Active Diagnosis of Hybrid Systems Guided by Diagnosability Properties

Transcription

1 Active Diagnosis of Hybrid Systems Guided by Diagnosability Properties Application to autonomous satellites Louise Travé-Massuyès 5 February 29

2 Motivation Control and autonomy of complex dynamic systems Physical plant: continuous behaviors Controller that imposes discrete switches between operating modes High need for availability Diagnosis and reconfiguration Reduce ground segment operations Far-space missions: need for autonomy 2

3 Diagnosis, diagnosability and active diagnosis Diagnosis aims at providing an estimation of the situation, normal or faulty, of the system, possibly making explicit the status of the different components. Diagnosability is the property of a system and its instrumentation that guarantees that different anticipated faulty situations can be determined with precision with a finite time delay. It determines the performance of the diagnosis module. The diagnosability property depends on: the system model the diagnosis approach the observation system Active diagnosis aims at refining an initial diagnosis by acting on the system to exhibit new symptoms. 3

4 Outline Hybrid modeling framework based on hybrid automata Diagnosis scheme of hybrid systems coupling discreteevent and continuous techniques Diagnosability analysis of multimode and hybrid systems Active diagnosis of hybrid systems guided by diagnosability properties The Attitude Control System (ACS), actuator fault diagnosis 4

5 Outline Hybrid modeling framework based on hybrid automata Diagnosis scheme of hybrid systems coupling discreteevent and continuous techniques Diagnosability analysis of multimode and hybrid systems Active diagnosis of hybrid systems guided by diagnosability properties The Attitude Control System (ACS), actuator fault diagnosis 5

6 Hybrid modeling framework () Hybrid system Nominal modes (continuous model) Inputs Discrete events Faulty modes (continuous model) Model-based diagnosis module Observable outputs D I A G N O S I S 6

7 Hybrid modeling framework (2) Hybrid System S = (", Q, #, T, C, (q," )) " = " o # " uo " F $ " uo Underlying discrete-event system M = (Q, ", T, q ) Underlying continuous system called the multimode system " = (#, Q, C, # ) f q2 q f uo q3 Q = {q, q 2, q 3, q 4 } = {f, uo, u, o, } + C i (ζ)= in every mode q i Q o F = {f } q4 7

8 FDI approach: consistency indicators eliminating non observable variables in C Physic laws: A set of constraints C C obs a set of constraints linking only observable variables (Analytic Redundancy Relations) k "C obs # C obs k if Cobs we associate a Boolean consistency indicator called residual and denoted r k is satisfied " r k = otherwise r k = Normal behavior: all residuals are null: [r,, r n ] T = For a fault F we associate a fault signature Sig(F) = [r,, r n ] T that models the expected behavior of residuals in this faulty situation 8

9 DES: the diagnoser approach () System model M = (Q,",T,q ) Q is the set of discrete states " is the set of discrete events " = " o # " uo T $ Q % " & Q is the partial transition function q is the initial state The Diagnoser of a discrete model M, is a deterministic state machine (Sampath, 995): Diag(M) = (Q D," o,t D,q ) - The non observable events are discarded (only observable events are represented) - States are labeled with non observable information (especially fault information) Note: The diagnoser can be used to perform on-line diagnosis and to check the diagnosability property 9

10 DES: the diagnoser approach (2) The diagnoser construction o q 2 u q 3 q 4 o 3 u (q,{ }) { (q 4,{F}),(q 6,{F2), (q 8,{ }) } (q 6,{F2}) f o o 3 q q 5 q 6 f 2 uo q 7 q 8 o 3 q 9 o 3 (q 2,{ }) (q 4,{ }) { (q 9, { }),(q 4,{F}) } F (F2)-uncertain state o 3 indeterminate cycle o 3 F i -indeterminate cycle: is a cycle composed by F i -uncertain states for which there exist two corresponding cycles in the original automaton: one involves only states that carry and the other involves states that do not carry the fault label F i in their labels in the diagnoser cycle

