Copyright © Vanderbilt University, Technical University of Budapest

Fault-Adaptive Control TechnologyF33615-99-C-3611 Gabor KarsaiGautam BiswasSherif Abdelwahed, Tivadar SzemethySriram Narasimhan, Tal Pasternak, John Ramirez

Gabor PeceliGyula Simon, Tamas Kovacshazy

Feng ZhaoXenofon Koutsoukos, Jim Kurien

ISIS, Vanderbilt University

Technical University of Budapest, Hungary

Xerox PARC

http://www.isis.vanderbilt.edu/Projects/Fact/Fact.htm

SEC PI Nov 01

Subcontractors & Collaborators

TU Budapest Reconfiguration

Transient Management

Xerox PARC Alternative Hybrid

Diagnostics

Boeing OCP Controller modeling OCP realization

Berkeley Modeling, FDIR

Georgia Tech Reconfiguration

technology

Northrop/Grumman FDIR

SEC PI Nov 01

Problem Description, ObjectiveProblem:To maintain control under fault conditionsTo maintain control under fault conditions

Goal: Technology and tool suite for Fault-Adaptive Control Components:

Modeling approach for capturing Hybrid and discrete models of the plant for both nominal and faulty

behavior Reconfigurable controllers

Mode identification and real-time fault-diagnostics Model-based hybrid and discrete approaches

Model-based dynamic selection/synthesis of regulatory controller structures

Algorithms for mitigating reconfiguration transientsSEC contribution:

Integrated Fault detection, isolation, and reconfigurable control

SEC PI Nov 01

Open Control Platform

Run-time execution environment for hosting:•Monitoring and controller software •Hybrid and discrete diagnostics modules•Controller object library and selector•Transient manager componentUse OCP as the underlying “OS”

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 Embedded

Models

EmbeddedModels

Visual modeling environment for creating:

•Hybrid bond-graph models

•Timed failure propagation graph models

•Controller models (supervisory and regulatory)

Technical Approach SummaryFrom models to a run-time system

SEC PI Nov 01

Hybrid ModelingNew developments

Fault detector specifications Variables –FD-> Alarms

Modulated components [nonlinearity] Variable –MOD-> (R,C,I,Sf,Se,TF,GY)

Controller modeling language SVC + Regulators

SEC PI Nov 01

FINITE AUTOMATON

Hybrid ObserverNew developments

Tracking autonomous changes

Modulated components

Observer is composed automatically from component models

PLANT

CONTROLLER

KALMAN FILTER

2N modes

AUTONOMOUS EVENTS

CONTROL EVENTS

RECALCULATE

HYBRID OBSERVERMODEL

S

EST:xk ,yk

uk yk

N switches

MODE CHANGES

SEC PI Nov 01

Hybrid Diagnosis

Time Line

Mode 1 Mode 2 Mode 3

Mode 4

Mode 5Fault Occurs

Fault Detecte

d

Tracked TrajectoryActual Trajectory

T1 T2 T3 T4 T5 T6

Mode 6

Mode 7

Fault Hypothesis: <mode,parameter>

If controller model is “correct”, fault must have occurred in

one of the modes in the mode trajectory

New Development: Solution of Hybrid Diagnosis problem for piecewise linear hybrid dynamical systems Presence of fault invalidates

tracked mode trajectory

Hypothesized fault mode

Known Controlled TransitionHypothesized

Autonomous Transition

Possible current modes

Hypothesized intermediate modes

Roll Back to find fault hypotheses

Roll Forward to confirm fault hypotheses

Catch up to current system mode to verify hypotheses against measurements

Note: Controller transitions known

Autonomous transitions have to be hypothesized

SEC PI Nov 01

Hybrid Diagnosis Methodology

Tracking, prediction, and analysis of system behavior under fault conditions across discrete mode changes

Deal with parametric faults (multiplicativemultiplicative) that occur as abrupt changes in parameter values

Fault Detection complicated – distinguish between mode change transients and fault transients

Sometimes fault detection occurs after mode change occurs Requires fast roll back process to identify correct model for fault isolation

