SEC PI Meeting

1
Fault-Adaptive 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
2
Objective

• Develop and demonstrate FACT tool suite
• Components
• Hybrid Diagnosis and Mode Identification System
• Discrete Diagnosis and Mode Identification System
• Dynamic Control Synthesis System
• Transient Management System

3
What to model?
4
System Architecture
Tools/components are model-based
5
Plant modeling Nominal behaviorDynamic Physical
Systems

• 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 (CDC99, HS00)
• compositional modeling using switched bond
  graphs
• Summary
• continuous discrete behavior gt hybrid
  modeling

6
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.

7
Plant modeling Nominal behaviorSwitched
Bond-Graph Implementation
Switched Bond-graph Model
Hybrid Observer
Continuous observer
A
yk
uk
B
z-1
C
System Generation
Hybrid Automata Generation
xk
Xk1
m1
m2
Hybrid Automata Model
m3
Mode switching logic
8
Plant modeling Nominal behaviorHybrid System
Model State-space switching

• 9 tuple HltI, S, f, C, U, f,, h, g, g gt
• 
  

sx
ss
Continuous model
Discrete Model

• I modes
• Sevents

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.
9
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

10
Plant modeling Nominal behaviorImplementation
of the observer switching
On-line Hybrid Observer
Embedded Switched Bond-graph Model
Not necessary to pre-calculate all the modes,
only the immediate follow-up modes are needed.
Generate Current State-Space Model (A,B,C,D)
High-level Mode (Switch settings)
Mode change Detector
Calculate transition conditions, next states
Recalculate Kalman Filter
uk,yk
Xk
Kalman Filter
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Plant modeling Nominal behaviorExample Hybrid
system Three tank model of a Fuel System
hi level of fluid in Tank i Hi height of
connecting pipe
R23v
R12v
4
ON
14
7
h1 ?H1 or h2?H2
h1 ltH1 and h2ltH2
C3
C1
C2
13
20
12
5
13
17
21
6
2
1
9
24
Sf1
Sf2
OFF
0
0
0
1
11
18
10
18
8
15
22
3
14
12
16
17
4
11
16
23
6
R1
R2
R12n
R23n
ON
h3 ltH3 and h4ltH4
h3 ?H3 or h4?H4
6 controlled junctions (1,2,3,5,7,8) 2 autonomous
junctions (4,6)
OFF
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Plant modeling Nominal behaviorHybrid Observer
Tracking tank levels through mode changes
h1
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
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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)

14
FDI for Continuous Dynamic Systems Hybrid Scheme
u
y
Plant
-
Nominal Parameters
Observer and mode detector
y
Hybrid models
Fault Parameters
mi
progressive monitoring
Fault detection Binary decision
hypothesis generation
hypothesis refinement
Symbol generation
r?
fh
fh
Parameter Estimation
Diagnosis models
Fault Isolation
u input vector, y measured output vector, y
predicted output using plant model, r y y,
residual vector, r? derived residuals mi
current mode, fh fault hypotheses
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FDI for Continuous Dynamic Systems Fault
detection Faults with quantifiable effects
System Generation
State-Space Models (A,B,C,D)
Quantitative Fault-effect Model (R1,R2)
Residual Generator Design
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FDI for Continuous Dynamic Systems Qualitative
FDI
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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FDI for Continuous Dynamic Systems Quantitative
Analysis Fault Refinement,Degradations
fh
fh
True Fault (C1) Other hypothesis (R12)
Multiple Fault Observers
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Hybrid DiagnosisIssues

• Fault Hypothesis generation back propagates to
  past modes
• Fault behavior prediction has to propagate
  forward across mode transitions
• Mode 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

• Qualitative fault description, propagations

20
Plant modeling Faulty behaviorDegradations and
precursors leading to discrete faults

• Hard/soft failures

Sequence of precursors leading to a failure mode
Degradations accumulate to a failure mode
FM
PC2
PC1
DE1
FM
DE2
Degradation
Precursor
Failure mode
Behavioral equation
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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

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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 lta,cgt ?
  b lta,bgt ? R2 ? ltb,cgt ? R3
• Intersection R1 R2 ? R3 R1 lta,b,cgt lta,bgt
  ? R2 ? ltb,cgt ? 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
Previously Hypothesized Set of Alarm Instances
Previously Hypothesized Set of Failure Modes
All disjunctions
Hk-1
P
Next Hypothesized Set of Alarm Instances
Any Set of Failure Modes
Set of Failure Mode Instances
T
Q
Ringing Alarms
Hk( Ak Q ) ? ((Hk-1 ? T) P)
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Transient ManagementTopics

• Transients in simple cascade compensation control
  loops using a reconfigurable PID controller
• Experimental testbed two-link planar robot arm
  for testing controller reconfiguration transients
  in highly nonlinear control loops
• Preliminary investigation of transients in
  model-based controllers

25
Controller output
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)
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Controller output
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)
27
Controller output
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)
28
Controller output
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)
29
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

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• First-order direct structure

34

• First-order resonator-based structure

35

• Second-order direct structure

36

• Second-order resonator-based structure

37

• Sixth-order direct structure

38

• Sixth-order resonator-based structure