11 Outline Hybrid modeling framework based on hybrid automata Diagnosis scheme of hybrid systems coupling discreteevent and continuous techniques Diagnosability analysis of multimode and hybrid systems Active diagnosis of hybrid systems guided by diagnosability properties The Attitude Control System (ACS), actuator fault diagnosis

12 Diagnosis scheme () PASSIVE DIAGNOSIS MODULE continuous inputs: u continuous outputs: y Residual Bench (Parity space approach) residuals Residual filter mode signature Abstraction of the continuous dynamics in terms of discrete events Observable events o Diagnoser of the hybrid system (built from the behavior automaton) diagnosis 2

13 Diagnosis scheme (2) PASSIVE DIAGNOSIS MODULE continuous inputs: u continuous outputs: y Residual bench residuals Residual filter mode signature Abstraction of the continuous dynamics in terms of discrete events Observable events " # o Diagnoser of the hybrid system (built from the behavior automaton) diagnosis 3

14 Reflexive, mirror and mode signatures Idea: to take any of the anticipated mode models as reference behavior. Mode signature: a theoretical signature that captures the expected values of all system residuals mode q i # x(n +) = A i x(n) + B i u(n) + E X i "(n) $ % y(n) = C i x(n) + D i u(n) + E Y i "(n) (u,y) " $ $ $ $ $ $ $ # R q.. R q i.. % ' ' ' ' ' ' S i/ : mirror signature of q S i/i = : reflexive signature of q i R q ' m Si/m : mirror signature of q i & The mode signature of q i, is the concatenation of all mirror signatures of q i Sig(q i ) = [S T i/ ST i/2,, ST i/m ]T, m is the mode number 4

15 Illustrative example Free-noise hypothesis " x(n +) = A i x(n) + B i u(n) # $ y(n) = C i x(n) + D i u(n) " A =.7 % #",5 4 & #,3 ",3 & #,6 ",3 & $ ' % ( % ( % ( #.7& A 2 =,6 A 3 =,6 A 4 =,3,6 % ( % ( % ( $ 6,8' $ ",3,9' $ ",6,9' " B = $ % " % " 2% $ ' ' B # 2 = B 3 = & $ ' B = $ ' 4 2 $ ' # & # & " c = % " $ ' c 2 = % " " $ ' C 4 = % C 3 = % $ ' $ ' # & # & # & # & f q2 q uo f o q3 q4 " D = D 2 = D 3 = D 4 = $ % ' # & 5

16 Illustrative example: parity space approach Parity order p= $ y (n #) ' & ) $ #,575,47,865 #,673' y 2 (n #) $ (n) = & ) & ) #,776 #,865' $ u (n #)' + & ) & ) %#,47 #,575,673,865 ( & y (n) ) %#,8367 #,673( % u (n) ( & ) % y 2 (n) ( " c $ y (n #) ' & ) $ #,278 #,958,2557 #,98' y 2 (n #) $ (n) = & ) & ) #,8 #,2557' $ u (n #)' + & ) & ) %,536 #,594 #,7,9799 ( & y (n) ) %#,9264,7 ( % u (n) ( & ) % y 2 (n) ( " c2 Computation form of residuals " c3 (n) = (,275 #,5437 #,3625,725) $ y (n #) ' & ) & y 2 (n #) ) +,9425,3625 & y (n) ) & ) % y 2 (n) ( $ & % ( ) u (n #)' ) u (n) ( " c4 (n) = (,275 #,5437 #,3625,725) $ y (n #) ' & ) & y 2 (n #) ) +,9425,3625 & y (n) ) & ) % y 2 (n) ( $ & % ( ) u (n #)' ) u (n) ( 6

17 Illustrative example: mode signatures Theoretical mode signatures Sig(q ) Sig(q 2 ) Sig(q 3 ) Sig(q 4 ) S/ S/2 S/3 S/ S2/ S2/2 S2/3 S2/ S3/ S3/2 S3/3 S3/ S4/ S4/2 S4/3 S4/