Issue: What to propagate across mode-change boundaries? To compare against current behavior, fault signatures have to be

generated by a quick roll forward processIssue: Autonomous changes cannot be correctly predicted. Tracking process invokes multiple paths

Parameter estimation Fault isolation refinement Fault magnitude determination

Issues Addressed:

SEC PI Nov 01

Fault Isolation & Identification

From Hybrid Bond

Graphs

RefinedCandidate Set

<fault,mode>current mode

Hypothesis Generation

(Back Propagation)

Candidate Set<fault,mode>

Qualitative Hypotheses Refinement

Forward Prop + Prog Monitoring

Quick Roll Forward

Transfer function Models

Past ModeTrajectory

Temporal Causal Graphs (TCGs)

RefinedCandidate Set

<fault,mode>current mode

Quantitative Hypotheses Refinement

Parameter Estimation

Observations

Signal to SymbolGenerator

Modemi

SEC PI Nov 01

Tank2C2

R3 R6

Tank1

C1 Tank3C3

R4R2

R1R5

Sf1Sf2

- Valve

C – Tank Capacity

R – Pipe Resistance

Sf – Flow Source

Hybrid bond graphs relate parameters to system dynamics

Hybrid System ExampleThree Tank System

hi = level of fluid in Tank i

Hi = height of connecting pipe

SEC PI Nov 01

Roll Back Process

•Qualitative Hypotheses Generation• Back propagate through TCG in current mode to identify candidates

• Back propagate across mode transitions using transition conditions (need to account for reset conditions, and change in plant configuration – invert qualitatively)

• Repeat same process for previous modes to identify more candidates

Fault: Leak in Drain Pipe

- Tank 1 Pressure

- Tank 2 Pressure

- Tank 3 Pressure

Transition

Fault Occurred

Fault Detected

System Autonomous Transition

Current Mode Candidates = C2+(0-+ ,-+- ,000 ), C1+(-+- ,0-+ ,000 ), R1- (0-+ ,00- ,000 ), R12- (0-+ ,0+- ,000 )

Previous Mode Candidates = C1+(-+- ,000 ,000 ), R1- (0-+ ,000 ,000 )

Example 1: Leak in pipe

SEC PI Nov 01

Quick Roll Forward

• Goal: Get to current mode, so parameter estimation can be applied to refine faults and identify fault magnitude

• Lemma: Sequence of k mode transitions in any order drives the system to the same final model

• Requires tracking of transients by progressive monitoringprogressive monitoring in continuous regions of space. Taylor series expansion defines qualitative fault signatures. Residual r(t) after fault can be described as:

• Progressive Monitoring: Match qualitative magnitude and slope of measurement signal transient against fault signature

)(!

)()(...

!2

)()(

!1

)()()()( 0

0

20

00

00 tRk

tttr

tttr

tttrtrtr k

kk

Fault signature: qualitative form of derivatives:

Qualitative form of

)(),....,(),( 000 trtrtr k

)(0),/()( 0 normalnormalbelowabovetr k

SEC PI Nov 01

Quick Roll Forward

• In continuous case, mismatch implies fault hypothesis is not consistent. However, in hybrid tracking, it may imply that we are not in the right mode. We need to identify the current mode (roll forward)identify the current mode (roll forward)

• All controlled transitions are known, but we have to hypothesize autonomous transitions since observer can no longer predict them correctly

• Use fault signatures to hypothesize mode transitions

- Tank 1 Pressure

- Tank 2 Pressure

- Tank 3 Pressure

Transition

Fault Occurred

Fault Detected

System Autonomous Transition

Current Mode Candidates = C1-(+-+ ,000 ,000 ), R1+ (0+- ,000 ,000 )

Signatures don’t match, therefore roll forward by hypothesizing mode transitions

Fault: Partialblock in pipe

Example 2: Block in Pipe

Progressive Monitoring with

Mode Changes

SEC PI Nov 01

Parameter Estimation (Real Time)

Derive transfer function model in current mode

derived from TCG (signal flow graph) using Mason’s gain rule. (Computational Complexity: Linear

in number of loops)

