ControlDesignandSimulationModuleJune2008,371894C-01Simulationisaprocessthatinvolvesusingsoftwaretorecreateandanalyzethebehaviorofdynamicsystems.Youusethesimulationprocesstolowerproductdevelopmentcostsbyacceleratingproductdevelopment.Youalsousethesimulationprocesstoprovideinsightintothebehaviorofdynamicsystemsyoucannotreplicateconvenientlyinthelaboratory.Forexample,simulatingajetenginesavestime,labor,andmoneycomparedtobuilding,testing,andrebuildinganactualjetengine.YoucanusetheLabVIEWControlDesignandSimulationModuletosimulateadynamicsystemoracomponentofadynamicsystem.Forexample,youcansimulateonlytheplantwhileusinghardwareforthecontroller,actuators,andsensors.IfyouarenewtotheControlDesignandSimulationModule,considercompletingtheGettingStartedwithSimulationtutorial.Inadditiontothetopicscontainedinthishelpfile,theLabVIEWControlDesignUserManualcontainsinformationaboutusingLabVIEWtodesign,analyze,anddeploycontrollersfordynamicsystems.ThefollowingtabledescribesthetasksyoucanperformwiththeControlDesignandSimulationModuleandthecomponentsyouuseforthesetasks.

Task ComponentDesign,analyze,anddeploycontrollersfordynamicsystemmodels

ControlDesignVIsandfunctions.YoualsocanusetheControlDesignMathScriptfunctionstodesignandanalyzecontrollers.

Configuresimulationparameters,includingtheordinarydifferentialequation(ODE)solver,anddefinethesimulationaspartofaLabVIEWblockdiagram

SimulationLoop

Build,simulate,anddeploydynamicsystemmodels,includingmodelsdevelopedwiththe

Simulationfunctions

LabVIEWSystemIdentificationToolkitortheControlDesignandSimulationModule.Executeoffline,RapidControlPrototype(RCP),andHardware-in-the-Loop(HIL)configurationsGenerateandcombineinputandfeedbacksignalsCollectanddisplaysimulationdata

Trimandlinearizeanonlineardynamicsystemmodel

Trim&LinearizeVIs;LinearizeSubsystemdialogbox

Determinetheoptimalparametersforadynamicsystemmodel,givenasetofconstraints

OptimalDesignVIs

ConvertamodeldevelopedinTheMathWorks,Inc.Simulink®applicationsoftwareintoLabVIEWblockdiagramcode

SimulationModelConverter

©2002–2008NationalInstrumentsCorporation.Allrightsreserved.

Version8.6Features(ControlDesignandSimulationModule)RefertotheLabVIEW8.6FeaturesandChangestopicforinformationaboutnewfeaturesinLabVIEW8.6.Refertothereadme_ControlandSim.htmlfile,locatedinthelabview\readmedirectory,foracompletelistofnewfeaturesandchanges,informationaboutupgradeandcompatibilityissuesspecifictodifferentversionsoftheControlDesignandSimulationModule,andinformationaboutknownissueswiththeControlDesignandSimulationModule8.6.

UsingSimulationSubsystemsOutsideaSimulationLoopYounowcanplaceasimulationsubsystemonablockdiagramoutsideaSimulationLoop.IfyourunasimulationsubsystemonablockdiagramoutsideaSimulationLoop,thesimulationsubsystemexecutesonestepoftheordinarydifferentialequationsolvereachtimethesimulationsubsystemiscalled.

PlacingConstraintsonanMPCControllerUsetheCDCreateMPCControllerVItocreateanMPCcontrollermodelwithconstraintsdefinedusingeitherthedualoptimizationorbarrierfunctionmethod.UsetheCDUpdateMPCWindowVItoprovidesetpointanddisturbanceprofilestotheMPCcontrollerduringimplementation.YoualsocanusetheCDSetMPCControllerVItoupdatespecifiedparameters,includinganyconstraints,ofanMPCcontrolleratruntime.RefertotheLabVIEWControlDesignUserManualformoreinformationaboutsettingconstraintsforanMPCcontroller.

