Control of Surge in Centrifugal Compressors by Active Magnetic Bearings: Theory and Implementation PDF
Preview Control of Surge in Centrifugal Compressors by Active Magnetic Bearings: Theory and Implementation
Advances in Industrial Control Forfurthervolumes: www.springer.com/series/1412 Se Young Yoon (cid:2) Zongli Lin (cid:2) Paul E. Allaire Control of Surge in Centrifugal Compressors by Active Magnetic Bearings Theory and Implementation SeYoungYoon PaulE.Allaire CharlesL.BrownDptofEl.&Comp.Eng. Dept.ofMechanical&AerospaceEngin. UniversityofVirginia UniversityofVirginia Charlottesville,USA Charlottesville,USA ZongliLin CharlesL.BrownDptofEl.&Comp.Eng. UniversityofVirginia Charlottesville,USA ISSN1430-9491 ISSN2193-1577(electronic) AdvancesinIndustrialControl ISBN978-1-4471-4239-3 ISBN978-1-4471-4240-9(eBook) DOI10.1007/978-1-4471-4240-9 SpringerLondonHeidelbergNewYorkDordrecht LibraryofCongressControlNumber:2012941917 ©Springer-VerlagLondon2013 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. 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Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) To OurFamilies Series Editors’ Foreword The series Advances in Industrial Control aims to report and encourage technol- ogy transfer in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. New theory, new controllers, actuators, sensors, new industrial processes, computer methods, new applications, new philosophies, ..., new challenges. Much of this development work resides in industrialreports,feasibilitystudypapersandthereportsofadvancedcollaborative projects.Theseriesoffersanopportunityforresearcherstopresentanextendedex- position of such new work in all aspects of industrial control for wider and rapid dissemination. Monographs in the Advances in Industrial Control series can be considered to range in type from the “art of the possible”, a “proof of principle” type and then a “state of the art” type, where the latter often reports on control as it exists in today’sindustry.Forexample,some“artofthepossible”monographsexploreanew theoreticaldevelopmentanddemonstratehowitmightfindapplicationinthecontrol field.AgoodexampleofthistypeofmonographisProcessControlbyJ.Baoand P.L.Lee(ISBN978-1-84628-892-0,2007).Othermonographsexaminethepresent “stateoftheart”ofcontrolanditstechnologyasfoundincurrentindustrialpractice and look at how better control might enhance efficiency and minimise pollution. RecentexemplarsofthiscategoryareAdvancedControlandSupervisionofMineral Processing Plants by D. Sbárbaro, R. del Villar (ISBN 978-1-84996-105-9, 2010) orthemonographHydraulicServo-systemsbyM.JelaliandA.Kroll(ISBN978-1- 85233-692-9,2002). However, this present, comprehensive Advances in Industrial Control mono- graph Surge Control of Active-Magnet-Bearing-Suspended Centrifugal Compres- sors:TheoryandImplementationbySeYoungYoon,ZongliLinandPaulE.Allaire isanexampleofthe“proofofconcept”monograph.Itisanexcellentadditiontothe seriessinceitscontenthasbroadbutcomplementarycontributionsfromanewtech- nology,fromadvancedcontrolandfromanadvancedcontrollerdemonstrationand assessmentusinganindustrial-standardexperimentalrig. The phenomenon of surge and stall in compressor technology is long standing andwhenthewidespreadindustrialuseofcompressorsisconsidered,asuccessful vii viii SeriesEditors’Foreword control strategy that optimally maximises performance and eliminates compressor downtimewouldbeofsignificanteconomicbenefittoindustry.Thisparticularcon- trolproblemhasreceivedexposureintheAdvancesinIndustrialControlseriespre- viouslythroughthepublishedmonographCompressorSurgeandRotatingStallby J.T.GravdahlandO.Egeland(ISBN978-1-85233-067-5,1999),amonographthat isoftencitedintheliteratureofthecompressorcontrolfield.Somerelatedmaterial canbefoundinanothermonographintheseries,namely,DynamicModellingofGas Turbines edited by G.G. Kulikov and H.A. Thompson (ISBN 978-1-85233-784-1, 2004). However,thismonographbySeYoungYoon,ZongliLinandPaulE.Allaireis distinctiveinthatitinvestigatestheparticulartechnologyofactive-magnet-bearing- suspendedcentrifugalcompressorsandassessestheauthors’ownoriginaladvanced control