Neural Network-Based State Estimation of Nonlinear Systems: Application to Fault Detection and Isolation

165 Pages·2010·7.149 MB·English

by  Heidar A. Talebi, Farzaneh Abdollahi, Rajni V. Patel, Khashayar Khorasani (auth.)

Lecture Notes
in Control and Information Sciences 395
Editors:M.Thoma,F.Allgo¨wer,M.Morari
Heidar A. Talebi, Farzaneh Abdollahi,
Rajni V. Patel, Khashayar Khorasani
Neural Network-Based State
Estimation of Nonlinear
Systems
Application to Fault Detection and Isolation
123
SeriesAdvisoryBoard
P.Fleming,P.Kokotovic,
A.B.Kurzhanski,H.Kwakernaak,
A.Rantzer,J.N.Tsitsiklis
Authors
HeidarA.Talebi FarzanehAbdollahi
DepartmentofElectricalEngineering DepartmentofElectricalEngineering
AmirkabirUniversityofTechnology AmirkabirUniversityofTechnology
424HafezAve. 424HafezAve.
15914Tehran 15914Tehran
Iran Iran
[email protected] f [email protected]
RajniV.Patel KhashayarKhorasani
DepartmentofElectrical&Computer DepartmentofElectrical&Computer
Engineering Engineering
UniversityofWesternOntario ConcordiaUniversity
1151RichmondStreetNorth 1455MaisonneuveBlvd.
LondonONN6A5B9 West,EV005.126
Canada MontrealQCH3G1M8
[email protected] Canada
[email protected]
ISSN0170-8643 e-ISSN1610-7411
ISBN978-1-4419-1437-8 e-ISBN978-1-4419-1438-5
DOI10.1007/978-1-4419-1438-5
SpringerNewYorkDordrechtHeidelbergLondon
LibraryofCongressControlNumber:2009940450
(cid:2)c SpringerScience+BusinessMedia,LLC2010
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Preface
Thestateofaprocessspecifiesitsbehavior,andmanycontrolschemessuchasin-
versedynamicsandfeedbacklinearizationrelyontheavailabilityofallthesystem
states.However,inmanypracticalsystemsonlytheinputandoutputofasystemare
measurable.Therefore,estimatingthestatesofasystemplaysacrucialroleinmon-
itoringtheprocess,detectinganddiagnosingoffaults,andachievingbetterperfor-
mance. Furthermore, most practical systems are nonlinear, and using linearization
or quasi-linearization methods limits the estimation accuracy to a small dynamic
range.Severalconventionalnonlinearobservershavebeenproposedduringthepast
coupleofdecades.However,mostofthisworkreliesonexactaprioriknowledge
of the system nonlinearities. This assumption is rarely satisfied for most practical
processes where determining an exact model is quite a difficult, if not impossible,
task. Robot manipulators with flexible joints or links are good examples of such
systems.Flexibilityinamanipulatorcausesextremedifficultyinmodelingmanip-
ulatordynamicsandbecomesapotentialsourceofuncertaintythatcandegradethe
performanceofthemanipulatorandinsomecasescanevendestabilizethesystem.
Thus,model-basedobserversarenotbestsuitedforsuchsystems.
Capabilitiesofneuralnetworksforidentification,observationandcontrolofnon-
linear systems have been investigated in both off-line and online environments. In
fact,theadaptivebehaviorofneuralnetworksmakesthempowerfultoolsforstate
observation without any a priori knowledge about the system dynamics. Several
neural network-based observers have been proposed in the literature for state esti-
mationofnonlinearsystems.However,mostofthesetechniquessufferfromrestric-
tive assumptions such as (a) a strictly positive real (SPR) condition on the output
errorequation,(b)scalar-valuednonlinearfunctions,(c)Linear-in-ParameterNeu-
ralNetworks(LPNN),(d)aspecialclassofnonlinearsystems(e.g.affinenonlinear
systems), (e) lack of proof of stability, and (f) a complex weight-updating mecha-
nism,whichpreventtheuseofsuchobserverstoreal-worldapplications.
Ontheotherhand,inmanycontrolapplicationsunpredictablebehaviorsuchas
poor performance or even unsafe operation can result from small abnormal devi-
ations (malfunctions) either in the sensors and actuators, or in the components of
theprocess.Hence,anexceptionallevelofautonomyisrequired.Recognizingthat
vii
viii Preface
fault detection and identification is an essential capability of an autonomous sys-
tem,thereisahighdemandfordevelopment ofnovelmethodsforfaultdetection,
isolation,andrecoverysystems.
