Backstepping Sliding Mode Control for the Displacement Tracking of Permanent Magnet Linear Synchronous Motor Based on Nonlinear Disturbance Observer

  • Hong-jiao Song
  • Le LiuEmail author
  • Man-jun Cai
  • Nuan Shao
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 582)


For the problem that the displacement tracking control accuracy of permanent magnet linear synchronous motor (PMLSM) is prone to be affected by the uncertain factors such as parameter perturbation, and load disturbance, a backstepping sliding mode control method is proposed based on the nonlinear disturbance observer in this paper. Firstly, the nonlinear disturbance observer is developed to observe the uncertainty dynamically, so as to improve the displacement tracking accuracy of the system. Secondly, the displacement tracking controllers of PMLSM are presented by combining the backstepping sliding mode control with the command filter, which enhance the anti-jamming capability of the system, and solve the “explosion of complexity” problem during using the conventional backstepping control. Theoretical analysis shows that all the signals of the resulting closed-loop system are uniformly ultimately bounded. Finally, the proposed control method in this paper is compared with the backstepping control method, and the simulation results verify the effectiveness of the proposed control method.


Permanent magnet linear synchronous motor Nonlinear disturbance observer Backstepping sliding mode control Command filter 



This work is supported by the National Natural Science Foundation of China under Grant 61803327, the Science and Technology Research Project in Colleges and Universities of Hebei Province under Grant Z2017041, the Key Research and Development Project of Hebei Province under Grant 18212109, the Research Foundation of Hebei University of Environmental Engineering under Grant BJ201604, and the Basic Research Specific Subject of Yanshan University under Grant 16LGA005.


  1. 1.
    Yahiaoui, M., Kechich, A., Bouserhane, I.K.: Design and development of permanent magnet linear synchronous motor. Indian J. Sci. Technol. 10(27), 1–4 (2017)Google Scholar
  2. 2.
    Ting, C.S., Liu, J.F., Liu, C.S., et al.: An adaptive FNN control design of PMLSM in stationary reference frame. J. Control Autom. Electr. Syst. 27(4), 391–405 (2016)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Cho, K., Kim, J., Choi, S.B., et al.: A high-precision motion control based on a periodic adaptive disturbance observer in a PMLSM. Trans. Mechatron. 20(5), 2158–2167 (2015)CrossRefGoogle Scholar
  4. 4.
    Kim, H., Son, J., Lee, J.: A high-speed sliding-mode observer for the sensorless speed control of a PMSM. IEEE Trans. Industr. Electron. 58(9), 4069–4077 (2011)CrossRefGoogle Scholar
  5. 5.
    Zhang, R.C., Zhao, H.C., Yu, J.Y.: A three dimensional self-adaptive region fuzzy guidance law based on RBF neural networks. Int. J. Model. Ident. Control 8(3), 184–190 (2009)CrossRefGoogle Scholar
  6. 6.
    Sun, N., Fang, Y.C., Chen H: Global sliding mode control of underactuated inertia wheel pendulum systems. Control Theory Appl. 33(5), 653–661 (2016)Google Scholar
  7. 7.
    Wei, Q.T., Chen, M., Wu, Q.X., et al.: Backstepping based attitude control for a quadrotor UAV with input saturation and attitude constraints. Control Theory Appl. 32(10), 1361–1369 (2015)zbMATHGoogle Scholar
  8. 8.
    He, Z.X., Liu, C.T., Zhang, Z.L.: Dynamic Surface adaptive integral terminal sliding mode control for theodolite rotating systems. Int. J. Model. Ident. Control 23(3), 222–229 (2015)CrossRefGoogle Scholar
  9. 9.
    Han, Y.X., Yu, J.P., Liu, Z.: Command filter based adaptive neural control for permanent magnet synchronous motor stochastic nonlinear systems with input saturation. Int. J. Model. Ident. Control 30(1), 38–47 (2018)CrossRefGoogle Scholar
  10. 10.
    Bu, W.X., Wu, X.Y., Chen, Y.X., et al.: Nonlinear disturbance observer sliding mode backstepping control of hypersonic vehicles. Control Theory Appl. 31(11), 1473–1479 (2014)Google Scholar
  11. 11.
    Chen, C.S., Lin, W.S.: Self-adaptive interval Type-2 neural fuzzy network control for PMLSM drives. Expert Syst. Appl. 38(12), 14679–14689 (2011)CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Hong-jiao Song
    • 1
  • Le Liu
    • 1
    Email author
  • Man-jun Cai
    • 1
  • Nuan Shao
    • 2
  1. 1.College of Electrical EngineeringYanshan UniversityQinhuangdaoChina
  2. 2.Hebei University of Environmental EngineeringQinhuangdaoChina

Personalised recommendations