ImplementationPaletteChangesTheControlDesign»Implementationpalettehasthefollowingchanges:

TheCDDiscreteStochasticState-SpacefunctionreplacestheCDDiscreteStochasticState-Space(External)functionandtheCDDiscreteStochasticState-Space(Internal)function.UsetheCDDiscreteStochasticState-SpacefunctionoutsideaSimulationLoop.UsethenewDiscreteStochasticState-SpacefunctioninsideaSimulationLoop.TheCDDiscreteObserverfunctionreplacestheCDPredictiveObserverfunction,theCDCurrentObserverCorrectorVI,andtheCDCurrentObserverPredictorVI.TheCDCurrentObserverCorrectorVIandtheCDCurrentObserverPredictorVInolongerareonthepalettebutstillworkinVIsyoucreatedinapreviousversionoftheControlDesignandSimulationModule.UsetheCDDiscreteObserverfunctionoutsideaSimulationLoop.UsethenewDiscreteObserverfunctioninsideaSimulationLoop.TheCDDiscreteKalmanFilterfunctionreplacestheCDDiscreteRecursiveKalmanCorrectorVIandtheCDDiscreteRecursiveKalmanPredictorVI.TheCDDiscreteRecursiveKalmanCorrectorVIandtheCDDiscreteRecursiveKalmanPredictorVInolongerareonthepalettebutstillworkinVIsyoucreatedinapreviousversionoftheControlDesignandSimulationModule.UsetheCDDiscreteKalmanFilterfunctionoutsideaSimulationLoop.UsethenewDiscreteKalmanFilterfunctioninsideaSimulationLoop.

TheSimulation»CDImplementationpalettehasbeenremoved.ThechangestotheControlDesign»ImplementationpalettealsoapplytotheSimulation»CDImplementationpalette.Additionally,theCDContinuousObserverfunctionandtheCDContinuousRecursiveKalmanFilterfunctionnowareontheSimulation»ContinuousLinearSystemspalette.

LabVIEWControlDesignAssistant3.0UsetheinteractiveLabVIEWControlDesignAssistanttodevelopmodelsthatreflectthebehaviorofsingle-inputsingle-output(SISO)systems.UsingtheControlDesignAssistant,youcanloadorcreateamodelofaplant,analyzethetimeorfrequencyresponse,andthensynthesizeacontroller.TheControlDesignAssistanthaswindowsinwhichyoucanimmediatelyseethemathematicalequationandgraphicalrepresentationthatdescribethemodel.Youalsocanviewtheresponsedataandtheconfigurationofthecontroller.SelectTools»ControlDesignandSimulation»LaunchControlDesignAssistanttolaunchtheControlDesignAssistantfromLabVIEW.

MathScriptNodeontheSimulationDiagramYounowcanplaceaMathScriptNodedirectlyonasimulationdiagram.

RelatedDocumentation(ControlDesignandSimulationModule)ThefollowingdocumentscontaininformationthatyoumightfindhelpfulasyouusetheLabVIEWControlDesignandSimulationModule.

GettingStartedwithLabVIEW—Thismanualcontainsanin-depthintroductiontoLabVIEW,includingseveraltutorialsthatshowcaseLabVIEWfeatures.LabVIEWFundamentals—ThismanualprovidesinformationaboutLabVIEWprogrammingconcepts,techniques,features,VIs,andfunctionsyoucanusetocreatemanytypesofapplications.LabVIEWControlDesignUserManual—ThismanualcontainsinformationaboutusingLabVIEWtodesign,analyze,anddeploycontrollersfordynamicsystems.GettingStartedwiththeLabVIEWReal-TimeModule—Thismanualintroducestheconceptsnecessarytocreatereal-timesimulations.Real-TimeExecutionTraceToolkitdocumentation.NI-CANHardwareandSoftwareManualNI-DAQmxHelpLabVIEWControlDesignandSimulationModuleReadme—Usethisfiletolearnimportantlast-minuteinformation,includinginstallationandupgradeissues,compatibilityissues,changesfromthepreviousversion,andknownissueswiththeControlDesignandSimulationModule.OpenthisreadmebyselectingStart»AllPrograms»NationalInstruments»LabVIEW»Readmeandopeningreadme_ControlandSim.htmlorbynavigatingtothelabview\readmedirectoryandopeningreadme_ControlandSim.html.LabVIEWControlDesignandSimulationModuleexampleVIs—Refertothelabview\examples\ControlandSimulationdirectoryforexampleVIsthatdemonstratecommontasksusingtheControlDesignandSimulationModule.YoualsocanaccesstheseVIsbyselectingHelp»FindExamplesandselectingToolkitsandModules»ControlandSimulationintheNIExampleFinderwindow.