strategies. The assessment takes place using “an industrial-size centrifugal compressortestrig...designed,built,andcommissionedbytheRotatingMachinery andControlsLaboratory(ROMAC)attheUniversityofVirginia”(USA).Adescrip- tionofthisexperimentalset-upcanbefoundinChap.4ofthemonograph. Access to and use of this industrial-sized test rig is just one of the distinctive featuresoftheresearchreportedinthemonograph.Anotherfeatureisthecompre- hensivenessofthecontentssincetheauthorshavetakenspecialcaretoaddressthe requirements of two readerships, one being readers from the control field, and the secondbeingamoregeneralengineeringreadership. Theindustrialandacademiccontrolcommunitywillbeinterestedintheoutcome ofthelinear-quadratic-Gaussian(LQG)andH∞ advancedcontroltrialsperformed usingtheexperimentalrig.Thisgroupofreaderswillalsofindthetechnicalknowl- edgeextractedintermsofmodelsandparametersneededforcomputersimulation tests before the instrumented control trials of value. However, to ensure that the industrial and academic control community can fully comprehend the fundamen- talsofcompressortechnologythereareinvaluableanddetailedpresentationsonthe problemofsurgeandstall(Chap.1),rotordynamics(Chap.2),magneticbearings (Chap.3)andontheexperimentalriganditsassociatedinstrumentation(Chap.4). In addition, to facilitate and ensure a full appreciation of the advanced control developments presented in Chaps. 7 and 8 by a more general readership from the mechanical, manufacturing, mechatronics, rotating machinery and other engineer- ingdisciplines,theauthorshaveincludedanintroductorychapteroncontrolsystems theory(Chap.6).Evenreadersfromthecontrolcommunitymightfindthischapter useful as a “refresher course” before reading the chapters covering the advanced LQGandH∞ controlstrategies. Theoriginalcontributionsmadebytheauthorsindescribingthevariousaspects of the technology, in devising and testing the advanced control strategies and the careful and thorough construction of this monograph make it a very welcome ad- dition to the Advances in Industrial Control series and to the wider literature of compressortechnology. IndustrialControlCentre M.J.Grimble Glasgow,Scotland,UK M.A.Johnson Preface Compressors are essential machines for a large number of modern manufacturing processes. Like the hearts pumping life to the production lines, compressors are vital to the operation of key industrial sectors, such as the petrochemical and the miningindustries,whichrelyoncompressorsforcriticaltasks,rangingfromtem- peraturecontroltogastransportationandmixing.Asaresult,therehavebeencon- tinualeffortsbytheacademicandindustrialcommunitiestoimprovethereliability and performance of such turbomachinery as new technologies become available. Active magnetic bearing (AMB) is one such enhancing technology that has been gaining strong momentum in recent years. Among other benefits, the low main- tenance requirements and small parasitic energy losses have made these bearings highly desirable for high performance compressors, particularly those designed to operateinharshorinaccessibleenvironments.Additionally,withtheirabilitytoac- tivelychangetherotor-dynamiccharacteristicsofthecompressorbycontrollingthe bearingparametersinrealtime,theAMBscanprovideasmootherandmorereliable operationofthecompressoroverawiderrangeofoperatingconditions. Stabilityisacriticalfactorthatlimitstheperformanceofcompressors.Themax- imummassflowoutputofacompressionsystemiscappedbychoke,whichisgen- erallynotadestabilizingphenomenon,anditiscausedbythecompressedmedium reaching sonic conditions.At the opposite end,the minimummass flow is limited by the compressor instabilities known as stall and surge. Stall is a localized phe- nomenon that can be observed in some compression systems, and it is sometimes accompaniedbyasuddendropintheaveragecompressoroutputflow.Ontheother hand, surge is a system-wide instability that is characterized by large amplitude oscillations in the output pressure and mass flow.These oscillations can cause ex- tensive damage to the compressor casing and internal components due to high