18 Abstraction of the continuous dynamics Assumption: the dynamics of discrete input events are slower than the continuous dynamics. Abstraction function f CS "DES : Q # T(Q) " $ Sig ( q i, q j ) a R oij % $ o Sig ( q i, q j ) a R uoij % $ o Sig if Sig(q i ) & Sig(q j ) if Sig(q i ) = Sig(q j ) The hybrid language " Sig = " Sig Sig o # " uo " hyb = "# " Sig * L(S) " # hyb Transient states f t : Q " T(Q,#) $ Q t (q i,q j ) a q ij 8

19 The behavior automaton The behavior automaton = the automaton representation of L(S) B A (S) = (Q beh," hyb,t beh,q ) Q beh = Q" Q t T beh " (Q beh # $ beh % Q beh ) & (q,") a f t (q,t(q,")) if q # Q and " # $ ' (( f % t ) 2 (q) if q # Q t and " # $ Sig 9

20 The behavior automaton: illustrative example R q u f q2 q uo f o q3 q4 + Sig(q )= Sig(q 2 )= Sig(q 3 )= Sig(q 4 )= uo q2 q2 R o32 q24 q3 uo3 R o3 q32 q3 R uo43 q43 q34 o R uo34 R 4 q4 The underlying CS The behavior automaton B A (S) 2

21 The behavior automaton: illustrative example R q u f q2 q uo f o q3 q4 + Sig(q )= Sig(q 2 )= Sig(q 3 )= Sig(q 4 )= uo q2 q2 R o32 q24 q3 uo3 R o3 q32 q3 R uo43 q43 q34 o R uo34 R 4 q4 The underlying CS The behavior automaton B A (S) 2

22 Extension of the diagnoser approach to hybrid systems Behavior automaton B A (S) Diagnoser approach Diagnoser of the hybrid system Diag(B A (S)) = (Q D," D,T D,q D ) Illustrative example 2 Ro3 (q,{ }) (q 3,{ }) (q 4,{ }) o 4 - The non observable events are discarded (only observable events are represented). - System modes are labeled with fault information. R 3 (q 2,{F}) Ro32 (q 24,{F}) 5 6 R4 (q 4,{F}) o Ro32 (q 3,{F}) 7 22

23 Passive diagnosis scheme: demonstration () Scenario: [(u o, t = 3s), (f, t = 5s), (, t = 7s), (o, t = 9s)] 2 Ro3 (q,{ }) (q 3,{ }) (q 4,{ }) o 4 R Ro32 f q2 q f uo q3 3 (q 2,{F}) (q 24,{F}) 5 6 R4 (q 4,{F}) o q4 o Ro32 7 (q 3,{F}) 23

24 Passive diagnosis scheme: demonstration (2) Scenario: [(u o, t = 3s), (f, t = 5s), (, t = 7s), (o, t = 9s)] 2 Ro3 (q,{ }) (q 3,{ }) (q 4,{ }) o 4 R Ro32 f q2 q f uo q3 3 (q 2,{F}) (q 24,{F}) 5 6 R4 (q 4,{F}) o q4 o Ro32 7 (q 3,{F}) 24

25 Passive diagnosis scheme: demonstration (3) Scenario: [(u o, t = 3s), (f, t = 5s), (, t = 7s), (o, t = 9s)] 2 Ro3 (q,{ }) (q 3,{ }) (q 4,{ }) o 4 R Ro32 f q2 q f uo q3 3 (q 2,{F}) (q 24,{F}) 5 6 R4 (q 4,{F}) o q4 o Ro32 7 (q 3,{F}) 25

26 Passive diagnosis scheme: demonstration (4) Scenario: [(u o, t = 3s), (f, t = 5s), (, t = 7s), (o, t = 9s)] 2 Ro3 (q,{ }) (q 3,{ }) (q 4,{ }) o 4 R Ro32 f q2 q f uo q3 3 (q 2,{F}) (q 24,{F}) 5 6 R4 (q 4,{F}) o q4 o Ro32 7 (q 3,{F}) 26