AdditionalLabVIEWdocumentation.YoumusthaveAdobeReader6.0.1orlaterinstalledtovieworsearchthePDFversionsofthesemanuals.RefertotheAdobeSystemsIncorporatedWebsitetodownloadAcrobatReader.RefertotheNationalInstrumentsProductManualsLibraryforupdateddocumentationresources.YoumustinstallthePDFstoaccessthemfromthishelpsystem.

NoteThefollowingresourcesofferusefulbackgroundinformationonthegeneralconceptsdiscussedinthisdocumentation.Theseresourcesareprovidedforgeneralinformationalpurposesonlyandarenotaffiliated,sponsored,orendorsedbyNationalInstruments.Thecontentoftheseresourcesisnotarepresentationof,maynotcorrespondto,anddoesnotimplycurrentorfuturefunctionalityintheControlDesignandSimulationModuleoranyotherNationalInstrumentsproduct.Åström,K.,andT.Hagglund.1995.PIDcontrollers:theory,design,andtuning.2ded.ISA.Balbis,Luisella.2006.Predictivecontroltoolkit.UKACCcontrol,2006.Minisymposia:87–96.Bertsekas,DimitriP.1999.NonlinearProgramming.2ded.Belmont,MA:AthenaScientific.Dorf,R.C.,andR.H.Bishop.2001.Moderncontrolsystems.9thed.UpperSaddleRiver,NJ:PrenticeHall.Franklin,G.F.,J.D.Powell,andA.Emami-Naeini.2002.Feedbackcontrolofdynamicsystems.4thed.UpperSaddleRiver,NJ:PrenticeHall.Franklin,G.F.,J.D.Powell,andM.L.Workman.1998.Digitalcontrolofdynamicsystems.3ded.MenloPark,CA:AddisonWesleyLongman,Inc.Kuo,BenjaminC.1992.DigitalControlSystems.2ded.Ft.Worth:SaundersCollege.Nise,NormanS.2000.Controlsystemsengineering.3ded.NewYork:JohnWiley&Sons,Inc.Ogata,Katsuhiko.1995.Discrete-timecontrolsystems.2ded.EnglewoodCliffs,N.J.:PrenticeHall.

Ogata,Katsuhiko.2001.Moderncontrolengineering.4thed.UpperSaddleRiver,NJ:PrenticeHall.Zhou,Kemin,andJohnC.Doyle.1998.Essentialsofrobustcontrol.UpperSaddleRiver,NJ:PrenticeHall.

Thefollowingbookscontaininformationabouttheordinarydifferentialequation(ODE)solverstheControlDesignandSimulationModuleuses.

Ascher,U.M.,andL.R.Petzold.1998.Computermethodsforordinarydifferentialequationsanddifferential-algebraicequations.Philadelphia:SocietyforIndustrialandAppliedMathematics.Shampine,LawrenceF.1994.Numericalsolutionofordinarydifferentialequations.NewYork:Chapman&Hall,Inc.

OrdinaryDifferentialEquationSolvers(ControlDesignandSimulationModule)Becausemanydynamicsystemmodelsconsistofdifferentialequations,youmustsolvethesedifferentialequationstoobservethebehaviorofthesimulatedsystem.LabVIEWincludesseveralordinarydifferentialequation(ODE)solversthatsolvetheseequations.Beforeyousimulateadynamicsystemmodel,youmustspecifyandconfiguretheODEsolverforthatsimulation.ODEsolversusemethodstoapproximatethesolutiontoadifferentialequation.TheODEsolversimplementthesemethodsinavarietyofways,eachwithvariousstrengthsandweaknesses.DefiningcharacteristicsofanODEsolverincludethefollowingqualities:

AccuracyororderStabilityComputationalspeedUseofafixedtimestepsizeversusavariabletimestepsizeUseofasinglestepversusmultiplestepsSuitabilityforstiffproblems

