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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. Objective. Develop and demonstrate FACT tool suite - PowerPoint PPT Presentation
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SEC PI Meeting10/00
Fault-Adaptive Control Technology
Gabor KarsaiGautam BiswasSriram NarasimhanTal PasternakGabor PeceliGyula SimonTamas KovacshazyFeng Zhao
ISIS, Vanderbilt University
Technical University of Budapest, Hungary
Xerox PARC
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Objective
Develop and demonstrate FACT tool suiteComponents: Modeling approach Hybrid Diagnosis and Mode Identification
System Discrete Diagnosis and Mode Identification
System Dynamic Control Synthesis System Transient Management System
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Model-based Approach
ModelingEnvironment
ModelDatabase
Run-time Environment•Hybrid/Discrete Diagnostics•Controller selection•Transient management•Run-time platform (OCP)
•Design-time and run-time activities are separated
•Technology target: run-time SW
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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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Run-time 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
EmbeddedModels
EmbeddedModels
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Modeling language summarySystem [plant] models
Physical components and assemblies Aspects:
Structure: hierarchy and interconnectivity Bond graph: quantitative/discrete nominal behavior,
discrepancies Local failures: failure modes, discrepancies,alarms Failure propagations: causal chain of events
Failure models Fine-grain: parametric failures in terms of bond-graph parameters Large-grain: (discrete) failure modes and their functional effects
(discrepancies) Multi-modal behavior
Switched junctions in the bond graph model Discrete modes in failure propagation graphs
Component types and system instances
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Modeling language summary
Functional models Modes contain Capabilities that reference
Parameters in Components
Controller models Hierarchical signal flow blocks
TBD: Sensor/actuator interfaces Controller characterization
Conditions for using a controller architecture
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Continuous behavior is interspersed with discontinuities Discontinuities attributed to
supervisory control and reconfiguration (fast switching) modeling abstractions (parameter & time-scale)
Modeling language based on hybrid bond graphs (Jour. Franklin Inst. ‘97) Bond graphs for energy-based modeling of
continuous behavior Switching junctions model controller and
autonomous jumps systematic principles: piecewise linearization
around operating points & derive transition conditions (CDC’99, HS’00)
Plant modeling: Nominal behaviorDynamic Physical Systems
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Plant modeling: Nominal behaviorExample Hybrid system: Three tank model of a Fuel System
ON
OFF
1,2,3,5,7,8:
soffi soni
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
C1 C2 C3
R2R12n R23n
7
h3 H3
orh4H4
ON
OFF
h1 H1
orh2H2
ON
OFF
4:
h1 <H1
andh2<H2
13 15
14
Sf1 Sf20 0 01
R1
21
22
2012
8
6
4
3
2111
1412
18
16 17
6:
59
10
11
13
15
16
17
18
23
24
6 controlled junctions (1,2,3,5,7,8)
2 autonomous junctions (4,6)
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Application example: Fuel System Control for Fighter/Attack Aircraft
P
P
PP
PP
P PLV
LV
IV IV
BP
BP
FM
FM
P Transfer Pump
LV Level Control ValveIV Interconnect Valve
BP Boost PumpFM Flow Meter
Fuel Quantity Sensor
Left Transfer Tank
Right Transfer Tank
Left Wing Tank
Right Wing Tank
Left FeedTank
Right FeedTank
Left Engine
Right Engine
Typical Fuel System Configuration
FEED
INTER-CONNECT
TRANSFER
Problems:•Maintain fuel flow to the engines•Maintain A/C center of gravity•Affected by modes of operation: attack, cruise,take-off, and landing•Compensate for component degradations and failures
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Simplified Fuel System Schematics
PumpTransferTank
FM
Pump
WingTank
Feed Tank Pump
Load(Engine
)
Detailed Model of AC Pump
One Side Only
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Hybrid Bond Graph Model (Simplified Fuel System)
Sfn
TF 0 131
1
Im1
2
RR1
Im2
MGY
a
45
67
8
Bond Graph Fragment: AC Pump
PumpBG Fragment
0
1Imp2
RRp3
CCW
PumpBG Fragment 10
Imp1
RRp1
CCTR
RRp2
0
1R
Rp4
RRp4
RRLoad1
Imp3
CCF
PumpBG Fragment
0 1
Controlled JunctionLevel Control Valve
Fuel System BG: one side
(valves – controlled junctions not shown)
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Plant modeling: Nominal behaviorUsing the Hybrid Bond-Graph
HybridBond-graph
Model
HybridBond-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
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Plant modeling: Nominal behaviorImplementation of the hybrid observer
EmbeddedHybrid
Bond-graphModel
EmbeddedHybrid
Bond-graphModel
Generate CurrentState-Space Model
(A,B,C,D)
RecalculateExtended Kalman Filter
Extended Kalman FilterExtended
Kalman Filter
uk,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)
Implement continuous +
switching behavior
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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
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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
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Diagnosis results
Measured variables e10 and f3 under fault conditions
.3
. 010
f
eactual
- - 3
- 0 01012
f
eR
- - 3
- - 0102
f
eC
- 03
01023
f
eR
- - 3
- 0 0101
f
eC
- 03
- -103
f
eC
- 0 03
- - 010
f
eRb
3
. 010
f
eactual
- - 3
- 0 01012
f
eR
- - 3
- 0 0101
f
eC
3
. 10
f
eactual
- - 3
- 0 01012
f
eR
- - 3
- 0 0101
f
eC
- - 3
- - 0102
f
eC
Qualitative diagnosis results
Step 0 Step 1 Step 2
For more details: see (i) Mosterman and Biswas, IEEE SMC’99
& (ii) Manders, Narasimhan, Biswas, & Mosterman, Safeprocess 2000.
