Advertisement

Cluster Computing

, Volume 22, Supplement 3, pp 7471–7480 | Cite as

Sliding mode control based on U model for nonlinear discrete system with modeling uncertainties

  • Fengxia XuEmail author
  • Xiaohui Song
  • Hongliang Ren
  • Shanshan Wang
Article
  • 82 Downloads

Abstract

In this paper, the high precision control problem is investigated for the nonlinear discrete system with modeling uncertainties. A new method based on nonlinear U model is proposed for sliding mode control, then based on which a new sliding mode observer is proposed firstly and a new adaptive reaching law is designed. The convergence of the designed sliding mode observer and the reach ability of the designed adaptive reaching law is proved respectively, then based on which and the Lyapunov’s stability theory the stability of the control system is proved. The observation error problem is also discussed, it is shown that the proposed sliding mode observer has a smaller observation error than the traditional method. Finally, two numerical example is given to illustrate the feasibility and superiority of the proposed design scheme.

Keywords

Nonlinear Uncertainty Sliding mode observer U-model Adaptive reaching law 

Notes

Acknowledgements

This work was supported by Heilongjiang Province Nature Science Foundation under Grant No. LC2015024.

References

  1. 1.
    Xu, F., Zhu, Q., Zhao, D., et al.: U-model based design methods for nonlinear control systems a survey of the development in the 1st decade. Control Decis. 28(7), 961–977 (2013)zbMATHGoogle Scholar
  2. 2.
    Zhu, Q.M., Warwick, K., Douce, J.L.: Adaptive general predictive controller for nonlinear systems. In: IEEE Proceedings D (Control Theory and Applications). IET Digital Library, vol. 138(1), 33–40 (1991)Google Scholar
  3. 3.
    Zhu, Q.M., Guo, L.Z.: A pole placement controller for non-linear dynamic plants. Proc. Inst. Mech. Eng. Part I 216(6), 467–476 (2002)Google Scholar
  4. 4.
    Zhu, Q., Wang, Y., Zhao, D., et al.: Review of rational (total) nonlinear dynamic system modeling, identification, and control. Int. J. Syst. Sci. 46(12), 2122–2133 (2015)CrossRefGoogle Scholar
  5. 5.
    Ali, S.Saad Azhar, Al-Sunni, F.M., Shafiq, M., et al.: U-model based learning feed forward control of MIMO nonlinear systems. Electr. Eng. (Archiv fur Elektrotechnik) 91(8), 405–415 (2010)CrossRefGoogle Scholar
  6. 6.
    Alipouri, Y., Poshtan, J.: Designing a robust minimum variance controller using discrete slide mode controller approach. ISA Trans. 52(2), 291–299 (2013)CrossRefGoogle Scholar
  7. 7.
    Soltanpour, M.R., Khooban, M.H., Soltani, M.: Robust fuzzy sliding mode control for tracking the robot manipulator in joint space and in presence of uncertainties. Robotica 32(03), 433–446 (2014)CrossRefGoogle Scholar
  8. 8.
    Moghaddam, E.T., Ganji, J.: Sliding mode control of magnetic levitation systems using hybrid extended kalman filter. Energy Sci. Technol. 2(2), 35–42 (2011)Google Scholar
  9. 9.
    Oveisi, A., Gudarzi, M.: Adaptive sliding mode vibration control of a nonlinear smart beam: a comparison with self-tuning Ziegler-Nichols PID controller. J. Low Freq. Noise Vib. Active Control 32(1), 41–62 (2013)CrossRefGoogle Scholar
  10. 10.
    Zhang, J.H., Wu, X.L., Li, Y., Huo, J.N.: Super twisting sliding mode control of nonlinear system based on U model control. In: Proceedings of the 35th Chinese Control Conference, pp. 3579–3583 (2016)Google Scholar
  11. 11.
    Deng, Y., Zhang, Y.: Sliding mode control for a class of nonlinear systems based on robust adaptive neural network estimation. Kybernetes 39(6), 888–899 (2010)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Hu, J., Zhu, D.: Vibration control of smart structure using sliding mode control with observer. J. Comput. 7(2), 411–418 (2012)CrossRefGoogle Scholar
  13. 13.
    Eun, Y., Kim, J.H., Kim, K., et al.: Discrete-time variable structure controller with a decoupled disturbance compensator and its application to a CNC servomechanism. IEEE Trans. Control Syst. Technol. 7(4), 414–423 (1999)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Hu, J., Wang, Z., Niu, Y., et al.: Hsliding mode observer design for a class of nonlinear discrete time delay systems: a delay fractioning approach. Int. J. Robust Nonlinear Control 22(16), 1806–1826 (2012)CrossRefGoogle Scholar
  15. 15.
    Wang, B., Wang, J.: Sliding mode control of surface-mount permanent-magnet synchronous motor based on error model with unknown load. J. Softw. 6(5), 819–825 (2011)Google Scholar
  16. 16.
    Neila, M.B.R., Tarak, D.: Adaptive terminal sliding mode control for rigid robotic manipulators. Int. J. Autom. Comput. 8(2), 215–220 (2011)CrossRefGoogle Scholar
  17. 17.
    Yang, C.C.: Adaptive nonsingular terminal sliding mode control for synchronization of identical \(\phi ^{6}\)oscillators. Nonlinear Dyn. 69, 21–33 (2012)CrossRefGoogle Scholar
  18. 18.
    Li, J., Su, H., Zhang, Y., et al.: Chattering free sliding mode control for uncertain discrete time-delay singular systems. Asian J. Control 15(1), 260–269 (2013)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Song, Z., Sun, K.: Adaptive back stepping sliding mode control with fuzzy monitoring strategy for a kind of mechanical system. ISA Trans. 53(1), 125–133 (2014)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Zarrabi, M.R., Farahi, M.H., Koshkouei, A.J., et al.: Embedding-based sliding mode control for linear time varying systems. Appl. Math. 2(4), 487–499 (2011)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Zhai, C.L., Wu, Z.M.: Variable Structure control method for discrete time systems. J. Shanghai Jiao Tong Univ. 34(5), 719–722 (2000)MathSciNetGoogle Scholar
  22. 22.
    Sarpturk, S.Z., Istefanopulos, Y., Kaynak, O.: On the stability of discrete-time sliding mode control systems. IEEE Trans. Autom. Control 32(10), 930–932 (1987)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Fengxia Xu
    • 1
    Email author
  • Xiaohui Song
    • 1
  • Hongliang Ren
    • 1
  • Shanshan Wang
    • 1
  1. 1.College of Computer and Control EngineeringQiqihar UniversityQiqiharChina

Personalised recommendations