ConsiderationsforEmbeddedTargets(ControlDesignandSimulationModule)IfyouinstallLabVIEWforaparticularembeddedtarget,youcanusetheLabVIEWControlDesignandSimulationModuletodevelopandexecutesimulationsonthattarget.RefertothedocumentationforthetargetyoupurchasedforinformationaboutdevelopingandexecutingVIsonthattarget.Whendevelopingasimulationforanembeddedtarget,takethefollowingfactorsintoconsideration:

YoucannotusetheTrim&LinearizeVIsorOptimalDesignVIswhendevelopingonanembeddedtarget.Therefore,LabVIEWdoesnotdisplaythesepaletteswhenyouareinanembeddedcontext.YoucanuseaConditionalDisablestructuretoenablereal-worldI/OwhenthesimulationisontheembeddedtargetandsimulatedI/OwhenthesamesimulationisrunningonaWindowscomputer.Usingthismethod,youdonothavetomodifytheVImanuallytousedifferentI/Ocodewhenyouswitchtargets.UseasfewSimulationfunctionsaspossible.CombineasmanysequentialtransformationsaspossibleintoasingleSimulationfunction.Forexample,insteadofusingthreeState-Spacefunctionstodescribeacontrollermodel,combinethosefunctionsintoasingleState-Spacefunction.

NoteYoucanusetheModelInterconnectionVIstocombinedynamicsystemmodels.

Considerthespeed/memorytrade-offwhenusingsimulationsubsystems.Usingfewersimulationsubsystemsmightincreaseexecutionspeedbutmightrequireyoutoduplicatecodeelsewhereonthesimulationdiagram.Considerusingfixedstep-sizeordinarydifferentialequation(ODE)solvers,thatis,thesolversnotmarked(variable).Variablestep-sizeODEsolversintroducecomputationaloverheadwhenchangingstepsizes.

NoteTheControlDesignandSimulationModuledoesnotguaranteeaccuracywhenusingtheBDForRosenbrock

ODEsolversonembeddedtargets.Ifthesesolversappeartoproduceinaccurateresultsonanembeddedtarget,chooseanotherODEsolver.

Glossary(ControlDesignandSimulationModule)A B C D E F H I L M N O P R S T

LabVIEWGlossary

AAckermann Atechniqueforplacingpolesinasystemmodel.Usethe

CDAckermannVItoimplementthistechnique.actuator Aphysicaldevicethatappliesthecontrolactiontotheplant.auto-covariance

Ameasureofhowcloselyavalueofastochasticprocess,suchasnoise,varieswiththesubsequentvalueofthatprocess.

Bbalancedsystemmodel

AsystemmodelwithidenticalcontrollabilityandobservabilitydiagonalGrammians.UsetheCDBalanceState-SpaceModel(Diagonal)VIandtheCDBalanceState-SpaceModel(Grammians)VItobalanceastate-spacesystemmodel.

Bodeplot

Aplotthatshowsthegainandphasemarginsofasystemmodelforacommonfrequencyrange.Bodeplotsshowhowcloseasystemmodelistoinstability.UsetheCDBodeVItocreateaBodeplotforasystemmodel.

CCGD CommonGraphDescription.TheformattheSimulation

ModelConverterusestostoreeachsystem,subsystem,block,andlinefromamodeldevelopedinTheMathWorks,Inc.Simulink®simulationenvironment.

constraints Seeinequalityconstraints.continuousmodel

Adynamicsystemmodelthatrepresentsreal-worldsignals,whichvarycontinuouslywithtime.Youcharacterizeacontinuousmodelbydifferentialequations.Seealsodiscretemodel.

controller Adevicethatregulatestheoperationofadynamicsystem.cost Thescalarvaluethatresultsfromsolvingacostfunction.costfunction

Aperformancemeasureyouwanttominimizewhendesigningoptimalparameters.Acostfunctionisafunctionalequationthatmapsasetofpointsinatimeseriestoasinglescalarvalue.

