HGO and neural network based integral sliding mode control for PMSMs with uncertainty


This paper proposes an integral sliding mode control that integrates a high-gain observer (HGO) and a radial basis function neural network (RBFNN) for a permanent magnet synchronous motor (PMSM) with uncertainty. Since the second-order motion equation of the PMSM is used to improve the control performance, the speed derivative, which cannot be measured directly, is required. Thus, the HGO is designed to estimate the unknown state (speed derivative). In addition, the RBFNN is designed to approximate the compounded disturbance including the lumped disturbance of system and the HGO error effect. Unlike previous studies, the output of the RBFNN is compensated by both the controller and the HGO to improve the system robustness and observer accuracy. The sliding function and the HGO error are both taken into account in the RBFNN to explicitly guarantee the stability of the whole system. To demonstrate the superiority of the proposed method, comparative simulations and experiments were carried out in different cases.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24


  1. 1.

    Kim, S.: Moment of inertia and friction torque coefficient identification in a servo drive system. IEEE Trans. Ind. Electron. 66(1), 60–70 (2019)

    Article  Google Scholar 

  2. 2.

    Thounthong, P., Sikkabut, S., Poonnoi, N., et al.: Nonlinear differential flatness based speed/torque control with state-observers of permanent magnet synchronous motor drives. IEEE Trans. Ind. Appl. 54(3), 2874–2884 (2018)

    Article  Google Scholar 

  3. 3.

    Chaoui, H., Khayamy, M., Okoye, O., et al.: Simplified speed control of permanent magnet synchronous motors using genetic algorithms. IEEE Trans. Power Electron. 34(4), 3563–3574 (2018)

    Article  Google Scholar 

  4. 4.

    Xu, Y., Hou, Y., Li, Z.: Robust predictive speed control for SPMSM drives based on extended state observers. J. Power Electron. 19(2), 497–508 (2019)

    Article  Google Scholar 

  5. 5.

    Chen, J., Yao, W., Ren, Y., et al.: Nonlinear adaptive speed control of a permanent magnet synchronous motor: a perturbation estimation approach. Control Eng. Pract. 85, 163–175 (2019)

    Article  Google Scholar 

  6. 6.

    Aghili, F.: Optimal feedback linearization control of interior PM synchronous motors subject to time-varying operation conditions minimizing power loss. IEEE Trans. Ind. Electron. 65(7), 5414–5421 (2018)

    Article  Google Scholar 

  7. 7.

    Xu, B., Shen, X., Ji, W., et al.: Adaptive nonsingular terminal sliding model control for permanent magnet synchronous motor based on disturbance observer. IEEE Access. 6, 48913–48920 (2018)

    Article  Google Scholar 

  8. 8.

    Preindl, M., Bolognani, S.: Model predictive direct speed control with finite control set of PMSM drive systems. IEEE Trans Power Electron. 28(2), 1007–1015 (2013)

    Article  Google Scholar 

  9. 9.

    Sousy, E., Fayez, F.: Robust recurrent wavelet interval type-2 fuzzy-neural-network control for DSP-based PMSM servo drive systems. J. Power Electron 13(1), 139–160 (2013)

    Article  Google Scholar 

  10. 10.

    Lin, F., Hung, Y., Ruan, K.: An intelligent second -order sliding-mode control for an electric power steering system using a wavelet fuzzy neural network. IEEE Trans. Fuzzy Syst. 22(6), 1598–1611 (2014)

    Article  Google Scholar 

  11. 11.

    Zhang, X., Sun, L., Zhao, K.: Nonlinear speed control for PMSM system using sliding-mode control and disturbance compensation techniques. IEEE Trans. Power Electron. 28(3), 1358–1365 (2013)

    Article  Google Scholar 

  12. 12.

    Li, S., Zong, K., Liu, H.: A composite speed controller based on a second-order model of permanent magnet synchronous motor system. Trans. Inst. Meas. Control 33(5), 522–541 (2011)

    Article  Google Scholar 

  13. 13.

    Bu, X., Wu, X., Zhang, R., et al.: Tracking differentiator design for the robust backstepping control of a flexible air-breathing hypersonic vehicle. J. Frankl. Inst. Eng. Appl. Math. 352(4), 1739–1765 (2015)

    MathSciNet  Article  Google Scholar 

  14. 14.

    Dai, X., Gao, Z., Breikin, T., et al.: High-gain observer-based estimation of parameter variations with delay alignment. IEEE Trans Autom. Control 57(3), 726–732 (2012)

    MathSciNet  Article  Google Scholar 

  15. 15.

    Liu, J., Vazquez, S., Wu, L., et al.: Extended state observer based sliding mode control for three-phase power converters. IEEE Trans. Ind. Electron. 64(1), 22–31 (2016)

    Article  Google Scholar 

  16. 16.

    Mercorelli, P.: A two-stage sliding-mode high-Gain observer to reduce uncertainties and disturbances effects for sensorless control in automotive applications. IEEE Trans. Ind. Electron. 62(9), 5929–5940 (2015)

    Article  Google Scholar 

  17. 17.

