International Journal of Control, Automation, and Systems

Institute of Control, Robotics and Systems (제어로봇시스템학회)
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Diagnosis of Linear Systems with Structured Uncertainties based on Guaranteed State Observation

  • Published : 2008.06.30
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Abstract

Reaching fault tolerance in technological systems requires to detect malfunctions. This paper presents a diagnostic method that is robust with respect to unknown-but-bounded uncertainties of the dynamical model and the measurements. By using models of the faultless and the faulty behaviours, a state-set observer computes polyhedral sets from which the consistency of the models with the interval measurements is determined. The diagnostic result is proven to be complete, i.e., the set of faults obtained by the diagnostic algorithm includes the actual fault. The algorithm is illustrated by an application example.

Keywords

References

  1. R. J. Patton, P. M. Frank, and R. N. Clark, Issues of Fault Diagnosis for Dynamic Systems, Springer, 2000
  2. M. Blanke, M. Kinnaert, J. Lunze, and M. Staroswiecki, Diagnosis and Fault-Tolerant Control, Springer, Heidelberg, 2006
  3. R. Isermann, "Modellgestutzte uberwachung und Fehlerdiagnose technischer Systeme, Teil 1," Automatisierungstechnische Praxis, vol. 5, pp. 9-20, 1996
  4. J. J. Gertler, Fault Detection and Diagnosis in Engineering Systems, Marcel Dekker, 1998
  5. J. C. Geromel and M. C. de Oliveira, "H2 and $H{\infty}$ robust filtering for convex bounded uncertain systems," IEEE Trans. on Automatic Control, vol. 46, no. 1, pp. 100-107, 2001 https://doi.org/10.1109/9.898699
  6. F. C. Schweppe, "Recursive state estimation: Unknown but bounded errors and system inputs," IEEE Trans. on Automatic Control, vol. 13, no. 1, pp. 22-28, February 1968 https://doi.org/10.1109/TAC.1968.1098790
  7. F. L. Chernousko, State Estimation for Dynamic Systems, CRC Press, 1994
  8. H. S. Witsenhausen, "Sets of possible states of linear systems given perturbed observations," IEEE Trans. on Automatic Control, vol. 13, no. 5, pp. 556-558, October 1968 https://doi.org/10.1109/TAC.1968.1098995
  9. L. Chisci, A. Garulli, and G. Zappa, "Recursive state bounding by parallelotopes," Automatica, vol. 32, no. 7, pp. 1049-1055, 1996 https://doi.org/10.1016/0005-1098(96)00048-9
  10. L. Jaulin, M. Kieffer, O. Didrit, and E. Walter, Applied Interval Analysis, Springer-Verlag, London, 2001
  11. V. Puig, J. Quevedo, T. Escobet, and S. de las Heras, "Passive robust fault detection approaches using interval models," Proc. of the 15th IFAC World Congress, Barcelona, 2002
  12. B. T. Polyak, S. A. Nazin, C. Durieu, and E. Walter, "Ellipsoidal parameter or state estimation under model uncertainty," Automatica, vol. 40, no. 7, pp. 1171-1179, 2004 https://doi.org/10.1016/j.automatica.2004.02.014
  13. T. Alamo, J. M. Bravo, and E. F. Camacho, "Guaranteed state estimation by zonotopes," Automatica, vol. 41, no. 6, pp. 1035-1043, 2005 https://doi.org/10.1016/j.automatica.2004.12.008
  14. P. Guerra, V. Puig, and A. Ingimundarson, "Robust fault detection using a consistencybased state estimation test considering unknown but bounded noise and parametric uncertainty," Proc. of European Control Conference, pp. 1595-1601, Kos, Greece, 2007
  15. J. S. Shamma and K.-Y. Tu, "Approximate setvalued observers for nonlinear systems," IEEE Trans. on Automatic Control, vol. 42, no. 5, pp. 648-658, May 1997 https://doi.org/10.1109/9.580870
  16. V. Puig, A. Stancu, and J. Quevedo, "Passive robust fault detection using a forward-backward test," Proc. of SAFEPROCESS, Beijing, China, 2006
  17. H. Janati Idrissi, F. Kratz, and J. Ragot, "Fault detection and isolation for uncertain systems," Proc. of IEEE Conference and Decision and Control, pp. 4748-4753, Las Vegas, 2002
  18. H. Janati Idrissi, O. Adrot, and J. Ragot, "Residual generation for uncertain models," Proc. of IEEE Conference and Decision and Control, pp. 590-595, Orlando, 2001
  19. A. Tzes and K. Le, "Fault detection for jump discrete systems," Proc. of American Control Conference, pp. 4496-4500, San Diego, 1999
  20. P. Kesavan and H. J. Lee, "A set based approach to detection and isolation of faults in multivariable systems," Computers and Chemical Engineering, vol. 25, pp. 925-940, 2001 https://doi.org/10.1016/S0098-1354(00)00315-X
  21. M. Witczak, J. Korbicz, and R. J. Patton, "A bounded-error approach to designing unknown input observers," Proc. of the 15th IFAC World Congress, Barcelona, 2002
  22. F. Hamelin and T. Boukhobza, "Geometricbased approach to fault detection for multilinear affine systems," Proc of the 16th IFAC World Congress, Prag, 2005
  23. F. Hamelin, H. Noura, and D. Sauter, "Fault detection method of uncertain system using interval model," Proc. of European Control Conference, pp. 826-831, Porto, 2001
  24. B. J. Kuipers, Qualitative Reasoning. Modeling and Simulation with Incomplete Knowledge, The MIT Press, 1994
  25. P. Planchon and J. Lunze, "Robust diagnosis using state-set observation," Proc. of SAFEPROCESS, Beijing, China, 2006
  26. J. S. Bay, Fundamentals of Linear State Space Systems, McGraw-Hill, 1999
  27. P. Planchon, Guaranteed Diagnosis of Uncertain Linear Systems using State-set Observation, Ph.D. Thesis, Ruhr-Universität Bochum, Logos-Verlag, Berlin 200
  28. S. S. Keerthi and E. G. Gilbert, "Computation of minimum-time feedback control laws for discrete time systems with state-control constraints," IEEE Trans. on Automatic Control, vol. 32, no. 5, pp. 432-435, May 1987 https://doi.org/10.1109/TAC.1987.1104625
  29. M. H. Karwan, V. Lotfi, J. Telgen, and S. Zionts, editors, Redundancy in Mathematical Programming, Springer, Berlin, 1983
  30. E. C. Kerrigan, Robust Constraint Satisfaction: Invariant Sets and Predictive Control, Ph.D. Thesis, University of Cambridge, Available online, November 2000