Ddesign Seeoptimaldesign.directfeedthrough

Arelationshipbetweenafunctioninputandafunctionoutputinwhichthefunctionusestheinputatthecurrentsteptocalculatetheoutputatthecurrentstep.Seealsoindirectfeedthrough.

discretemodel

Adynamicsystemmodelthatrepresentssignalsthataresampledatdiscontinuousintervalsintime.Youcharacterizeadiscretemodelbydifferenceequations.Seealsocontinuousmodel.

distributedparametermodel

Aphysicalmodelthatyoucandescribewithpartialdifferentialequations.Seealsolumpedparametermodel.

dynamicsystem

Asystemwhosebehaviorvarieswithtime.

dynamicsystemmodel

Adifferentialordifferenceequationthatrepresentsthebehaviorofallorpartofadynamicsystem.

Eempiricalmodeling

Amodelingtechniqueinwhichyouuseexperimentaldatatodefineadynamicsystemmodel.Seealsophysicalmodeling.

Ffeedbackcycle

Acycleinwhichdatafloworiginatesfromanoutputofafunctionorsubsystemandterminatesasaninputofthesamefunctionorsubsystem.Seealsoindirectfeedthrough.

HHIL Hardware-in-the-loop.Asimulationconfigurationinwhichyoutest

acontrollerimplementationwithasimulatedsystem.SeealsoRCP.

Iindirectfeedthrough

Arelationshipbetweenafunctioninputandafunctionoutputinwhichthefunctiondoesnotusetheinputatthecurrentsteptocomputetheoutputatthecurrentstep.Seealsodirectfeedthrough.

inequalityconstraints

Anyrestrictionsyouplaceonhowtheoptimaldesignprocessdeterminesoptimalparametervalues.Youcandefineinequalityconstraintsforthecontrolaction,theoutput,therateofchangeofthecontrolaction,andtherateofchangeoftheoutput.

InputNode AcollectionofinputterminalsattachedtotheSimulationLoop.UsetheInputNodetoconfiguresimulationparametersprogrammatically.SeealsoOutputNode.

Llinearmodel Adynamicsystemmodelthatobeystheprinciplesof

superpositionandhomogeneity.Seealsononlinearmodel.

linearize Aprocedurethatapproximatesthebehaviorofanonlinearmodel.Seealsotrim.

lumpedparametermodel

Aphysicalmodelyoucandescribewithanordinarydifferentialequation.Seealsodistributedparametermodel.

Mmodel Seedynamicsystemmodel.

Nnonlinearmodel

Adynamicsystemmodelthatdoesnotobeytheprinciplesofsuperpositionorhomogeneity.Seealsolinearmodel.

Ooffline Asimulationconfigurationinwhichyouusesoftwaretosimulate

thecontrollerandthesystemyouwanttocontrol.Nohardwareisinvolvedinanofflinesimulation.

optimaldesign

Theprocessofselectingparametervaluesthatmaximizeameasureofperformance.

OutputNode

AnoutputterminalontheSimulationLoop.UsetheOutputNodetoviewanyerrorsthesimulationdiagramgenerates.SeealsoInputNode.

Pparameterbounds

Anyrestrictionsyouplaceonpossibleparametervaluesduringtheoptimaldesignprocess.Theoptimaldesignprocessdoesnotconsideranyparametervaluesoutsidetheboundsyoudefine.

parameterdesign

Seeoptimaldesign.

parametermesh

Asetofpointsthatdefinesthedistributionpatternsofsetsofparametervaluesandthenumberofsetstogenerate.

period TheamountoftimeinwhichadiscretelinearSimulationfunctionmustcomplete.

physicalmodeling

Amodelingtechniqueinwhichyouusethelawsofphysicstodefineadynamicsystemmodel.Seealsoempiricalmodeling.

plant Adynamicsystemwhosebehavioryouwanttoobserve,replicate,ormanipulate.

RRCP Rapidcontrolprototype.Asimulationconfigurationinwhichyou

testplanthardwarewithasoftwaremodelofthecontroller.SeealsoHIL.

Ssimulationdiagram

ALabVIEWdiagramthatallowsyoutouseSimulationfunctionswithinaSimulationLooporsimulationsubsystem.Asimulationdiagram,likeotherLabVIEWdiagrams,hasthefollowingsemanticproperties:Theorderofoperationsisnotcompletelyspecifiedbytheuser.Theorderofoperationsisimpliedbydatainterdependencies.Afunctioncanexecuteonlyafterallnecessaryinputshavebecomeavailable.Outputsaregeneratedafterafunctioncompletesexecution.

