Control of Axially Moving Systems PDF
Preview Control of Axially Moving Systems
Keum-Shik Hong Li-Qun Chen Phuong-Tung Pham Xiao-Dong Yang Control of Axially Moving Systems Control of Axially Moving Systems · · Keum-Shik Hong Li-Qun Chen · Phuong-Tung Pham Xiao-Dong Yang Control of Axially Moving Systems Keum-ShikHong Li-QunChen SchoolofMechanicalEngineering SchoolofMechanicsandEngineering PusanNationalUniversity Science Busan,Korea(Republicof) ShanghaiUniversity Shanghai,China Phuong-TungPham SchoolofMechanicalEngineering Xiao-DongYang PusanNationalUniversity SchoolofMechanicalEngineering Busan,Korea(Republicof) BeijingUniversityofTechnology Beijing,China ISBN978-981-16-2914-3 ISBN978-981-16-2915-0 (eBook) https://doi.org/10.1007/978-981-16-2915-0 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNatureSingapore PteLtd.2022 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. 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The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore Preface Thisbookprovidesacompletein-depthunderstandingofthederivationoftheequa- tionsofmotionandcontrolofvariousaxiallymovingsystems(AMSs)describedby string,beam,belt,andplatemodels.Additionally,approximatemodelsdiscretized frompartialdifferentialequations(PDEs)usingapproximatemethodsareintroduced inthisbook.TherelationshipbetweenthesystemparametersoftheAMSsandthe dynamicbehaviorsoftheAMSsisemphasized.Also,thedesignofcontrolstrategies foraxiallymovingsystemsispresented.Basedonasubsequentdiscussion,conclu- sionsaredrawn,andfuturedirectionsonaxiallymovingsystemsareproposed.The contentsofthisbookarebrieflydescribedasfollows. Chapter 1 introduces industrial axially moving systems and the motivation to studytheaxiallymovingsystems.Thischapteralsogivesabroadoverviewofthe dynamicsandcontrolofaxiallymovingsystems. Chapter2coversthedynamicsofaxiallymovingstrings.ThePDEsthatdescribe thevibrationoftravelingstrings(withconstantortime-varyingvelocity)aredevel- oped using the Hamilton principle. The effects of nonlinear factors, such as axial deformationandviscoelasticityofmaterials,arealsoconsidered.Variousboundary conditions are further investigated in this chapter. In addition to the exact model describedbyPDEs,approximatemodelscharacterizedbyordinarydifferentialequa- tions (ODEs) are also derived. Subsequently, the dynamic behaviors of axially movingstringsareanalyzed. Chapter3providesacompletediscussiononthedynamicsoftheaxiallymoving beam.Theequationsofmotionofmovingbeamsarederivedbasedondiversebeam theories: the Euler–Bernoulli, Rayleigh, and Timoshenko beam theories. Besides, other aspects of axially moving beams, such as the cantilever beam, viscoelastic beam,fluid-conveyingpipe,nanoscalebeam,andcompositebeam,arealsocovered. The approximate models and dynamic behaviors of moving beams are further analyzedinthischapter. Chapter4discussesthedesignofthecontrolschemesforaxiallymovingstrings and beams. The control methods that use an ODE model, such as model-based feedback control and variable structure control, are presented in the first half of thischapter.TheremainderofthischapterfocusesondesigningPDE-basedcontrol schemes: transfer function method, wave cancelation approach, boundary controls v vi Preface based on the Lyapunov method, adaptive control, and hybrid control methods. Numerical simulations are also shown to verify the effectiveness of the control schemes. Chapters5and6areconcernedwithaxiallymovingbelts.Chapter5introduces the dynamics of various axially moving belts, whereas Chap. 6 covers boundary controlsofmovingbeltsbasedontheLyapunovmethod. Chapter 7 is the first of two sections on axially moving plates, which provides thederivationsofthemathematicalmodeloforthotropic,isotropic,andcomposite moving plates. The remainder of Chap. 7 discusses the approximate models and dynamicbehaviorsofaxiallymovingplates.Chapter8isconcernedwiththecontrol ofaxiallymovingplatesbasedonvelocityregulation. Chapter9presentsseveralconclusionsandfinallymakesfutureresearchdirections foraxiallymovingsystems. Busan,Korea(Republicof) Keum-ShikHong Shanghai,China Li-QunChen Busan,Korea(Republicof) Phuong-TungPham Beijing,China Xiao-DongYang Acknowledgments In preparing this book, Keum-Shik Hong and Phuong-Tung Pham were supportedbytheNationalResearchFoundation(NRF)ofKoreaundertheauspicesoftheMinistry ofScienceandICT,Korea(grantno.NRF-2020R1A2B5B03096000). Contents 1 Introduction ................................................... 1 1.1 IndustrialAxiallyMovingSystems ............................ 1 1.2 DynamicsofAxiallyMovingSystems ......................... 5 1.3 ControlofAxiallyMovingSystems ........................... 7 References ..................................................... 9 2 StringModel ................................................... 13 2.1 Introduction ............................................... 13 2.2 DynamicModelsofAxiallyMovingStrings .................... 14 2.2.1 LinearModel ........................................ 14 2.2.2 StringswithTime-VaryingVelocity ..................... 17 2.2.3 LargeAmplitudeVibration ............................ 18 2.2.4 Varying-LengthStrings ............................... 19 2.2.5 ViscoelasticStrings .................................. 23 2.2.6 StringswithNon-homogenousBoundaries ............... 27 2.3 ApproximateModel ........................................ 28 2.4 DynamicAnalysisofStringModel ............................ 