Fault Detection and Diagnosis in Nonlinear Systems: A Differential and Algebraic Viewpoint PDF
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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 Springer Complexity is an interdisciplinary program publishing the best research and academic-level teaching on both fundamental and applied aspects of complex systems – cutting across all traditional disciplines of the natural and life sciences, engineering, economics,medicine,neuroscience,socialandcomputerscience. Complex Systems are systems that comprise many interacting parts with the ability to generate anew qualityof macroscopic collectivebehavior themanifestations of whichare the spontaneous formation of distinctive temporal, spatial or functional structures. Models of such systems can be successfully mapped onto quite diverse “real-life” situations like theclimate,thecoherentemissionoflightfromlasers,chemicalreaction-diffusionsystems, biologicalcellularnetworks, thedynamicsofstockmarketsandoftheinternet,earthquake statistics and prediction, freeway traffic, the human brain, or the formation of opinions in socialsystems,tonamejustsomeofthepopularapplications. Although their scope and methodologies overlap somewhat, one can distinguish the following main concepts and tools: self-organization, nonlinear dynamics, synergetics, turbulence,dynamicalsystems,catastrophes,instabilities,stochasticprocesses,chaos,graphs and networks, cellular automata, adaptive systems, genetic algorithms and computational intelligence. ThethreemajorbookpublicationplatformsoftheSpringerComplexityprogramarethe monograph series“Understanding ComplexSystems”focusing on thevariousapplications of complexity, the “Springer Series in Synergetics”, which is devoted to the quantitative theoreticalandmethodological foundations,andthe“SpringerBriefsinComplexity”which are concise and topical working reports, case-studies, surveys, essays and lecture notes of relevance to the field. In addition to the books in these two core series, the program also incorporatesindividualtitlesrangingfromtextbookstomajorreferenceworks. 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 ViktorJirsa,CentreNationaldelaRechercheScientifique(CNRS),Universite´delaMe´diterrane´e,Marseille, France JanuszKacprzyk,SystemResearch,PolishAcademyofSciences,Warsaw,Poland KunihikoKaneko,ResearchCenterforComplexSystemsBiology,TheUniversityofTokyo,Tokyo,Japan ScottKelso,CenterforComplexSystemsandBrainSciences,FloridaAtlanticUniversity,BocaRaton,USA 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 boththeircomposition–typicallymanydifferentkindsofcomponentsinteracting simultaneouslyandnonlinearlywitheachotherandtheirenvironmentsonmultiple levels–andintherichdiversityofbehaviorofwhichtheyarecapable. TheSpringerSeriesinUnderstandingComplexSystemsseries(UCS)promotes new strategies and paradigms for understanding and realizing applications of complex systems research in a wide variety of fields and endeavors. UCS is explicitlytransdisciplinary.Ithasthreemaingoals:First,toelaboratetheconcepts, methodsandtoolsofcomplexsystemsatalllevelsofdescriptionandinallscientific fields,especiallynewlyemergingareaswithinthelife,social,behavioral,economic, neuro-andcognitivesciences(andderivativesthereof);second,toencouragenovel applicationsoftheseideasinvariousfieldsofengineeringandcomputationsuchas robotics,nano-technologyandinformatics;third,toprovidea singleforumwithin whichcommonalitiesanddifferencesintheworkingsofcomplexsystemsmaybe discerned,henceleadingtodeeperinsightandunderstanding. UCS will publish monographs, lecture notes and selected edited contributions aimedatcommunicatingnewfindingstoalargemultidisciplinaryaudience. Forfurthervolumes: http://www.springer.com/series/5394 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 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’slocation,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer. PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter.Violations areliabletoprosecutionundertherespectiveCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. While the advice and information in this book are believed to be true and accurate at the date of publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) 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
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