Design of unknown input observers for non-linear stochastic systems and their application to robust fault diagnosis

• Autorzy: Witczak M. , Korbicz J. , Józefowicz R.
• Języki publikacji: EN

Abstrakty

EN

The paper deals with the problem of designing filters for non-linear discrete-time stochastic systems. In particular, it is shown how to design an unknown input filter for a single (constant) unknown input distribution matrix, which guarantees that the effect of a fault will not be decoupled from the residual. Subsequently, the problem of using one, fixed disturbance distribution matrix is eliminatek by using the interacting multiple models algorithm to select an appropriate unknown input distribution matrix from a predefined set of matrices. The final part of the paper shows an illustrative example, which confirms the effectiveness of the proposed approach.

Słowa kluczowe

EN

fault diagnosis; unknown input; unscented Kalman filter; interactive multiple models; non-linear systems

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2013
• Tom: Vol. 42, no. 1
• Strony: 227--256
• Opis fizyczny: Bibliogr. 26 poz., il., wykr.

Twórcy

autor

Witczak M.

• Institute of Control and Computation Engineering University of Zielona Góra ul. Podgórna 50, 65–246 Zielona Góra, Poland

autor

Korbicz J.

• Institute of Control and Computation Engineering University of Zielona Góra ul. Podgórna 50, 65–246 Zielona Góra, Poland

autor

Józefowicz R.

• Institute of Control and Computation Engineering University of Zielona Góra ul. Podgórna 50, 65–246 Zielona Góra, Poland

Bibliografia

• 1. BLOM, H.A.P and BAR-SHALOM, Y. (1988) The interacting multiple model algorithm for systems with markovian switching coefficients. IEEE Transactions on Automatic Control, 33 (8), 780–783.
• 2. BOUTAYEB, M. and AUBRY, D. (1999) A strong tracking extended Kalman observer for nonlinear discrete-time systems. IEEE Transactions on Automatic Control, 44 (8), 1550–1556.
• 3. CHEN, J. and PATTON, R.J. (1999) Robust Model Based Fault Diagnosis for Dynamic Systems. Kluwer Academic Publishers, London.
• 4. CHEN, W., KHAN, A.Q., ABID, M. and DING, S.X. (2011) Integrated design of observer-based fault detection for a class of uncertain non-linear systems. International Journal of Applied Mathematics and Computer Science, 21 (4), 619–636.
• 5. DING, S.X. (2008) Model-based Fault Diagnosis Techniques: Design Schemes, Algorithms and Tools. Springer-Verlag, Berlin.
• 6. DUCARD, G. (2009) Fault-tolerant Flight Control and Guidance Systems: Practical Methods for Small Unmanned Aerial Vehicles. Springer-Verlag, Berlin.
• 7. FRANC, P.M. and MARCU, T. (2000) Diagnosis strategies and systems. principles, fuzzy and neural approaches. In: H. N. Teodorescu, D. Mlynek, A. Kandel and H. J. Zimmermann, eds., Intelligent Systems and Interfaces. Kluwer Academic Publishers, Boston.
• 8. HAMMOURI, H., KABORE, P., OTHMAN, S. and BISTON, J. (1999) Observerbased approach to fault detection and isolation for nonlinear systems. IEEE Trans. Automatic Control, 44(10), 1879–1884.
• 9. HAMMOURI, H., KABORE, P., OTHMAN, S. and BISTON, J. (2002) Failure diagnosis and nonlinear observer. application to a hydraulic process. Journal of The Franklin Institute, 339(4–5), 455–478.
• 10. ISERMAN, R. (2011) Fault Diagnosis Applications: Model Based Condition Monitoring, Actuators, Drives, Machinery, Plants, Sensors, and Fault–tolerant Systems. Springer-Verlag, Berlin.
• 11. JULIER, S.J. and UHLMANN, J.K. (2004) Unscented filtering and estimation. Proceedings of the IEEE, 92(3), 401–422.
• 12. KABORE, R. and WANG, H. (2001) Design of fault diagnosis filters and fault tolerant control for a class of nonlinear systems. IEEE Trans. Automatic Control, 46(11), 1805–1809.
• 13. KANDEPU, R., FOSS, B. and IMSLAND, L. (2008) Applying the unscented kalman filter for nonlinear state estimation. Journal of Process Control, 18 (7-8), 753–768.
• 14. KEMIR, K., BEN HMIDA, F., RAGOT, J. and GOSSA, M. (2011) Novel optimal recursive filter for state and fault estimation of linear systems with unknown disturbances. International Journal of Applied Mathematics and Computer Science, 21(4), 629–638.
• 15. KOENIG, D. and MAMMAR, S. (2002) Design of a class of reduced unknown inputs non-linear observer for fault diagnosis. In: Proc. American Control Conference, ACC, Arlington, USA.
• 16. KORBICZ, J. KOŚCIELNY, J., KOWALCZUK, Z. and CHOLEWA, W., eds. (2004) Fault diagnosis. Models, Artificial Intelligence, Applications. Springer Verlag, Berlin.
• 17. MAHMOUD, M., JIANG, J. and ZHANG, Y. (2003) Active Fault Tolerant Control Systems: Stochastic Analysis and Synthesis. Springer Verlag, Berlin.
• 18. NOURA, H., THEILLIOL, D., PONSART, J. and CHAMSEDDINE, A. (2003) Fault-tolerant Control Systems: Design and Practical Applications. Springer Verlag, Berlin.
• 19. PARTEW, A.M., MARQUEZ, H.J. and ZHAO, Q. (2005) H1 synthesis of unknown input observers for non-linear lipschitz systems. International Journal of Control, 78(15), 1155–1165.
• 20. PUIG, V. (2010) Fault diagnosis and fault tolerant control using set-membership approaches: Application to real case studies. International Journal of Applied Mathematics and Computer Science, 20(4), 619–635, 2010.
• 21. TONG, S., YANG, G. and ZHANG, W. (2011) Observer-based fault-tolerant control againts sensor failures for fuzzy systems with time delays. International Journal of Applied Mathematics and Computer Science, 21(4), 617–628.
• 22. UPPAL, F.J., PATTON, R.J. andWITCZAK,M. (2006) A neuro-fuzzymultiplemodel observer approach to robust fault diagnosis based on the DAMADICS benchmark problem. Control Engineering Practice, 14(6), 699–717.
• 23. WALTER, E. and PRONZATO, L. (1996) Identification of Parametric Models from Experimental Data. Springer, London.
• 24. WANG, S.H., DAVISON, E.J. and DORATO, P. (1975) Observing the states of systems with unmeasurable disturbances. IEEE Transactions on Automatic Control, 20(5), 716–717.
• 25. WITCZAK, M. (2007) Modelling and Estimation Strategies for Fault Diagnosis of Non-linear Systems. Springer Verlag, Berlin.
• 26. WITCZAK, M. and PRETKI, P. (2007) Design of an extended unknown input observer with stochastic robustness techniques and evolutionary algorithms. International Journal of Control, 80(5), 749–762.