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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
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Discrete Fault ModelsTimed Failure Propagation Graph
Failure Mode
Discrepancy
D +Alarm
Sensor
Time Interval
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Discrete Fault ModelsGraphical Representation in GME
Propagation Attributes:•Time delay•Likelihood
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Discrete Fault ModelsResearch Issues: Managing complexity in models
Locality: Some phenomenon are not local (e.g. fire in the
engine) or are a composite of local phenomena To provide useful information the diagnosis must
trace failures to individual components Failure Modes are attributes of components
Hierarchy For scalability it is important that the model
accommodates diagnosis with different resolution An FPG at one level will often incorporate Failure
Modes of components at a lower level
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Discrete Fault ModelsResearch Issues: Semantics of models
Failure Mode: A condition of a component, which manifests in
abnormal behavior. Structural defect: parameter deviation Failure modeled as “input”
Discrepancy: An abnormal change in system state
Transition into abnormal state Normal state, but abnormal transition
Fault Propagation: Ordering of events Where an event is a region in the extended system state space
Input x State x Next State
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Discrete Fault ModelsResearch Issues: Expressing Constraints and
Interactions Incompatibility
When symptoms (or causes) can not co-occur (stuck_open stuck_closed)
Additivity When the combination of effects produces an extra
effect (primary and backup fail)
Cancellation When effects negate, decrease, or mask each other
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Discrete Fault ModelsResearch Issues: TFPG, FSM and Diagnostics
A model of a system as a timed (non-deterministic) Finite State Automata provides sufficient information to draw the full TFPGDiagnosis can be performed using a partial TFPG model of the system
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Discrete Fault ModelsResearch Issues: Implementing the Discrete Diagnostics
Extended Relational Algebra Relational Algebra is used in databases to
manipulate relations Extended Relational Algebra allows nested relations This allows to model logical constraints involving
arbitrary logical expressions
Role Discrete fault models as FSM-s The complex state transition function of FSM-s can
be represented using the Extended Relational Algebra and OBDD-s as the physical data structure
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Component Digraph
A link represents the fact that the faulty operation of the source component results in the faulty operation of the destination componentA Transition Event represents the cause and nature of the change: <triggering event, current state, next state>Failure Propagation Graph links each transition event to its immediate successor. Only failure trajectories are represented
Discrete Fault ModelsRelating an FPG to FSM
FlowController
Flow SensorPipeValve
V
FC
FS P
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Discrete Fault ModelsRelating an FPG to FSM: Example
Controller
FlowIndicator
PressureSensor
SC
VC VO
VE, VD
VE
F1 F1
VD VD
C2
C1 C3
C4
VE
VD
PE
PD
Pump
Controller
Valve
POFF PON
PD PE
PD
PE
FON
F2F2
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Discrete Fault ModelsRelating an FPG to FSM: Composed FSM
1 = (C1,nf,np)
2 = (C2,nf,np)
3 = (C3,f,pp) 4 = (C4,nf,np)
3 = (C3,nf,pp)
1 = (C1,nf,pp)
2 = (C2,f,pp) 4 = (C4,f,pp)
2 = (C2,nf,pp)
4 = (C4,nf,pp)
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10,11 11,12
1,5
{pp}{pp}
{nf}
{F1}
4,8
{nf}
{F1}
3,7
{nf,pp}
{F1}
7,8
{nf}
6,7
{nf,pp}
9,13
{F1}
{nf,pp}
12,16
{nf,pp}
{F1}11,15
{nf,pp}
{F1}
1,9
{nf,pp}
{F2}
2,10
{pp}
{F2}
6,14
{pp}
{F2}
8,16
{nf,pp}
{F2}
{nf}
2,6
{F1}
7,15
{nf,pp}
{F2}
{pp}
4,12
{F2}
3,11
{pp}
{F2}
9,10
{pp}
10,14
{pp}
{F1}
{F2}
5,13
{nf,pp}
15,16
{nf,pp}
13,14{pp}
5,6
{nf}
14,15
{nf,pp}
Discrete Fault ModelsRelating an FPG to FSM: FPG
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Discrete Fault Models Diagnosis using Extended Relational Models
Contents of the hypothesis set: State (Which nodes are we “in”) Failure modes (Which got us “here”)
All combinationsPreviously
HypothesizedSet of Alarm
Instances
RingingAlarms
Next HypothesizedSet of Alarm
Instances
PreviouslyHypothesizedSet of Failure
Modes
Any Set of Failure Modes
Set of Failure Mode
Instances
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Discrete Fault Models Summary
Extended Relational Models offer a general formalism to express causality relations between failures and their symptoms, as well as constraints, interactions and compositionExtended Relational Models can also represent ordering of transition events in a dynamic systemFailure Propagation Graphs have been disambiguated by redefining them with a precise mapping to the Extended Relational Model
See MSc thesis of Tal Pasternak on ISIS website
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Towards an OCP implementation:Model-based software generation
Software models:• Controllers • Datatypes• Architectures
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PlansVanderbilt/ISIS Improve modeling language Finish implementing Hybrid Diagnostics Develop controller selection component Fuel system example Integration with OCP
Technical University of Budapest Transient management techniques Controller examples
Xerox/PARC Data processing for fault detection
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