vi- brationalloads.Theycanevenleadtoacatastrophicmechanicalfailureofthecom- pressoriftheyarenotaddressedproperly.Aconservativewayofdealingwithsurge istoavoidit,byoperatingfarawayfromtheinstability.Amoreefficientwayisto implementanactivemethodtostabilizesurgeandstall,sothatthestableoperating regionofthecompressionsystemisextended,resultinginbothhigherproductivity andsaferoperation. ix x Preface Unfortunately,amajorityofcurrentcompressorsoperateconservativelytoavoid surge. In other words, many compressors trade the peak performance at the maxi- mumpressureriseforthestabilityatthehighermassflowrates.Thefocusinsurge avoidanceisonguaranteeingthemechanicalintegrityofthemachinesandthesafety oftheworkplacebykeepingaprecautionarymarginbetweentheoperatingoutput flows and the known surge points. Additionally, a reset mechanism is built in the systemthatquicklyreleasesthebuilt-uppressureinthecompressorifsurgeisde- tectedbythedifferentsafetytriggers.Anactivesurgecontroller,ontheotherhand, stabilizes the compressor flow during the initiation of surge, effectively extending theoperationalrangeofthecompressorwithnolossinperformance.Theimplemen- tationofacontrolmechanismismuchrarerinindustrialapplicationsthanthesurge avoidancestrategiesforseveralreasons.Themainreasonis thatthemodifications tocompressorsinthefieldrequiredfortheinstallationofasurgecontrolmechanism are very often complicated and involve very specialized equipments. More impor- tantly, there has not been an univocal experimental demonstration of the potential benefits that an effective surge controller could offer to an actual industrial-size compressor. Recently, promising results have been presented in the literature on an active surgecontrolschemethatmodulatestheimpellerpositiontostabilizetheflowinan AMBsupportedsinglestagecentrifugalcompressor.WiththeAMBactingasahigh bandwidthactuatortoregulatethedisplacementoftheimpeller,thecompressorflow statescanberestoredtotheequilibriumoperatingpointduringtheearlystagesofthe surgeinstability,whentheamplitudeofthelimitcycleisrelativelysmall.Themain advantageofthisactivesurgecontrolschemeisthatitcanbeeasilyimplementedin existingAMBsuspendedcompressors,generallywithasimplemodificationinthe controlsoftware. Thepurposeofthisbookistopresentthefundamentalsontheintegrationofthe AMBsforthesuspensionoftherotorincompressors,andhowthisrelativelynew bearing technology can be employed to actively control and potentially eliminate the compressor surge. The material presented here is intended to serve as a com- prehensivereferenceintheareasofcompressorsurgecontrolandAMBapplication inturbomachinery.Forreaderswhoareunfamiliarwithcompressors,rotordynam- ics and magnetic bearings, brief introductions to these topics are presented in the earlierchaptersofthisbook.Abriefdiscussiononcompressorsandcompressorin- stabilities is presented in Chap. 1, where the literature on the surge modeling and controlisalsoreviewed.Chapter2containsareviewofthebasictheoriesandtools inthestudyofrotordynamics.Chapter3presentsabriefdiscussionontheoperat- ingprinciplesoftheAMBsandasummaryofthepotentialbenefitsthatcomefrom theimplementationofthisbearingtechnologyincompressors.BothChaps.2and3 areintendedtobeaself-containedreferenceforcontrolengineers. Inordertodevelopthetheoryinaphysicalcontext,andtoprovideexperimental validation of the theory developed throughout this book, an industrial-sized AMB suspendedcompressorsystemwasdesigned,constructedandcommissionedforthe study of surge control. A thorough description of this compressor test rig is pre- sented in Chap. 4. This description includes the integration of the AMBs to the Preface xi compressor for rotor support and for surge control. The derivation of the dynamic modelsforboththeAMB/rotorsystemandthecompressionsystemflow,alongwith their experimental validations, are presented in Chaps. 