SimulationLoop

Thestructurethatexecutesthesimulationdiagramovermultipletimesteps.

skew TheamountoftimebywhichyouwanttodelaytheexecutionofadiscretelinearSimulationfunction.

SQP SequentialQuadraticProgramming.Ageneral-purposenumericaloptimizationalgorithm.

subsystem AsectionofasimulationdiagramyourepresentwithasingleiconinsteadofmultipleSimulationfunctionsandwires.

Ttime-invariantmodel

Adynamicsystemmodelwhoseparametersdonotchangewithtime.

time-variantmodel

Adynamicsystemmodelwhoseparameterschangewithtime.

trim Aprocedurethatsearchesforthevaluesofstatesandinputsthatproduceoutputand/orstatederivativeconditionsyouspecify.Seealsolinearize.

BuildingandConfiguringSimulations(ControlDesignandSimulationModule)UsetheLabVIEWControlDesignandSimulationModuletobuildasimulationdiagram,whichgraphicallydisplaysadynamicsystemmodelinLabVIEW.YoubuildandexecuteasimulationdiagrambyplacingSimulationfunctionsandotherLabVIEWVIsandstructuresinsidetheSimulationLoop.Thesimulationdiagramthenusesanordinarydifferentialequation(ODE)solvertocomputethebehaviorofthedynamicsystemmodel.ThesimulationdiagramsupportsstandardLabVIEWdebuggingtechniques.Youcanuseexecutionhighlighting,breakpoints,probes,customprobes,andsingle-steppingonthesimulationdiagram.

(Windows)Toviewrelatedtopics,clicktheLocatebutton,shownatleft,inthetoolbaratthetopofthiswindow.TheLabVIEWHelphighlightsthistopicintheContentstabsoyoucannavigatetherelatedtopics.

ConceptsUsethisbooktolearnaboutconceptsintheLabVIEWControlDesignandSimulationModule.RefertotheHow-Tobookforstep-by-stepinstructionsforusingtheControlDesignandSimulationModule.

(Windows)Toviewrelatedtopics,clicktheLocatebutton,shownatleft,inthetoolbaratthetopofthiswindow.TheLabVIEWHelphighlightsthistopicintheContentstabsoyoucannavigatetherelatedtopics.

UnderstandingDynamicSystemModels(ControlDesignandSimulationModule)Adynamicsystemmodelisamathematicalrepresentationofthedynamicsbetweentheinputsandoutputsofadynamicsystem.Yougenerallyrepresentdynamicsystemmodelswithdifferentialordifferenceequations.Thefollowingfigureshowsasampledynamicsystem.

Thedynamicsysteminthepreviousfigurerepresentsaclosed-loopsystem,alsoknownasafeedbacksystem.Inclosed-loopsystems,thecontrollermonitorstheoutputoftheplantandadjuststheactuatorstoachieveaspecifiedresponse.Youcanusephysicallawsorexperimentaldatatodevelopadynamicsystemmodel.Thefollowingsectionsdescribefeaturesofboththephysicalmodelingandtheempiricalmodelingtechniques.

PhysicalModelsThelawsofphysicsdefinethephysicalmodelofasystem.Thefollowingsectionsdescribevariousclassificationsandfeaturesofphysicalmodels.LumpedversusDistributedParameterModelsIfyoucanuseanordinarydifferentialequationtodescribeaphysicalsystem,theresultingmodelisalumpedparametermodel.Ifyoucanuseapartialdifferentialequationtodescribeasystem,theresultingmodelisadistributedparametermodel.LinearversusNonlinearModelsDynamicsystemmodelsareeitherlinearornonlinear.Alinearmodelobeystheprincipleofsuperpositionandhomogeneity.Thefollowingequationsaretrueforlinearmodels.y1=f(u1)

y2=f(u2)