...,2,1,1 ),()(

)()(

1

kyituzh

zgty kj

u

j

ij

ki

2221212112121

1

1222212111

2

122112

2211221

1

111

731

1111111

1

111

},{},{

RRCCRRCCRRCCz

RCRCRCRCzh

RCCg

RCCRCCz

Cg

efyfu

Parameterized (symbolic)

Transfer Function Model of

Three Tank System

SEC PI Nov 01

Parameter Estimation (Real Time)

Initiate fault observer filter for each fault hypothesissubstitute nominal values for all but the faulty parameter

Initiate least squares estimator for parameter estimationcompute parameter values from g and h estimates. Check consistency

Test for convergence as more measurements obtained identifies true fault candidateconsistency implies predicted parameter value substituted into model again tracks system accurately

SEC PI Nov 01

Discrete Diagnostics AlgorithmNew developments

Correct diagnosis of graphs with loopsDiagnostics with ranked hypothesesStarted: Discrete diagnostics for hybrid systems

The FPG structure is dependent on the mode

RefineHypothesis(set Alarms) { static set NewFailureModes, NewMissingUpstream, MissingAncestors, PromotedNewFailureModes; const static map Descendant, Ancestor; NewFailureModes = RelationalProduct(Descendant,Alarms) && (-Hypotheses); Hypotheses |= NewFailureModes; // Add NewFailureModes to hypothesis set MissingAncestors = (RelationalProduct(Alarms,Ancestor) && (-MissingUpstream) && (-AlreadyRinging)); NewMissingUpstream = RelationalProduct(Hypotheses,Descendant) && MissingAncestors; MissingUpstream |= NewMissingUpstream; AlreadyRinging |= Alarms; // Increment rank of faults which have new supporting alarms and no new missing upstream alarms PromotedNewFailureModes = RelationalProduct(Descendant,Alarms) &&

(-RelationalProduct(Descendant,NewMissingUpstream));}

SEC PI Nov 01

Descendants:FModes X Alarms

AlarmsAlarms

X &

-

Hypo

U Hypo’Hypo’

Ancestors:Alarms X Alarms

X

MissingUpstream

AlreadyRinging

&

- -

&Missing

Upstream’U

AlreadyRinging’U

X

&PromotedFModes

PromotedFModes

Discrete Diagnostics AlgorithmAlgorithm flow

SEC PI Nov 01

Combine the results of multiple (2) diagnostic reasonersMaps the specific hypotheses into Bond Graph elements

Intersecting subsets(Listed by ANY(Listed by EACH(TopRank by ANY(TopRank by EACH

Agreement: when ||

Fusion algorithmIntegrating the hybrid and discrete diagnostics

All dynamic data (incl. diagnostics results) is available via the Active State Model

SEC PI Nov 01

Controller ReconfigurationModel

Problem SettingThe SystemA hybrid system H with:• Linear cont. dynamics: fq = Aqx+Bqu• Piecewise-linear (PL) discrete constraints: Invq, Initq, Gq,q’ are PL

The specificationthe system has to remain in a given safe region defined by a set of PL constraints.

PiecewiseLinearHybrid System

Configurationengine

Diagnoser

Observer

•detects faulty components• provides the current value of the system parameters • provides enough information to observe the current state

Controller

• compute the current system state• adjust the controller for the new system parameters • assumes finite control policies• provide stable and efficient transitions between controllers

components

measurements

of variables,

states parametersupdate

control

input

SensorsAlarms

Samplers

SwitchesValves

Regulators

SEC PI Nov 01

Current systems data

Hybrid System

Controller Synthesis

Discrete Abstraction• Divide the state space into finite set of regions • In any region, the system can be driven to the adjacent regions

Supervisory Control• based on the abstract state machine obtained by the partition • it is required to move the system from current region to safe region• movement is based on the discrete supervisor

Continuous Control• continuous controller is established for each region• drive the system from a region to the guard (surface) of the next one.

