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On nonlinear systems diagnosis using differential and algebraic methods. (English) Zbl 1167.93010
Summary: We tackle the diagnosis problem in nonlinear systems under failure using differential algebra. Three examples are presented in order to apply the proposed methodology. Numerical simulations of these examples are presented to illustrate the effectiveness of the suggested approach.

MSC:
93B07 Observability
93B25 Algebraic methods
93C15 Control/observation systems governed by ordinary differential equations
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[1] Willsky, A.S., A survey of design methods for failure detection in dynamic system, Automatica, 12, 601-611, (1976) · Zbl 0345.93067
[2] Frank, P.M.; Ding, X., Survey of robust residual generation and evaluation methods in observer-based fault detection systems, J. proc. control, 7, 403-424, (1997)
[3] Iserman, R., Process fault detection based on modeling and estimation methods: a survey, Automatica, 20, 4, 387-404, (1984)
[4] Frank, P.M., Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy: a survey, Automatica, 26, 459-474, (1990) · Zbl 0713.93052
[5] Frank, P.M.; Ding, X., Frequency domain approach to optimally robust residual generation and evaluation for model based fault diagnosis, Automatica, 20, 5, 789-804, (1994) · Zbl 0799.93018
[6] Alcorta García, E.; Frank, P.M., Deterministic nonlinear observer-based approaches to fault diagnosis: a survey, Control eng. practice, 5, 663-670, (1997)
[7] Wünnenberg. Observer-based fault detection in dynamic system, Reihe 8, No. 222, VDI-Fortschrittsber., VDI-Verlag, Düsseldorf, Germany, 1990.
[8] Seliger, R.; Frank, P.M., Robust observer-based fault diagnosis in nonlinear uncertain systems, (), 145-187
[9] Diop, S.; Martínez-Guerra, R., An algebraic and data derivative information approach to nonlinear systems diagnosis, (), 2334-2339
[10] S. Diop, R. Martínez-Guerra, On an algebraic and differential approach of nonlinear systems diagnosis, in: Proceedings of the IEEE Conference of Decision and Control, CDC01, Orlando, FL, USA, pp. 585-589.
[11] Viswanadham, N.; Srichander, R., Fault detection using unknown-input observers, Control theory adv. technol., 3, 91-101, (1987)
[12] Kudva, P.; Viswanadham, N.; Ramakrishna, A., Observers for linear systems with unknown inputs, IEEE trans. autom. control, 25, 113-115, (1980) · Zbl 0443.93012
[13] Baseville, X.; Nikoforov, I.V., Detection of abrupt changes. theory and application, (1993), Prentice-Hall Englewood Cliffs, NJ
[14] Chen, J.; Patton, R.J., Robust model-based fault diagnosis for dynamic systems, (1998), Kluwer Academic publishers Boston
[15] De Persis, C.; Isidori, A., A geometric approach to nonlinear fault detection and isolation, IEEE trans. autom. control, 46, 6, 853-865, (2001) · Zbl 1009.93003
[16] Massoumnia, M.A.; Verghese, G.C.; Willsky, A.S., Failure detection and identification, IEEE trans. autom. control, 34, 316-321, (1989) · Zbl 0682.93061
[17] Patton, R.J.; Frank, P.M.; Clark, R.N., Fault diagnosis in dynamic systems, theory and application, (1989), Prentice-Hall Englewood Cliffs, NJ
[18] Staroswiecki, M.; Comtet-Varga, G., Fault detectability and isolability in algebraic dynamic systems, () · Zbl 1007.93029
[19] Szigeti, F.; Vera, C.E.; Bokor, J.; Edelmayer, A., Inversion based fault detection and isolation, (), 1005-1010
[20] M. Fliess, C. Join, H. Mounier, An introduction to nonlinear fault diagnosis with application to a congested internet router, in: C.T. Abdalah, J. Chiasson (Eds.), Advances in Communication Control Networks, Lecture Notes in Control and Information Sciences, vol. 308, Springer, Berlin, pp. 327-343.
[21] Fliess, M.; Join, C.; Sira-Ramírez, H., Robust residual generation for linear fault diagnosis: an algebraic setting with examples, Int. J. control, 14, 77, 1223-1242, (2004) · Zbl 1073.93527
[22] C. Join, H. Sira-Ramírez, M. Fliess, Control of an uncertain three-tank system via on-line parameter identification and fault detection, in: Proceedings of World IFAC Conference, Prague, July 2005.
[23] R. Martínez-Guerra, R. Garrido, A. Osorio Mirón, High-gain nonlinear observers for the fault detection problem: application to a bioreactor, in: A.B. Kurzhanski, A.L. Fradkov (Eds.), IFAC Publications, Editorial Elsevier Science Ltd., Amsterdam, Nonlinear Control Systems, vol. 3, pp. 1567-1572, 2002, ISBN 0-08-043560-2.
[24] Martínez-Guerra, R.; Garrido, R.; Osorio Mirón, A., The fault detection problem in nonlinear systems using residual generators, IMA J. math. control inf., 22, 119-136, (2005) · Zbl 1109.93015
[25] Frank, P.M., Enhancement of robustness in observer-based fault detection, Int. J. control, 59, 955-981, (1994) · Zbl 0813.93003
[26] Chen, J.; Patton, R.J.; Zhang, H.Y., Design of unknown input observers and robust fault detection filters, Int. J. control, 63, 85-105, (1996) · Zbl 0844.93020
[27] Martínez-Guerra, R.; De León-Morales, J., Nonlinear estimators: a differential algebraic approach, Appl. math. lett., 9, 4, 21-25, (1996) · Zbl 0873.93016
[28] Martínez-Guerra, R.; Ramírez Palacios, I.R.; Alvarado-Trejo, E., On parametric and state estimation: application to a simple Academic example, (), 764-765
[29] Hammouri, H.; Kinnaert, M.; El Yaagoubi, E.H., Observer based approach to fault detection and isolation for nonlinear systems, IEEE trans. autom. control, 44, 10, (1999) · Zbl 0956.93005
[30] Fliess, M., A note on the invertibility of non-linear input – output differential systems, Syst. control lett., 8, 147-151, (1986) · Zbl 0634.93035
[31] R. Martínez-Guerra, S. Diop, R. Garrido, A. Osorio Mirón, Diagnosis of nonlinear systems using a reduced order fault observer: application to a bioreactor, in: Journées Franco-Mexicaines d’Automatique Appliquée, IRCCyN, Nantes, France, 12-14, September 2001.
[32] Martínez-Guerra, R.; Mendoza-Camargo, J., Observers for a class of Liouvillian and nondifferentially flat systems, IMA J. math. control inf., 21, 493-509, (2004) · Zbl 1069.93005
[33] Kolchin, E.R., Differential algebra and algebraic groups, (1973), Academic Press New York · Zbl 0264.12102
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