The objective of this monograph is to address the problem of state estimation,
systemidentificationandobserver-basedfaultdetectionandisolation(FDI)fornon-
linear systems. Towards this end, a neural network-based adaptive observer for a
generalmodelofMIMOnonlinearsystemsisfirstproposedwithnoaprioriknowl-
edge about the system nonlinearities. The neural network is nonlinear in its pa-
rametersandcanbeappliedtomanysystemswitharbitrarydegreesofnonlinearity
andcomplexity.Theonlineweight-updatingmechanismisamodifiedversionofthe
backpropagationalgorithmwithasimplestructuretogetherwithane-modification
termthatisaddedforenhancedrobustnesstounmodelleddynamicsanduncertain-
ties.TheSPRassumptionimposedontheoutputerrorequationisalsorelaxed.The
proposedstructureisthenemployedforthesystemidentificationproblem.Thepro-
posed state estimation scheme is employed to develop a new observer-based fault
detectionandisolationscheme.Severaltypesoffaults,namelyactuatorbiasfaults,
actuatorgainfaults,andsensorbiasfaultsareconsidered.Theproposedmethodre-
liesononlyoutputmeasurementsandisalsorobusttodynamicuncertaintiesaswell
asdisturbancesandmeasurementnoise.Moreover,thefaultdetection,isolation,and
estimationstepsareallunified,i.e.,neitherextrameasured/calculatedsignalsnora
separate fault isolation policy is required to isolate the faults. For each developed
algorithm, mathematical proofs of stability are given by using Lyapunov’s direct
method. The effectiveness of our proposed state estimation/identification/fault de-
tectionapproachesisdemonstratedthroughextensivesimulationsaswellasexper-
imentations that are carried out on highly nonlinear systems. The case studies in-
cludeflexible-jointandflexible-linkmanipulators,satelliteattitudecontrolsystems
withreactionwheelandmagnetorquertypeofactuators(simulations),anda3DOF
macro-micro manipulator and a 6 DOF industrial manipulator, namely the PUMA
560(experiments).
Thefundingformuchoftheresearchdescribedinthismonographwasprovided
by the Natural Sciences and Engineering Research Council (NSERC) of Canada
(PatelandKhorasani),byaTier-ICanadaResearchChair(Patel),byaninfrastruc-
ture grant from the Canada Foundation for Innovation awarded to the University
of Western Ontario (Patel), by the Faculty of Engineering and Computer Science
(Khorasani),andTier-IConcordiaUniversityResearchChair(Khorasani).
June2009, H.A.Talebi
F.Abdollahi
R.V.Patel
K.Khorasani
Contents
1 Introduction................................................... 1
1.1 Preamble.................................................. 1
1.2 Background ............................................... 7
1.2.1 MultilayerNeuralNetworks........................... 7
1.3 Outline ................................................... 13
2 NeuralNetwork-BasedStateEstimationSchemes.................. 15
2.1 Introduction ............................................... 15
2.2 ProblemFormulation ....................................... 15
2.3 Linear-in-ParameterNeuralNetwork-BasedObserver ............ 17
2.4 Nonlinear-in-ParameterNeuralNetwork-BasedObserver ......... 21
2.5 ACaseStudy:ApplicationtoStateEstimationofFlexible-Joint
Manipulators .............................................. 26
2.5.1 ManipulatorModel................................... 27
2.6 SimulationResults ......................................... 28
2.6.1 ASingle-linkFlexible-JointManipulator ................ 28
2.6.2 ATwo-linkFlexible-JointManipulator .................. 31
2.7 Conclusions ............................................... 34
3 NeuralNetwork-BasedSystemIdentificationSchemes ............. 37
3.1 Introduction ............................................... 37
3.2 AParallelIdentificationScheme ............................. 38
3.2.1 LPNNParallelIdentifier.............................. 40
3.2.2 NLPNNParallelIdentifier............................. 41
3.3 ASeries-ParallelIdentificationScheme ........................ 45
3.4 ACasestudy:ApplicationtoaFlexible-LinkManipulator ........ 46
3.5 SimulationResults ......................................... 48
3.5.1 ATwo–LinkManipulator ............................. 49
3.5.2 TheSpaceStationRemoteManipulatorSystem(SSRMS) . 49
3.5.3 Generalization....................................... 53
3.6 ExperimentalResultsonaMacro-MicroManipulatorSystem...... 53
ix
x Contents
3.7 Conclusions ............................................... 58
4 AnActuatorFaultDetectionandIsolationScheme:Experimentsin
RoboticManipulators .......................................... 61
4.1 Introduction ............................................... 61
4.2 NeuralNetworkStructureforActuatorFaultDetection .......... 63
4.3 CaseStudy1:ApplicationtoSatelliteAttitudeControlSubsystems. 66
4.3.1 SystemDynamics.................................... 66
4.3.2 ReactionWheelModel ............................... 67
