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

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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

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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.

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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)

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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:

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)

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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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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

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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

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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

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

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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