Skip to main content

Variable Structure Systems with Terminal Sliding Modes

  • Chapter
  • First Online:
Variable Structure Systems: Towards the 21st Century

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 274))

Abstract

In this chapter, we discuss recent developments in a special topic of Variable Structure Systems, namely, the terminal sliding mode control. Dynamic properties of the terminal sliding mode control systems are explored and their applications in single input single output (SISO) systems and multi input multi output (MIMO) systems are presented. Further improvements of the particular sliding mode control strategy are suggested.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bartolini, G., Ferrara, A., Levant, A., and Usai, E. (1999). On second order sliding mode controllers. Variable Structure Systems, Sliding Mode and Nonlinear Control. K. D. Young and U. Ozguner (Eds.), Lecture Notes in Control and Information Sciences, Springer Verlag, 247, 329–350.

    Google Scholar 

  2. Bhat, S. P. and Berstein D. S. (1997). Finite time stability of homogeneous systems. Proc. American Control Conference, 2513–1514.

    Google Scholar 

  3. Feng, Y., Han F., Yu, X., Stonier, D. and Man Z. (2000). Tracking precision analysis of terminal sliding mode control systems with saturation functions. Advances in Variable Structure Systems: Analysis, Integration and Applications, Yu X. and Xu. J.-X. (eds), pp. 325–334, World Scientific, Singapore.

    Google Scholar 

  4. Feng, Y., Yu, X. and Man, Z. (2001). Non singular terminal sliding mode control and its applications to robot manipulators. Proceedings of 2001 IEEE International Symposium on Circuits and Systems, III, pp. 545–548, Sydney May 2001.

    Google Scholar 

  5. Fuller, A. T. (1973). Proof of the time optimality of a predictive control strategy for systems of higher order. International Journal of Control, 18(6), 1121–1127.

    Article  MATH  MathSciNet  Google Scholar 

  6. Gulko, F. B., Ya Kogan, B., Ya. Lerner, A., Mikhailov, N. N. and Bovoseltseva, Zh. A. (1964). A prediction method using high speed analog computers and its applications. Automation and Remote Control, 25(6), 803–813.

    Google Scholar 

  7. Haimo, V. T. (1986). Finite time controllers. SIAM Journal of Control and Optimization, 24. 760–770.

    Article  MATH  MathSciNet  Google Scholar 

  8. Isidori, A. (1989). Nonlinear Control Systems. Springer-Verlag, Berlin, Heidelberg.

    MATH  Google Scholar 

  9. Jefferey, A. (1994). Table of Integrals, Series and Products. Academic Press, Inc., 5th Edition.

    Google Scholar 

  10. Lewis, F. L., Abdallah, C. T. and Dawson, D. M. (1993). Control of Robot Manipulators. Macmillan Publishing.

    Google Scholar 

  11. Levant, A. (1993). Sliding order and sliding accuracy in sliidng mode control. International Journal of Control, 58, 1247–1263.

    Article  MATH  MathSciNet  Google Scholar 

  12. Man, Z., Paplinski, A. P. and Wu, H. R. (1994). A robust MIMO terminal sliding mode control for rigid robotic manipulators. IEEE Transactions on Automat. Control, 39, 2464–2469.

    Article  MATH  MathSciNet  Google Scholar 

  13. Man, Z. and Yu, X. (1997). Terminal sliding mode Control of MIMO systems. IEEE Transactions on Circuits and Systems — Part I, 44, 1065–1070.

    Article  MathSciNet  Google Scholar 

  14. Man, Z., O’Day, M. and Yu, X. (1999). A robust adaptive terminal sliding mode control for rigid robotic systems. J. Intelligent & Robotic Systems, 24, 23–41.

    Article  MATH  Google Scholar 

  15. Man, Z. and Yu, X. (1997). Adaptive terminal sliding mode tracking control for rigid robotic manipulators with uncertain dynamics. JSME International Journal, 40(3), 493–502.

    Google Scholar 

  16. Ryan, E.P. (1982). Optimal Relay and Saturating Control System Synthesis, Peter Peregrinus Ltd. London.

    Google Scholar 

  17. Sira-Ramirez, H. (1989). Sliding regimes in general nonlinear systems: A relative degree approach. International Journal of Control, 50 1487–1506.

    Article  MATH  MathSciNet  Google Scholar 

  18. Slotine, J.-J. E. and Li, W. (1991). Applied Nonlinear Control. Prentice-Hall, Englewood Cliffs, NJ.

    MATH  Google Scholar 

  19. Utkin, V.I. (1992). Sliding Modes in Control Optimization. Springer Verlag, Berlin, Heidelberg.

    MATH  Google Scholar 

  20. Wu, Y., Yu, X. and Man, Z. (1998). Terminal sliding mode control design for uncertain dynamic systems. Systems and Control Letters, 34(5), 281–288.

    Article  MATH  MathSciNet  Google Scholar 

  21. Xia, Y., Yu, X., Ledwich, G. and Oghanna, W. (2000). Self-tuning relay control design for MIMO systems with fast convergence. IEEE Trans. Circuits and Systems — Part I, 47(10), 1548–1552.

    Article  Google Scholar 

  22. Xia, Y., Yu, X. and Oghanna, W. (2000). Adaptive robust fast control for induction motors. IEEE Trans. Industrial Electronics, 47(4), 854–862.

    Article  Google Scholar 

  23. Xu, J.-X. and Cao, W. J. (2000). Synthesized sliding mode control of a single-link flexible robot. International Journal of Control, 73(3), 197–209.

    Article  MATH  MathSciNet  Google Scholar 

  24. Yu, X. and Man, Z. (1996). Model reference adaptive control systems with terminal sliding modes. International Journal of Control, 64(6), 1165–1176.

    Article  MATH  MathSciNet  Google Scholar 

  25. Yu, X. and Man, Z. (1998). Multi-input uncertain linear systems with terminal sliding mode control. Automatica, 34(3), 389–392.

    Article  MATH  MathSciNet  Google Scholar 

  26. Yu, X. and Man, Z. (1996). On finite time convergence: Terminal sliding modes. Proceedings of 1996 International Workshop on Variable Structure Systems, 164–168, Tokyo Japan.

    Google Scholar 

  27. Yu, X. and Xu, J.-X. (1996). A novel nonlinear signal derivative estimator. Electronics Letters, 31(16), 445–1447.

    Google Scholar 

  28. Zak, M. (1989). Terminal attractors in neural networks. Neural Networks, 2, 259–274.

    Article  Google Scholar 

  29. Zinober, A. S. I. (1993). Variable Structure and Lyapunov Control. Springer-Verlag, London.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Yu, X., Man, Z. (2002). Variable Structure Systems with Terminal Sliding Modes. In: Yu, X., Xu, JX. (eds) Variable Structure Systems: Towards the 21st Century. Lecture Notes in Control and Information Sciences, vol 274. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45666-X_5

Download citation

  • DOI: https://doi.org/10.1007/3-540-45666-X_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42965-4

  • Online ISBN: 978-3-540-45666-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics