Advertisement

Nonlinear Dynamics

, Volume 93, Issue 4, pp 2273–2282 | Cite as

Chattering reduced sliding mode control for a class of chaotic systems

  • Shuyi Lin
  • Weidong Zhang
Original Paper
  • 79 Downloads

Abstract

This paper presents a sliding mode control scheme for chaotic systems. Finite time stability of the system states is realized by implementing the proposed controller, which is designed on the basis of a nonlinear sliding surface and a new sliding mode reaching law. The new reaching law contributes good control performance in terms of system reaching time and input chattering reduction. Principles for controller parameter selection are given in detail. Simulation results of two controlled chaotic systems are provided to demonstrate effectiveness of the proposed method.

Keywords

Chaotic control Reaching time reduction Chattering reduction Finite time stability 

Notes

Acknowledgements

The authors thank the editor and anonymous reviewers for their valuable remarks and helpful suggestions. This study is partly supported by the National Natural Science Foundation of China (U1509211, 61473183, 61627810).

References

  1. 1.
    Ott, E., Grebogi, C., Yorke, J.A.: Controlling chaos. Phys. Rev. Lett. 64(11), 1196 (1990)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Yu, Y., Jia, H., Li, P., Su, J.: Power system instability and chaos. Electr. Power Syst. Res. 65(3), 187–195 (2003)CrossRefGoogle Scholar
  3. 3.
    Jimenez-Triana, A., Chen, G., Gauthier, A.: A parameter-perturbation method for chaos control to stabilizing upos. IEEE Trans. Circuits Syst. II Express Briefs 62(4), 407–411 (2015)CrossRefGoogle Scholar
  4. 4.
    Feng, G., Chen, G.: Adaptive control of discrete-time chaotic systems: a fuzzy control approach. Chaos Solitons Fractals 23(2), 459–467 (2005)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Chen, S., Lü, J.: Synchronization of an uncertain unified chaotic system via adaptive control. Chaos Solitons Fractals 14(4), 643–647 (2002)CrossRefMATHGoogle Scholar
  6. 6.
    Fuh, C.C., Tsai, H.H., Yao, W.H.: Combining a feedback linearization controller with a disturbance observer to control a chaotic system under external excitation. Commun. Nonlinear Sci. Numer. Simul. 17(3), 1423–1429 (2012)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Pai, M.C.: Global synchronization of uncertain chaotic systems via discrete-time sliding mode control. Appl. Math. Comput. 227, 663–671 (2014)MathSciNetMATHGoogle Scholar
  8. 8.
    Ni, J., Liu, L., Liu, C., Hu, X., Shen, T.: Fixed-time dynamic surface high-order sliding mode control for chaotic oscillation in power system. Nonlinear Dyn. 86(1), 401–420 (2016)CrossRefMATHGoogle Scholar
  9. 9.
    Park, J.H.: Synchronization of genesio chaotic system via backstepping approach. Chaos Solitons Fractals 27(5), 1369–1375 (2006)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Yu, J., Chen, B., Yu, H., Gao, J.: Adaptive fuzzy tracking control for the chaotic permanent magnet synchronous motor drive system via backstepping. Nonlinear Anal. Real World Appl. 12(1), 671–681 (2011)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Zhou, P., Zhu, P.: A practical synchronization approach for fractional-order chaotic systems. Nonlinear Dyn. 89, 1719–1726 (2017)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Wu, Z.G., Shi, P., Su, H., Chu, J.: Sampled-data fuzzy control of chaotic systems based on a t–s fuzzy model. IEEE Trans. Fuzzy Syst. 22(1), 153–163 (2014)CrossRefGoogle Scholar
  13. 13.
