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Robust H ∞ sliding mode observer design for fault estimation in a class of uncertain nonlinear systems with LMI optimization approach

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Abstract

This paper presents a new approach for the design of robust H ∞ sliding mode observer (SMO) for a class of Lipschitz nonlinear systems where both faults and uncertainties are considered. A sufficient condition using linear matrix inequality (LMI) optimization is derived to guarantee the asymptotically stability of the estimation error dynamics and compute the observer gains. A fault estimation scheme is presented where the estimation signal can approximate the fault to some degree of accuracy. Our design approach has some advantages. The Lipschitz constant of the nonlinear term in the system and the disturbance attenuation level are maximized simultaneously through convex multiobjective optimization. For this reason, the Lipschitz constant is suitable to a large class of uncertain nonlinear systems. Moreover, the fault estimation is much more robust against disturbances and nonlinear uncertainty and can preserve the fault signal shape effectively. Finally, a simulation study on a robotic arm system is presented to show the effectiveness of this approach.

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References

  1. R. J. Patton and R. Clark, Issues of Fault Diagnosis for Dynamics Systems, Springer, Berlin, Heidelberg, New York, 2000.

    Google Scholar 

  2. J. Chen and R. J. Patton, Robust Model-based Fault Diagnosis for Dynamics Systems, Kluwer Academic Publishers, 1999.

  3. J. J. Gertler, Fault Detection and Diagnosis in Engineering Systems, Marcel Dekker, New York, 1998.

    Google Scholar 

  4. P. M. Frank, “Fault diagnosis in dynamics systems using analytical and knowledge-based redundancy-a survey and some new results,” Automatica, vol. 26, no. 3, pp. 459–474, 1990.

    Article  MATH  Google Scholar 

  5. E. Y. Chow and A. S. Willsky, “Analytical redundancy and the design of robust detection systems,” IEEE Trans. on Automatic Control, vol. 43, no. 7, pp. 143–161, 1984.

    MathSciNet  Google Scholar 

  6. R. Isermann, “Process fault detection based on modelling and estimation methods,” Automatica, vol. 20, no. 4, pp. 827–846, 1984.

    Article  Google Scholar 

  7. C. Edwards, S. K. Spurgeon, and R. J. Patton, “Sliding mode observers for fault detection and isolation,” Automatica, vol. 36, no. 4, pp. 541–553, 2000.

    Article  MathSciNet  MATH  Google Scholar 

  8. C. Edwards and S. K. Spurgeon, “A sliding mode observers based FDI scheme for the ship benchmark,” European Journal of Control, vol. 6, pp. 341–356, 2000.

    Google Scholar 

  9. C. P. Tan and C. Edwards, “Sliding mode observers for detection and reconstruction of sensor faults,” Automatica, vol. 38, no. 10, pp. 1815–1821, 2002.

    Article  MathSciNet  MATH  Google Scholar 

  10. C. P. Tan and C. Edwards, “Sliding mode observers for robust detection and reconstruction of actuator and sensor faults,” International Journal of Robust Nonlinear Control, vol. 13, no. 5, pp. 443–463, 2003.

    Article  MathSciNet  MATH  Google Scholar 

  11. T. Floquet, J. P. Barbot, W. Perruquetti, and M. Djemai, “On the robust fault detection via a sliding mode disturbance observer,” International Journal of Control, vol. 77, no. 7, pp. 622–629, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  12. E. Yaz and A. Azemi, “Sliding mode observer for nonlinear models with unbounded noise and measurement uncertainties,” Journal of Dynamics and Control, vol. 3, no. 3, pp. 217–235, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  13. T. Floquet and J. P. Barbot, “Super twisting algorithm-based step-by-step sliding mode observers for nonlinear systems with unknown inputs,” Inter national Journal of Systems Science, vol. 38, no. 10, pp. 803–815, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  14. X. G. Yan and C. Edwards, “Nonlinear robust fault reconstruction and estimation using a sliding mode observer,” Automatica, vol. 43, no. 9, pp. 1605–1614, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  15. R. Raoufi, H. J. Marquez, and A. S. I. Zinober, “H ∞ sliding mode observers for uncertain nonlinear Lipschitz systems with fault estimation synthesis,” International Journal of Robust and Nonlinear control, vol. 20, no. 16, pp. 1785–1801, 2010.

