Robust sensor fault estimation for descriptor-LPV systems with unmeasurable gain scheduling functions: application to an anaerobic bioreactor

Francisco-Ronay López-Estrada; Jean-Christophe Ponsart; Didier Theilliol; Carlos-Manuel Astorga-Zaragoza; Jorge-Luis Camas-Anzueto

International Journal of Applied Mathematics and Computer Science (2015)

  • Volume: 25, Issue: 2, page 233-244
  • ISSN: 1641-876X

Abstract

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This paper addresses the design of a state estimation and sensor fault detection, isolation and fault estimation observer for descriptor-linear parameter varying (D-LPV) systems. In contrast to where the scheduling functions depend on some measurable time varying state, the proposed method considers the scheduling function depending on an unmeasurable state vector. In order to isolate, detect and estimate sensor faults, an augmented system is constructed by considering faults to be auxiliary state vectors. An unknown input LPV observer is designed to estimate simultaneously system states and faults. Sufficient conditions to guarantee stability and robustness against the uncertainty provided by the unmeasurable scheduling functions and the influence of disturbances are synthesized via a linear matrix inequality (LMI) formulation by considering H∞ and Lyapunov approaches. The performances of the proposed method are illustrated through the application to an anaerobic bioreactor model.

How to cite

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Francisco-Ronay López-Estrada, et al. "Robust sensor fault estimation for descriptor-LPV systems with unmeasurable gain scheduling functions: application to an anaerobic bioreactor." International Journal of Applied Mathematics and Computer Science 25.2 (2015): 233-244. <http://eudml.org/doc/270771>.

@article{Francisco2015,
abstract = {This paper addresses the design of a state estimation and sensor fault detection, isolation and fault estimation observer for descriptor-linear parameter varying (D-LPV) systems. In contrast to where the scheduling functions depend on some measurable time varying state, the proposed method considers the scheduling function depending on an unmeasurable state vector. In order to isolate, detect and estimate sensor faults, an augmented system is constructed by considering faults to be auxiliary state vectors. An unknown input LPV observer is designed to estimate simultaneously system states and faults. Sufficient conditions to guarantee stability and robustness against the uncertainty provided by the unmeasurable scheduling functions and the influence of disturbances are synthesized via a linear matrix inequality (LMI) formulation by considering H∞ and Lyapunov approaches. The performances of the proposed method are illustrated through the application to an anaerobic bioreactor model.},
author = {Francisco-Ronay López-Estrada, Jean-Christophe Ponsart, Didier Theilliol, Carlos-Manuel Astorga-Zaragoza, Jorge-Luis Camas-Anzueto},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {fault diagnosis; fault estimation; LPV systems; observer design; descriptor system},
language = {eng},
number = {2},
pages = {233-244},
title = {Robust sensor fault estimation for descriptor-LPV systems with unmeasurable gain scheduling functions: application to an anaerobic bioreactor},
url = {http://eudml.org/doc/270771},
volume = {25},
year = {2015},
}

TY - JOUR
AU - Francisco-Ronay López-Estrada
AU - Jean-Christophe Ponsart
AU - Didier Theilliol
AU - Carlos-Manuel Astorga-Zaragoza
AU - Jorge-Luis Camas-Anzueto
TI - Robust sensor fault estimation for descriptor-LPV systems with unmeasurable gain scheduling functions: application to an anaerobic bioreactor
JO - International Journal of Applied Mathematics and Computer Science
PY - 2015
VL - 25
IS - 2
SP - 233
EP - 244
AB - This paper addresses the design of a state estimation and sensor fault detection, isolation and fault estimation observer for descriptor-linear parameter varying (D-LPV) systems. In contrast to where the scheduling functions depend on some measurable time varying state, the proposed method considers the scheduling function depending on an unmeasurable state vector. In order to isolate, detect and estimate sensor faults, an augmented system is constructed by considering faults to be auxiliary state vectors. An unknown input LPV observer is designed to estimate simultaneously system states and faults. Sufficient conditions to guarantee stability and robustness against the uncertainty provided by the unmeasurable scheduling functions and the influence of disturbances are synthesized via a linear matrix inequality (LMI) formulation by considering H∞ and Lyapunov approaches. The performances of the proposed method are illustrated through the application to an anaerobic bioreactor model.
LA - eng
KW - fault diagnosis; fault estimation; LPV systems; observer design; descriptor system
UR - http://eudml.org/doc/270771
ER -