5 and 7. The experimental identification of the system dynamics included in these chapters will demonstrate thattheassumptionsmadeinthederivationofthemathematicalmodelsaresound. ThesemodelswillserveasthebasisonwhichtheAMBlevitationcontrollerandthe activesurgecontrolleraredesigned,inChaps.7and8,respectively. InthedesignoftheAMBlevitationcontroller,performanceandrobustnessspec- ifications that are desirable for AMB suspended compressors are included in the discussion.Inthedesignofthesurgecontroller,theperformancedegradationofthe surgecontrollerduetodynamiclimitationsintheAMBsystemwillbestudied.For bothcontrollers,thetheoreticalderivationisaccompaniedbytheexperimentaldata toshowtheireffectivenessinindustrial-sizecompressors. Finally,itisimportanttonotethatthisbookisnotintendedtobereferencemate- rialforgeneraldesignandoperationofcompressors.Thereexistsanextensivelistof excellentreferencesonthetopicsofcompressordesignandflowmodeling.Instead, thisbookisintendedtoserveasaguidefortheapplicationoftheAMBtechnology in turbomachinery, and to demonstrate the advantages that this rotor support sys- temcanprovideinthestabilizationofthecompressorsurgeforaparticulargroup ofsinglestagecentrifugalcompressors.Sinceactivemagneticbearingsplayacen- tral role in the surge control method to be presented in the book, their theory and applicationsareextensivelydiscussed.Thestabilizationofthecompressorsurgeis mainlydiscussedfromacontroltheoryperspective. This book builds on years of work invested by many engineers and scientists fromtheRotatingMachineryandControls(ROMAC)LaboratoryattheUniversity of Virginia. The authors would like to acknowledge those who participated in the different stages of the research presented here. The derivation of the theoretical concept for the surge control strategy presented here, as well as the design and the initial preparation of the experimental setup, was executed in the early stages of this project by the team led by Professor Eric Maslen and Dr. Dorsa Sanadgol. TheexperienceinindustrialcompressorsbroughtbyKinTienLimandtheadvice ofProfessorChrisGoyneinexperimentalfluiddynamictestingcametobeofgreat valueduringtheconstructionandcommissioningofthecompressortestrig.Finally, theauthorswouldalsoliketoexpresstheirappreciationforthegenerousdonations madebyKobeSteelLtd.,Kobe,Japan,andtheconstantsupportandfundingbythe ROMACLaboratoryanditsindustrialpartnersaroundtheworld. Charlottesville,Virginia,USA SeYoungYoon ZongliLin PaulE.Allaire Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 CompressorsandCompressorSystems . . . . . . . . . . . . . . . 1 1.2 ActiveMagneticBearingsinCompressors . . . . . . . . . . . . . 4 1.3 CompressorInstability . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3.1 Stall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.2 Surge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 CompressorSurgeModeling . . . . . . . . . . . . . . . . . . . . 10 1.5 SurgeAvoidanceandSuppression . . . . . . . . . . . . . . . . . . 11 1.5.1 SurgeAvoidance . . . . . . . . . . . . . . . . . . . . . . . 12 1.5.2 SurgeSuppressionandControl . . . . . . . . . . . . . . . 13 1.6 ObjectivesofThisBook . . . . . . . . . . . . . . . . . . . . . . . 15 2 IntroductiontoRotorDynamics. . . . . . . . . . . . . . . . . . . . . 17 2.1 Föppl/JeffcottSingleMassRotor . . . . . . . . . . . . . . . . . . 18 2.1.1 UndampedFreeVibration . . . . . . . . . . . . . . . . . . 20 2.1.2 DampedFreeVibration . . . . . . . . . . . . . . . . . . . 22 2.1.3 ForcedSteadyStateResponse . . . . . . . . . . . . . . . . 23 2.2 RotorGyroscopicEffects . . . . . . . . . . . . . . . . . . . . . . 27 2.2.1 RigidCircularRotoronFlexibleUndampedBearings . . . 28 2.2.2 ModelofRigidCircularRotorwithGyroscopic Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.2.3 UndampedNaturalFrequenciesoftheCylindricalMode . . 31 2.2.4 UndampedNaturalFrequenciesoftheConicalMode . . . 32 2.3 InstabilityduetoAerodynamicCrossCoupling. . . . . . . . . . . 36 2.3.1 AerodynamicCrossCouplinginTurbines . . . . . . . . . 36 2.3.2 AerodynamicCrossCouplinginCompressors . . . . . . . 37 2.4 Rotor-DynamicSpecificationsforCompressors . . . . . . . . . . 38 2.4.1 LateralVibrationAnalysis . . . . . . . . . . . . . . . . . . 39 2.4.2 RotorStabilityAnalysis . . . . . . . . . . . . . . . . . . . 43 2.5 RotorFiniteElementModeling . . . . . . . . . . . . . . . . . . . 47 2.5.1 DiscretizingRotorintoFiniteElements . . . . . . . . . . . 47 xiii
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