Skip to main content
SpringerLink
Log in

Chattering free adaptive fuzzy terminal sliding mode control for second order nonlinear system

  • Published:
Journal of Control Theory and Applications Aims and scope Submit manuscript

Abstract

A novel fuzzy terminal sliding mode control (FTSMC) scheme is proposed for position tracking of a class of second-order nonlinear uncertain system. In the proposed scheme, we integrate input-output linearization technique to cancel the nonlinearities. By using a function-augmented sliding hyperplane, it is guaranteed that the output tracking error converges to zero in finite time which can be set arbitrarily. The proposed scheme eliminates reaching phase problem, so that the closed-loop system always shows invariance property to parameter uncertainties. Fuzzy logic systems are used to approximate the unknown system functions and switch item. Robust adaptive law is proposed to reduce approximation errors between true nonlinear functions and fuzzy systems, thus chattering phenomenon can be eliminated. Stability of the proposed control scheme is proved and the scheme is applied to an inverted pendulum system. Simulation studies are provided to confirm performance and effectiveness of the proposed control approach.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. I. Utkin. Variable structure systems with sliding modes[J]. IEEE Trans. on Automatic Control, 1977, 22(2): 212–222.

    Article  MathSciNet  Google Scholar 

  2. K. D. Young, V. I. Utkin, U. Ozguner. A control engineer’s guide to sliding mode control[J]. IEEE Trans. on Control Systems Technology, 1999, 7(3): 328–342.

    Article  Google Scholar 

  3. V. I. Utkin. Sliding Mode Control in Electromechanical Systems[M]. London: Taylor Francis, 1999.

    Google Scholar 

  4. H. Elmali, N. Olgac. Robust output tracking control of nonlinear MIMO systems via sliding mode technique[J]. Automatica, 1992, 28(1): 145–151.

    Article  MathSciNet  Google Scholar 

  5. J.E. Slotine, W. Li. Applied Nonlinear Control[M]. Englewood Cliffs, NJ: Prentice-Hall, 1991.

    Google Scholar 

  6. Z. Man, A. P. Paplinski, H. Wu. A robust MIMO terminal sliding mode control scheme for rigid robot manipulators[J]. IEEE Trans. on Automatic Control, 1994, 39(12): 2464–2469.

    Article  MathSciNet  Google Scholar 

  7. Y. Wu, Z. Man. Terminal sliding mode control design for uncertain dynamic systems[J]. Systems & Control Letters, 1998, 34(5): 281–287.

    Article  MathSciNet  Google Scholar 

  8. C. Tao, J. S. Taur, M. Chan. Adaptive fuzzy terminal sliding mode controller for linear systems with mismatched time-varying uncertainties[J]. IEEE Trans. on Systems, Man and Cybernetics, Part B, 2004, 34(1): 255–262.

    Article  Google Scholar 

  9. K. B. Park, J. Lee. Comments on “A robust MIMO terminal sliding mode control scheme for rigid robot manipulators”[J]. IEEE Trans. Automatic Control, 1996, 41(5): 761–762.

    Article  MathSciNet  Google Scholar 

  10. Y. Feng, X. Yu, Z. Man. Non-singlar terminal sliding mode control of rigid robot manipulators[J]. Automatica, 2002, 38(12): 2159–2167.

    Article  MathSciNet  Google Scholar 

  11. K. B. Park, T. Tsuiji. Terminal sliding mode control of second-order nonlinear uncertain systems[J]. Int. J. of Robust and Nonlinear Control, 1999, 9(11): 769–780.

    Article  Google Scholar 

  12. B. Yoo, W. Ham. Adaptive fuzzy sliding mode control of nonlinear system[J]. IEEE Trans. on Fuzzy Systems, 1998, 6(2): 315–321.

    Article  Google Scholar 

  13. Y. R. Hwang, M. Tomizuka. Fuzzy smoothing algorithms for variable structure systems[J]. IEEE Trans. on Fuzzy Systems, 1994, 2(4): 227–284.

    Article  Google Scholar 

  14. J. Wang, A. B. RAD, P. Chan. Indirect adaptive fuzzy sliding mode control: Part I: fuzzy switching[J]. Fuzzy Sets and Systems, 2001, 122(1): 21–30.

    Article  MathSciNet  Google Scholar 

  15. R. Wai, C. Lin, C. F. Hsu. Adaptive fuzzy sliding-mode control for electrical servo drive[J]. Fuzzy Sets and Systems, 2004, 143(2): 295–310.

    Article  MathSciNet  Google Scholar 

  16. L. Wang. A Course in Fuzzy Systems and Control[M]. Upper Saddle River, NL: Prentice-Hall, 1997.

    Google Scholar 

  17. J. Liu. Matlab Simulation For Sliding Mode Control[M]. Beijing: Tsinghua University Press, 2005.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing, 100083, China

    Jinkun Liu

  2. State Key Laboratory of Intelligent Technology and Systems, Tsinghua University, Beijing, 100084, China

    Fuchun Sun

Authors
  1. Jinkun Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fuchun Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported by the National Natural Science Foundation of China (No. 60474025, 90405017).

Jinkun LIU was born in Heilongjiang Province, 1965. He received Ph.D. degree in department of automatic control from Northeastern University, China in 1997. Having been a two-year post-doctor at automatic department in Zhejiang University from 1997 to 1999, he joined department of automatic control, Beijing University of Aeronautics and Astronautics as an associate professor. His research includes motion control, intelligent control and robust control.

Fuchun SUN received the B.S. and M.S. degrees from Naval Aeronatical Engineering Academy, Yantai, China, in 1986 and 1989, respectively, and Ph.D. degree from the Department of Computer Science and Technology, Tsinghua University, Beijing, China, in 1998. He worked over four years for the Department of Automatic Control at Naval Aeronautical Engineering Academy. From 1998 to 2000 he was a Postdoctoral Fellow of the Department of Automation at Tsinghua University, Beijing, China. Now he is a professor in the Department of Computer Science and Technology, Tsinghua University, Beijing, China. His research interests include intelligent control, network control and management, neural networks, fuzzy systems, variable structure control, nonlinear systems and robotics. Dr. Sun is a member of the IEEE Control System Society. He is the recipient of the excellent Doctoral Dissertation Prize of China in 2000.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, J., Sun, F. Chattering free adaptive fuzzy terminal sliding mode control for second order nonlinear system. J. Control Theory Appl. 4, 385–391 (2006). https://doi.org/10.1007/s11768-006-5334-6

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11768-006-5334-6

Keywords

Search

Navigation