Model-Based FDI : the control approach

Transcription

1 Model-Baed FDI : he conrol approach M. Saroweck LAIL-CNRS EUDIL, Unver Llle I Olne of he preenaon Par I : model Sem, normal and no normal condon, fal Par II : he decon problem problem eng noe, drbance, ncerane Par III : fal deecon par pace, oberver baed approache Par IV : fal olaon dreconal, rcred redal Conclon 1

2 Par I : model em : a e of nerconneced componen, fal : preven componen o perform her fncon varable and me conno varable/conno me, conno varable/dcree me, dcree varable/dcree me fal model addve, mlplcave, probabl drbon Wha a em? A em a e of nerconneced componen Each componen acheve ome fncon of nere becae eplo ome phcal prncple whch are epreed b ome relaonhp beween he me evolon of ome em varable. Relaonhp are called conran, Tme evolon of a varable called rajecor. 2

3 The ank eample Poble fncon : orage of lqd, decoplng moohng of he op flow, mng of wo dfferen lqd, ec. Whaever fncon, he ank nrodce a mahemacal conran beween ome varable, namel dl d q q o Conrolled em Acaor : allow o chooe, beween all he poble em rajecore, he one whch wll brng ome epeced rel acheve ome gven objecve. Eablh ome conran beween he proce varable and ome conrol varable, whch called ''conrol gnal''. Conrol gnal : generaed b hman operaor or b conrol algorhm. Cloed loop conrol : he acal vale of ome em varable m be known. Senor : componen whch provde h nformaon. 3

4 4 Acaor eample : np valve Analog valve On-off valve p k q α 1 q q Senor eample : level enor Analog enor conran Qanzed enor 1 2 n l [a,b[ [b,c[ [,l ma ] l

5 5 Conrolled em e of nerconneced componen whch nclde proce componen, acaor, enor and conrol algorhm Eample ank np valve op ppe level enor level conrol algorhm q q d dl o α 1 q q l k q o, Σ N l 1 > < l l l l M m

6 6 Normal and no-normal condon, fal Normal operaon : he mlaneo occrence of wo aon 1 componen perform properl her agned fncon he reall behave a he degner epec conran appled o he varable are he nomnal one IF NOT : INTERNAL FAULT 2 neracon beween he em and envronmen are compable wh he em' objecve. IF NOT : EXTERNAL FAULT Eample of nernal fal Proce fal : he ank leakng. Acaor fal : he np valve blocked open. Senor fal : noe ha mproper acal characerc q q q d dl l o α α 1 q q, 1 Σ µ N l

7 Eample of eernal fal Conrol algorhm objecve : l mn l l ma canno be acheved for oo large op flow 2 1 q d o > l α l In he preence of a leak n he ank nernal fal, he em objecve ma ll be acheved provded he above neqal doe no hold for he overall op flow mn Dfferen knd of model em' fncon, em' archecre he componen and her nerconneon, em' behavor he e of he conran whch lnk he em varable. Degn of MB FDI algorhm behavor model 3 bac feare : varable, me and conran. 7

8 Bac modellng feare Varable whoe me evolon of nere for FDI Bond-graph : power and energ varable conrolled em : conrol and nformaon gnal varable o be condered : all qane conraned b he em componen proce, acaor, enor, algorhm Se of vale varale can be agned qanave varable qalave varable ordered or no abrp ranon avoded ng fzz e. 8

9 Tme conno me dcree me ampled daa em drven b a clock even drven em Conran Markov proper Whole pa hor mmarzed b he em' ae Sae evolon onl depend on crren ae and np Conno me, conno varable algebrac and dfferenal eqaon Comper-baed mearemen, conrol and pervon dcree me, algebrac and dfference eqaon Qalave varable logc eqaon, aomaa, Per ne, e of rle. 9

10 1 Normal operaon Conno varable/dcree me Phcal law obeed b he healh proce componen ae pace, mearemen, operang range,,,,,, 1 h P g v f Eample : Lnear em h H H C v E B A 1

11 11 Fal operaon Mlplcave fal :,,,,, 1 g v f,,,,,,, 1 g v f ϕ ϕ From mlplcave o addve fal 1 C v E B A 1 C C v E E B B A A

12 12 Addve fal Acaor fal : F B, F Senor fal : F, F C 1 F C F Ev B A ϕ Change n acal drbon 1 P P

13 Qalave varable / dcree me Eample : eqenal lnear em gae arra, nchroneo clock {,1}, wo operaor and, conan amplng rae Normal operaon Fal model 1 A B C 1 [ A B ] e [ C ] e j Dfferen fal H : Normal operaon em behavor obe normal ae and mearemen eqaon em behavor obe fal ae and mearemen eqaon wh ϕ. H :Faloccr ϕ φ eample : fal on enor : g ϕ ϕ ke 13

14 Par II : The decon problem Two problem eng Obervaon : Z col [U, Y ] U col,-1, - Y col,-1, - Hpohee checkng H he daa have been prodced b he healh em H 1 he daa canno have been prodced b he healh em Change pon deecon H all he daa have been prodced b he healh em H 1 he daa have been prodced b he healh em nll ome me nan; he canno have been prodced b he healh em afer ha me 14

15 No noe, no nceran, no drbance 1 f,, ϕ g, ϕ fal deecon fndanneger and a e E ch ha Z E for whch he healh em prodce he obervaon Z fal olaon fndanneger and a e E.. Z E, ϕ φ for whch he fal em prodce he obervaon Z No noe, no nceran 1 f,, v, ϕ g, ϕ fal deecon fndanneger and a e E ch ha Z E, v V for whch he healh em prodce he obervaon Z fal olaon fndanneger and a e E.. Z E, ϕ φ, v V for whch he fal em prodce he obervaon Z 15

16 1 No noe f,, v,, ϕ g, ϕ, fal deecon fndanneger and a e E.. Z E, v V, Θ for whch he healh em prodce he obervaon Z fal olaon fndanneger and a e E.. Z E, ϕ φ, v V, Θ for whch he fal em prodce he obervaon Z Deermnc deecabl / olabl Non deecable fal Z E healh em OR fal Non olable fal Z E j fal OR fal j 16

17 Sochac em 1 Mearemen noe g, ϕ,, Ξ,, f,, v,, ϕ P, Ξ, are bonded e : forge he drbon, do a for nknown np Sacal decon : replace characerc vecor b condonal probabl π Z Proba {Z Z /fal preen} Sochac deecabl / olabl Generalzaon An nknown em np, em parameer can be decrbed b ome probabl drbon Non-deecable fal π Z π Z Non-olable fal π Z π j Z 17

18 Par III : Fal deecon The problem Bld a paron no wo clae E and E 1 ch ha Z E decde H and Z E 1 decde H 1 Dffcl : he nknown nknown nal condon v nknown np nknown or nceran parameer mearemen noe 1 Elmnae he nknown : analc redndanc approach 2 Emae he nknown : oberver baed approach 18

19 19 Unknown ae : Analc redndanc Obervaon Tranformaon,, 1 g f,, k k U g k k k,, U G Y Ξ,, ] [ U G Y Ξ Ψ Ψ Ξ Ψ Ξ Ψ Ψ ],, [ ], [ ] [ 1 U U Y Analc redndanc relaon Decon ], [ ], [ ] [ Ξ Ξ Ψ Ψ Z U Y ω { }, ; Z Z E ω Y U E

20 2 Unknown ae : oberver Smlaon of he em behavor Dcrepance hold be zero Eample em mlaor error, 1 g f r Ce e Ae e C B A C B A Oberver General cae K ch ha when no fal 1 ] [ Ce e e KC A e C Ke B A C B A,, 1 g K f lm

21 Y E U Unknown np 1 Par pace Y Tranformaon 1 f,, v g, v, G, U, V, Ξ Ψ [ U, Ξ ] Ψ[ Y ] 1 Ψ [, U, V, Ξ ] Rob redndanc relaon ω [ Z, Ξ ] 21

22 Unknown np 2 Eence condon : ome bem whch no affeced b he nknown np Eqvalen aemen : a ranformaon z T. z1 1 f1 z1, z2 1 f2 z1, z2,, v 1 g1 z1, 2 g2 z1, z2, v, An oberver can be degned from bem 1. Unknown np 3 Y E U 22

23 Unknown np 4 When no decoplng poble? No rob oberver, no rob redndanc relaon Se heorec approach 1 { Z ; V V ; ω Z, V, } E How o deermne Lnear eample E PY E E QU RV 1 RV Unknown np 5 Y E E E U 23

24 Uncerane Same a nknown np Par IV : Fal olaon 24

25 Problem Se whch are characerc of each fal whch mgh occr Y E E 2 E 1 U Dreconal and rcred redal Dreconal redal characerc e pace of dmenon one Srcred redal characerc e pace of gven dmenon Fal 3 Fal Fal

26 Compaon / evalaon form 1 f,, ϕ g, ϕ ω[ Z, Φ ] Sppoe can be wren ω ω where [ Z, Φ ] c[ Z,] ωe[ Z, Φ ] ω e [ Z,] Then r ωc[ Z,] ωe[ Z, Φ ] r when no fal occr { Z ; r [ Z,] } E ω c Srcred redal Le Φ col ϕ, ϕ 1,... ϕ when fal preen Sppoe here e a be of componen of ω e 1 ω e [ Z, Φ ], Φ φ ω e Then, nder fal, he redal vecor belong o a gven bpace Ω. Srcred redal : he bpace Ω are dfferen. Degn of rcred redal ng elmnaon n redndanc relaon or pecal oberver degn 26

27 Conclon On model Componen relaed model Hgher abracon level ranformaon n he ae pace Noe, drbance, ncerane Poble knowledge abo he fal Toward hbrd model 27

28 On decon Real me decon of nere Geomerc / acal opmzaon fale alarm, med deecon rae deecon dela Rob decon procedre Logcall ond decon procedre ee IMALAIA On he FDI cone Real me eploaon cone FDI for Fal Toleran Conrol fal accomodaon conrol reconfgraon goal reconfgraon conrol, degraded conrol, change of operang mode, manenance FDI for manenance Sem degn for FDI / FTC enor, acaor elecon 28