Nonlinear diagnostic filter design: algebraic and geometric points of view

Shumsky, Alexey ; Zhirabok, Alexey

International Journal of Applied Mathematics and Computer Science, Tome 16 (2006), p. 115-127 / Harvested from The Polish Digital Mathematics Library

Résumé

The problem of diagnostic filter design is studied. Algebraic and geometric approaches to solving this problem are investigated. Some relations between these approaches are established. New definitions of fault detectability and isolability are formulated. On the basis of these definitions, a procedure for diagnostic filter design is given in both algebraic and geometric terms.

Détail

Publié le : 2006-01-01

Zbl 1334.93081

EUDML-ID : urn:eudml:doc:207769

Bibliographie

[000] Alcorta-Garcia E. and Frank P.M. (1997): Deterministic nonlinear observer-based approach to fault diagnosis: A survey. - Contr. Eng. Pract., Vol. 5, No. 5, pp. 663-670.

[001] Birk J. and Zeitz M. (1988): Extended Luenberger observer for nonlinear multivariable systems. - Int. J. Contr., Vol. 47, No. 6, pp. 1823-1836. | Zbl 0648.93022

[002] Chen J. and Patton R.J. (1994): A reexamination of fault detectability and isolability in linear dynamic systems. - Proc. Int. Symp. Safeprocess'94, Espoo, Finland, pp. 590-596.

[003] Chow E.Y. and Willsky A.S. (1984): Analytical redundancy and the design of robust failure detection systems. - IEEE Trans. Automat. Contr., Vol. AC-29, No. 7, pp. 603-614. | Zbl 0542.90040

[004] De Persis C. and Isidori A. (2001): A geometric approach to nonlinear fault detection and isolation. - IEEE Trans. Automat. Contr., Vol. AC-46, No. 6, pp. 853-865. | Zbl 1009.93003

[005] Ding X. and Frank P.M. (1990): Nonlinear observer design via an extended canonical form. - Syst. Contr. Lett., Vol. 15, pp. 313-322. | Zbl 0724.93009

[006] Edelmayer A., Bokor J., Szabo Z. and Szigeti F. (2004): Fault reconstruction by means of system inversion: a geometric approach to fault detection and isolation in nonlinear systems. - Int. J. Appl. Math. Comput. Sci., Vol. 14, No. 2, pp. 189-199. | Zbl 1083.93008

[007] Frank P.M. (1990): Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy - A survey and some new results. - Automatica, Vol. 26, No. 3, pp. 459-474. | Zbl 0713.93052

[008] Frank P.M. (1996): Analytical and qualitative model-based fault diagnosis - A survey and some new results. - Europ. J. Contr., Vol. 2, No. 1, pp. 6-28. | Zbl 0857.93015

[009] Frank P.M. and Ding X. (1997): Survey of robust residual generation and evaluation methods in observer-based fault detection systems. - J. Process Contr., Vol. 7, No. 3, pp. 403-424.

[010] Gauthier J. and Kupca I. (2000): Deterministic Observation Theory and Application. - Cambridge: Cambridge Univ. Press.

[011] Gertler J. and Kunwer M.M. (1993): Optimal residual decoupling for robust fault diagnosis. - Proc. Int. Conf. Tooldiag'93, Toulouse, France, pp. 436-452. | Zbl 0817.93039

[012] Isidori A. (1989): Nonlinear Control Systems. - London: Springer. | Zbl 0693.93046

[013] Hartmanis J. and Stearns R. (1966): Algebraic Structure Theory of Sequential Machines. - New York: Prentice Hall. | Zbl 0154.41701

[014] Join C., Ponsart J-C. and Sauter D. (2002a): Fault detection and isolation via nonlinear filters. - Proc. 15-th IFAC World Congress,Barcelona, Spain, (on CD ROM).

[015] Join C., Ponsart J-C. and Sauter D. (2002b): Sufficient conditions to fault isolation in nonlinear systems: a geometric approach. - Proc. 15-th IFACs World Congress, Barcelona, Spain, (on CD ROM).

[016] Korn G.A. and Korn T.M. (1961): Mathematical Handbook. - New York: McGraw-Hill.

[017] Massoumnia M.A. (1986): A geometric approach to the synthesis of failure detection filters. - IEEE Trans. Automat. Contr., Vol. AC-31, No. 9, pp. 839-846. | Zbl 0599.93017

[018] Massoumnia M.A., Verghese G.C. and Willsky A.S. (1989): Failure detection and identification. - IEEE Trans. Automat. Contr., Vol. AC-34, No. 3, pp. 316-323. | Zbl 0682.93061

[019] Mironovskii L.A. (1980): Functional diagnosis of dynamic systems. - Automat. Remote Contr., Vol. 41, No. 8, pp. 120-128.

[020] Misawa E.A. and Hedrick J.K. (1989): Nonlinear observers - A state-of-the-art survey. - J. Dynam. Syst. Meas. Contr., Vol. 111, No. 9, pp. 344-352. | Zbl 0695.93106

[021] Park J., Rizzoni G. and Ribbens W.B. (1994): On the representation of sensor faults in fault detection filters. - Automatica, Vol. 30, No. 11, pp. 1793-1795. | Zbl 0925.93875

[022] Shumsky A.Ye. (1988): Model of the faults for discrete systems and its application to the problem of fault diagnosis. - Electronnoye Modelirovanie, Vol. 10, No. 4, pp. 56-61, (in Russian).

[023] Shumsky A.Ye. (1991): Fault isolation in nonlinear systems via functional diagnosis. - Automat. Remote Contr., Vol. 52, No. 12, pp. 148-155.

[024] Shumsky A.Ye. and Zhirabok A.N. (2005): Nonlinear diagnostic filter design: algebraic and geometric points of view. - Proc. 16-th IFAC WorldCongress, Prague, Czech Republic, (on CD ROM). | Zbl 1334.93081

[025] Zhirabok A.N. and Shumsky A.Ye. (1987): Functional diagnosis of continuous dynamic systems described by equations whose right-hand side is polynomial. - Automat. Remote Contr., Vol. 48, No. 8, pp. 154-164, (in Russian issue).

[026] Zhirabok A.N. and Shumsky A.Ye. (1993a): Controllability, Observability, Decomposition of Nonlinear Dynamic Systems. - Vladivostok: Far State Technical University Press, (in Russian).

[027] Zhirabok A.N. and Shumsky A.Ye. (1993b): A new mathematical techniques for nonlinear systems research. - Proc. 12-th IFAC World Congress, Sydney, Australia, Vol. 3, pp. 485-488.

[028] Zhirabok A.N. (1997): Fault detection and isolation: Linear and nonlinear systems. - Prep. Int. Symp. Safeprocess'97, Hull, UK, pp. 903-908.