27 Passive diagnosis scheme: demonstration (5) Scenario: [(u o, t = 3s), (f, t = 5s), (, t = 7s), (o, t = 9s)] 2 Ro3 (q,{ }) (q 3,{ }) (q 4,{ }) o 4 R Ro32 f q2 q f uo q3 3 (q 2,{F}) (q 24,{F}) 5 6 R4 (q 4,{F}) o q4 o Ro32 7 (q 3,{F}) 27

28 Passive diagnosis scheme: demonstration (6) Scenario: [(u o, t = 3s), (f, t = 5s), (, t = 7s), (o, t = 9s)] 2 Ro3 (q,{ }) (q 3,{ }) (q 4,{ }) o 4 R Ro32 f q2 q f uo q3 3 (q 2,{F}) (q 24,{F}) 5 6 R4 (q 4,{F}) o q4 o Ro32 7 (q 3,{F}) 28

29 Passive diagnosis scheme: demonstration (7) Scenario: [(u o, t = 3s), (f, t = 5s), (, t = 7s), (o, t = 9s)] 2 Ro3 (q,{ }) (q 3,{ }) (q 4,{ }) o 4 R Ro32 f q2 q f uo q3 3 (q 2,{F}) (q 24,{F}) 5 6 R4 (q 4,{F}) o q4 o Ro32 7 (q 3,{F}) 29

30 Outline Hybrid modeling framework based on hybrid automata Diagnosis scheme of hybrid systems coupling discreteevent and continuous techniques Diagnosability analysis of multimode and hybrid systems Active diagnosis of hybrid systems guided by diagnosability properties The Attitude Control System (ACS), actuator fault diagnosis 3

31 Diagnosability of multimode systems Mode diagnosability definition Two modes q i and q j are diagnosable if Sig(q i ) Sig(q j ) Mutual diagnosability definition Two modes q i and q j are not mutually diagnosable if S i/i = S i/j = [,, ] T and S j/i = S j/j = [,,] T = R qi q i R qj q j = 3 rd diagnosability definition Two modes q i and q j are q k -3 rd diagnosable if S i/k S j/k q i q j R qk q k Propositions Two modes q i and q j are diagnosable iff they are mutually or 3 rd diagnosable The multimode system is diagnosable iff all modes are diagnosable (Cocquempot et al. 24) 3

32 Diagnosability of multimode systems: illustrative example Sig(q )= Sig(q 2 )= Sig(q 3 )= Sig(q 4 )= modes q and q 2 are mutual diagnosable modes q and q 2 are not 3 rd diagnosable modes q and q 2 are diagnosable modes q 3 and q 4 are not mutually diagnosable modes q 3 and q 4 are not 3 rd diagnosable modes q 3 and q 4 are not diagnosable The underlying CS 32

33 Diagnosability of hybrid systems The hybrid system Diagnosability definition for hybrid systems S = (", Q, #, T, C, (q," )) is diagnosable if the language * L(S) is diagnosable. " hyb Sufficient criteria CS criterion: the hybrid system is diagnosable if the underlying continuous system is diagnosable. DES criterion: the hybrid system is diagnosable if the underlying discreteevent system is diagnosable. Necessary and sufficient criterion The hybrid system S is not diagnosable iff the diagnoser built from the behavior automaton Diag(B A (S)) contains an indeterminate cycle. 33

34 Diagnosability of hybrid systems: example Sig Sig2 Sig2 Sig3 Sig4 Diagnosability of the hybrid system 34

35 Outline Hybrid modeling framework based on hybrid automata Diagnosis scheme of hybrid systems coupling discreteevent and continuous techniques Diagnosability analysis of multimode and hybrid systems Active diagnosis of hybrid systems guided by diagnosability properties The Attitude Control System (ACS), actuator fault diagnosis 35

