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Robust fault detection and estimation for descriptor systems based on multi-models concept

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Abstract

This paper addresses the robust fault detection and estimation problem of nonlinear descriptor system with unknown inputs observers. The considered nonlinear descriptor system is transformed into an equivalent multi-models form by using the Takagi-Sugeno (T-S) approach. Two cases are considered: the first one deals with the multi-models based on measurable decision variables and the second one assumes that these decision variables are unmeasurable. Then, a residual generator based on an unknown observer is designed for both fault detection and estimation. Stability analysis and gain matrices determination are performed by resolving a set of Linear Matrices Inequalities (LMIs) for both cases. The performances of the proposed fault detection and estimation method is successfully applied to an electrical circuit.

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References

  1. G. D. A. T. Vemuri, M. M. Polycarpou, and A. R. Ciric, “Fault diagnosis of differential-algebraic systems,” IEEE Trans. on Systems, Man, and Cybernetics, Part A: Systems and Humans, vol. 31, no. 2, pp. 143–152, March 2001.

    Article  Google Scholar 

  2. D. Koenig, “Observer design for unknown input nonlinear descriptor systems via convex optimization,” IEEE Trans. on Automatic Control, vol. 51, no. 6, pp. 1047–1052, June 2006.

    Article  MathSciNet  Google Scholar 

  3. H. Hamdi, M. Rodrigues, C. Mechmeche, D. Theilliol, and N. BenHadj Braiek, “Fault detection and isolation in linear parameter-varying descriptor systems via proportional integral observer,” International Journal of Adaptive Control and Signal Processing, vol. 26, pp. 224–240, 2012.

    Article  MathSciNet  Google Scholar 

  4. J. L. Chen, “Robust ESPR analysis and control for uncertain continuous-time descriptor systems,” International Journal of Control, Automation, and Systems, vol. 8, no. 1, pp. 8–15, 2010.

    Article  Google Scholar 

  5. J. Sjoberg, “Some results on optimal control for non-linear descriptor systems,” Sweden Studies in Science and Technology, Thesis No. 1227, 2006.

  6. M. Darouach and M. Boutayeb, “Design of observers for descriptor systems,” IEEE Trans. on Automatic Control, vol. 40. no. 7, pp. 1323–1327, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  7. M. Rodrigues, D. Theilliol, M. Adam-Medina, and D. Sauter, “A fault detection and isolation scheme for industrial systems based on multiple operating models,” Control Engineering Practice, vol. 16, pp. 225–239, 2008.

    Article  Google Scholar 

  8. T. Taniguchi, K. Tanaka, and H. O. Wang, “Fuzzy descriptor systems and nonlinear model following control,” IEEE Trans. on Fuzzy Systems, vol. 8, no. 4, pp. 442–452, August 2000.

    Article  Google Scholar 

  9. Y. Wang, Z. Q. Sun, and F. C. Sun, “Robust fuzzy control of a class of nonlinear descriptor systems with time-varying delay,” International Journal of Control, Automation and Systems, vol. 2, no. 1, pp. 76–82, March 2004.

    Google Scholar 

  10. Z. Gao and S. X. Ding, “Fault reconstruction for Lipschitz nonlinear descriptor systems via linear matrix inequality approach” Circuits Syst. Signal Process, vol. 27, pp. 295–308, 2008.

    Article  MathSciNet  MATH  Google Scholar 

  11. Z. Gao and S. X. Ding, “Actuator fault robust estimation and fault-tolerant control for a class of nonlinear descriptor systems” Automatica, vol. 43, pp. 912–920, 2007.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Laboratory for Advanced Systems (LSA), Polytechnic School of Tunisia, Tunis, Tunisia

    Habib Hamdi, Chokri Mechmeche & Naceur Benhadj Braiek

  2. Laboratory Automation and Engineering Process (LAGEP), CNRS UMR 5007, University Lyon1, Lyon1, France

    Mickael Rodrigues

Authors
  1. Habib Hamdi
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  2. Mickael Rodrigues
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  3. Chokri Mechmeche
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  4. Naceur Benhadj Braiek
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Corresponding author

Correspondence to Mickael Rodrigues.

Additional information

Recommended by Editorial Board member Bin Jiang under the direction of Editor Young-Hoon Joo.

Habib Hamdi received his Master degree in Automatic Control from the High School of Sciences and Techniques of Tunis, University of Tunis, in 2005, he is currently a member of Laboratory for Advanced Systems at the Tunisia Polytechnic School, University of Carthage. His current research interests are focused on fault diagnosis, multi-models, LPV systems, descriptor systems, observers, stability and LMI.

Mickael Rodrigues received his Ph.D. degree in Automatic Control from the Department of Automatic Control of the Henri Poincaré University of Nancy 1 from the Centre de Recherche en Automatique de Nancy (CRAN) in 2005. Since 2006, he is currently an associate professor in Claude Bernard University of Lyon1 with the Automatic and Process Control Laboratory (LAGEP), France. His current research interests are focused on model-based fault diagnosis, fault tolerant control, multi-models, LPV systems, descriptor systems, observers, stability and LMI.

Chokri received his Ph.D. degree in Automatic Control from the Henri Poincaré University of Nancy 1 with the Centre de Recherche en Automatique de Nancy (CRAN) in 1995. Since 2000, he has been with the Department of Electrical Engineering at the High School for Science and Technology in Tunis, University of Tunis, Tunisia where he is currently an associate professor. His current research interests include nonlinear dynamical systems, observer design, Fault detection, and their applications.

Naceur Benhadj Braiek has obtained his Ph.D. from the University of Science and Technology of Lille — France in 1990 and the Science State Doctorate from the National School of Engineers of Tunis in 1995. Currently, he is a professor at the High School of Sciences and Techniques of Tunis, University of Tunis, and head of the research laboratory “Laboratory for Advanced Systems” at the Tunisia Polytechnic School, University of Carthage. His area of interest includes modeling, control and optimization of nonlinear dynamical systems.

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Hamdi, H., Rodrigues, M., Mechmeche, C. et al. Robust fault detection and estimation for descriptor systems based on multi-models concept. Int. J. Control Autom. Syst. 10, 1260–1266 (2012). https://doi.org/10.1007/s12555-012-0622-z

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  • DOI: https://doi.org/10.1007/s12555-012-0622-z

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