SEC PI Meeting06/00
Fault-Adaptive Control Technology
Gabor KarsaiGautam BiswasSriram NarasimhanTal PasternakGabor PeceliGyula SimonTamas KovacshazyFeng Zhao
ISIS, Vanderbilt University
Technical University of Budapest, Hungary
Xerox PARC
SEC PI Meeting06/00
Objective
Develop and demonstrate FACT tool suiteComponents: Hybrid Diagnosis and Mode Identification
System Discrete Diagnosis and Mode Identification
System Dynamic Control Synthesis System Transient Management System
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What to model?
Plant Model
Nominal Model
Fault Model
Observation Model Control Model
What and how to observe? What and how to control? How sensors and
controllers are related?
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System Architecture
Reconfigurable Monitoring and Control System
Hybrid Observer
Hybrid Diagnostics
Failure Propagation Diagnostics
Active Model
Controller Selector
Monitor/ Controller
Library
Transient Manager
Reconfiguration Controller
Fault Detector
Tools/components are model-based
SEC PI Meeting06/00
Continuous behavior is mixed with discontinuities Discontinuities attributed to
modeling abstractions (parameter & time-scale) 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 Systems
SEC PI Meeting06/00
Plant modeling: Nominal behavior
Switched bond-graphs Bond-graph: energy-based model of
continuous plant behavior in terms of effort & flow variables (effort x flow = power),
Switched bond-graph: introduce switchable (on/off) junctions for hybrid modeling
components (R,I,C), transformers and gyrators, junctions, effort and flow sources.
SEC PI Meeting06/00
Plant modeling: Nominal behaviorSwitched Bond-Graph Implementation
SwitchedBond-graph
Model
SwitchedBond-graph
Model
Hybrid AutomataGeneration
HybridAutomata
Model
Hybrid Observer
B z-1 C
A
xk
Xk+1
yk
uk
m3
m1 m2
Mode switching logic
Continuous observer
System Generation
SEC PI Meeting06/00
Plant modeling: Nominal behaviorHybrid System Model: State-space + switching
9 tuple: H=<9 tuple: H=<UUffhh g g>> x s
x
Continuous model:
))(x(t),u(thyiα
))(),(( tutxfxi
Discrete Model
II :I: modes
events
Interactions XIXg :
y(y+)
Multiple mode transitions may occur at same time point t0
ji results in g(x)x and ),( uxhyi which causesfurther
transitions.
f
g
h
yy+
x+
u
. xi
j
i
x+
(State mapping)(Event generation)
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Plant modeling: Nominal behaviorNon-autonomous mode switching
Operation mode changes High-level user mode switching Low-level component/subsystem switching
Mapping of high-level control commands into low-level switching actions
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Plant modeling: Nominal behaviorImplementation of the observer switching
EmbeddedSwitched
Bond-graphModel
EmbeddedSwitched
Bond-graphModel
Generate CurrentState-Space Model
(A,B,C,D)
RecalculateKalman Filter
Kalman FilterKalman Filteruk,yk Xk
Calculate: transition conditions,
next states
On-line Hybrid Observer
Mode change
Detector
Not necessary to pre-calculate all the modes, only the immediate follow-up modes are needed.