36 Active diagnosis PROBLEM the diagnosis returned by the passive diagnosis scheme is ambiguous (the diagnoser state is uncertain) focused reconfiguration requirement Active diagnosis the active diagnosis consists on performing control actions in order to disambiguate or precise the system state the active diagnosis can be performed in an uncertain state: that belongs to an indeterminate cycle that does not belong to an indeterminate cycle! the system can be diagnosable or not ( Sampath 98) 36

37 Controllable and induced controllable paths Controllable events: discrete control inputs and events corresponding to spontaneous mode changes when the continuous dynamics model of the source mode is controllable: " c # " o Induced controllable events: events that model the response of the hybrid system after a control action (continuous control input/discrete control input): " hybic = " ic # " Sig ic $ " hyb Reaction of the continuous dynamics: Reaction of the discrete dynamics: " Sig ic # " Sig " ic # " A controllable path in the behavior automaton is a string of induced-controllable events and consecutive controllable events: s " L(S) # ($ c % $ hybic ) * A controllable path in the behavior automaton corresponds to a observable controllable path in the hybrid system diagnoser 37

38 The active diagnoser () the active diagnoser : (Q D act, T D act, " c # " hybic, q act ) embedded in the classic hybrid diagnoser controllability consideration: contains only controllable paths safety considerations: only control inputs enabled in all possible fault situations can be performed f N f 2 qf qf2 c c c 2 q F q F2 q F2 Classic diagnoser (q F,{F}) (q F2,{F2}) (qf,{f}) (qf2,{f2}) c c 2 (q F,{F}) (q F2,{F2}) 38

39 The active diagnoser (2) the active diagnoser : (Q D act, T D act, " c # " hybic, q act ) embedded in the classic hybrid diagnoser controllability consideration: contains only controllable paths safety considerations: only control inputs enabled in all possible fault situations can be performed f N f 2 qf qf2 c c c 2 q F q F2 q F2 Classic diagnoser (q F,{F}) (q F2,{F2}) (qf,{f}) (qf2,{f2}) c c 2 (q F,{F}) (q F2,{F2}) 39

40 The active diagnoser (3) the active diagnoser : (Q D act, T D act, " c # " hybic, q act ) embedded in the classic hybrid diagnoser controllability consideration: contains only controllable paths safety considerations: only control inputs enabled in all possible fault situations can be performed f N f 2 qf qf2 c c c 2 q F q F2 q F2 Active diagnoser (q F,{F}) (q F2,{F2}) (qf,{f}) (qf2,{f2}) c c 2 (q F,{F}) (q F2,{F2}) 4

41 The active diagnoser (4) the active diagnoser : (Q D act, T D act, " c # " hybic, q act ) embedded in the classic hybrid diagnoser controllability consideration: contains only controllable paths safety considerations: only control inputs enabled in all possible fault situations can be performed f N f 2 qf qf2 c c c 2 q F q F2 q F2 Active diagnoser (q F,{F}) (q F2,{F2}) (qf,{f}) (qf2,{f2}) c 4

42 The active diagnoser seen as a AND-OR Graph state node c q D c 3 Mapping between the active diagnoser and the AND-OR graph q D2 q D6 initial state: uncertain state " Q D act c 2 ic o3 ic o4 state nodes (OR): start of actions observation node ic o q D4 qd3 ic q D5 q D7 q D8 observations nodes (AND): end of actions actions: a " 2 # c observations: o " ic # $ hybic target states: certain states (or more certain) 42

43 Conditional planning for active diagnosis The active diagnosis is formulated as a conditional planning problem The research of an active diagnosis plan is achieved by the exploration of the AND-OR graph corresponding to the active diagnoser A Mini-Max algorithm is implemented for graph exploration An active diagnosis plan is guaranteed if it guarantees to reach a certain state of the active diagnoser from the starting uncertain state 43