Hybrid model parameters

current discrete state

current continuous state

Global discreteobserver

Local continuousobserver

discrete input

continuous input

global abstract control

local detailed control

Discrete andcontinuousdiagnoser

Controller ReconfigurationApproach

SEC PI Nov 01

Curr

ent

Focu

s

Controller:

• <S, P, x> • Parameter Design Procedures• Resource Requirements

- run-time cost- design proc cost- reconfiguration cost

• Performance metrics•Settling time, overshoot

• Reconfiguration Support•Initial state •Injection sequence

S: signal flow graphP: parameter setx: state variables

Services are used:

- off-line (design-time) by system designer- on-line (run-time) by designer/constructor algorithms

Transient managementReconfigurable controller description

SEC PI Nov 01

Curr

ent

Focu

s

The Supervisory Controller supports the following Controller specification techniques:

• Set <S, P> given

• Design S given, P calculated based on control objective

• ConstructSelect from given {Si} <Sopt, Popt> based on control objective

[Initial values for x are calculated by the Transient Management Algorithm]

Transient managementController specification in SVC

SEC PI Nov 01

[Controller Services]

Curr

ent

Focu

s

Construct decision making: Constraint satisfaction (optimization) based on

• Performance requirements• Resource requirements

Performance specifications[Supervisory Controller]

Available resources[Current System State]

Resource requirements Performance metrics

Transient managementController description hierarchy

Abstract controller (root)Controller variantsPhysical realizations (HW/SW)

SEC PI Nov 01

Real-life example:Aircraft Fuel System

Obtained engineering documents and simulation data from BoeingBuilt Hybrid Bond Graph model of the systemStarted testing the HOBS and DIAG components using simulated data

SEC PI Nov 01

Schematic of Fuel Transfer Systems and GME model

JoinFour

LWTP

Component-Based Hierarchical GME Model

Fuel Transfer Schematic

Symmetric Transfer and Wing tanks

Two Feed Tanks that supply fuel to engine

Controller maintains fuel supply and CG of aircraft

Behavior: Complex Hybrid Dynamics

Multiple pumps and pathways to accommodate pump failure and leaks

SEC PI Nov 01

Fuel Transfer Schematic and Bond Graph

Hybrid Bond Graph Model of System

Hybrid Bond Graph: Topological Model of energy + signal model f system

Captures hybrid state space + temporal causal model of system dynamics

Faults parameterized in representation

(pump failures + pipe and tank leaks + valve failures)

Used for hybrid observer + fault detection, isolation, and identification

Enables tracking of system behavior in nominal plus faulty modes of operation

SEC PI Nov 01

Project Tasks/Schedule/Status

2000 2001 2002 2003

Lab prototype Prototype HOBs, TCGFPG diag,

Transient mgmt tech

Embeddable version ControllerModeling

Reconfig mgr

Embedded version

Plant Modeling

Framework

1st OCP Integration

Analysis technologyAnalysis technology

Analysis tools:Diagnosability (FPG)Feasibility (HYB)Consistency/completeness (RC)

SEC PI Nov 01

Next MilestonesNext 6 months

Implement CML run-time support Hierarchical FSM for supervisory control Regulator blocks (OCP components)

Finish improved discrete diagnosticsImplement prototype controller selectorTrials on the A/C fuel systemIntegrate on OCPIntegrate with Xerox

SEC PI Nov 01

Technology Transition/Transfer

Boeing IVHM Group Aircraft Fuel System models (DEMO) Testing fault diagnostics using simulated data

(provided by Boeing) Plan: Develop a full FACT application using the

fuel system as example

GE Aircraft Engines First contact with their Advanced Controls

group Potential collaborations

NASA Intelligent System Group Recently started project Application area: advanced life-support system

SEC PI Nov 01

Program Issues

PARC integration workOCP: Specific challenge problem(s) Precise documentation

Transfer to other DoD programs

SEC PI Nov 01

Pump

GO BACK

SEC PI Nov 01

LWTP

Pump Pipe1

Tank

GO BACK

SEC PI Nov 01

Tank

GO BACK

SEC PI Nov 01

Pipe

GO BACK

SEC PI Nov 01

JoinFour

GO BACK