Analysis and Control of Chaos in Permanent Magnet Synchronous Motor

Year 2023, , 1217 - 1225, 18.12.2023

Abdallah Moussa Yaya , Yılmaz Uyaroğlu

https://doi.org/10.16984/saufenbilder.1286774

Abstract

This paper explores the chaotic dynamics exhibited by a Permanent Magnet Synchronous Motors (PMSM) through an analysis of Lyapunov exponents and equilibrium points. Subsequently, the study focuses on controlling the motor's chaotic behavior under specific parameter conditions using a straightforward controller. The approach employed in this paper involves utilizing a single-state feedback controller as the resolution method. The derived control law enables the stabilization of the motor's state around a reference state, even in the presence of parameter uncertainties, thereby preventing chaotic behavior. To illustrate the proposed method, numerical simulations were conducted in MATLAB, showcasing the practical application of this approach. The simulation results demonstrate the success of the controller used.

Keywords

Chaos, chaotic system, chaos control, PMSM

References

• [1] R. Krishnan, “Application Characteristics of Permanent Magnet Synchronous and Brushless dc Motors for Servo Drives,” IEEE Transactions on Industry Applications, vol. 27, no. 5, pp. 986–996, 1991.
• [2] D. P. Iracleous, N. Mastorakis, and T. H. Piraeus, “Application of passivity control theory to chaotic systems,” 2004.
• [3] M. Babaei, J. Nazarzadeh, and J. Faiz, “Nonlinear feedback control of chaos in synchronous reluctance motor drive systems,” 2008 IEEE International Conference on Industrial Technology, 2008.
• [4] J. Hu, L. Liu, and D. Wei Ma, “Robust nonlinear feedback control of a chaotic permanent-magnet synchronous motor with a load torque disturbance,” Journal of the Korean Physical Society, vol. 65, no. 12, pp. 2132–2139, 2014.
• [5] J. Hu, Y. Qiu, and H. Lu, “Adaptive robust nonlinear feedback control of chaos in PMSM system with modeling uncertainty,” Applied Mathematical Modelling, vol. 40, no. 19–20, pp. 8265–8275, Oct. 2016.
• [6] (陈强) C. Q. et al., “Full-order sliding mode control of uncertain chaos in a permanent magnet synchronous motor based on a fuzzy extended state observer,” Chinese Physics B, vol. 24, no. 11, pp. 110504–110504, Nov. 2015.
• [7] S. Luo, “Adaptive fuzzy dynamic surface control for the chaotic permanent magnet synchronous motor using Nussbaum gain,” Chaos, vol. 24, no. 3, Sep. 2014.
• [8] J. Yu, J. Gao, Y. Ma, H. Yu, and S. Pan, “Robust adaptive fuzzy control of chaos in the permanent magnet synchronous motor,” Discrete Dynamics in Nature and Society, vol. 2010, 2010.
• [9] H. H. Choi, “Adaptive control of a chaotic permanent magnet synchronous motor,” Nonlinear Dyn, vol. 69, no. 3, pp. 1311–1322, Aug. 2012.
• [10] L. Wang, J. Fan, Z. Wang, B. Zhan, and J. Li, “Dynamic Analysis and Control of a Permanent Magnet Synchronous Motor With External Perturbation,” Journal of Dynamic Systems Measurement and Control-transactions of The Asme, vol. 138, no. 1, 2016.
• [11] M. Ataei, A. Kiyoumarsi, and B. Ghorbani, “Control of chaos in permanent magnet synchronous motor by using optimal Lyapunov exponents placement,” Phys Lett A, vol. 374, no. 41, pp. 4226–4230, 2010, Accessed: Apr. 22, 2023. [Online]. Available: https://www.academia.edu/9295607/C ontrol_of_chaos_in_permanent_magn et_synchronous_motor_by_using_opti mal_Lyapunov_exponents_placement
• [12] Q. Donglian, W. Jia-jun, and Z. Guangzhou, “Passive control of Permanent Magnet Synchronous Motor chaotic systems,” Journal of Zhejiang University-SCIENCE A, 2005.
• [13] X. Chen, J. Hu, Z. Peng, and C. Yuan, “Bifurcation and chaos analysis of torsional vibration in a PMSM-based driven system considering electromechanically coupled effect,” Nonlinear Dyn, vol. 88, no. 1, pp. 277– 292, Apr. 2017.
• [14] D. Li, S. L. Wang, X. H. Zhang, D. Yang, and H. Wang, “Impulsive control of permanent magnet synchronous motors with parameters uncertainties,” Chinese Physics B, vol. 17, no. 5, pp. 1678–1684, May 2008.
• [15] W. Du-Qu and Z. Bo, “Controlling chaos in permanent magnet synchronous motor based on finitetime stability theory,” Chinese Physics B, vol. 18, no. 4, pp. 1399–1403, 2009.
• [16] J. TU and Q. Zhou, “DESIGN AND IMPLEMENTATION OF THE CRYING VOICE DETECTION CIRCUIT IN THE BABY’S SUPERVISION SYSTEM,” Review of Computer Engineer Studies, vol. 1, no. 1, pp. 13–16, Sep. 2014.
• [17] J. Zhou, Y. Luo, Z. Li, and C. Kang, “ANALYSIS OF FOREST FIRE SURVEILLANCE & PREWARNING APPLICATION SYSTEM BASED ON POWER GRID GIS,” Review of Computer Engineer Studies, vol. 1, no. 1, pp. 23–28, Sep. 2014.
• [18] U. J. Das, “Effects of non-newtonian parameter on unsteady MHD free convective mass transfer flow of a viscoelastic fluid past an infinite vertical porous plate with constant suction and heat, sink,” International Journal of Heat and Technology, vol. 31, no. 2, pp. 87–93, 2013.
• [19] B. Buonomo, O. Manca, S. Nardini, and P. Romano, “Thermal and fluid dynamic analysis of solar chimney building systems,” International Journal of Heat and Technology, vol. 31, no. 2, pp. 119–126, 2013.
• [20] L. Marietta and G. Evola, “Thermodynamic analysis of a hybrid photovoltaic/thermal solar collector,” International Journal of Heat and Technology, vol. 31, no. 2, pp. 135– 142, 2013.
• [21] M.G. Reddy, “Influence of thermal Radiation on Natural Convection Boundary Layer Flow of a Nanofluid Past a Vertical Plate with Uniform Heat Flux | IIETA,” International Journal of Heat and Technology, 2013. https://www.iieta.org/journals/ijht/pap er/10.18280/ijht.320101 (accessed Apr. 02, 2023).
• [22] K. Rajagopal, A. Karthikeyan, and P. Duraisamy, “Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine Systems,” Nonlinear Engineering, vol. 6, no. 2, pp. 79–87, Jun. 2017.
• [23] 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.
• [24] X. Liao and P. Yu, “Absolute Stability of Nonlinear Control Systems,” vol. 25, 2008.