Skip to main content
SpringerLink
Log in

Design of robust fault detection observer for Takagi-Sugeno models using the descriptor approach

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

Abstract

This paper deals with the design of a robust fault detection observer for a Takagi-Sugeno (T-S) fuzzy model affected by sensor and actuator faults and unknown bounded disturbances simultaneously. An observer based on the technique of descriptor systems is studied. Indeed, by considering faults as auxiliary state variables, both states and faults are estimated simultaneously. In order to guarantee the best robustness to disturbances and sensitivity to faults, the developed observer combine the H −/H ∞ performances. Then, based on Lyapunov method, asymptotic stability conditions are given to design the observer parameters. In order to get convenient and reliable faults estimator in computations, an iterative linear matrix inequality (LMI) algorithm is developed. This algorithm, solved easily using existing numerical tools, allows to minimize influences of disturbances and maximize the ones of faults. Finally, a numerical example is proposed to illustrate the effectiveness of the result.

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. J. Gertler, “Analytical redundancy methods in fault detection and isolation,” Proc. of the IFAC Symposium Safeprocess, Baden-Baden, pp. 9–21, 1991.

  2. M. Blanke, M. Kinnaert, J. Lunze, and M. Staroswiecki, Diagnosis and Fault-tolerant Control, 2nd edition, Springer, 2006.

  3. R. J. Patton, P. M. Frank, and R. Clark, Issues of Fault Diagnosis For Dynamic Systems, Springer-Verlag, London, 1999.

    Google Scholar 

  4. S. X. Ding, L. Guo, and P. Frank, “Parametrization of linear observers and its application to observer design,” IEEE Trans. on Automatic Control, vol. 39, pp. 1648–1652. 1994.

    Article  MathSciNet  MATH  Google Scholar 

  5. P. Frank, “Enhancement of robustness in observer based fault detection,” International Journal of Control, vol. 59, pp. 955–981, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  6. C. Edwards, S. K. Spurgeon, and R. J. Patton, “Sliding mode observers for fault detection and isolation,” Automatica, vol. 36, pp. 541–553, 2000.

    Article  MathSciNet  MATH  Google Scholar 

  7. T.-M. Guerra, A. Kruszewski, and M. Bernal, “Control law proposition for the stabilization of discrete Takagi-Sugeno models,” IEEE Trans. on Fuzzy Systems, vol. 17, no. 3, pp. 724–731, 2009.

    Article  Google Scholar 

  8. J. Lunze and J. Schroder, “Sensor and actuator fault diagnosis of systems with discrete inputs and out puts,” IEEE Trans. Syst., Man, Cybern. B, vol. 34, no. 2, pp. 1096–1107, 2004.

    Article  Google Scholar 

  9. M. Bouattour, M. Chadli, A. El Hajjaji, and M. Chaabane, “H ∞ state and faults estimation for T-S models and application to fault diagnosis,” Proc. of the 7th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, pp. 492–497, Barcelona, 30 June–03 July 2009.

  10. M. Bouattour, M. Chadli, A. El Hajjaji, and M. Chaabane, “H ∞ sensor faults estimation for T-S models using descriptor techniques: application to fault diagnosis,” Proc. of IEEE International Conferences on Fuzzy Systems, pp 251–255, Jeju Island, Korea, August 20–24, 2009.

  11. J. Guoa, X. Huangaand, and Y. Cui, “Design and analysis of robust fault detection filter using LMI tools,” Computers and Mathematics with Applications, vol. 57, pp. 1743–1747, 2009.

    Article  MathSciNet  Google Scholar 

  12. J. Liang Wang, G. H. Yang, and J. Liu, “An LMI approach to H − index and mixed H −/H ∞ fault detection observer design,” Automatica, vol. 43, pp. 1656–1665, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  13. J. Liu, J. Liang Wang, and G. H. Yang, “An LMI approach to minimum sensitivity analysis with application to fault detection,” Automatica, vol. 41, no. 11, pp. 1995–2004, 2005.

    Article  MathSciNet  MATH  Google Scholar 

  14. M. Zhong, S. X. Ding, J. Lam, and H. Wang, “An LMI approach to design robust fault detection Filter for uncertain LTI systems,” Automatica, vol. 39, pp. 543–550, 2003.

    Article  MathSciNet  MATH  Google Scholar 

  15. H. Wang, J. Wang, J. Liu, and J. Lam “Iterative LMI approach for robust fault detection observer design,” Proc. of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii USA, 2003.

  16. Z. Gao, X. Shi, and S. X. Ding, “Fuzzy statedisturbance observer design for T-S fuzzy systems with application to sensor fault estimation,” IEEE Trans. on System, Man, and Cybernetics -Part B, vol. 38, no. 3, 2008.

  17. L. Tao, G. Lei, W. Lingyao, and W. Xinjiang, “Robust fault detection filter design for uncertain LTI systems based on new bounded real lemma,” International Journal of Control, Automation, and Systems, vol. 7, no. 4, pp. 644–650, 2009.