    Cunha, J., Costa, R., Lizarralde, F.: Peaking free variable structure control of uncertain linear systems based on a high-gain observer. Automatica 45(5), 1156–1164 (2009)

    MathSciNet  Article  Google Scholar 

  18. 18.

    Khalil, H., Praly, L.: High-gain observers in nonlinear feedback control. Int. J. Robust Nonlinear Control 24(6), 993–1015 (2014)

    MathSciNet  Article  Google Scholar 

  19. 19.

    Prasov, A., Khalil, H.: A nonlinear high-gain observer for systems with measurement noise in a feedback control framework. IEEE Trans. Autom. Control 58(3), 569–580 (2013)

    MathSciNet  Article  Google Scholar 

  20. 20.

    Niu, X., Zhang, C., Li, H.: Active disturbance attenuation control for permanent magnet synchronous motor via feedback domination and disturbance observer. IET Control Theory Appl. 11(6), 807–815 (2017)

    MathSciNet  Article  Google Scholar 

  21. 21.

    Zhao, L., Huang, J., Liu, H., et al.: Second-order sliding-mode observer with online parameter identification for sensorless induction motor drives. IEEE Trans. Ind. Electron. 61(10), 5280–5289 (2014)

    Article  Google Scholar 

  22. 22.

    Wang, H., Ge, X., Liu, Y.: Second-order sliding-mode MRAS observer based sensorless vector control of linear induction motor drives for medium-low speed maglev applications. IEEE Trans. Ind. Electron. 65(12), 9938–9952 (2018)

    Article  Google Scholar 

  23. 23.

    Biricik, S., Komurcugil, H.: Optimized sliding mode control to maximize existence region for single-phase dynamic voltage restorers. IEEE Trans. Ind. Informat. 12(4), 1486–1497 (2016)

    Article  Google Scholar 

  24. 24.

    Sira-Ramirez, H., Linares-Flores, J., Garcia-Rodriguez, C., et al.: On the control of the permanent magnet synchronous motor: an active disturbance rejection control approach. IEEE Trans. Control Syst Technol. 22(5), 2056–2063 (2014)

    Article  Google Scholar 

  25. 25.

    Liu, X., Shan, Z.B., Li, Y.C.: Dynamic boundary layer based neural network quasi-sliding mode control for soft touching down on asteroid. Adv. Space Res. 59(8), 2173–2185 (2017)

    Article  Google Scholar 

  26. 26.

    He, W., Huang, B., Dong, Y., et al.: Adaptive neural network control for robotic manipulators with unknown deadzone. IEEE Trans. Cybern. 48(9), 2670–2682 (2018)

    Article  Google Scholar 

  27. 27.

    Kenne, G., Fotso, A., Lamnabhi, L.: A new adaptive control strategy for a class of nonlinear system using RBF neuro-sliding-mode technique: application to SEIG wind turbine control system”. Int. J. Control 90(4), 855–872 (2017)

    MathSciNet  Article  Google Scholar 

  28. 28.

    Liu, L., Wang, D., Peng, Z., et al.: Bounded neural network control for target tracking of underactuated autonomous surface vehicles in the presence of uncertain target dynamics. IEEE Trans. Neural Netw. Learn. Syst. 30(4), 1241–1249 (2019)

    MathSciNet  Article  Google Scholar 

  29. 29.

    Xu, B., Wang, D., Zhang, Y., et al.: DOB based neural control of flexible hypersonic flight vehicle considering wind effects. IEEE Trans. Ind. Electron. 64(11), 8676–8685 (2017)

    Article  Google Scholar 

  30. 30.

    Yin, Y., Liu, J., Sanchez, J., et al.: Observer-based adaptive sliding mode control of NPC converters: an RBF neural network approach. IEEE Trans. Power Electron. 34(4), 3831–3841 (2019)

    Article  Google Scholar 

  31. 31.

    Kommuri, S., Defoort, M., Karimi, H., et al.: A robust observer based sensor fault-tolerant control for PMSM in electric vehicles. IEEE Trans. Ind. Electron. 63(12), 7671–7681 (2016)

    Article  Google Scholar 

  32. 32.

    Golubev, A., Krishchenko, A., Tkachev, S.: Stabilization of nonlinear dynamic systems using the system state estimates made by the asymptotic observer. Autom. Remote Control 66(7), 1021–1058 (2005)

    MathSciNet  Article  Google Scholar 

Download references


Funding was provided by Fundamental Research Funds for the Central Universities (CN) (xjj2018007).

Author information



Corresponding author

Correspondence to Lihui Yang.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ge, Y., Yang, L. & Ma, X. HGO and neural network based integral sliding mode control for PMSMs with uncertainty. J. Power Electron. (2020). https://doi.org/10.1007/s43236-020-00111-w

Download citation


  • Permanent magnet synchronous motor
  • Integral sliding mode control
  • High-gain observer
  • Radial basis function neural network
  • Parameter adaptive algorithm