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Analysis of Dynamic Behavior of Permanent Magnet Synchronous Motors and Controlling Chaos with Nonlinear Output Regulation

Year 2020, Volume: 9 Issue: 1, 154 - 171, 30.01.2020
https://doi.org/10.28948/ngumuh.630680

Abstract

In this paper, the dynamic behavior of permanent magnet
synchronous motors and the nonlinear output regulation of them for constant
reference signals are studied. The dynamic analysis is based on previous studies
and new results related to chaos phenomena are obtained. With the state
feedback control law, regulation of motor velocity and direct-axis current is
achieved for known and unknown load torque at constant operating points.
Moreover, the control law is enhanced in the sense of robustness with respect
to parameter uncertainties by utilizing an augmented system with integral
operators. 

References

  • [1] N. Hemati and H. Kwatny, “Bifurcation of equilibria and chaos in permanent-magnet machines,” in Decision and Control, 1993., Proceedings of the 32nd IEEE Conference on, Dec 1993, pp. 475–479 vol.1.
  • [2] 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, Jan 1994.
  • [3] 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, Mar 2002.
  • [4] Z. Jing, C. Yu, and G. Chen, “Complex dynamics in a permanent-magnet synchronous motor model,” Chaos, Solitons & Fractals, vol. 22, no. 4, pp. 831 – 848, 2004.
  • [5] Q. Dong-lian, W. Jia-jun, and Z. Guang-zhou, “Passive control of permanent magnet synchronous motor chaotic systems,” Journal of Zhejiang University SCIENCE A, vol. 6, no. 7, pp. 728–732, 2005.
  • [6] H. 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.
  • [7] H.-p. Ren, D. Liu, and J. Li, “Delay feedback control of chaos in permanent magnet synchronous motor,” Proceedings of the Csee, vol. 6, p. 033, 2003.
  • [8] D. Q. Wei, B. Zhang, D. Y. Qiu, and X. S. Luo, “Effects of current time-delayed feedback on the dynamics of a permanent-magnet synchronous motor,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 57, no. 6, pp. 456–460, June 2010.
  • [9] 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.
  • [10] A. Loria, “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, Sept 2009.
  • [11] 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.
  • [12] M. Ataei, A. Kiyoumarsi, and B. Ghorbani, “Control of chaos in permanent magnet synchronous motor by using optimal lyapunov exponents placement,” Physics Letters A, vol. 374, no. 41, pp. 4226–4230, 2010.
  • [13] T. Chuansheng, L. Hongwei, and D. Yuehong, “Robust optimal control of chaos in permanent magnet synchronous motor with unknown parameters.” Journal of Electrical Systems, vol. 11, no. 4, pp. 376 – 383, 2015.
  • [14] Z. Ping and J. Huang, “Global robust output regulation for a class of multivariable systems and its application to a motor drive system,” in Proceedings of the 2011 American Control Conference. 1em plus 0.5em minus 0.4em IEEE, 2011, pp. 4560–4565.
  • [15] ——, “A control problem of pm synchronous motor by internal model design,” in 2011 50th IEEE Conference on Decision and Control and European Control Conference, Dec 2011, pp. 5383–5388.
  • [16] W. Yu, “Passive equivalence of chaos in lorenz system,” IEEE transactions on circuits and systems. 1, Fundamental theory and applications, vol. 46, no. 7, pp. 876–878, 1999.
  • [17] A. Isidori and C. I. Byrnes, “Output regulation of nonlinear systems,” IEEE Transactions on Automatic Control, vol. 35, no. 2, pp. 131–140, 1990.
  • [18] J. Huang and Z. Chen, “A general framework for tackling the output regulation problem,” IEEE Transactions on Automatic Control, vol. 49, no. 12, pp. 2203–2218, 2004.
  • [19] D. Q. Wei, L. Wan, X. S. Luo, S. Y. Zeng, and B. Zhang, “Global exponential stabilization for chaotic brushless dc motors with a single input,” Nonlinear Dynamics, vol. 77, no. 1, pp. 209–212, 2014.
  • [20] Y. Yu, X. Guo, and Z. Mi, “Adaptive robust backstepping control of permanent magnet synchronous motor chaotic system with fully unknown parameters and external disturbances,” Mathematical Problems in Engineering, vol. 2016, 2016.
  • [21] P. Zhou, R.-j. Bai, and J.-m. Zheng, “Stabilization of a fractional-order chaotic brushless dc motor via a single input,” Nonlinear Dynamics, vol. 82, no. 1-2, pp. 519–525, 2015.
  • [22] P. Krause, Analysis of electric machinery, ser. McGraw-Hill series in electrical and computer engineering. 1em plus 0.5em minus 0.4em McGraw-Hill, 1986.
  • [23] Z.-M. Ge and C.-M. Chang, “Chaos synchronization and parameters identification of single time scale brushless {DC} motors,” Chaos, Solitons & Fractals, vol. 20, no. 4, pp. 883 – 903, 2004.
  • [24] C. Sparrow, The Lorenz equations: bifurcations, chaos, and strange attractors. 1em plus 0.5em minus 0.4em Springer Science & Business Media, 2012, vol. 41.
  • [25] S. Vaidyanathan and C. Volos, Advances and Applications in Nonlinear Control Systems. 1em plus 0.5em minus 0.4em Springer, 2016, vol. 635.
  • [26] H. Khalil, Nonlinear Systems, ser. Pearson Education. 1em plus 0.5em minus 0.4em Prentice Hall, 2002.