44 Active diagnosis: illustrative example h h 2 h 3 V V 2 fault F Modes Valve V F,F 2, F 3 open 2F, 2F 2, 2F 3 3F, 3F 2, 3F 3 fault F 2 fault F 3 close close Valve V 2 open open close h = " r = h < " r 4 = h 2 = " r 2 = h 2 < " r 5 = h 3 = " r 3 = h 3 < " r 6 = OR (F, {F}) (F2, {F2}) (F3, {F3}) closev (3F2, {F2}) (2F, {F}) (2F, {F}) (2F2, {F2}) (2F3, {F3}) (2F2, {F2}) (2F3, {F3}) closev 2 (23F2, {F2}) (23F3, {F3}) (3F3, {F3}) ic R o4 AND OR AND ic R o ic R ic Active diagnosis plan: [closev, if R ic R o3 closev 2 else [ ] ] 44

45 Outline Hybrid modeling framework based on hybrid automata Diagnosis scheme of hybrid systems coupling discreteevent and continuous techniques Diagnosability analysis of multimode and hybrid systems Active diagnosis of hybrid systems guided by diagnosability properties The Attitude Control System (ACS), actuator fault diagnosis 45

46 Hybrid model based diagnosis applied to the Attitude Control System (ACS) Torque setpoint r T rq controller Torque " setpoint$ $ for each $ wheel $ # reaction wheels T cmd T cmd 2 T cmd 3 T cmd 4 % ' ' ' ' & # " & % ( %" 2 ( % " 3 ( % $ ( " 4 ' r H rwsc, T r rqsc satellite Attitude quaternion Rotation vector r " S / R Kinetic momentum theorem: d dt / R [ H r G ] = d [ H r GSatellite + H r GWheels ] = M r GFext = T r rq dt / R Reference frame change: d dt / R d dt / R [ H r GSatellite ] = d [ H r GSatellite ] + " r S / R # H r Satellite dt / R [ H r Wheels ] = d [ H r Wheels ] + " r S / R # H r Wheels dt / R 46

47 ACS: satellite equations r r H GSatellite = I G " S / R # d dt / R d dt / R r " S / R = [I G r " S / R ] + I G r " S / R = r T rq sc # d [ H r GWheels ] dt / S due to wheel the rotation r r [I G " S / R ] + I G " S / R = T r rq sc # d [ H r GWheels ] dt / S % p( ' * q ' *, r % ' T rq sc = ' & r ' ) & T rqsc T rqsc 2 T rqsc 3 ( * *, r % ' H rwsc = ' * ' ) &,. p = 6 qr + 6 (T rq sc # H rwsc ). - q = 7 (T rq sc2 # H rwsc2 ).. r = # 6 pq + 6 (T rq sc # H rwsc 3 3 ) /. r H rwsc H rwsc H rwsc2 H rwsc 3 ( * * * ) + # r " S / R $ H r 4 24 GWheels 43 due to the Gyroscopic coupling Polynomial non-linearity 47

48 ACS: reaction wheel equations T rwi = T roti " f viscous H rwi I $ T roti = " m i T cmd i if T cmd i # T rotmax & % " mi & ' Sign(T cmd i )T rotmax otherwise Motor torque limitation (3 configurations) " Sign( H rwi ) f Coulomb (Static friction: 2 configurations) % ' H rwi = " # T rw i if " # T rwi $ H rwmax & (' Sign(" # T rwi )H rwmax otherwise Wheel velocity limitation (3 configurations) Connection equations: r T rqsc " $ T = C $ as $ $ # T rw T rw2 T rw3 T rw4 % ' ' ' ' & r H rqsc " $ T = C $ as $ $ # H rw H rw2 H rw3 H rw4 % ' ' ' ' & C T as = Spin axe configuration " % $ ' $.77.5 (.5 ' $.77 (.5 (.5' $ ' #.77 (.5.5 & 48

49 ACS: the hybrid model Saturation non linearities are modeled by piece-wise affine functions NOMINAL BEHAVIOR The system is the synchronous product of 5 components: the 4 wheels + the satellite: =2 nominal modes (+ physical consideration) nominal mode of the satellite 2 4 = 2736 nominal modes of the system FAULT BEHAVIOR actuator faults: F, F2, F3, F4 that model motor failures of each wheel each fault may occur in any nominal mode 2 2 = 4 fault modes for each wheel SYSTEM MODES (2+4) 4 = modes single fault assumption: = modes 49

