Skip to main content
SpringerLink
Log in

Dynamic integral sliding mode for MIMO uncertain nonlinear systems

  • Technical Notes and Correspondence
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

In this paper the authors propose a novel sliding mode control methodology for Multi-Input and Multi-Output (MIMO) uncertain nonlinear systems. The proposed approach synthesizes dynamic sliding mode and integral sliding mode control strategies into dynamic integral sliding mode. The new control laws establish sliding mode without reaching phase with the use of an integral sliding manifold. Consequently, robustness against uncertainties increases from the very beginning of the process. Furthermore, the control laws considerably alleviate chattering along the switching manifold. In addition, the performance of the controller boost up in the presence of uncertainties. A comprehensive comparative analysis carried out with dynamic sliding mode control and integral sliding mode control demonstrates superiority of the newly designed control law. A chatter free regulation control of two uncertain nonlinear systems with improved performance in the presence of uncertainties ensures the robustness of the proposed dynamic integral sliding mode controller.

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. C. Edwards and S. K. Spurgeon, Sliding Mode Control: Theory and Applications, Taylor and Francis, London, 1998.

    Google Scholar 

  2. V. I. Utkin, Sliding Mode Control in Electromechanical Systems, Taylor and Francis, 1999.

  3. S. H. Zak and S. Hui, “On variable structure output feedback controllers for uncertain dynamic systems,” IEEE Trans. on Automatic Control, vol. 38, no. 10, pp. 1509–1512, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  4. C. Edwards and S. K. Spurgeon, “Sliding mode stabilization of uncertain systems using only output information,” International Journal of Control, vol. 62, no. 5, pp. 1129–1144, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  5. K. K. Shyu, Y. W. Tasi, and C. K. Lai, “A dynamic output feedback controller for mismatch uncertain variable structure systems,” Automatica, vol. 37, no. 5, pp. 775–779, 2001.

    MATH  MathSciNet  Google Scholar 

  6. J. M. Andrade-Da Silva, C. Edwards, and S. K. Spurgeon, “Sliding-mode output-feedback control based on LMIs for plants with mismatched uncertainties,” IEEE Trans. on Ind. Electronics, vol. 56, no. 9, pp. 3675–3683, 2009.

    Article  Google Scholar 

  7. J.-L. Chang, “Dynamic output integral slidingmode control with disturbance attenuation,” IEEE Trans. on Automatic Control, vol. 54, no. 11, pp. 2653–2658, 2009.

    Article  Google Scholar 

  8. W. J. Cao and J.-X. Xu, “Nonlinear integral-type sliding surface for both matched and unmatched uncertain systems,” IEEE Trans. on Automatic Control, vol. 49, no. 8, pp. 1355–1360, 2004.

    Article  MathSciNet  Google Scholar 

  9. Y.-J. Cheon, “Sliding mode control of spacecraft with actuator dynamics,” Trans. on Control Automation, and Systems Engineering, vol. 4, no. 2, pp. 169–175, 2002.

    MathSciNet  Google Scholar 

  10. H. Sira-Ramirez, “A dynamical variable structure control strategy in asymptotic output tracking problems,” IEEE Trans. on Automatic Control, vol. 38, no. 4, pp. 615–620, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  11. G. Bartolini, A. Ferrara, and E. Usai, “Chattering avoidance by second order sliding mode control,” IEEE Trans. on Automatic Control, vol. 43, no. 2, pp. 241–246, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  12. L. Fridman and A. Levant, Higher order sliding modes, In W. Perruquetti, J. P. Barbot, eds., Sliding mode Control in Engineering, Marcel Dekker, Inc., 53–101, 2002.

  13. A. Levant, “Sliding order and sliding accuracy in sliding mode control,” International Journal of Control, vol. 58, no. 6, pp. 1247–1267, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  14. T. Floquet, J. P. Barbot, and W. Perruquetti, “Higher order sliding mode stabilization for a class of nonholonomic perturbed systems,” Automatica, vol. 39, no. 6, pp. 1077–1083, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  15. S. Laghrouche, F. Plestan, and A. Alain Gluminea, “Higher order sliding mode control based on integral sliding mode,” Automatica, vol. 43, no. 3, pp. 531–537, 2007.

