This paper deals with residual generation methods for nonlinear model-based fault detection and isolation (FDI) systems. More specifically, a differential relationship between nonlinear parity space residuals (based on analytical redundancy relations) and high-gain observer-based residuals is emphasized. The first part of this paper presents the nonlinear affine state space model, which is considered to generate residuals in the following. In order to design the high-gain observer, a nonlinear transformation is used to put the model under its observable canonical form (OCF). The two residual generation approaches are detailed in the second part. The result of the paper is then established: we express explicitly a differential relationship between the two residuals and so extend in a more general framework the well known result that was established for linear and linearizable systems by input/output injection. A model of a series DC motor is considered to illustrate the theoretical result and simulations results are presented.
Alcorta-Garcia, E. and Frank, P.1997: Deterministic nonlinear observer-based approaches to fault diagnosis: a survey. Control Engineering Practice5, 663-670.
2.
Chen, J. and Patton, R. J.1999: Robust model-based fault diagnosis for dynamic systems. Boston: Kluwer Academic.
3.
Chiasson, J. N. and Bodson, M.1993: Nonlinear control of a shunt DC motor. IEEE Transactions on Automatic Control38, 1662-1666.
4.
Chow E. Y. and Willsky, A. S.1984: Analytical redundancy and the design of robust failure detection systems. IEEE Transactions on Automatic control29, 602-615.
5.
Cocquempot, V. and Christophe, C. 2000: On the equivalence between observer-based and parity space approaches for FDI in nonlinear systems. In: IFAC International Symposium on Safety in Technical Processes Safeprocess 2000, Budapest, 232-237.
6.
Comtet-Varga, G. 1997: Surveillance des systémes non linéaires. Application aux machines asynchrones. PhD thesis, Université des Sciences et Technologies de Lille.
7.
Conte, G., Moog, C. and Perdon, A.1998: Nonlinear control systems. New York: Springer.
8.
Cox, D., Little, J. and O’Shea, D.1992: Ideals, varieties and algorithms. New York: Springer.
9.
Diop, S.1991: Elimination in control theory. Mathematical Control Signal systems4, 17-32.
10.
Frank, P. M., Ding, B. and Koppen-Selinger, B. 2000: Current developments in the theory of FDI. In: Proceedings of SAFEPROCESS 2000, Vol. 1, Budapest, 16-27.
11.
Gauthier, J. P., Hammouri, H. and Othman, S.1992: A simple observer for nonlinear systems applications to bioreactors. IEEE Transactions on Automatic Control37, 875-880.
12.
Gertler, J.1998: Fault detection and diagnosis in engineering systems. New York: Marcel Dekker.
13.
Gertler, J. 2000: All linear methods are equal and extendable to nonlinearities. In: Proceedings of SAFEPROCESS 2000, Vol. 1, Budapest, 52-63.
14.
Isermann, R.1984: Process fault detection based on modelling and estimation methods. Automatica20, 387-404.
15.
Isermann, R.1993: Fault diagnosis of machines via parameter estimation and knowledge processing. Automatica29, 815-835.
16.
Isidori, A.1995: Nonlinear Control Systems, third edition. New York: Springer.
17.
Jiang, B. and Staroswiecki, M.2002: Adaptive observer design for robust fault estimation. International Journal of Systems Science, 33, 767-775.
18.
Jiang, B., Cocquempot, V. and Christophe, C. 2002: Sliding mode observer based fault diagnosis in nonlinear systems. Proc. of IFAC World Congress’ 02, Barcelona, 674-679.
19.
Kinnaert, M. 2003: Fault diagnosis based on analytical models for linear and nonlinear systems a tutorial. IFAC Conference Safeprocess’03Washington, DC, 37-50.
20.
Nijmeijer, H. and Fossen, T. I.1999: New directions in nonlinear observer design. Volume 244 of Lecture Notes in Control and Information Sciences. Behin, Springer.
21.
Patton, R. J. and Chen, J.1991a: A re-examination of the relationships between parity space and observer-based approaches in fault diagnosis. Revue Européenne Diagnostic et Sûr-eté de fonctionnement1, 183-200.
22.
Patton, R. J. and Chen, J. 1991b: A review of parity space approaches to fault diagnosis. IFAC/IMACS Safeprocess Conference, Baden Baden, 239-255.
23.
Patton, R. J.Frank, P. M. and Clark, R.1989: Fault diagnosis in dynamic systems: theory and application. In Systems and control engineering series. EnglewoodCliffs, NJ:Prentice Hall.
24.
Persis, C. De and Isidori, A. 1999: On the problem of residual generation for fault detection in non-linear systems and some related facts. ECC’99 (CDrom), Karlshruhe.
25.
Ritt, J. F.1950: Differential algebra. Providence, RI: American Mathematical Society.
26.
Staroswiecki, M. and Comtet-Varga, G. 1999: Fault detectability and isolability in algebraic dynamic systems. ECC’99 (CDrom), Karlsruhe.
27.
Staroswiecki, M. and Comtet-Varga, G.2001: Analytic redundancy relations for fault detection and isolation in algebraic dynamic systems. Automatica37, 687-699.
28.
Staroswiecki, M., Cocquempot, V. and Cassar, J.-Ph. 1991: Optimal Design of F.D.I. systems via parity space and observer based approches. In: IECON’91, Kobe, 143-147.
29.
Wü nnenberg, J. 1990: Observer-based fault detection in dynamic systems. PhD thesis, University of Duisburg, VDI-Fortschrittsber, Reihe 8, No. 222.
30.
Zhang, Q., Basseville, M. and Benveniste, A.1998: Fault detection and isolation in nonlinear dynamical systems: a combined input output and local approach. Automatica34, 1359-1374.