    Young, K.D., Utkin, V.I., Ozguner, U.: A control engineer’s guide to sliding mode control. In: 1996 IEEE international workshop on variable structure systems, VSS’96, proceedings, pp 1–14. IEEE (1996)Google Scholar
  14. 14.
    Chiang, T.Y., Hung, M.L., Yan, J.J., Yang, Y.S., Chang, J.F.: Sliding mode control for uncertain unified chaotic systems with input nonlinearity. Chaos Solitons Fractals 34(2), 437–442 (2007)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Dadras, S., Momeni, H.R., Majd, V.J.: Sliding mode control for uncertain new chaotic dynamical system. Chaos Solitons Fractals 41(4), 1857–1862 (2009)CrossRefMATHGoogle Scholar
  16. 16.
    Wang, H., Zz, Han, Qy, Xie, Zhang, W.: Sliding mode control for chaotic systems based on LMI. Commun. Nonlinear Sci. Numer. Simul. 14(4), 1410–1417 (2009a)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Wang, H., Han, Z.Z., Xie, Q.Y., Zhang, W.: Finite-time chaos control via nonsingular terminal sliding mode control. Commun. Nonlinear Sci. Numer. Simul. 14(6), 2728–2733 (2009b)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Aghababa, M.P., Khanmohammadi, S., Alizadeh, G.: Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique. Appl. Math. Model. 35(6), 3080–3091 (2011)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Pan, Y., Yang, C., Pan, L., Yu, H.: Integral sliding mode control: performance, modification and improvement. IEEE Trans. Ind. Inform. (2017).  https://doi.org/10.1109/TII.2017.2761389
  20. 20.
    Li, H., Liao, X., Li, C., Li, C.: Chaos control and synchronization via a novel chatter free sliding mode control strategy. Neurocomputing 74(17), 3212–3222 (2011)CrossRefGoogle Scholar
  21. 21.
    Zhang, X., Liu, X., Zhu, Q.: Adaptive chatter free sliding mode control for a class of uncertain chaotic systems. Appl. Math. Comput. 232, 431–435 (2014)MathSciNetMATHGoogle Scholar
  22. 22.
    Fallaha, C.J., Saad, M., Kanaan, H.Y., Al-Haddad, K.: Sliding-mode robot control with exponential reaching law. IEEE Trans. Ind. Electron. 58(2), 600–610 (2011)CrossRefGoogle Scholar
  23. 23.
    Liu, L., Han, Z., Li, W.: Global sliding mode control and application in chaotic systems. Nonlinear Dyn. 56(1), 193–198 (2009)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Lü, J., Chen, G.: A new chaotic attractor coined. Int. J. Bifurc. Chaos 12(03), 659–661 (2002)MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    Li, Z., Park, J.B., Joo, Y.H., Zhang, B., Chen, G.: Bifurcations and chaos in a permanent-magnet synchronous motor. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 49(3), 383–387 (2002)CrossRefGoogle Scholar
  26. 26.
    Gao, W., Hung, J.C.: Variable structure control of nonlinear systems: a new approach. IEEE Trans. Ind. Electron. 40(1), 45–55 (1993)CrossRefGoogle Scholar
  27. 27.
    Gao, T., Chen, G., Chen, Z., Cang, S.: The generation and circuit implementation of a new hyper-chaos based upon Lorenz system. Phys. Lett. A 361(1), 78–86 (2007)CrossRefMATHGoogle Scholar
  28. 28.
    Fridman, L., Shtessel, Y., Edwards, C., Yan, X.G.: Higher-order sliding-mode observer for state estimation and input reconstruction in nonlinear systems. Int. J. Robust Nonlinear Control 18(4–5), 399–412 (2008)MathSciNetCrossRefMATHGoogle Scholar
  29. 29.
    Bartolini, G., Pisano, A., Usai, E.: An improved second-order sliding-mode control scheme robust against the measurement noise. IEEE Trans. Autom. Control 49(10), 1731–1737 (2004)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of AutomationShanghai Jiao Tong UniversityShanghaiChina
  2. 2.School of Computer Engineering and ScienceShanghai UniversityShanghaiChina

Personalised recommendations