Skip to main content

Advances in High Order and Adaptive Sliding Mode Control – Theory and Applications

  • Chapter
Sliding Modes after the First Decade of the 21st Century

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 412))

Abstract

The objective of this chapter is to present advanced control methodologies of uncertain nonlinear systems. Firstly, adaptive sliding mode controller that retains the system’s robustness in the presence of the bounded uncertainties/perturbations with unknown bounds is proposed. Due to the on-line adaptation, the proposed approach allows reducing control chattering. Secondly, a high order sliding mode control strategy that features a priory knowledge of the convergence time is presented. Finally, the output feedback second order sliding mode controller is presented and discussed. The control algorithms are applied to experimental set-up equipped by electrical or electropneumatic actuators.

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. Bouri, M., Thomasset, D.: Sliding control of an electropneumatic actuator using an integral switching surface. IEEE Trans. Control Syst. Tech. 9, 368–375 (2001)

    Article  Google Scholar 

  2. Filippov, A.F.: Differential Equations with Discontinuous Right-Hand side. Kluwer Academic Publishers, Dordrecht (1992)

    Google Scholar 

  3. Fliess, M.: Generalized controller canonical form for linear and nonlinear dynamics. IEEE Trans. Autom. Control 35, 994–1000 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  4. Girin, A., Plestan, F., Brun, X., Glumineau, A.: A third order sliding mode controller based on integral sliding mode for an electropneumatic system. In: IEEE Conference on Decision and Control CDC 2006, San Diego, California (2006)

    Google Scholar 

  5. Girin, A.: Contribution à la commande non linéaire d’un système électropneumatique pour une utilisation aéronautique: application sur un benchmark dédié (In French). Ph.D. Thesis, Ecole Centrale and University of Nantes (2007)

    Google Scholar 

  6. Girin, A., Plestan, F., Brun, X., Glumineau, A.: Robust control of an electropneumatic actuator: application to an aeronautical benchmark. IEEE Trans. Control Syst. Tech. 17, 633–645 (2009)

    Article  Google Scholar 

  7. Girin, A., Plestan, F.: A new experimental setup for a high performance double electropneumatic actuators system. In: American Control Conference ACC 2009, Saint Louis, Missouri (2009)

    Google Scholar 

  8. Laghrouche, S., Plestan, F., Glumineau, A.: Practical higher order sliding mode control: optimal control based approach and application to electromechanical systems. In: Edwards, C., Fossas Colet, E., Fridman, L. (eds.) Advances in Variable Structure and Sliding Mode Control. LNCIS, vol. 334, pp. 169–191. Springer, Berlin (2006)

    Chapter  Google Scholar 

  9. Laghrouche, S., Smaoui, M., Plestan, F., Brun, X.: Higher order sliding mode control based on optimal approach of an electropneumatic actuator. Int. J. Control 79, 119–131 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Laghrouche, S., Plestan, F., Glumineau, A.: Higher order sliding mode control based on integral sliding surface. Automatica 43, 531–537 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  11. Levant, A.: Sliding order and sliding accuracy in sliding mode control. Int. J. Control 58, 1247–1263 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  12. Levant, A.: Robust exact differentiation via sliding mode technique. Automatica 34, 379–384 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  13. Levant, A.: Homogeneity approach to high-order sliding mode design. Automatica 41, 823–830 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  14. Paul, A.K., Mishra, J.K., Radke, M.G.: Reduced order sliding mode control for pneumatic actuator. IEEE Trans. Control Syst. Tech. 2, 271–276 (1994)

    Article  Google Scholar 

  15. Plestan, F., Glumineau, A., Laghrouche, S.: A new algorithm for high order sliding mode control. International Journal of Robust and Nonlinear Control 18, 441–453 (2008)

    Article  MathSciNet  Google Scholar 

  16. Plestan, F., Shtessel, Y., Brégeault, V., Poznyak, A.: New methodologies for adaptive sliding mode control. International Journal of Control 83, 1907–1919 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  17. Plestan, F., Moulay, E., Glumineau, A., Cheviron, T.: Output feedback sampling control: a robust solution based on second order sliding mode. Automatica 46, 1096–1100 (2010)

    Article  MATH  Google Scholar 

  18. Rekasius, Z.V.: An alternate approach to the fixed terminal point regulator problem. IEEE Trans. Automat. Control 9, 290–292 (1964)

    Article  Google Scholar 

  19. Rengifo-Rodas, C., Plestan, F., Aoustin, Y.: Optimal control of a neuromusculoskeletal model: a second order sliding mode solution. In: Int. Workshop on Variable Structure Systems (VSS), Antalya, Turkey (2008)

    Google Scholar 

  20. Sesmat, S., Scavarda, S.: Static characteristics of a three way servovalve. In: Conf. Fluid Power Tech., Aachen, Germany (1996)

    Google Scholar 

  21. Sira-Ramirez, H.: An algebraic approach to sliding mode control. In: Zinober, A.S.I. (ed.) Variable Structure and Lyapunov Control. LNCIS, vol. 193, pp. 23–49. Springer, London (1994)

    Chapter  Google Scholar 

  22. Smaoui, M., Brun, X., Thomasset, D.: Robust position control of electropneumatic system using second order sliding mode. In: IEEE International Symposium on Industrial Electronics, Ajaccio, France (2004)

    Google Scholar 

  23. Traoré, D., Plestan, F., Glumineau, A., de Léon-Morales, J.: Sensorless induction motor: high order sliding mode controller and adaptative interconnected observer. IEEE Trans. Indus. Electron. 55, 3818–3827 (2008)

    Article  Google Scholar 

  24. Utkin, V.I., Shi, J.: Integral sliding mode in systems operating under uncertainty. In: IEEE Conference on Decision and Control CDC 1996, Kobe, Japan (1996)

    Google Scholar 

  25. VanLoan, C.F.: Computing integrals involving the matrix exponential. IEEE Trans. Automat. Control 23, 395–404 (1978)

    Article  MathSciNet  Google Scholar 

  26. Yang, L., Lilly, J.H.: Sliding mode tracking for pneumatic muscle actuators in bicep/triceps pair configuration. In: American Control Conference ACC 2003, Denver, Colorado (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Plestan, F., Brégeault, V., Glumineau, A., Shtessel, Y., Moulay, E. (2011). Advances in High Order and Adaptive Sliding Mode Control – Theory and Applications. In: Fridman, L., Moreno, J., Iriarte, R. (eds) Sliding Modes after the First Decade of the 21st Century. Lecture Notes in Control and Information Sciences, vol 412. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22164-4_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-22164-4_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22163-7

  • Online ISBN: 978-3-642-22164-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics