Open Access Open Access  Restricted Access Subscription or Fee Access

Control of a Permanent Magnet Synchronous Motors Based on the Nonlinear Dynamic Inversion Approach

Sabrine Jebri(1*), Khaled Nouri(2)

(1) Laboratory of Advanced Systems, Polytechnic School of Tunis, University of Carthage, Tunisia
(2) Laboratory of Advanced Systems, Polytechnic School of Tunis, University of Carthage, Tunisia
(*) Corresponding author



This paper proposes a new method for tracking and control current and speed for a Permanent Magnet Synchronous Motor (PMSM). The proposed tracking approach is based on the Nonlinear Dynamic Inversion (NDI). The novelty aspect is shown on the current and speed dependency with amplitude. Based on previous work, an accurate nonlinear model of PMSM has been used to perform the proposed approach. An advanced NDI tracking control is then considered and a comparative study between desired and simulation direct current and speed tracking control is established. Two PMSMs are considered to verify the proposed approach. Simulation results replicate clearly the desired data at different amplitude. A validity approach, named Abacus, is proposed to compare simulated and desired data to draw up operating domains. The obtained result using NDI Control method showed a difference less than 1% for the maximal speed rotor Ω at different current level and rotor speed for both tow PMSMs. Moreover, the dΩ/dt validity abacuses present an error less than 0.2% at the low-speed rotor and current. Besides, the current error between estimated and simulation NDIC results.
Copyright © 2018 Praise Worthy Prize - All rights reserved.


Nonlinear Dynamic Inversion Approach; PMSM; Direct Current Tracking Control; Speed Tracking Control; Amplitude Dependence; Validity Abacus

Full Text:



G. Wang, H. Zhan, G. Zhang, X. Gui, and D. Xu, “Adaptive compensation method of position estimation harmonic error for EMF-based observer in sensorless IPMSM drives,” IEEE Trans. Power Electron., vol. 29, no. 6, pp. 3055–3064, Jun. 2014.

C. Elmas and O. Ustun, A hybrid controller for the speed control of a permanent magnet synchronous motor drive, Control Engineering Practice, vol.16, pp.260-270, 2008.

J. Zhou and Y. Wang, Real-time nonlinear adaptive backstepping speed control for a pm synchronous motor, Control Engineering Practice, vol.13, pp.1259-1269, 2005.

M. Sekour, K. Hartani, A. Draou, and A. Allali, “Sensorless fuzzy direct torque control for high performance electric vehicle with four in-wheel motors,” J. Electr. Eng. Technol., vol. 8, no. 3, pp. 530–543, May 2013.

D. Q. Dang, N. T. T. Vu, H. H. Choi, and J. W. Jung, “Neural-fuzzy control of interior permanent magnet synchronous motor: Stability analysis and implementation,” J. Electr. Eng. Technol., vol. 8, no. 6, pp. 1439–1450, Nov. 2013.

F. Niu, , B. Wang, A. S. Babel,K. Li, and E. G. Strangas “Comparative Evaluation of Direct Torque Control Strategies for Permanent Magnet Synchronous Machines “,54:495–503,2007 IEEE Transactions on Power Electronics, Vol.31, Issue.2, February. 2016 .

W. Wang , J . Zhang , M. Cheng and R. Cao“Direct Torque Control of Five-leg Dual-PMSM Drive Systems for Fault-tolerant Purposes“,J P E, Vol. 17, No. 1, January 2017.

J. W. Jung, V. Q. Leu, T. O. Do, I.K. Kim and H. H. Choi “Adaptive PID Speed Control Design for Permanent Magnet Synchronous Motor Drives“, IEEE Transactions on Power Electronics ,Vol.30,P900 - 908, February 2015.

J. W. Jung, Y. S. Choi, V. Q. Leu, and H. H. Choi, “Fuzzy PI-type current controllers for permanent magnet synchronous motors,” IET Electr. Power Appl., vol. 5, no. 1, pp. 143–152, Jan. 2011.

A. V. Sant and K. R. Rajagopal, “PM synchronous motor speed control using hybrid fuzzy-PI with novel switching functions,” IEEE Trans. Magn., vol. 45, no. 10, pp. 4672–4675, Oct. 2009.

B. V. L. Reddy, U. A. and T.S. Rao, “A Closed Loop Speed Control of PMSM Drive Using Fuzzy Logic Controller,” IJIR,Vol.2,P778-784. 2016.

S. P. Singh, A. K.Gautam, Jyoti Dubey, J. P. Pandey and R. P. Payasi, “Performance Comparison of PMSM Drive using PI and Fuzzy Logic based controllers,” IEEE Uttar Pradesh Section International Conference on Electrical, Computer and Electronics Engineering (UPCON) ,India, December 2016.

V. Q. Leu, H. H. Choi, and J. W. Jung, “Fuzzy sliding mode speed controller for PM synchronous motors with a load torque observer,” IEEE Trans. Power Electron., vol. 27, no. 3, pp. 1530–1539, Mar. 2012

T. D. Do, H. H. Choi, and J. W. Jung, “SDRE-based near optimal control system design for PM synchronous motor,” IEEE Trans. Ind. Electron., vol. 59, no. 11, pp. 4063–4074, Nov. 2012.

T. D. Do, S. Kwak, H. H. Choi, and J. W. Jung, “Suboptimal control scheme design for interior permanent magnet synchronous motors: An SDRE-based approach,” IEEE Trans. Power Electron., vol. 29, no. 6, pp. 3020–3031, Jun. 2014.

K. Jezernik, J. Korelic, and R. Horvat, “PMSM sliding mode FPGA-based control for torque ripple reduction,” IEEE Trans. Power Electron., vol. 28, no. 7, pp. 3549–3556, Jul. 2013.

G. O. Guardabassi and S. M. Savaresi, “Approximate linearization via feedback – an overview,” Automatica, Vol. 37, pp. 1 – 15, Janvier 2001.

N. Hovakimyan, E. Lavretsky, and C. Cao, “Adaptive dynamic inversion via time-scale separation,” in Proc. 45th IEEE Conf. Decision and Control, San Diego, CA, pp. 1075 – 1080,December 2006.

H. Geng, S. Xiao,W. Yang and G. Yang. Nonlinear dynmic inversion approach applied to pitch control of wind turbines. In Proceeding of the 11th World Congress on Intelligent Control and Automation,2014.

P. B. Acquatella, W. Falkena, E. van Kampen, and Q. P. Chu,“Robust nonlinear spacecraft attitude control using incremental nonlinear dynamic inversion,” in Proceedings of the AIAA Guidance, Navigation, and Control Conference and Exhibit, Minneapolis, Minn, USA, August 2012.

S.Jebri, H. Loussifi and K. Nouri “Two mass modelling and nonlinear dynamic inversion of motor drive systems” 16th International Conference on STA Control and Computer Engineering Conference, IEEE, TUNISIA, December 2015.

S.Jebri,K. Nouri and L. Bouslimi, “Speed tracking control performance with frequency and amplitude dependence”, International Conference on Advanced Systems and Electric Technologies (IC_ASET), Hammamet, Tunisia, jan 2017.

R.Ouhibi and K. Nouri, “Internal Model Controller for Variable-Speed Wind Turbines at High Wind Speeds” International Journal of Energy Science 6 (1), 43-51, 2016

M. Koç, J. Wang, T. Sun,” An Inverter Nonlinearity Independent Flux Observer for Direct Torque Controlled High Performance Interior Permanent Magnet Brushless AC Drives” IEEE Trans. Power Electron, Volume:PP , Issue: 99, February 2016.

Kendouci, K., Mazari, B., Benhadria, M.R., Speed tracking control of PMSM using backstepping controller-simulation and experimentation, (2010) International Review of Electrical Engineering (IREE), 5 (6), pp. 2630-2636.

Ch. Uma Maheswara Rao, Bala Murali Krishna.V, A. Laxmi Soundarya, N. Krishna Kumari, “Field Oriented Control of PMSM with Model Reference Adaptive Control Using Fuzzy-PI Controller”, IJCTA, Vol. 8, No. 1, pp. 95-107, Jan-June 2015.

Ismagilov, F., Uzhegov, N., Vavilov, V., Gusakov, D., Design Aspects of a High-Speed High-Voltage PMSM for Aerospace Application, (2017) International Review of Aerospace Engineering (IREASE), 10 (3), pp. 122-130.

Del Pizzo, A., Di Noia, L., Rizzo, R., Energy Storage System Sizing for a Twin Engine Four-Seat Aircraft Electrical Propulsion, (2017) International Review of Aerospace Engineering (IREASE), 10 (6), pp. 315-322.

Abouelella, M., Zaid, S., Mahgoub, O., El-Shafei, A., New Current Trajectory for Field Weakening Control of PMSM in Wide Speed Range, (2016) International Review of Electrical Engineering (IREE), 11 (1), pp. 45-54.

Karttunen, J., Kallio, S., Peltoniemi, P., Honkanen, J., Silventoinen, P., Inverse-Based Current Harmonic Controller for Multiphase PMSMs, (2016) International Review of Electrical Engineering (IREE), 11 (4), pp. 359-369.


  • There are currently no refbacks.

Please send any question about this web site to
Copyright © 2005-2022 Praise Worthy Prize