Fault Detection and Diagnosis in Nonlinear Systems: A Differential and Algebraic Viewpoint

143 Pages·2014·4.507 MB·English

by  Rafael Martinez-Guerra, Juan Luis Mata-Machuca (auth.)

Understanding Complex Systems
Rafael Martinez-Guerra
Juan Luis Mata-Machuca
Fault Detection
and Diagnosis
in Nonlinear
Systems
A Diff erential and Algebraic Viewpoint
Springer Complexity
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EditorialandProgrammeAdvisoryBoard
HenryAbarbanel,InstituteforNonlinearScience,UniversityofCalifornia,SanDiego,USA
DanBraha,NewEnglandComplexSystemsInstituteandUniversityofMassachusettsDartmouth,USA
Pe´ter E´rdi, Center for Complex Systems Studies, Kalamazoo College, USA and Hungarian Academy
ofSciences,Budapest,Hungary
KarlFriston,InstituteofCognitiveNeuroscience,UniversityCollegeLondon,London,UK
HermannHaken,CenterofSynergetics,UniversityofStuttgart,Stuttgart,Germany
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France
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KunihikoKaneko,ResearchCenterforComplexSystemsBiology,TheUniversityofTokyo,Tokyo,Japan
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Markus Kirkilionis, Mathematics Institute and Centre for Complex Systems, University of Warwick,
Coventry,UK
Ju¨rgenKurths,NonlinearDynamicsGroup,UniversityofPotsdam,Potsdam,Germany
AndrzejNowak,DepartmentofPsychology,WarsawUniversity,Poland
LindaReichl,CenterforComplexQuantumSystems,UniversityofTexas,Austin,USA
PeterSchuster,TheoreticalChemistryandStructuralBiology,UniversityofVienna,Vienna,Austria
FrankSchweitzer,SystemDesign,ETHZurich,Zurich,Switzerland
DidierSornette,EntrepreneurialRisk,ETHZurich,Zurich,Switzerland
StefanThurner,SectionforScienceofComplexSystems,MedicalUniversityofVienna,Vienna,Austria
Understanding Complex Systems
FoundingEditor:S.Kelso
Future scientific and technological developments in many fields will necessarily
dependuponcomingtogripswithcomplexsystems.Suchsystemsarecomplexin
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Rafael Martinez-Guerra • Juan Luis Mata-Machuca
Fault Detection and Diagnosis
in Nonlinear Systems
A Differential and Algebraic Viewpoint
123
Rafael Martinez-Guerra Juan Luis Mata-Machuca
Departamento de Control Automatico Unidad Profesional Interdisciplinaria
CINVESTAV-IPN en Ingenieria y Tecnologias Avanzadas
Mexico, D.F. Instituto Politecnico Nacional
Mexico Academia de Mecatronica
Mexico, D.F.
Mexico
ISSN1860-0832 ISSN1860-0840(electronic)
ISBN978-3-319-03046-3 ISBN978-3-319-03047-0 (eBook)
DOI10.1007/978-3-319-03047-0
SpringerCham HeidelbergNewYorkDordrechtLondon

Library of Congress Control Number: 2013953239
(cid:2)c Springer International Publishing Switzerland 2014
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Tomywifeandsons
Marilen,RafaelandJuanCarlos.
Tomyparentsandbrothers
Carlos,Virginia,Victor,Arturo,
Carlos,JavierandMarisela.
RafaelMart´ınez-Guerra
Tomystudents
JuanLuisMata-Machuca