Sabit Mıknatıslı Senkron Motorun Dinamik Davranış Analizi ve Doğrusal Olmayan Kontrolör ile Kaos Kontrolü

Year 2020, Volume: 9 Issue: 1, 154 - 171, 30.01.2020
https://doi.org/10.28948/ngumuh.630680

Abstract

Bu çalışmada sabit mıknatıslı senkron motorların dinamik davranışları analizi edilmiş ve sabit referans sinyali için doğrusal olmayan çıkış regülasyon kontrolü işlenmiştir. Dinamik analiz literatürde va rolan çalışmalara dayandırılarak kaos fenomenine ilişkin yeni sonuçlar elde edilmiştir. Belirli ve belirsiz yük torkları altında sabit çalışma noktasında motor hız regülasyonu ve direkt eksen akımı durum geri beslemesi kontrolü ile sağlanmıştır. Bunun ötesinde kontrol kuralı integral içeren yardımcı sistem vasıtasıyla parametre belirsizliklerine karşı dayanıklılık anlamında geliştirilmiştir.

References

  • [1] N. Hemati and H. Kwatny, “Bifurcation of equilibria and chaos in permanent-magnet machines,” in Decision and Control, 1993., Proceedings of the 32nd IEEE Conference on, Dec 1993, pp. 475–479 vol.1.
  • [2] 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, Jan 1994.
  • [3] 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, Mar 2002.
  • [4] Z. Jing, C. Yu, and G. Chen, “Complex dynamics in a permanent-magnet synchronous motor model,” Chaos, Solitons & Fractals, vol. 22, no. 4, pp. 831 – 848, 2004.
  • [5] Q. Dong-lian, W. Jia-jun, and Z. Guang-zhou, “Passive control of permanent magnet synchronous motor chaotic systems,” Journal of Zhejiang University SCIENCE A, vol. 6, no. 7, pp. 728–732, 2005.
  • [6] H. 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.
  • [7] H.-p. Ren, D. Liu, and J. Li, “Delay feedback control of chaos in permanent magnet synchronous motor,” Proceedings of the Csee, vol. 6, p. 033, 2003.
  • [8] D. Q. Wei, B. Zhang, D. Y. Qiu, and X. S. Luo, “Effects of current time-delayed feedback on the dynamics of a permanent-magnet synchronous motor,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 57, no. 6, pp. 456–460, June 2010.
  • [9] 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.
  • [10] A. Loria, “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, Sept 2009.
  • [11] 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.
  • [12] M. Ataei, A. Kiyoumarsi, and B. Ghorbani, “Control of chaos in permanent magnet synchronous motor by using optimal lyapunov exponents placement,” Physics Letters A, vol. 374, no. 41, pp. 4226–4230, 2010.
  • [13] T. Chuansheng, L. Hongwei, and D. Yuehong, “Robust optimal control of chaos in permanent magnet synchronous motor with unknown parameters.” Journal of Electrical Systems, vol. 11, no. 4, pp. 376 – 383, 2015.
  • [14] Z. Ping and J. Huang, “Global robust output regulation for a class of multivariable systems and its application to a motor drive system,” in Proceedings of the 2011 American Control Conference. 1em plus 0.5em minus 0.4em IEEE, 2011, pp. 4560–4565.
  • [15] ——, “A control problem of pm synchronous motor by internal model design,” in 2011 50th IEEE Conference on Decision and Control and European Control Conference, Dec 2011, pp. 5383–5388.
  • [16] W. Yu, “Passive equivalence of chaos in lorenz system,” IEEE transactions on circuits and systems. 1, Fundamental theory and applications, vol. 46, no. 7, pp. 876–878, 1999.
  • [17] A. Isidori and C. I. Byrnes, “Output regulation of nonlinear systems,” IEEE Transactions on Automatic Control, vol. 35, no. 2, pp. 131–140, 1990.
  • [18] J. Huang and Z. Chen, “A general framework for tackling the output regulation problem,” IEEE Transactions on Automatic Control, vol. 49, no. 12, pp. 2203–2218, 2004.
  • [19] D. Q. Wei, L. Wan, X. S. Luo, S. Y. Zeng, and B. Zhang, “Global exponential stabilization for chaotic brushless dc motors with a single input,” Nonlinear Dynamics, vol. 77, no. 1, pp. 209–212, 2014.
  • [20] Y. Yu, X. Guo, and Z. Mi, “Adaptive robust backstepping control of permanent magnet synchronous motor chaotic system with fully unknown parameters and external disturbances,” Mathematical Problems in Engineering, vol. 2016, 2016.
  • [21] P. Zhou, R.-j. Bai, and J.-m. Zheng, “Stabilization of a fractional-order chaotic brushless dc motor via a single input,” Nonlinear Dynamics, vol. 82, no. 1-2, pp. 519–525, 2015.
  • [22] P. Krause, Analysis of electric machinery, ser. McGraw-Hill series in electrical and computer engineering. 1em plus 0.5em minus 0.4em McGraw-Hill, 1986.
  • [23] Z.-M. Ge and C.-M. Chang, “Chaos synchronization and parameters identification of single time scale brushless {DC} motors,” Chaos, Solitons & Fractals, vol. 20, no. 4, pp. 883 – 903, 2004.
  • [24] C. Sparrow, The Lorenz equations: bifurcations, chaos, and strange attractors. 1em plus 0.5em minus 0.4em Springer Science & Business Media, 2012, vol. 41.
  • [25] S. Vaidyanathan and C. Volos, Advances and Applications in Nonlinear Control Systems. 1em plus 0.5em minus 0.4em Springer, 2016, vol. 635.
  • [26] H. Khalil, Nonlinear Systems, ser. Pearson Education. 1em plus 0.5em minus 0.4em Prentice Hall, 2002.
There are 26 citations in total.