50 ACS: redundancy relations () modes 3 analytic redundancy relations for each mode r i = f i (T cmd,t cmd 2,T cmd 3,T cmd 4, T cmd, T cmd 2, T cmd 3, T cmd 4, p, r, q, p, r, q, p, r, q ) r i2 = f i2 (T cmd,t cmd 2,T cmd 3,T cmd 4, T cmd, T cmd 2, T cmd 3, T cmd 4, p, r, q, p, r, q, p, r, q ) r i3 = f i3 (T cmd,t cmd 2,T cmd 3,T cmd 4, T cmd, T cmd 2, T cmd 3, T cmd 4, p, r, q, p, r, q, p, r, q ) pre-computed analytic redundancy relations the system is diagnosable (all modes are mutually diagnosable) 5

51 ACS: redundancy relations (2) w w2 w3 w4 satellite S Wheel Wheel 2 Wheel 3 Wheel 4 w w w2 w2 w3 w3 w4 w4 w w2 w3 w4 ON-LINE ANALYTIC REDUNDANCY RELATIONS GENERATION 3 generic analytic redundancy relations (using non linear functions) non r linear non = f linear (T cmd,t cmd 2,T cmd 3,T cmd 4, T cmd, T cmd 2, T cmd 3, T cmd 4, p, r, q, p, r, q, p, r, q ) non r linear non 2 = f linear 2 (T cmd,t cmd 2,T cmd 3,T cmd 4, T cmd, T cmd 2, T cmd 3, T cmd 4, p, r, q, p, r, q, p, r, q ) non r linear non 3 = f linear 3 (T cmd,t cmd 2,T cmd 3,T cmd 4, T cmd, T cmd 2, T cmd 3, T cmd 4, p, r, q, p, r, q, p, r, q ) From a current mode we instantiate the residuals of all the possible destination modes (in the worst case 3 ( 3 4 )=243 residuals) 5

52 ACS: demonstration T rot " T rotmax q N T rot2 q N F q N2 F " T rotmax T rot = T " T rot = rotmax T rot2 T rot2 " T rotmax H rw " H rwmax Sign(# ) > T rot3 = T rotmax H rw2 T rot4 " H rwmax Sign(# 2 ) < " T rotmax f at t= 5s """ # H rw " H rwmax Sign(# ) > T rot3 = T rotmax H rw2 T rot4 " H rwmax Sign(# 2 ) < " T rotmax T rot3 <.5Nm """ "# H rw " H rwmax Sign(# ) > T rot3 " T rotmax H rw2 T rot4 " H rwmax Sign(# 2 ) < " T rotmax H rw3 " H rwmax Sign(# 3 ) > H rw4 " H rwmax Sign(# 4 ) < H rw3 " H rwmax Sign(# 3 ) > H rw4 " H rwmax Sign(# 4 ) < H rw3 " H rwmax Sign(# 3 ) > H rw4 " H rwmax Sign(# 4 ) < Fault scenario (q N, { }) (q NF, { }) (q NF2, { }) (q NF3, { }) (q NF4, { }) (q N2, { }) (q N2F, { }) Numbers associated to diagnoser states 52

53 Conclusions and perspectives Contributions The hybrid modeling framework that allows us to couple continuous diagnosis knowledge and discrete-event information The passive diagnosis scheme The diagnosability analysis of multimode and hybrid systems, definition and diagnosability criteria The active diagnosis scheme formulated as a conditional planning problem based on the new concept of active diagnoser The diagnosis of the Attitude Control system Perspectives The use of concurrent hybrid automata to perform diagnosis in a distributed way To couple mode estimation and hybrid state estimation to define continuous control strategy for active diagnosis The improvement of the active diagnosis algorithm to take into account fault probabilities and command costs 53