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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

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fault adaptive control technology

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
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
system architecture
System Architecture

Tools/components are model-based

plant modeling nominal behavior dynamic 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 (CDC’99, HS’00)

compositional modeling: using switched bond graphs

Summary:

continuous + discrete behavior => hybrid modeling

Plant modeling: Nominal behaviorDynamic Physical Systems
plant modeling nominal behavior
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.

plant modeling nominal behavior switched bond graph implementation
Plant modeling: Nominal behaviorSwitched Bond-Graph Implementation

Switched

Bond-graph

Model

Hybrid Observer

Continuous observer

A

uk

yk

System Generation

B

z-1

C

Hybrid Automata

Generation

Xk+1

xk

m1

m2

Hybrid

Automata

Model

m3

Mode switching logic

plant modeling nominal behavior hybrid system model state space switching

f

g

y+

y

a

j

ha

i

x+

g

x+

fa

.

x

i

u

Plant modeling: Nominal behaviorHybrid System Model: State-space + switching

sx

ss

Continuous model:

9 tuple: H=<I, S, f, C, U, f,,h, g, g >

Discrete Model

  • I: modes

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.

plant modeling nominal behavior non autonomous mode switching
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
plant modeling nominal behavior implementation of the observer switching
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

plant modeling nominal behavior example hybrid system three tank model of a fuel system

V1

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 System

hi = level of fluid in Tank i

Hi = height of connecting pipe

R12v

R23v

4:

ON

14

7

h1 <H1

and

h2<H2

h1H1

or

h2H2

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

h3H3

or

h4H4

6 controlled junctions (1,2,3,5,7,8)

2 autonomous junctions (4,6)

OFF

plant modeling nominal behavior hybrid observer tracking tank levels through mode changes

V1

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 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

plant modeling faulty behavior fault categories
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)
fdi for continuous dynamic systems hybrid scheme
FDI for Continuous Dynamic SystemsHybrid Scheme

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

fdi for continuous dynamic systems fault detection faults with quantifiable effects

ymeas

r

Residual

Generator

yest

FDI for Continuous Dynamic SystemsFault detection:Faults with quantifiable effects

System Generation

State-Space

Models

(A,B,C,D)

Quantitative

Fault-effect

Model

(R1,R2)

Residual

Generator

Design

fdi for continuous dynamic systems qualitative fdi

fh

r

rs

Detect

discrepancy

Generate

faults

Predict

behavior

fh, p

e6- =>R -leak , I+rad-out , R-hy-blk

fh

progressive

monitoring

Magnitude: low, high

Slope:below, above normal

discontinuous change

R -leak --> e6 = < -,+,- >

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

fdi for continuous dynamic systems quantitative analysis fault refinement degradations
FDI for Continuous Dynamic Systems Quantitative Analysis: Fault Refinement,Degradations

fh’

fh

True Fault (C1) Other hypothesis (R12)

Multiple Fault Observers

hybrid diagnosis issues
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
plant modeling faulty behavior faults with discrete effects

F3

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 effects
  • Qualitative fault description, propagations
plant modeling faulty behavior degradations and precursors leading to discrete faults
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

PC1

PC2

FM

DE1

FM

DE2

Degradation

Precursor

Failure mode

Behavioral equation

plant modeling faulty behavior obdd based discrete diagnostics
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
obdd based discrete diagnostics relations between sets
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  R3R1 = { <a,b,c> | <a,b>  R2  <b,c>  R3 }

Superposition R1 = R2R3R1 = { s | (s  R2)  (s  R3) 

 s2 ,s3 ((s2  R2)  (s3 R2)  (s =s2 s3)}

obdd based discrete diagnostics hypothesis calculation
OBDD-based discrete diagnostics Hypothesis Calculation

Previously

Hypothesized

Set of Alarm

Instances

Previously

Hypothesized

Set of Failure

Modes

All disjunctions

Hk-1

P

Any Set of

Failure

Modes

Next

Hypothesized

Set of Alarm

Instances

Set of

Failure Mode

Instances

T

Q

Ringing

Alarms

Hk=( Ak ;Q )  ((Hk-1  T) ; P)

transient management topics
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
slide25

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)

slide26

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)

slide27

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)

slide28

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)

conclusions
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
plant modeling nominal behavior hybrid observer for tracking behavior
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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