About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 495126, 11 pages
http://dx.doi.org/10.1155/2014/495126
Research Article

A Strange Double-Deck Butterfly Chaotic Attractor from a Permanent Magnet Synchronous Motor with Smooth Air Gap: Numerical Analysis and Experimental Observation

1Department of Physics and Electronics Science, Binzhou University, Binzhou 256604, China
2Department of Industry Design, Tianjin University of Science and Technology, Tianjin 300457, China
3Department of Electrical and Mining Engineering, University of South Africa, Florida 1710, South Africa
4Department of Automation, Tianjin University of Science and Technology, Tianjin 300457, China
5Department of Automation, Nankai University, Tianjin 300071, China

Received 30 April 2014; Accepted 1 July 2014; Published 17 July 2014

Academic Editor: Roberto Barrio

Copyright © 2014 Zhonglin Wang 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. 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, Section A: General, Atomic and Solid State Physics, vol. 363, no. 1-2, pp. 71–77, 2007. View at Publisher · View at Google Scholar · View at Scopus
  2. C. Mademlis and V. G. Agelidis, “On considering magnetic saturation with maximum torque to current control in interior permanent magnet synchronous motor drives,” IEEE Transactions on Energy Conversion, vol. 16, no. 3, pp. 246–252, 2001. View at Publisher · View at Google Scholar · View at Scopus
  3. T. D. Batzel and K. Y. Lee, “Electric propulsion with sensorless permanent magnet synchronous motor: implementation and performance,” IEEE Transactions on Energy Conversion, vol. 20, no. 3, pp. 575–583, 2005. View at Publisher · View at Google Scholar · View at Scopus
  4. L. Jolly, M. A. Jabbar, and L. Qinghua, “Optimization of the constant power speed range of a saturated permanent-magnet synchronous motor,” IEEE Transactions on Industry Applications, vol. 42, no. 4, pp. 1024–1030, 2006. View at Publisher · View at Google Scholar · View at Scopus
  5. J. H. Lee, Y. J. Jang, and J. P. Hong, “Characteristic analysis of permanent magnet-assisted synchronous reluctance motor for high power application,” Journal of Applied Physics, vol. 97, no. 10, Article ID 10Q503, 2005. View at Publisher · View at Google Scholar · View at Scopus
  6. X. Zhang, X. Wang, J. Du, and R. Tang, “Amelioration of coreless permanent-magnet disk synchronous motor based on FEM: motor with wedge airgap,” Journal of Iron and Steel Research International, vol. 13, no. 1, pp. 427–432, 2006. View at Publisher · View at Google Scholar · View at Scopus
  7. L. Qi, X. Wang, J. Du, F. ZHAO, and R. TANG, “Magnetic field analysis of disk coreless permanent magnet synchronous motor based on thickness variation Halbach array,” Journal of Iron and Steel Research International, vol. 13, no. 1, pp. 439–443, 2006. View at Publisher · View at Google Scholar · View at Scopus
  8. S. Chi, Z. Zhang, and L. Xu, “Sliding-mode sensorless control of direct-drive PM synchronous motors for washing machine applications,” IEEE Transactions on Industry Applications, vol. 45, no. 2, pp. 582–590, 2009. View at Publisher · View at Google Scholar · View at Scopus
  9. N. Park, M. Jang, J. Lee, K. Hong, and J. Kim, “Performance improvement of a PMSM sensorless control algorithm using a stator resistance error compensator in the low speed region,” Journal of Power Electronics, vol. 10, no. 5, pp. 485–490, 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. S. Chakraborty, E. Keller, A. Ray, and J. Mayer, “Detection and estimation of demagnetization faults in permanent magnet synchronous motors,” Electric Power Systems Research, vol. 96, pp. 225–236, 2013. View at Publisher · View at Google Scholar · View at Scopus
  11. 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
  12. M. Zribi, A. Oteafy, and N. Smaoui, “Controlling chaos in the permanent magnet synchronous motor,” Chaos, Solitons & Fractals, vol. 41, no. 3, pp. 1266–1276, 2009. View at Publisher · View at Google Scholar · View at Scopus
  13. W. Xue, Y. L. Guo, and Z. Q. Chen, “Analysis of chaos and circuit implementation of a permanent magnet synchronous motor,” Acta Physica Sinica, vol. 58, no. 12, pp. 8146–8151, 2009. View at MathSciNet · View at Scopus
  14. Z. J. Jing, C. Yu, and G. R. 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 Scopus
  15. H. H. Choi, “Adaptive control of a chaotic permanent magnet synchronous motor,” Nonlinear Dynamics, vol. 69, no. 3, pp. 1311–1322, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. D. Wei, B. Zhang, and X. Luo, “Adaptive synchronization of chaos in permanent magnet synchronous motors based on passivity theory,” Chinese Physics B, vol. 21, no. 3, Article ID 030504, 2012. View at Publisher · View at Google Scholar · View at Scopus
  17. M. Ataei, A. Kiyoumarsi, and B. Ghorbani, “Control of chaos in permanent magnet synchronous motor by using optimal Lyapunov exponents placement,” Physics Letters, Section A: General, Atomic and Solid State Physics, vol. 374, no. 41, pp. 4226–4230, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  18. K. Mischaikow and M. Mrozek, “Chaos in the Lorenz equations: a computer assisted proof. Part II: details,” Mathematics of Computation, vol. 67, no. 223, pp. 1023–1046, 1998. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. K. Mischaikow, M. Mrozek, and A. Szymczak, “Chaos in the Lorenz equations: a computer assisted proof Part III: classical parameter values,” Journal of Differential Equations, vol. 169, no. 1, pp. 17–56, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. M. Bask and R. Gençay, “Testing chaotic dynamics via Lyapunov exponents,” Physica D: Nonlinear Phenomena, vol. 114, no. 1-2, pp. 1–2, 1998. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. A. Algaba, F. Fernández-Sánchez, M. Merino, and A. J. Rodríguez-Luis, “Centers on center manifolds in the Lorenz, Chen and Lü systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 4, pp. 772–775, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. S. Cang, G. Qi, and Z. Chen, “A four-wing hyper-chaotic attractor and transient chaos generated from a new 4-D quadratic autonomous system,” Nonlinear Dynamics, vol. 59, no. 3, pp. 515–527, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. Z. H. Wang, G. Qi, Y. Sun, B. J. van Wyk, and M. A. van Wyk, “A new type of four-wing chaotic attractors in 3-D quadratic autonomous systems,” Nonlinear Dynamics, vol. 60, no. 3, pp. 443–457, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. S. Cang, Z. Chen, and Z. Yuan, “Analysis and circuit implementation of a new four-dimensional non-autonomous hyper-chaotic system,” Acta Physica Sinica, vol. 57, no. 3, pp. 1493–1501, 2008. View at Scopus
  25. L. Liu, C. Liu, and Y. Zhang, “Theoretical analysis and circuit implementation of a novel complicated hyperchaotic system,” Nonlinear Dynamics, vol. 66, no. 4, pp. 707–715, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus