FaultAdaptive Control Technology. Gabor Karsai Gautam Biswas Sriram Narasimhan Tal Pasternak Gabor Peceli Gyula Simon Tamas Kovacshazy Feng Zhao. ISIS, Vanderbilt University Technical University of Budapest, Hungary Xerox PARC. Objective. Develop and demonstrate FACT tool suite
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Gabor Karsai
Gautam Biswas
Sriram Narasimhan
Tal Pasternak
Gabor Peceli
Gyula Simon
Tamas Kovacshazy
Feng Zhao
ISIS, Vanderbilt University
Technical University of Budapest, Hungary
Xerox PARC
Tools/components are modelbased
Continuous behavior is mixed with discontinuities
Discontinuities attributed to
modeling abstractions (parameter & timescale)
supervisory control and reconfiguration (fast switching)
Implement discontinuities as transitions in continuous behavior
systematic principles: piecewise linearization around operating points & derive transition conditions (CDC’99, HS’00)
compositional modeling: using switched bond graphs
Summary:
continuous + discrete behavior => hybrid modeling
Plant modeling: Nominal behaviorDynamic Physical Systemscomponents (R,I,C), transformers and gyrators, junctions, effort and flow sources.
Switched
Bondgraph
Model
Hybrid Observer
Continuous observer
A
uk
yk
System Generation
B
z1
C
Hybrid Automata
Generation
Xk+1
xk
m1
m2
Hybrid
Automata
Model
m3
Mode switching logic
g
y+
y
a
j
ha
i
x+
g
x+
fa
.
x
i
u
Plant modeling: Nominal behaviorHybrid System Model: Statespace + switchingsx
ss
Continuous model:
9 tuple: H=<I, S, f, C, U, f,,h, g, g >
Discrete Model
S:events
Interactions
(State mapping)
(Event generation)
x
g :y(y+) S
Multiple mode transitions may occur at same time point t0
results in
and
which causes
further transitions.
Online Hybrid Observer
Embedded
Switched
Bondgraph
Model
Not necessary to precalculate all
the modes, only the immediate
followup modes are needed.
Generate Current
StateSpace Model
(A,B,C,D)
Highlevel Mode
(Switch settings)
Mode change
Detector
Calculate:
transition conditions,
next states
Recalculate
Kalman Filter
uk,yk
Xk
Kalman Filter
Tank 1
Tank 2
Tank 3
V5
Sf2
Sf1
h1
h2
h3
R23n
H4
H3
R12n
H1
H2
V2
V3
V4
V6
R1
R2
R23v
R12v
15
1,2,3,5,7,8:
ON
soni
soffi
OFF
Plant modeling: Nominal behaviorExample Hybrid system: Three tank model of a Fuel Systemhi = level of fluid in Tank i
Hi = height of connecting pipe
R12v
R23v
4:
ON
14
7
h1 <H1
and
h2<H2
h1H1
or
h2H2
C3
C1
C2
13
20
5
12
13
17
1
2
6
21
9
24
Sf1
Sf2
OFF
11
0
0
1
0
18
10
18
8
15
3
22
14
12
16
17
4
11
16
23
6:
R1
R12n
R23n
R2
ON
h3 <H3
and
h4<H4
h3H3
or
h4H4
6 controlled junctions (1,2,3,5,7,8)
2 autonomous junctions (4,6)
OFF
Tank 1
Tank 2
Tank 3
V5
Sf2
Sf1
h1
h2
h3
R23n
H4
H3
R12n
H1
H2
V2
V3
V4
V6
R1
R2
R23v
R12v
Plant modeling: Nominal behaviorHybrid Observer: Tracking tank levels through mode changesh1
Mode 1: 0 t 10: Filling tanks
v1, v3, & v4 open, v2, v5, & v6: closed
h2
Mode 2: 10 t 20: Draining tanks
v2, v3, v4, & v6 open, v1, & v5: closed
Mode 3: 20 t : Tank 3 isolated
v3 open, all others: closed
: actual measurement
: predicted measurement
h3
u
y
Plant

Nominal
Parameters
Observer and mode detector
ŷ
Hybrid models
Fault
Parameters
mi
progressive monitoring
hypothesis
refinement
hypothesis
generation
Symbol generation
Fault detection
[Binary decision]
r
fh
fh’
Parameter
Estimation
Diagnosis models
Fault Isolation
u = input vector, y = measured output vector, ŷ = predicted output using plant model, r = y – ŷ, residual vector, r= derived residualsmi= current mode, fh = fault hypotheses
ymeas
r
Residual
Generator
yest
FDI for Continuous Dynamic SystemsFault detection:Faults with quantifiable effectsSystem Generation
StateSpace
Models
(A,B,C,D)
Quantitative
Faulteffect
Model
(R1,R2)
Residual
Generator
Design
fh
r
rs
Detect
discrepancy
Generate
faults
Predict
behavior
fh, p
e6 =>R leak , I+radout , Rhyblk
fh
progressive
monitoring
Magnitude: low, high
Slope:below, above normal
discontinuous change
R leak > e6 = < ,+, >
FDI for Continuous Dynamic Systems Qualitative FDIFault Isolation Algorithm
1. Generate Fault Hypotheses: Backward Propagation on Temporal Causal Graph
2. Predict Behavior for each hypothesized fault: Generate Signatures by Forward Propagation
3. Fault Refinement and Isolation: Progressive Monitoring
fh’
fh
True Fault (C1) Other hypothesis (R12)
Multiple Fault Observers
C1
DY6
FM1
DY7
DY12
DY4
FM2
DY5
DY8
DY11
DY3
C2
F2
DY2
FM3
DY9
DY10
FM4
DY1
F1
Failure Mode
Discrepancy
“Alarmed” Discrepancy
Plant modeling: Faulty behaviorFaults with discrete effectsSequence of precursors
leading to a failure mode
Degradations accumulate
to a failure mode
PC1
PC2
FM
DE1
FM
DE2
Degradation
Precursor
Failure mode
Behavioral equation
R1, R2, R3P(A) P(B) relations between subsets of A, B
Relational Product R1 = R2 ; R3 R1= { <a,c>  b <a,b> R2 <b,c> R3 }
Intersection R1 = R2 R3R1 = { <a,b,c>  <a,b> R2 <b,c> R3 }
Superposition R1 = R2R3R1 = { s  (s R2) (s R3)
s2 ,s3 ((s2 R2) (s3 R2) (s =s2 s3)}
Previously
Hypothesized
Set of Alarm
Instances
Previously
Hypothesized
Set of Failure
Modes
All disjunctions
Hk1
P
Any Set of
Failure
Modes
Next
Hypothesized
Set of Alarm
Instances
Set of
Failure Mode
Instances
T
Q
Ringing
Alarms
Hk=( Ak ;Q ) ((Hk1 T) ; P)
4
state zeroing
3
scaled SS
direct form
2
1
0
1
0
50
100
150
200
250
300
350
400
450
500
Time (sec)
Plant output
2
1.5
1
0.5
0
0
50
100
150
200
250
300
350
400
450
500
Time (sec)
4
state zeroing
3
scaled SS
direct form
2
1
0
1
0
50
100
150
200
250
300
350
400
450
500
Time (sec)
Plant output
2
1.5
1
0.5
0
0
50
100
150
200
250
300
350
400
450
500
Time (sec)
4
state zeroing
3
scaled SS
direct form
2
1
0
1
0
50
100
150
200
250
300
350
400
450
500
Time (sec)
Plant output
2
1.5
1
0.5
0
0
50
100
150
200
250
300
350
400
450
500
Time (sec)
4
state zeroing
3
scaled SS
direct form
2
1
0
1
0
50
100
150
200
250
300
350
400
450
500
Time (sec)
Plant output
2
1.5
1
0.5
0
0
50
100
150
200
250
300
350
400
450
500
Time (sec)