References

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  1. Aguilera-González, A., Astorga-Zaragoza, C.M., Adam-Medina, M., Theilliol, D., Reyes-Reyes, J. and Garcia-Beltrán, C.-D. (2013). Singular linear parameter-varying observer for composition estimation in a binary distillation column, IET Control Theory & Applications 7(3): 411-422. 
  2. Alcorta-García, E., Saucedo-Flores, S. and Díaz-Romero, D.A. (2014). Intelligent fault diagnosis in nonlinear systems, Intelligent Automation and Soft Computing 20(2): 201-212. 
  3. Astorga-Zaragoza, C.M., Theilliol, D., Ponsart, J.C. and Rodrigues, M. (2011). Observer synthesis for a class of descriptor LPV systems, American Control Conference, ACC 2011, San Francisco, CA, USA, pp. 722-726. Zbl06141808
  4. Blesa, J., Rotondo, D., Puig, V. and Nejjari, F. (2014). FDI and FTC of wind turbines using the interval observer approach and virtual actuators/sensors, Control Engineering Practice 24: 138-155. 
  5. Chadli, M., Abdo, A. and Ding, S.X. (2013a). H / H ∞ fault detection filter design for discrete-time Takagi-Sugeno fuzzy system, Automatica 49(7): 1996-2005. 
  6. Chadli, M., Aouaouda, S., Karimi, H. and Shi, P. (2013b). Robust fault tolerant tracking controller design for a VTOL aircraft, Journal of the Franklin Institute 350(350): 2627-2645. Zbl1287.93024
  7. Chadli, M. and Darouach, M. (2011). Robust admissibility of uncertain switched singular systems, International Journal of Control 84(10): 1587-1600. Zbl1236.93107
  8. Chen, J. and Patton, R.J. (1999). Robust Model-based Fault Diagnosis for Dynamic Systems, Kluwer Academic Publishers, Norwell, MA. Zbl0920.93001
  9. Ding, S.X. (2008). Model-Based Fault Diagnosis Techniques: Design Schemes, Algorithms and Tools, Springer, Berlin/Heidelberg. 
  10. Duan, G.R. (2010). Analysis and Design of Descriptor Linear Systems, Springer, New York, NY. Zbl1227.93001
  11. Frank, P. (1996). Analytical and qualitative model-based fault diagnosis - a survey and some new results, European Journal of Control 2(1): 6-28. Zbl0857.93015
  12. Gertler, J. (1997). Fault detection and isolation using parity relations, Control Engineering Practice 5(5): 653-661. 
  13. Hamdi, H., Rodrigues, M., Mechmeche, C. and Braiek, N.B. (2012a). Robust fault detection and estimation for descriptor systems based on multi-models concept, International Journal of Control, Automation and Systems 10(6): 1260-1266. 
  14. Hamdi, H., Rodrigues, M., Mechmeche, C. and Theilliol, D. (2012b). Fault detection and isolation for linear parameter varying descriptor systems via proportional integral observer, International Journal of Adaptive Control and Signal Processing 26(3): 224-240. Zbl1309.93030
  15. Hwang, I., Sungwan, K., Youdan, K. and Seah, C. (2010). A survey of fault detection, isolation, and reconfiguration methods, IEEE Transactions on Control Systems Technology 18(3): 636-653. 
  16. Ichalal, D., Marx, B., Ragot, J. and Maquin, D. (2010). State estimation of Takagi-Sugeno systems with unmeasurable premise variables, IET Control Theory & Applications 4(5): 897. Zbl1290.93107
  17. Isermann, R. (1984). Process fault detection based on modeling and estimation methods - a survey, Automatica 20(4): 387-404. Zbl0539.90037
  18. Kamidi, R. (2000). Controllability and observability of polytopic linear models, Technical report, Eindhoven University of Technology, Eindhoven. 
  19. Lendek, Z., Guerra, T.M., Babuˆska, R. and De Schutter, B. (2011). Stability Analysis and Nonlinear Observer Design Using Takagi-Sugeno Fuzzy Models, Studies in Fuzziness and Soft Computing, Vol. 262, Springer, Berlin/Heidelberg. 