32 2.4.1 EquilibriumSolution ................................. 34 2.4.2 StabilityAnalysis .................................... 34 2.4.3 BifurcationandChaoticDynamics ..................... 37 References ..................................................... 49 3 BeamModel ................................................... 53 3.1 Introduction ............................................... 53 3.2 DynamicModelsofAxiallyMovingBeams .................... 54 3.2.1 Euler–BernoulliBeam ................................ 54 3.2.2 Varying-LengthBeam ................................ 57 3.2.3 ViscoelasticBeams ................................... 59 3.2.4 RayleighBeam ...................................... 61 3.2.5 TimoshenkoBeam ................................... 64 3.2.6 BeamswithNonhomogenousBoundaries ................ 67 3.2.7 Fluid-ConveyingPipe ................................ 83 3.2.8 NanoscaleBeams .................................... 85 vii viii Contents 3.2.9 LaminatedCompositeBeams .......................... 87 3.3 ApproximateModel ........................................ 89 3.4 DynamicAnalysisofBeamModels ........................... 92 3.4.1 EquilibriumSolutions ................................ 92 3.4.2 StabilityAnalysis .................................... 93 3.4.3 BifurcationandChaoticDynamics ..................... 104 References ..................................................... 121 4 ControlofAxiallyMovingStringsandBeams ..................... 125 4.1 ControlBasedonanODEModel ............................. 125 4.1.1 Model-BasedFeedbackControl ........................ 126 4.1.2 SlidingModeControl ................................. 131 4.1.3 ControlBasedonRegulatingAxialVelocity ............. 133 4.2 ControlBasedonaPDEModel .............................. 139 4.2.1 TransferFunction-BasedMethod ....................... 139 4.2.2 WaveCancellationMethod ............................ 144 4.2.3 BoundaryControlBasedontheLyapunovMethod ........ 147 4.2.4 AdaptiveControl ..................................... 159 4.3 HybridControlMethods ..................................... 164 4.4 SimulationExamples ....................................... 165 References ..................................................... 171 5 BeltModel ..................................................... 173 5.1 Introduction ............................................... 173 5.2 DynamicModelsofAxiallyMovingBelts ..................... 174 5.2.1 BeltModelUsingaClosed-FormStrain ................. 174 5.2.2 BeltModelUsingApproximateStrains .................. 177 5.2.3 ViscoelasticBelt ..................................... 179 5.2.4 ShearDeformationandRotaryInertia ................... 180 5.2.5 TransverseVibration ................................. 182 5.2.6 BeltswithNonhomogenousBoundaries ................. 182 5.3 ApproximateModel ........................................ 199 5.4 DynamicAnalysisofBeltModels ............................ 201 5.4.1 EquilibriumSolutions ................................ 201 5.4.2 StabilityAnalysis .................................... 203 5.4.3 BifurcationandChaoticDynamics ..................... 210 References ..................................................... 218 6 ControlofAxiallyMovingBelts ................................. 221 6.1 BoundaryControlBasedontheLyapunovMethod .............. 221 References ..................................................... 231 7 PlateModel .................................................... 233 7.1 Introduction ............................................... 233 7.2 DynamicModelsofAxiallyMovingPlates ..................... 234 7.2.1 ElasticPlate ......................................... 234 7.2.2 ViscoelasticPlate .................................... 239 Contents ix 7.2.3 LaminatedCompositePlate ........................... 241 7.3 ApproximateModels ........................................ 244 7.4 DynamicAnalysisofPlateModels ............................ 249 7.4.1 EquilibriumSolutionsandStabilityofanIsotropic Plate ............................................... 250 7.4.2 EquilibriumSolutionsandStabilityofanOrthotropic Plate ............................................... 256 References ..................................................... 263 8 ControlofAxiallyMovingPlatesandMembranes ................. 265 8.1 ControlBasedonRegulatingAxialVelocity .................... 265 Reference ...................................................... 272 9 ConclusionsandFutureDirections ............................... 273 9.1 ConcludingRemarks ........................................ 273 9.2 FutureDirections ........................................... 276 AppendixA ....................................................... 279 AppendixB ....................................................... 281 AppendixC ....................................................... 283 AppendixD ....................................................... 287 AppendixE ....................................................... 291 AppendixF ....................................................... 297 Index ............................................................. 315 Abbreviations AMS Axiallymovingsystem DIQM Differentialandintegralquadraturemethod IPDE Integro-partialdifferentialequation ODE Ordinarydifferentialequation PDE Partialdifferentialequation SMC Slidingmodecontrol VSC Variablestructurecontrol xi
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