Centre de Recherche en Automatique de Nancy CNRS UMR 7039

1. Centre de Recherche en Automatique de Nancy CNRS UMR 7039 Système tolérant aux défauts: reconfiguration et/ou restructuration basée sur la fiabilité sous contrainte de  performances dynamiques F. Guenab, D.Theilliol, P.Weber

2. Centre de Recherche en Automatique de Nancy CNRS UMR 7039 Groupe de Recherche SURFDIAG : SUReté de Fonctionnement et DIAgnostic des systèmes Pr. Didier MAQUIN Equipe Projet SYstèmes Distribués et Embarqués Réactifs aux fautes Pr. Dominique SAUTER Intelligent Fault Tolerant Control in Integrated Systems European project reference (IFATIS EU-IST-2001-32122)

3. OUTLINES • Introduction & Problem statement • The Fault Tolerant Control System • Reliability Computation • Controller Synthesis • FTC design: a Unified Strategy • Application • System description • Results and comments • Conclusion

4. OUTLINES • Introduction & Problem statement • The Fault Tolerant Control System • Reliability Computation • Controller Synthesis • FTC design: a Unified Strategy • Application • System description • Results and comments • Conclusion

5. Behaviour Bof the closed-loop system Bspecif U xY B0 Control specifications: requirements on the closed-loop system Bc Behaviour of the system Behaviour Bof the open loop system U xY B0

6. Behaviour Bof the faulty closed-loop system Bspecif U xY Bf Bc Problem statement Behaviour Bof the fault-free closed-loop system Bspecif U xY B0 Control specifications: requirements on the closed-loop system Bc

7. A solution: Fault Tolerant Control !!! Behaviour Bof the faulty closed-loop system with controller re-design Bspecif Bf Bnew c • Fault Tolerant Control system • System capable to maintain current performances closed to desirable performances • and stability conditions in the presence of component and/or instrument faults ; • Acceptreduced performance as a trade-off.

8. Faulty case • Standard control problem => γ, S, θ, U • θ parameters of system • γ Global objectives Staroswiecki & Gehin, 2001 γf, Sa, θa, U • UControl law classes • S Structure Fault tolerant control System Passive Method Active Method γ, S, Q, U Accommodation Reconfiguration Restructuration ^ ^ γ, s, b, V γo, S, q, V Fault Tolerant Control SystemS

9. What is possible to do? • Depends on the fault characteristics, - Faults are more or less critical, - Number of faults occuring at the same time, - Fault location, - Effects on the system performances (transfer from fault to outputs). • Depends on the system and instrumentation - Number and location of instruments (sensors and actuators), - Properties of the system (controllability, Observability), - Structural Redundancies, - Remaining potential in the actuating effort.

10. Fault Faulty cases By replacing or isolating faulty parts, or using them under degraded conditions, there exists M possible Working Modes System structure S1 objectives 1 parameter 1 control law u1 structure SM How to choose the best structure in sense of criterion J, allowing to reach the global objectives or ? objectives M parameter M control law uM Problem formulation: assumption • Standard control problem Fault-free case System nominal objectives nominal structure nominal parameter nominal control law

11. s1 s2 s3 Fault si WM0 WM0’ f s1 s2 s3 n subsystems s4 sn si s4 sn Problem formulation

12. Fault WM0 WM0’ f n subsystems Problem formulation WM1 n1 subsystems WMm n2 subsystems WMM nM subsystems

13. s1 s2 s3 si Fault s4 sn WM0 WM0’ S1 S2 S3 f n subsystems Si S4 Sn Problem formulation WM1 n1 subsystems WMm n2 subsystems WMM nM subsystems

14. Fault Fault WM0 WM0’ f n subsystems Problem formulation WM1 n1 subsystems WMm ????? n2 subsystems WMM nM subsystems

15. Rg(t) 1 t 0 Reliability function

16. R* Reliabilityfunction Rg(t) 1 tf t 0

17. FTC system WM n°3 WM n°1 WM n°2 Reliability function Rg(t) 1 R* tf t 0

18. Objectives Fault Free Case Fault Objective of FTC Fault g0 FAULTS Faulty Case g2 WM0 WM0’ FTC g1 f n subsystems U,Y U0,Y0 U1,Y1 U2,Y2 Problem formulation WM1 n1 subsystems WMm ????? n2 subsystems WMM nM subsystems

19. Fault Faulty cases By replacing or isolating faulty parts, or using them under degraded conditions, there exists M possible Working Modes Reliability System Wu, 2001a Bonivento et al., 2003 structure S1 objectives 1 Wu, 2001b parameter 1 Wu and Patton. 2003 control law u1 Wu, 2004 Srichander and Walker, 1993 Mahmoud et al., 2003 structure SM How to choose the best structure in sense of criterion J, allowing to reach the global objectives or ? objectives M parameter M control law uM Problem formulation Principle behind the solution • Standard control problem Fault-free case System nominal objectives nominal structure nominal parameter nominal control law

