Google Scholar · View at Scopus
  7. A. Loría, “Robust linear control of (chaotic) permanent-magnet synchronous motors with uncertainties,” IEEE Transactions on Circuits and Systems. I. Regular Papers, vol. 56, no. 9, pp. 2109–2122, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. M. Messadi, A. Mellit, K. Kemih, and M. Ghanes, “Predictive control of a chaotic permanent magnet synchronous generator in a wind turbine system,” Chinese Physics B, vol. 24, no. 1, Article ID 010502, 2015. View at Publisher · View at Google Scholar · View at Scopus
  9. Z. Li, B. Zhang, and Z. Y. Mao, “Entrainment and migration control of permanent-magnet synchronous motor system,” Control Theory and Applications, vol. 19, no. 1, pp. 53–56, 2002. View at Google Scholar
  10. H. C. Cho, K. S. Lee, and M. S. Fadali, “Adaptive control of pmsm systems with chaotic nature using lyapunov stability based feedback linearization,” International Journal of Innovative Computing, Information and Control, vol. 5, no. 2, pp. 479–488, 2009. View at Google Scholar · View at Scopus
  11. D. Q. Wei, B. Zhang, X. S. Luo, S. Y. Zeng, and D. Y. Qiu, “Effects of couplings on the collective dynamics of permanent-magnet synchronous motors,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 60, no. 10, pp. 692–696, 2013. View at Publisher · View at Google Scholar · View at Scopus
  12. G. Maeng and H. H. Choi, “Adaptive sliding mode control of a chaotic nonsmooth-air-gap permanent magnet synchronous motor with uncertainties,” Nonlinear Dynamics, vol. 74, no. 3, pp. 571–580, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. T.-B.-T. Nguyen, T.-L. Liao, and J.-J. Yan, “Adaptive sliding mode control of chaos in permanent magnet synchronous motor via fuzzy neural networks,” Mathematical Problems in Engineering, vol. 2014, Article ID 868415, 11 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. J. P. Yu, B. Chen, and H. S. Yu, “Fuzzy-approximation-based adaptive control of the chaotic permanent magnet synchronous motor,” Nonlinear Dynamics, vol. 69, no. 3, pp. 1479–1488, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. Y.-F. Yang, M.-Z. Luo, S.-B. Xing, X.-X. Han, and H.-Q. Zhu, “Analysis of chaos in permanent magnet synchronous generator and optimal output feedback H control,” Acta Physica Sinica, vol. 64, no. 4, Article ID 040504, 2015. View at Publisher · View at Google Scholar · View at Scopus
  16. J.-H. Hao, X.-W. Wang, and H. Zhang, “Chaotic robust control of permanent magnet synchronous motor system under uncertain factors,” Acta Physica Sinica, vol. 63, no. 22, Article ID 220203, 2014. View at Publisher · View at Google Scholar · View at Scopus
  17. S. H. Luo, “Adaptive fuzzy dynamic surface control for the chaotic permanent magnet synchronous motor using Nussbaum gain,” Chaos, vol. 24, no. 3, Article ID 033135, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. D. Q. Wei, X. S. Luo, B. H. Wang, and J. Q. Fang, “Robust adaptive dynamic surface control of chaos in permanent magnet synchronous motor,” Physics Letters A, vol. 363, no. 1-2, pp. 71–77, 2007. View at Publisher · View at Google Scholar · View at Scopus
  19. A. N. Njah, “Tracking control and synchronization of the new hyperchaotic Liu system via backstepping techniques,” Nonlinear Dynamics, vol. 61, no. 1-2, pp. 1–9, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. X. Wang and J. Zhang, “Tracking control and the Backstepping design of synchronization controller for Chen system,” International Journal of Modern Physics B, vol. 25, no. 28, pp. 3815–3824, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  21. N. Chen, S. Q. Xiong, B. Liu, and W. H. Gui, “Adaptive backstepping control of permanent magnet synchronous motor chaotic system,” Journal of Central South University (Science and Technology), vol. 45, no. 1, pp. 99–104, 2014. View at Google Scholar
  22. X. Ge and J. Huang, “Chaos control of permanent magnet synchronous motor,” in Proceedings of the 8th International Conference on Electrical Machines and Systems, pp. 484–488, Nanjing, China, September 2006. View at Scopus
  23. C. M. Kwan and F. L. Lewis, “Robust backstepping control of induction motors using neural networks,” IEEE Transactions on Neural Networks, vol. 11, no. 5, pp. 1178–1187, 2000. View at Publisher · View at Google Scholar · View at Scopus
  24. A. Stotsky, I. Kanellakopoulus, and P. Kokotovic, Nonlinear and Adaptive Control Design, John Wiley & Sons, New York, NY, USA, 1995.
  25. A. Harb and W. Ahmad, “Control of chaotic oscillators using a nonlinear recursive backstepping controller,” in Proceedings of the IASTED Conference on Applied Simulations and Modeling, pp. 451–453, Crete, Greece, June 2002.
  26. J.-H. Hu and J.-B. Zou, “Adaptive backstepping control of permanent magnet synchronous motors with parameter uncertainties,” Control and Decision, vol. 21, no. 11, pp. 1264–1269, 2006. View at Google Scholar · View at Scopus