Nonlinear Dynamics Induced by Coil Heat in the PMDC Motor and Control

Year 2024, Volume: 6 Issue: 4, 228 - 236

Arnaud Ngonting Topy , Justin Roger Mboupda Pone , Alex Stéphane Kemnang Tsafack , André Cheukem

https://doi.org/10.51537/chaos.1462132

Abstract

In this paper, the interesting dynamics of chaos induced by the effect of the variation of internal average heat during operation in the DC motor control by the full bridge drive are analyzed. By using simple powerful tools of analyzing nonlinear dynamical systems like phase portraits, time traces and frequency spectrum in the MATLAB-SIMULINK environment, we showed that under certain conditions, the PMDC motor develops different behaviors so as periodic limited, and chaotic attractors, when the motor drive different form of external load torque and the windings resistance variation. This paper presents the first studies on the variation of the average heat of the motor and the amplitude of the triangular load torque to produce the strange phenomena like chaos as far as our knowledge go. A chaos control of the unstable regime is proposed to stabilize the PM DC motor in a desire regime. This contribution is very important in industry because some unexplained dynamical behaviors of the DC motor driven by a full bridge now can be avoided.

Keywords

PM DC motor, Triangular load torque, Windings coil heat, Phase portraits, Periodic oscillations, Torus, Chaos, Chaos control

Ethical Statement

The authors declare that they have no conflict interest regarding the publication of this paper

Supporting Institution

none

Project Number

100

Thanks

The authors would like to thank Prof Sifeu Takougang for carefully reading the manuscript

References

• Abdullah, M. A., F. R. Tahir, and K. M. Abdul-Hassan, 2016 Sliding mode control-based chaos stabilization in pm dc motor drive. Iraqi Journal for Electrical & Electronic Engineering 12.
• Arat, H. T., 2018 Numerical comparison of different electric motors (im and pm) effects on a hybrid electric vehicle. Avrupa Bilim ve Teknoloji Dergisi pp. 378–387.
• Ayan, S. ¸S. and A. Kurt, 2018 Computational bifurcation analysis to find dynamic transitions of the corticotroph model. Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering 60: 41–64.
• Bonnett, A. H., 2001 Operating temperature considerations and performance characteristics for ieee 841 motors. IEEE Transactions on Industry Applications 37: 1120–1131.
• Chau, K. and Z. Wang, 2011 Introduction to chaos theory and electric drive systems .
• Chergui, H. et al., 2020 Commande Directe Du Couple d’un Moteur Asynchrone avec la Reconstitution de l’Algorithme Des Commutations par la Logique Floue. Ph.D. thesis.
• Dalcalı, A., 2018 Optimal design of high performance interior pm motor for electric vehicle. The International Journal of Energy and Engineering Sciences 3: 46–54.
• Fussell, B., 1993 Thermal effects on the torque-speed performance of a brushless dc motor. In Proceedings of Electrical/Electronics Insulation Conference, pp. 403–411, IEEE.
• Gieras, J. F., 2009 Permanent magnet motor technology: design and applications. CRC press.
• Junak, J., G. Ombach, and D. Staton, 2008 Permanent magnet dc motor brush transient thermal analysis. In Proceedings of the 2008 International Conference on Electrical Machines, pp. 978–1.
• Klein, F. N. and M. E. Kenyon, 1984 Permanent magnet dc motors design criteria and operation advantages. IEEE transactions on industry applications pp. 1525–1531.
• Liao, Y., F. Liang, and T. A. Lipo, 1995 A novel permanent magnet motor with doubly salient structure. IEEE transactions on industry applications 31: 1069–1078.
• Malvino, A., 1993 Electronic principles.
• Minghui, Z. and L. Weiguo, 2010 Transient coupled electromagnetic thermal analysis of a permanent magnet brushless dc motor. In 2010 International Conference on Computer, Mechatronics, Control and Electronic Engineering, volume 4, pp. 221–224, IEEE.
• Moustafa, E., A.-A. Sobaih, B. Abozalam, and A. S. A. Mahmoud, 2021 Period-doubling bifurcation analysis and chaos control for load torque using flc. Complex & Intelligent Systems 7: 1381– 1389.
• Okafor, N., 2013 Analysis and control of nonlinear phenomena in electrical drives. Ph.D. thesis, Newcastle University.
• Okafor, N., D. Giaouris, and B. Zahawi, 2015 Analysis and control of fast scale bifurcation in series connected dc drive operating in continuous conduction mode. In IECON 2015-41st Annual Conference of the IEEE Industrial Electronics Society, pp. 000667– 000671, IEEE.
• Okafor, N., D. Giaouris, B. Zahawi, and S. Banerjee, 2010a Analysis of fast-scale instability in dc drives with full-bridge converter using filippov’s method .
• Okafor, N., B. Zahawi, D. Giaouris, and S. Banerjee, 2010b Chaos, coexisting attractors, and fractal basin boundaries in dc drives with full-bridge converter. In Proceedings of 2010 IEEE International Symposium on Circuits and Systems, pp. 129–132, IEEE.
• Öztürk, H., 2020 A novel chaos application to observe performance of asynchronous machine under chaotic load. Chaos Theory and Applications 2: 90–97.
• Parsa, L. and H. A. Toliyat, 2005 Five-phase permanent-magnet motor drives. IEEE Transactions on Industry applications 41: 30–37.
• Pillay, P. and R. Krishnan, 1989 Modeling, simulation, and analysis of permanent-magnet motor drives. i. the permanent-magnet synchronous motor drive. IEEE Transactions on industry applications 25: 265–273.
• Pisarchik, A. N. and U. Feudel, 2014 Control of multistability. Physics Reports 540: 167–218.
• Poliashenko, M. and C. K. Aidun, 1995 A direct method for computation of simple bifurcations. Journal of Computational Physics 121: 246–260.
• Sprott, J. C., 2011 A proposed standard for the publication of new chaotic systems. International Journal of Bifurcation and Chaos 21: 2391–2394.
• Tahir, F. R., K. M. Abdul-Hassan, M. A. Abdullah, V.-T. Pham, T. M. Hoang, et al., 2017 Analysis and stabilization of chaos in permanent magnet dc motor driver. International Journal of Bifurcation and Chaos 27: 1750173.
• Toufouti, R., S. Meziane, and H. Benalla, 2007 Direct torque control strategy of induction motors. Acta Electrotechnica et Informatica 1: 1–7.
• Tsafack, A. S. K., R. Kengne, A. Cheukem, J. R. M. Pone, and G. Kenne, 2020 Chaos control using self-feedback delay controller and electronic implementation in ifoc of 3-phase induction motor. Chaos Theory and Applications 2: 40–48.
• Yu, J., T. Zhang, and J. Qian, 2011 Electrical motor products: international energy-efficiency standards and testing methods. Elsevier.