20. Fault Faulty cases By replacing or isolating faulty parts, or using them under degraded conditions, there exists M possible Working Modes System structure S1 objectives 1 parameter 1 control law u1 Control objectives structure SM How to choose the best structure in sense of criterion J, allowing to reach the global objectives or ? objectives M parameter M control law uM Problem formulation Principle behind the solution • Standard control problem Fault-free case System nominal objectives nominal structure nominal parameter nominal control law

21. Fault Faulty cases By replacing or isolating faulty parts, or using them under degraded conditions, there exists M possible Working Modes Reliability System structure S1 objectives 1 parameter 1 control law u1 Control objectives structure SM How to choose the best structure in sense of criterion J, allowing to reach the global objectives or ? objectives M parameter M control law uM Problem formulation Principle behind the solution • Standard control problem Fault-free case System nominal objectives nominal structure nominal parameter On-line nominal control law

22. OUTLINES • Introduction & Problem statement • The Fault Tolerant Control System • Reliability Computation • Controller Synthesis • FTC design: a Unified Strategy • Application • System description • Results and comments • Conclusion

23. OUTLINES • Introduction & Problem statement • The Fault Tolerant Control System • Reliability Computation • Controller Synthesis • FTC design: a Unified Strategy • Application • System description • Results and comments • Conclusion

24. Optimal structure : structure which ensures the required global objective m closed to nominal one with: • the highest expected reliability under a threshold Fault time represents period between fault occurrence (new structure is applied) and the end of expected mission Reliability computation assumption After a fault is occured, FDI module generates suitable information

25. Global objective um Failure rates Reliability 1 i n Local objectives Reliability computation principle For each Working Mode m System Subsystem 1 Subsystem i Subsystem n

26. ith subsystem i=1,…,n mth structure (or WM) m=1,…,M i: baseline failure rate g(x): function (independent of time) incorporates the effects of applied loads x: load image For g(x),exponential form is mostly used due to its simplicity Failure rate function Operating conditions evolution from one WM to an other generate failure rate modification. According to Proportionals Hazard Model (Cox, 1972),

27. For g(x),exponential form is mostly used due to its simplicity Failure rate function

28. ith subsystem reliability for the mth structure for a desired time life Td Reliability function time represents period between fault occurrence (new structure is applied) and the end of expected mission

29. s1 s2 s3 si s4 sn Serial case Parallel case Reliability function

30. OUTLINES • Introduction & Problem statement • The Fault Tolerant Control System • Reliability Computation • Controller Synthesis • FTC design: a Unified Strategy • Application • System description • Results and comments • Conclusion

31. global objectives local references local outputs Case study Hierarchical structures

32. with or Nominal controller design Fault-free case

33. FDI f Nominal controller design Faulty case

34. FDI with f Nominal controller design Faulty case

35. FDI Extension of Revisited PIM f Nominal controller design Faulty case

36. FDI with Extension of Revisited PIM f Nominal controller design Faulty case

37. Numerical sample

38. s1 s2 s3 si s4 sn Performance criteria

39. s1 s2 s3 si s4 sn Performance criteria

40. s1 s2 s3 si s1 s2 s3 s4 sn si s4 sn Performance criteria

41. X X X X X s1 s2 s3 X si s4 sn Performance criteria

42. OUTLINES • Introduction & Problem statement • The Fault Tolerant Control System • Reliability Computation • Controller Synthesis • FTC design: a Unified Strategy • Application • System description • Results and comments • Conclusion

43. Fault WM0 WM0’ f n subsystems FTC system design

44. Fault WM0 WM0’ f n subsystems FTC system design WM1 n1 subsystems WMm ????? n2 subsystems WMM nM subsystems

45. WM1 n1 subsystems Fault ????? WMm WM0 WM0’ For all possible references and local objectives S1 S2 S3 n2 subsystems f n subsystems Si + WMM S4 Sn nM subsystems FTC system design Local level s1 s2 s3 si s4 sn

46. Global objectives Fault Global reliability WM0 WM0’ f n subsystems Static criteria Dynamic criteria FTC system design Global level WM1 n1 subsystems WMm n2 subsystems WMM nM subsystems

47. Global objectives Fault Global reliability WM0 WM0’ with f n subsystems Static criteria Dynamic criteria FTC system design Global level WM1 n1 subsystems WMm ????? n2 subsystems WMM nM subsystems

48. FTC system design Reliability FDI 2 1 Dynamic Performances Static Performances 3 4

49. 2 1 3 4 FTC system design => Efficient FTC system

50. FDI Controller f General scheme FTC system Reference Input Plant Y U