Details

Primary Language English
Subjects Electrical Engineering
Journal Section Electrical and Electronics Engineering
Authors

Handan Nak 0000-0002-6642-3546

Ali Fuat Ergenc 0000-0003-2782-5566

Publication Date January 30, 2020
Submission Date October 8, 2019
Acceptance Date December 12, 2019
Published in Issue Year 2020 Volume: 9 Issue: 1

Cite

APA Nak, H., & Ergenc, A. F. (2020). Analysis of Dynamic Behavior of Permanent Magnet Synchronous Motors and Controlling Chaos with Nonlinear Output Regulation. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, 9(1), 154-171. https://doi.org/10.28948/ngumuh.630680
AMA Nak H, Ergenc AF. Analysis of Dynamic Behavior of Permanent Magnet Synchronous Motors and Controlling Chaos with Nonlinear Output Regulation. NOHU J. Eng. Sci. January 2020;9(1):154-171. doi:10.28948/ngumuh.630680
Chicago Nak, Handan, and Ali Fuat Ergenc. “Analysis of Dynamic Behavior of Permanent Magnet Synchronous Motors and Controlling Chaos With Nonlinear Output Regulation”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 9, no. 1 (January 2020): 154-71. https://doi.org/10.28948/ngumuh.630680.
EndNote Nak H, Ergenc AF (January 1, 2020) Analysis of Dynamic Behavior of Permanent Magnet Synchronous Motors and Controlling Chaos with Nonlinear Output Regulation. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 9 1 154–171.
IEEE H. Nak and A. F. Ergenc, “Analysis of Dynamic Behavior of Permanent Magnet Synchronous Motors and Controlling Chaos with Nonlinear Output Regulation”, NOHU J. Eng. Sci., vol. 9, no. 1, pp. 154–171, 2020, doi: 10.28948/ngumuh.630680.
ISNAD Nak, Handan - Ergenc, Ali Fuat. “Analysis of Dynamic Behavior of Permanent Magnet Synchronous Motors and Controlling Chaos With Nonlinear Output Regulation”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 9/1 (January 2020), 154-171. https://doi.org/10.28948/ngumuh.630680.
JAMA Nak H, Ergenc AF. Analysis of Dynamic Behavior of Permanent Magnet Synchronous Motors and Controlling Chaos with Nonlinear Output Regulation. NOHU J. Eng. Sci. 2020;9:154–171.
MLA Nak, Handan and Ali Fuat Ergenc. “Analysis of Dynamic Behavior of Permanent Magnet Synchronous Motors and Controlling Chaos With Nonlinear Output Regulation”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, vol. 9, no. 1, 2020, pp. 154-71, doi:10.28948/ngumuh.630680.
Vancouver Nak H, Ergenc AF. Analysis of Dynamic Behavior of Permanent Magnet Synchronous Motors and Controlling Chaos with Nonlinear Output Regulation. NOHU J. Eng. Sci. 2020;9(1):154-71.

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