    MathSciNet  MATH  Google Scholar 

  16. A. Sellami, D. Arzelier, R. Mhiri, and J. Zrida, “A sliding mode control approach for systems subjected to a norm-bounded uncertainty,” International Journal of Robust and Nonlinear Control, vol. 17, no. 4, pp. 327–346, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  17. C. Edwards and S. K. Spurgeon, “On the development of discontinuous observers,” International Journal of Control, vol. 59, no. 5, pp. 1221–1229, 1994.

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

  19. M. Abbaszadeh and H. J. Marquez, “LMI optimization approach to robust H ∞ observer design and static feedback stabilization for discrete-time nonlinear uncertain systems,” International Journal of Robust and Nonlinear Control, vol. 19, no. 3, pp. 313–340, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  20. V. I. Utkin, Sliding Modes in Control Optimization, Springer-verlag, Berlin, 1992.

    Book  MATH  Google Scholar 

  21. R. Rajamani and Y. Cho, “Existence and design of observers for nonlinear systems,” International Journal of Control, vol. 69, no. 5, pp. 717–731, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  22. P. Gahinet, A. Nemirovski, A. Laub, and M. Chilali, LMI Control Toolbox, User Guide, MathWorks, 1995.

    Google Scholar 

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Authors and Affiliations

  1. Higher School of Sciences and Techniques of Tunis, University of Tunis, 5 street Taha Hussein, B.P. 56-1008, Tunis, Tunisia

    Slim Dhahri, Anis Sellami & Fayçal Ben Hmida

Authors
  1. Slim Dhahri
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  2. Anis Sellami
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  3. Fayçal Ben Hmida
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Correspondence to Slim Dhahri.

Additional information

Recommended by Editorial Board member Izumi Masubuchi under the direction of Editor Yoshito Ohta.

Slim Dhahri received his Master degree in Automatic Control from Higher School of Sciences and Techniques of Tunis, Tunisia (E.S.S.T.T.), in 2006. Currently, he is a research member in research unit on control, monitoring and safety of systems (C.3.S.) at E.S.S.T.T. and he is working toward a Ph.D. degree in Electrical Engineering. His research interests include sliding mode and fault detection and isolation (F.D.I.) of linear and nonlinear systems.

Anis Sellami was born in Tunisia, in 1967. He obtained his HABILITATION diploma at Sciences Faculty of Tunis, Tunisia in 2008, and his Ph.D. in Electrical Engineering at National School of Engineers of Tunis, Tunisia in 1999, and an Master in Automatic Control and a B.A. in Technical Sciences at ESSTT, Tunis, Tunisia in 1993 and 1990, respectively. From 1999 to 2008, he was an assistant professor at ESSTT. Since December 2008 he is a professor (University Lecturer) with the Electrical Engineering Department, ESSTT, Tunisia. His research interests robust control with sliding mode and photovoltaic systems.

Fayçal Ben Hmida received his B.S. in Electrical Engineering from the E.S.S.T.T., Tunisia, in 1991. In 1992, he obtained his Master degree in Automatic and Informatics at the Aix-Marseille III University, France, and a Ph.D. in Productique and Informatics at the same university in 1997. Since 1998, he joined the E.S.S.T.T at Tunis University as an Assistant Professor. Now, he is a member in research unit on C3S at E.S.S.T.T. His main research includes fault detection and isolation (FDI), robust estimation and robust filtering.

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Dhahri, S., Sellami, A. & Hmida, F.B. Robust H ∞ sliding mode observer design for fault estimation in a class of uncertain nonlinear systems with LMI optimization approach. Int. J. Control Autom. Syst. 10, 1032–1041 (2012). https://doi.org/10.1007/s12555-012-0521-3

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  • DOI: https://doi.org/10.1007/s12555-012-0521-3

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