4.3.3 SimulationResults ................................... 69
4.4 CaseStudy2:ApplicationtoRoboticManipulators .............. 71
4.4.1 SystemDynamics.................................... 72
4.4.2 ExperimentalSetup .................................. 73
4.5 Conclusions ............................................... 78
5 ARobustActuatorGainFaultDetectionandIsolationScheme ..... 83
5.1 Introduction ............................................... 83
5.2 ProblemStatement ......................................... 84
5.3 NeuralNetwork-BasedFaultDetectionandEstimationScheme.... 85
5.3.1 FaultDetectionandIsolationPolicy..................... 87
5.3.2 StabilityAnalysis .................................... 87
5.4 A Case Study: Application to a Satellite’s Attitude Control
Subsystem ................................................ 93
5.5 SimulationResults ......................................... 93
5.6 Conclusions ............................................... 95
6 ARobustSensorandActuatorFaultDetectionandEstimation
Approach ..................................................... 99
6.1 Introduction ............................................... 99
6.2 ProblemStatement .........................................100
6.3 NeuralNetwork-BasedFaultDetectionandEstimationScheme
forSensor/ActuatorFaults ...................................101
6.3.1 FaultDetectionandIsolationPolicy.....................103
6.3.2 SystemIdentification,FaultDetection,andStabilityAnalysis103
6.4 A Case Study: Application to a Satellite’s Attitude Control
Subsystem ................................................109
6.4.1 DynamicModeling...................................109
6.4.2 MagnetorquerModel(ACSActuator) ...................109
6.4.3 Actuator(Magnetorquer)Fault ........................111
6.4.4 MagnetometerModel(ACSSensor) ....................112
6.5 SimulationResults .........................................113
6.6 Conclusions ...............................................117
Contents xi
A PreliminaryDefinitions .........................................131
A.1 Norms....................................................131
A.2 UltimateBoundedness[1] ...................................132
A.3 PositiveRealandStrictlyPositiveReal[2] .....................132
B Flexible-JointManipulatorModel ...............................133
B.1 HarmonicDrive............................................133
B.2 Flexible-jointManipulatorDynamics..........................136
B.2.1 DynamicModelofaTwo-LinkPlanarManipulator[3].....137
B.2.2 TheEffectofJointFlexibilityonManipulatorModel[3]...139
C NeuralNetworkLearningRulesforTheorem6.1 ..................141
D StabilityConditionsofTheorem6.1-Part2 .......................145
References.....................................................147
Index .............................................................153
List of Figures
1.1 High-gainobserverforasysteminobservabilitynormalform[4].... 4
1.2 Somecommonchoicesfortheactivationfunctionsofmultilayer
neuralnetworks............................................. 9
1.3 Athreelayerneuralnetwork................................... 9
1.4 AthreelayerneuralnetworktrainingbyerrorBP................. 10
2.1 Thestructureoftheproposedneuralnetworkobserver. ............ 17
2.2 Theschematicofflexible-jointmanipulator[3]................... 27
2.3 Thestateresponsesofthesingle-linkflexible-jointmanipulator
usingNLPNN .............................................. 30
2.4 Thestateresponsesofthesingle-linkflexible-jointmanipulator
usingNLPNNafterthelearningstops .......................... 31
2.5 Thestateresponsesofthesingle-linkflexible-jointmanipulatorto
0.1sint+0.2sin2t+0.05sin4t trajectory......................... 32
2.6 Thestateresponsesofthesingle-linkflexible-jointmanipulatorto
0.075sin3t trajectoryduringrecallphase ........................ 33
2.7 Thestateresponsesofthetwo-linkflexible-jointmanipulatorafter
learningperiod.............................................. 34
2.8 Thestateresponsesoftheflexible-jointmanipulatorforNLPNN
andLPNNobserverschemes.................................. 35
3.1 Thestructureofneuralnetworkidentifier(parallelmodel).......... 39
3.2 Thestructureofneuralnetworkidentifier(series-parallelmodel). ... 46
3.3 Simulationresultsforatwo-linkmanipulator(parallelmodel) ...... 50
3.4 Simulationresultsforatwo-linkmanipulator(series-parallelmodel). 51
3.5 SchematicofCanadarm2[5]. ................................. 52
3.6 SimulationresultsfortheSSRMS(a) .......................... 54
3.7 SimulationresultsfortheSSRMS(b)........................... 55
3.8 Generalizationresultsforatwo-linkflexiblemanipulator .......... 56
3.9 TheactualMacro-MicroManipulatortest-bed. .................. 57
3.10 ExperimentalresultsfortheM3test-bed ........................ 59
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