    Article  MATH  MathSciNet  Google Scholar 

  16. A. Levant and L. Alelishvili, “Integral high-order sliding modes,” IEEE Trans. on Automatic Control, vol. 52, no. 7, pp. 1278–1282, 2007.

    Article  MathSciNet  Google Scholar 

  17. K. Furuta, and Y. Pan, “Variable structure control with sliding sector,” Automatica, vol. 36, pp. 211–228, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  18. H. Sira-Ramirez, “On the dynamical sliding mode control of nonlinear systems,” International Journal Control, vol. 57, no. 5, pp. 1039–1061, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  19. M. Fliess, “Generalized controller canonical form for linear systems and nonlinear dynamics,” IEEE Trans. on Automatic Control, vol. 35,no. 9, pp. 994–1001, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  20. M. Fliess, Nonlinear control theory and differential algebra. In C. Byrnes, A. Kurzhanski, (Eds), Modeling and Adaptive Control. vol. 105 of Lecture notes in Control and Information Sciences, Springer-Verlag, New York, pp. 134–145, 1988.

    Google Scholar 

  21. A. Isidori, Nonlinear Control Systems, 3rd Ed., Springer-Verlag, 1995.

  22. M. Iqbal, A. I. Bhatti, S. Iqbal, and Q. Khan, “Robust parameter estimation of nonlinear systems using sliding mode technique,” IEEE Trans. on Ind. Electronics, published online: March, 2010.

Download references

Author information

Authors and Affiliations

  1. Department of Electronic Engineering, Mohammad Ali Jinnah University (MAJU) Islamabad Campus, Islamabad, Pakistan

    Qudrat Khan, Aamer Iqbal Bhatti & Sohail Iqbal

  2. Department of Computer Engineering, Centre for Advanced Studies in Engineering (CASE), Islamabad, Pakistan

    Mohammad Iqbal

Authors
  1. Qudrat Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Aamer Iqbal Bhatti
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sohail Iqbal
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mohammad Iqbal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qudrat Khan.

Additional information

Recommended by Editorial Board member Guang-Hong Yang under the direction of Editor Jae Weon Choi. This research work is conducted at Control and Signal Processing Research (CASPR) Group.

Qudrat Khan is a postgraduate student with the Department of Electronic Engineering Mohammad Ali Jinnah University Islamabad, Pakistan. His professional interests are observer design and parameter estimation, theory of sliding mode control and its application and analytical dynamics.

Aamer Iqbal Bhatti got his Bachelor’s degree in Electrical Engineering from UET Lahore in 1993; Masters in Control Systems from Imperial College of Science, Technology & Medicine, London, in 1994. He did his Ph.D. and postdoctorial research in Control Engineering in 1998, 1999 from Leicester University UK. Currently, he is a Professor of DSP and Control Systems. His research interests are sliding mode applications and radar signal processing and have published more than 68 refereed research papers.

Sohail Iqbal is doing his Ph.D. from Mohammad Ali Jinnah University, Islamabad. Currently, he is with university of Leicester, UK as Research Fellow. His research interests are control theory & robotics systems emphasizing on higher order sliding mode theory and parallel robotic manipulators.

Mohammad Iqbal is a Ph.D. candidate at Center for Advanced Studies in Engineering (CASE), Islamabad. He is the first author and co-author of more than 16 refereed international publications. His research interests are controls & DSP applications emphasizing fault diagnosis of uncertain nonlinear dynamic systems.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khan, Q., Bhatti, A.I., Iqbal, S. et al. Dynamic integral sliding mode for MIMO uncertain nonlinear systems. Int. J. Control Autom. Syst. 9, 151–160 (2011). https://doi.org/10.1007/s12555-011-0120-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-011-0120-8

Keywords

Search

Navigation