High-level Mode
(Switch settings)
SEC PI Meeting06/00
Plant modeling: Nominal behaviorExample Hybrid system: Three tank model of a Fuel System
ON
OFF
1,2,3,5,7,8:
soffisoni
R23v
hi = level of fluid in Tank i
Hi = height of connecting pipe
V1 V5Tank 1 Tank 2 Tank 3
h1 h2 h3
H1 H2
H3H4
V2 V3 V4 V6R1 R2
Sf1 Sf2
R12v
R12n
R23n
R23v
h3 <H3
andh4<H4
R12v
Sf1 Sf20 0 01
C1 C2 C3
R1 R2R12n R23n
21
22
2012
8
7
6
4
3
2111
1412
18
16 17
h3 H3
orh4H4
ON
OFF
6:
h1 H1
orh2H2
ON
OFF
4:
h1 <H1
andh2<H25
13 15
910
11
13
14
15
16
17
18
23
24
6 controlled junctions (1,2,3,5,7,8)
2 autonomous junctions (4,6)
SEC PI Meeting06/00
Plant modeling: Nominal behaviorHybrid Observer: Tracking tank levels through mode changes
Mode 1: 0 t 10: Filling tanks v1, v3, & v4 open, v2, v5, & v6: closed
Mode 2: 10 t 20: Draining tanksv2, v3, v4, & v6 open, v1, & v5: closed
Mode 3: 20 t : Tank 3 isolatedv3 open, all others: closed
h1
h2
h3
: actual measurement
: predicted measurement
V1 V5Tank 1 Tank 2 Tank 3
h1 h2 h3
H1 H2
H3H4
V2 V3 V4 V6R1 R2
Sf1 Sf2
R12v
R12n
R23n
R23v
SEC PI Meeting06/00
Plant modeling: Faulty behaviorFault categories
Sensor/actuator/parameter faults Quantitative description
Component failure modes Qualitative description
Hard/soft failures Precursors and degradations
Failure propagations Analytic redundancy (quantitative) Causal propagation (qualitative) Cascade effects (discrete event) Secondary failure modes (discrete) Functional impact (discrete)
SEC PI Meeting06/00
fh’
u
Observer and mode detector
Planty
r
ŷ
Fault detection[Binary decision]
mi
u = input vector, y = measured output vector, ŷ = predicted output using plant model, r = y – ŷ, residual vector, r= derived residuals mi = current mode, fh = fault hypotheses
Hybrid models
Diagnosis models
hypothesis
generation
hypothesis
refinement
progressive monitoring
Fault Isolation
-NominalParameters
FaultParameters
Symbol generation
fh
FDI for Continuous Dynamic Systems Hybrid Scheme
ParameterEstimation
SEC PI Meeting06/00
FDI for Continuous Dynamic Systems Fault detection: Faults with quantifiable effects
State-Space Models
(A,B,C,D)
Quantitative Fault-effect
Model(R1,R2)
ResidualGenerator
Design
ResidualGenerat
or
ymeas
yest
r
System Generation
SEC PI Meeting06/00
FDI for Continuous Dynamic Systems Qualitative FDI
Detect discrepancy
Generatefaults
Predictbehavior
progressive
monitoring
r rsfh
fh, p
fh
Magnitude: low, highSlope:below, above normal discontinuous change
e6- =>R -
leak , I+rad-out , R-
hy-blk
R -leak --> e6 = < -,+,- >
Fault 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
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G en erate P aram eter izedS ta te E q u ation M od e l
P aram eter E st im ation(S y stem IDm eth o d s)
D ecis io nP roced u re
FDI for Continuous Dynamic Systems
Quantitative Analysis: Fault Refinement,Degradations
True Fault (C1) Other hypothesis (R12)
fh
fh’
Multiple Fault Observers
SEC PI Meeting06/00
Hybrid DiagnosisIssues
Fault Hypothesis generation back propagates to past modesFault behavior prediction has to propagate forward across mode transitionsMode identification and fault isolation go hand in hand -- need multiple fault observers tracking behavior till true fault is isolated.Computationally intensive problem
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Plant modeling: Faulty behaviorFaults with discrete effects
FM1
FM2
FM3
FM4
C1
DY4
DY3
DY6 DY7
DY8DY5
DY2
DY1DY9 DY10
DY11
DY12
C2
Failure Mode Discrepancy “Alarmed” Discrepancy
F1
F3
F2
Qualitative fault description, propagations
SEC PI Meeting06/00
Plant modeling: Faulty behaviorDegradations and precursors leading to discrete faults
Hard/soft failures
Degradation
Precursor
Failure mode
DE1
Behavioral equation
DE2
FM
FM
Degradations accumulate to a failure mode