    Article  Google Scholar 

  18. M. Chadli, A. Akhenak, J. Ragot, and D. Maquin, “State and unknown input estimation for discrete time multiple model,” Journal of the Franklin Institute, vol. 346, no. 6, pp. 593–610, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  19. M. Chadli, A. Akhenak, J. Ragot, and D. Maquin, “On the design of observer for unknown inputs fuzzy models,” International Journal of Automation and Control, vol. 2, no. 1, pp. 113–125, 2008.

    Article  Google Scholar 

  20. R. Orjuela, B. Marx, D. Maquin, and J. Ragot, “On the simultaneous state and unknown input estimation of complex systems via a multiple model strategy,” IET CTA, vol. 3, no. 7, pp. 877–890, 2009.

    MathSciNet  Google Scholar 

  21. K. Zhang, B. Jiang, and V. Cocquempot, “Adaptive observer-based fast fault estimation,” International Journal of Control, Automation, and Systems, vol. 6, no. 3, pp. 320–326, June 2008.

    Google Scholar 

  22. N. Essounbouli and A. Hamzaoui, “Direct and indirect robust adaptive fuzzy controllers for a class of nonlinear systems,” International Journal of Control, Automation and Systems, vol. 4, no. 2, pp. 146–154, 2006.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of “modélisation, Information et Systèmes”, UPJV-MIS, University of Picardie Jules Verne, 7 Rue Moulin neuf, 80000, Amiens, France

    Maha Bouattour, Mohammed Chadli & Ahmed El Hajjaji

  2. Electrical Engineering Department, National Engineering School of Sfax, Route Soukra, BP 1173, 3038, Sfax, Tunisie

    Maha Bouattour & Mohamed Chaabane

Authors
  1. Maha Bouattour
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohammed Chadli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mohamed Chaabane
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ahmed El Hajjaji
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammed Chadli.

Additional information

Recommended by Editorial Board member Bin Jiang under the direction of Editor Young Il Lee.

Maha Bouattour was born in Sfax, Tunisia, in 1981. She received her Master degrees in Electrical Engineering from the National Engineering School of Sfax, Tunisia, in 2005, and her Ph.D. degree in Electrical Engineering from the University of Picardie Jules Verne, France, and the National Engineering School of Sfax, in 2010. She is an assistant with the Preparatory Engineering Institute of Sfax, since 2009. Her current research interests include fuzzy control and fault tolerant control.

Mohammed Chadli was born in Oued-Zem, Morocco. He received his Master degree (DEA) from INSA of Lyon, France in 1999 and his Ph.D. thesis from CRAN-INPL of Nancy-France in 2002. From 1999 to 2004, he was an associate researcher in CRAN-INPL. Since 2004, he has been an Associate Professor at the University of Picardie Jules Verne and a researcher in the ‘Modélisation, Information et Systèmes’ Laboratory (MIS) in Amiens, France. His research interests include, on the theoretical side, analysis and control of singular (switched) systems, analysis and control of fuzzy/multiple model approach, robust control, model-based diagnosis, fault detection and isolation (FDI), fault tolerant control (FTC), analysis and control via LMI optimization techniques and Lyapunov methods. On the application side he is mainly interested in automotive control.

Mohamed Chaabane is working as a professor in automatic control at National School of Engineers of Sfax (ENIS), Tunisia. He received his Doctorate degree in Electrical Engineering from the University of Nancy, France in 1991. He was an Associate Professor at the University of Nancy and was a researcher at Center of Automatic Control of Nancy (CRAN) from 1988–1992. Since 1997, he is holding a research position at Automatic Control Unit, ENIS. The main research interests are in the filed of robust and optimal control, delay systems, descriptor systems. Currently, he is an associate editor of journal IJ-STA International Journal on Sciences and Techniques of Automatic control & computer engineering (www.statn.com).

Ahmed El Hajjaji received his Ph.D. and “Habilitation à diriger les recherches” degrees in automatic control from the University of Picardie Jules Verne, France, in 1993 and 2000, respectively. He was an Associate Professor in the same university from 1994 to 2003. He is currently a Full Professor and Director of the Electrical Engineering department in University of Picardie Jules Verne. Since 2001, he has also been also the head of the research team of control and vehicle of Modeling, Information and Systems (MIS) laboratory. His current research interests include fuzzy control, vehicle dynamics, Fault Tolerant Control (FTC), neural networks, maglev systems, and renewable energy systems.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bouattour, M., Chadli, M., Chaabane, M. et al. Design of robust fault detection observer for Takagi-Sugeno models using the descriptor approach. Int. J. Control Autom. Syst. 9, 973–979 (2011). https://doi.org/10.1007/s12555-011-0519-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-011-0519-2

Keywords

Search

Navigation