[ Log In | Register]
! Skip Navigation Links
Skip Navigation Links
Image of Discontinuity, Nonlinearity and Complexity
ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Stable and Unstable Behaviors for Brushless Motor with Harmonic Disturbance via Discrete Implicit Maps

Discontinuity, Nonlinearity, and Complexity 7(4) (2018) 463--477 | DOI:10.5890/DNC.2018.12.010

Jianzhe Huang

Department of Power and Energy Engineering, Harbin Engineering University, Harbin, 150001, China

Download Full Text PDF

 

Abstract

Dynamic model for brushless motor in the rotating frame is studied in this paper, where a periodic disturbance is introduced in the quadrature-axis voltage. The methodology of discrete implicit maps is adopted to investigate the dynamical response of such brushless motor system. Multiple closed semi-analytic bifurcation routes for period-1 motions are found by varying frequency of disturbance of the quadrature-axis voltage. The stability conditions for periodic motions will be given through eigenvalue analysis. From the semi-analytical prediction of period-1 motions, the corresponding frequency-amplitude characteristics are obtained. Finally, the stable and unstable period-1 motions will be presented numerically. With such discrete implicit maps method, the unstable motion of such brushless motor with strong nonlinearity can be obtained. Compared to the method of generalized harmonic balance, the dimension of Jacobian matrix can be dramatically decreased and the numerical error can be avoided without using QR algorithm.

Acknowledgments

This study is supported by the National Natural Science Foundation of China (Grant no. 51375104), Heilongjiang Province Funds for Distinguished Young Scientists (Grant no. JC 201405), China Postdoctoral Science Foundation (Grant no. 2015M581433), and Postdoctoral Science Foundation of Heilongjiang Province (Grant no. LBH-Z15038).

References

  1. [1]  Li, D., Wang, S.L., Zhang, X.H., and Yang, D. (2009), Fuzzy impulsive control of chaos in permanent magnet synchronous motors with parameter uncertainties, Acta Phys. Sin, 58, 1432-1440.
  2. [2]  Hernandez-Guzman, V.M., Santibanez, V., and Zavala-Rio, A. (2010), A saturated PD controller for robots equipped with brushless DC-motors, Robotica, 28, 405-411
  3. [3]  Ogasawara, S. and Akagi, H. (1991), An approach to position sensorless drive for brushless dc motors, IEEE Transactions on Industry Applications, 27(5), 928-933
  4. [4]  Hemati, N. (1992), The global and local dynamics of direct-drive brushless dc motors, Proc. Of the 1992 IEEE Int. Conf. Robotics and Automat., 2, 1858-1863.
  5. [5]  Hemati, N. (1993), Dynamic analysis of brushless motors based on compact representations of equations of motion, Proc. of 1993 IEEE indust. Appl. Soc. Ann. I Mtg., 1, 51-58.
  6. [6]  Kang, S.J. and Sul, S.K. (1995), Direct torque control of brushless dc motor with nonideal trapezoidal back EMF, IEEE Trans. Power Electron., 10(6), 796-802.
  7. [7]  Rubaai, A., Kotaru, R., and KankamM.D. (2000), A continually online-trained neural network controller for brushless dc motor drives, IEEE Trans. Ind. Appl., 36(2), 475-483.
  8. [8]  Ge, Z.M. and Chang C.M. (2004), Chaos synchronization and parameters identification of single time scale brushless dc motors, Chaos, Solitons and Fractals, 20(4), 883-903.
  9. [9]  Lee, B.K. and Ehsani, M. (2003), Advanced simulation model for brushless dc motor drives, Electric Power Components and Systems, 31(9), 841-868.
  10. [10]  Jabbar, M.A., Phyu, H.N., Liu, Z. and Bi, C. (2004), Modeling and numerical simulation of a brushless permanentmagnet dc motor in dynamic conditions by time-stepping technique, IEEE Transactions on Industry Applications, 40(3), 763-770.
  11. [11]  Luo, S.H., Wang, J.X., and Wu, S.L. (2014), Chaos RBF dynamics surface control of brushless dc motor with time delay based on tangent barrier Lyapunov function, Nonlinear Dyn., 78(2), 1193-1204.
  12. [12]  Luo, S.H.,Wu, S.L., and Gao, R.Z. (2015), Chaos control of the brushless direct current motor using adaptive dynamic surface control based on neural with the minimum weights, Chaos, 25(7), 073102 (8 pages).
  13. [13]  Zhang, F., Lin, D., Xiao, M., and Li, H. (2014), Dynamical behaviors of the chaotic brushless dc motors model, Complexity, 21(4), 79-85.
  14. [14]  Jagiela, M. and Gwozdz, J. (2015), Steady-state time-periodic finite element analysis of a brushless dc motor drive considering motion, Archives of Electrical Engineering, 64(3), 471-486.
  15. [15]  Luo, A.C.J. (2012), Continuous Dynamical Systems, L&H Scientific: Glen Carbon.
  16. [16]  Wang, F.X. and Luo, A.C.J. (2012), On the Stability of a Rotating Blade with Geometric Nonlinearity, Journal of Applied Nonlinear Dynamics, 1(3), 263-286.
  17. [17]  Leonov, G.A., Kiseleva, M.A., Kuznetsov, N.V., and Neittaanmaki, P. (2013), Hidden Oscillations in Drilling Systems: Torsional Vibrations, Journal of Applied Nonlinear Dynamics, 2(1), 83-94.
  18. [18]  Heckman, C.R. and Rand R.H. (2012), Asymptotic Analysis of the Hopf-Hopf Bifurcation in a Time-delay System, Journal of Applied Nonlinear Dynamics, 1(2), 159-171.
  19. [19]  Luo, A.C.J. and Jin H.X. (2014), Bifurcation Trees of Period-m Motions to Chaos in a Time-Delayed, Quadratic Nonlinear Oscillator under a Periodic Excitation, Discontinuity, Nonlinearity, and Complexity, 3(1), 87-107.
  20. [20]  Sah, S.M. and Rand R.H. (2016), Delay Terms in the Slow Flow, Journal of Applied Nonlinear Dynamics, 5(4), 471- 484.
  21. [21]  Luo, A.C.J. (2015), Periodic flows in nonlinear dynamical systems based on discrete implicitmaps, Int. J. Bifurc. Chao, 25, 1550044 (62 pages).
  22. [22]  Luo, A.C.J. and Guo, Y. (2015), A semi-analytical prediction of periodicmotions in Duffing oscillator throughmapping structures, Discont, Nonlinearity Complexity, 4(2), 121-50.
  23. [23]  Guo, Y and Luo, A.C.J. (2017), Periodic motions in a double-well Duffing oscillator under periodic excitation through discrete mappings, Int. J. Dyn. Control, 5(2), 223-238.
  24. [24]  Luo, A.C.J. and Xing, S.Y. (2016), Multiple bifurcation tress of period-1 motions to chaos in a periodically forced, time-delayed, hardening Duffing oscillator, Chaos, Solitons and Fractals, 89, 405-434.
  25. [25]  Xing, S.Y. and Luo A.C.J. (2017), Towards Infinite Bifurcation Trees of Period-1Motions to Chaos in a Time-delayed, Twin-well Duffing Oscillator, Journal of Vibration Testing and System Dynamics, 1(4), 353-392.

Copyright © 2011-2023 L & H Scientific Publishing. All rights reserved. Wildcard SSL Certificates