PC2PC1Sequence of precursors leading to a failure mode
SEC PI Meeting06/00
Plant modeling: Faulty behaviorOBDD-based discrete diagnostics
•OBDD-based reasoning can rapidly calculate next-state sets (including non-deterministic transitions)
•All relations are represented as Ordered Binary Decision Diagrams
SEC PI Meeting06/00
OBDD-based discrete diagnosticsRelations Between Sets
R1, R2, R3 P(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 R3 R1 = { <a,b,c> | <a,b> R2 <b,c> R3 }
Superposition R1 = R2 R3 R1 = { s | (s R2) (s R3)
s2 ,s3 ((s2 R2) (s3 R2) (s =s2 s3 )}
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OBDD-based discrete diagnostics Hypothesis Calculation
Hk=( Ak ; Q ) ((Hk-1 T) ; P)
All disjunctionsPreviously HypothesizedSet of Alarm
Instances
RingingAlarms
Next HypothesizedSet of Alarm
Instances
P
Hk-1
PreviouslyHypothesizedSet of Failure
Modes
T
Any Set of Failure Modes
Set of Failure Mode
Instances
Q
SEC PI Meeting06/00
Transient ManagementTopics
Transients in simple cascade compensation control loops using a reconfigurable PID controllerExperimental testbed: two-link planar robot arm for testing controller reconfiguration transients in highly nonlinear control loopsPreliminary investigation of transients in model-based controllers
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0 50 100 150 200 250 300 350 400 450 500-1
0
1
2
3
4
Time (sec)
Controller output
state zeroingscaled SS direct form
0 50 100 150 200 250 300 350 400 450 5000
0.5
1
1.5
2
Time (sec)
Plant output
SEC PI Meeting06/00
0 50 100 150 200 250 300 350 400 450 500-1
0
1
2
3
4
Time (sec)
Controller output
state zeroingscaled SS direct form
0 50 100 150 200 250 300 350 400 450 5000
0.5
1
1.5
2
Time (sec)
Plant output
SEC PI Meeting06/00
0 50 100 150 200 250 300 350 400 450 500-1
0
1
2
3
4
Time (sec)
Controller output
state zeroingscaled SS direct form
0 50 100 150 200 250 300 350 400 450 5000
0.5
1
1.5
2
Time (sec)
Plant output
SEC PI Meeting06/00
0 50 100 150 200 250 300 350 400 450 500-1
0
1
2
3
4
Time (sec)
Controller output
state zeroingscaled SS direct form
0 50 100 150 200 250 300 350 400 450 5000
0.5
1
1.5
2
Time (sec)
Plant output
SEC PI Meeting06/00
Conclusions
Summary Experimental hybrid observer Prototype discrete diagnostics algorithm First cut of model building tool Transient management experiments
Finish modeling tool Develop integrated software Controller selection component Integrated demonstration Cooperation with Boeing IVHM
Fuel system example
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Backup slides
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Plant modeling: Nominal behaviorHybrid Observer for Tracking Behavior
Switched Bond-Graph Implementation Algorithmically generate a hybrid automata
from the switched bond-graph. The states of the HA will represent the discrete mode-space of the plant
Derive standard state-space models for each mode and use a standard observer (e.g. Kalman filter) to track the plant in that mode
When a mode-change happens, switch to a new observer
SEC PI Meeting06/00
Z-1
u(n) y(n)
a1
b0
b1
x(n)
x(n+1)
Z-1
u(n)
y(n)
r0-1
w0
d
x(n+1)
x(n)
If u n( )1 for n,
then x na
( )1
1 1as n.
If un( )1 for n,then xn( )1as n.
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First-order direct structure
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First-order resonator-based structure
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Second-order direct structure
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Second-order resonator-based structure
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Sixth-order direct structure
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Sixth-order resonator-based structure