  20. Lofberg, J. (2004). A toolbox for modeling and optimization in MATLAB, Proceedings of the Computer Aided Control System Design Conference, Taipei, Taiwan, pp. 284-289. 
  21. López-Estrada, F.-R., Ponsart, J., Theilliol, D. and Astorga-Zaragoza, C.-M. (2013). Fault estimation observer design for descriptor-LPV systems with unmeasurable gain scheduling functions, 2nd International Conference on Control and Fault-Tolerant Systems (SYSTOL), Nice, France, pp. 269-274. Zbl1334.93036
  22. López-Estrada, F.R., Ponsart, J.C., Theilliol, D., Astorga-Zaragoza, C.-M. and Aberkane, S. (2014a). Fault diagnosis based on robust observer for descriptor-LPV systems with unmeasurable scheduling parameters, 19th World Congress of the International Federation of Automatic Control, Cape Town, South Africa, pp. 1079-1084. 
  23. López-Estrada, F.-R., Ponsart, J., Theilliol, D. and Astorga-Zaragoza, C.-M. (2014b). Robust sensor FDI observer for polytopic descriptor-LPV systems with unmeasurable scheduling varying parameter, American Control Conference, Portland, OR, USA. 
  24. Lunze, J., Blanke, M., Staroswiecki, M. and Kinnaert, M. (2006). Diagnosis and Fault-Tolerant Tolerant Control, Springer, Berlin/Heidelberg. Zbl1126.93004
  25. Martínez-Sibaja, A., Astorga-Zaragoza, C.M., Alvarado-Lassman, A., Posada-Gómez, R., Aguila-Rodríguez, G., Rodríguez-Jarquin, J. and Adam-Medina, M. (2011). Simplified interval observer scheme: A new approach for fault diagnosis in instruments, Sensors 11(1): 612-622. 
  26. Masubuchi, I., Kato, J., Saeki, M. and Ohara, A. (2004). Gain-scheduled controller design based on descriptor representation of LPV systems: Application to flight vehicle control, 43rd IEEE Conference on Decision and Control, Atlantis, Paradise Island, The Bahamas, Vol. 1, pp. 815-820. 
  27. Montes de Oca, S., Puig, V. and Blesa, J. (2011). Robust fault detection based on adaptive threshold generation using interval LPV observers, International Journal of Adaptive Control and Signal Processing 26(3): 258-283. Zbl06141811
  28. Nagy-Kiss, A.M., Marx, B., Mourot, G., Schutz, G. and Ragot, J. (2011a). Observers design for uncertain Takagi-Sugeno systems with unmeasurable premise variables and unknown inputs. application to a wastewater treatment plant, Journal of Process Control 21(7): 1105-1114. 
  29. Nagy Kiss, A.M., Marx, B., Mourot, G., Schutz, G. and Ragot, J. (2011b). State estimation of two-time scale multiple models. Application to wastewater treatment plant, Control Engineering Practice 19(11): 1354-1362. 
  30. Samy, I., Postlethwaite, I. and Gu, D.-W. (2011). Survey and application of sensor fault detection and isolation schemes, Control Engineering Practice 19(7): 658-674. 
  31. Theilliol, D. and Aberkane, S. (2011). Design of LPV observers with unmeasurable gain scheduling variable under sensors faults, IFAC World Congress, Milan, Italy, pp. 7613-7618. 
  32. Wang, J.L., Yang, G.-H. and Liu, J. (2007). An LMI approach to index and mixed fault detection observer design, Automatica 43(9): 1656-1665. Zbl1128.93321
  33. Xu, S. and Lam, J. (2006). Robust Control and Filtering of Singular Systems, Springer, Berlin/Heidelberg. Zbl1114.93005
  34. Yoneyama, J. (2009). H ∞ filtering for fuzzy systems with immeasurable premise variables: An uncertain system approach, Fuzzy Sets and Systems 160(12): 1738-1748. Zbl1175.93137

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