Preface
Thisbookisaboutfaultsaspectsofdetectionanddiagnosisproblemsinnonlinear
systemswhicharerepresentedbyordinarydifferentialequationsfromadifferential
andalgebraicviewpoint.Thisframeworksoimportantforfaultdetectionanddiag-
nosis,isnotcommonlyfoundintextbooks.Aprominentroleisplayedbythetype
ofmathematicaltoolusedwhichisthemainingredienttothesolutionofsomereal
problems. The background material needed to understand this book is differential
algebraanddifferentialequations.Thisbookcanbeusedbystudentswithastrong
first year of algebra and differential equations, it is oriented mainly toward upper
divisionengineeringandsciencestudents.Itcanalsobeusedforagraduatecourse.
We have rather tried to unify the theory as much as possible with the practice by
focussing attention on a greatest number of techniques or procedures to tackle the
generalproblem.Ourgoalinthisbookistodeveloptechniquesusingauxiliarysys-
temsnamedalso“observers”tosolvethefaultdetectionanddiagnosisproblemin
nonlinearsystems.Thelevelofrigorishigh,andalmosteverythingisproved.We
havetriedtodevelopproofsthataddinsighttothetheoremsandthatareimportant
methods.Wehaveavoidedtheintroductionofsomeconceptsinordertomakethe
bookmorewidelyreadable,butthemainideascaneasilybeseeninthisbook.
Theplanofthebookisasfollows:
Infirsttwochapters,speciallychapters1and2,givearatherintensiveandcom-
plete study of the fault detection problem using residual generators by consider-
ingtwotypesoffaultswithapplicationtoanelectromechanicalpositioningsystem
and a Continuous Stirred Tank Reactor (CSTR). Chapters 3 and 4 are devoted to
faultdiagnosisproblem.Weintroducesomeconceptssuchasthe“differentialtran-
scendence degree” to attack this problem, as well as we introduce the concept of
“diagnosabilitycondition”basedonalgebricityofthefaultandweestablishsome
strongresultsontheminimalnumberofmeasurementswhichareprovedusingthe
differential transcendence degree with application to a bioreactor model and a hy-
draulic system. In chapter 5 is studied a fault detection method to detect the belt
breakdowninanexperimentalbeltdrivesystemusingaproportionalreducedorder
vii
viii Preface
observer.Inchapter6isdealtthefaultdiagnosisproblemusingtheleftinvertibility
condition,troughtheconceptofdifferentialoutputrank,themethodologyistested
inanexperimentalimplementationofathree-tanksystem.Inchapter7isboarded
defaultestimationproblemusingaslidingmodeobserverandthesocalledLinear
time-varying(LTV)differentiators.Inchapter8istackledthediagnosisproblemfor
non-differentiallyflatandLiouvilliansystemsbyusingtheconceptsofdifferential
transcendence degree and Hardy differential field. Finally, chapter 9 is devoted to
thediagnosisproblemusingapolynomialobservertobetestedintheexperimental
settingAmiraDTS200(three-tanksystem).
Me´xicoCity,Me´xico RafaelMart´ınez-Guerra
July2013 JuanLuisMata-Machuca
Contents
1 Thefaultdetectionprobleminnonlinearsystemsusingresidual
generators..................................................... 1
1.1 Introduction ............................................... 1
1.2 Observationproblem........................................ 2
1.3 Fundamentalproblemofresidualgeneration ................... 5
1.3.1 Residualgeneratorstability............................ 5
1.4 Faultdetection ............................................ 9
1.4.1 Constantfaultcase .................................. 9
1.4.2 Time-varyingfaultcase .............................. 13
1.5 Numericalexample......................................... 15
References..................................................... 19
2 FaultDetectioninCSTRUsingNonlinearObservers............... 21
2.1 Introduction ............................................... 21
2.2 Basicdefinitions ........................................... 22
2.3 Statementoftheproblem .................................... 23
2.3.1 Observersynthesis ................................... 24
2.4 ApplicationtoaCSTR ...................................... 24
2.5 Numericalresults........................................... 29
2.6 Concludingremarks ........................................ 29
References..................................................... 30
3 Diagnosisofnonlinearsystemsusingtheconceptofdifferential
transcendencedegree ........................................... 33
3.1 Introduction ............................................... 33
3.2 Statementoftheproblem .................................... 35
3.2.1 Onthediagnosabilitycondition ........................ 37
3.2.2 Ontheminimalnumberofmeasurements................ 38
3.2.3 Someproperties ..................................... 38
3.2.4 Examples........................................... 39
3.3 Reducedorderuncertaintyobserversynthesis ................... 40
ix