f(u1+u2)=f(u1)+f(u2)=y1+y2f(au1)=af(u1)=ay1whereu1andu2arethesysteminputs,y1andy2arethesystemoutputs,andaisaconstant.Conversely,nonlinearmodelsdonotobeytheprinciplesofsuperpositionorhomogeneity.Nonlineareffectsinreal-worldsystemsincludesaturation,dead-zone,friction,backlash,andquantizationeffects;relays;switches;andratelimiters.Manyreal-worldsystemsarenonlinear,thoughyoucanlinearizenonlinearmodelstosimplifyadesignoranalysisprocedure.Time-VariantversusTime-InvariantModelsDynamicsystemmodelsareeithertime-variantortime-invariant.Theparametersofatime-variantmodelchangewithtime.Forexample,youcanuseatime-variantmodeltodescribethemassofanautomobile.Asfuelburns,themassofthevehiclechangeswithtime.Conversely,theparametersofatime-invariantmodeldonotchangewithtime.Foranexampleofatime-invariantmodel,considerasimplerobot.Generally,thedynamiccharacteristicsofrobotsdonotchangeovershort

periodsoftime.ContinuousversusDiscreteModelsDynamicsystemmodelsareeithercontinuousordiscrete.Bothcontinuousanddiscretesystemmodelscanbelinearornonlinearandtime-invariantortime-variant.Continuousmodelsdescribehowthebehaviorofasystemvariescontinuouslywithtime,whichmeansyoucanobtainthepropertiesofasystematanycertainmomentfromthecontinuousmodel.Discretemodelsdescribethebehaviorofasystematseparatetimeinstants,whichmeansyoucannotobtainthebehaviorofthesystembetweenanytwosamplingpoints.Continuoussystemmodelsareanalog.Youderivecontinuousmodelsofaphysicalsystemfromdifferentialequationsofthesystem.Thecoefficientsofcontinuousmodelshaveclearphysicalmeanings.Forexample,youcanderivethecontinuoustransferfunctionofaresistor-capacitor(RC)circuitifyouknowthedetailsofthecircuit.ThecoefficientsofthecontinuoustransferfunctionarethefunctionsofRandCinthecircuit.Youusecontinuousmodelsifyouneedtomatchthecoefficientsofamodeltosomephysicalcomponentsinthesystem.Discretesystemmodelsaredigital.Youderivediscretemodelsofaphysicalsystemfromdifferenceequationsorbyconvertingcontinuousmodelstodiscretemodels.Incomputer-basedapplications,signalsandoperationsaredigital.Therefore,youcanusediscretemodelstoimplementadigitalcontrollerortosimulatethebehaviorofaphysicalsystematdiscreteinstants.Youalsocanusediscretemodelsintheaccuratemodel-baseddesignofadiscretecontrollerforaplant.

EmpiricalModelsEmpiricalmodelsusedatagatheredfromexperimentstodefinethemathematicalmodelofasystem.Tosomedegree,physicalmodelsareempiricalbecauseyouexperimentallydeterminecertainconstantsusedtodevelopthemodel.Avarietyofempiricalmodelingmethodsexist.Onemethodofempiricalmodelingusestablesofexperimentaldatathatrepresentthesystemyouwanttomodel.Anothermethodfordevelopingmodelsusessystemidentificationmethods.Systemidentificationmethodsusemeasureddatatocreatedifferentialordifferenceequationrepresentationsthatmodelthedata.

NoteYoucanusetheLabVIEWSystemIdentificationToolkittoconstructmodelsbyusingsystemidentificationmethods.

LinearModelFormsYoucanusetheControlDesignandSimulationModuletorepresentcontinuousanddiscretelinearmodelsinthefollowingthreeforms:

TransferFunction—Thesemodelsusepolynomialfunctionstodefinetherelationshipbetweentheinputsandoutputsofadynamicsystem.Youanalyzetransferfunctionmodelsinthefrequencydomain.Zero-Pole-Gain—Thesemodelsaretransferfunctionmodelsthatyourewritetoshowthegainandthelocationsofthezerosandpolesofthedynamicsystem.Youanalyzezero-pole-gainmodelsinthefrequencydomain.State-Space—Thesemodelsrepresentthedynamicsystemintermsofphysicalstates.Continuousstate-spacemodelsusefirst-orderdifferentialequationstodescribethedynamicsystem,whereasdiscretestate-spacemodelsusefirst-orderdifferenceequations.Youanalyzestate-spacemodelsinthetimedomain.

SISOvs.MIMOModelsWhenyouconfigureacontinuousordiscretetransferfunction,zero-pole-gain,orstate-spacefunction,youcanusetheconfigurationdialogboxtospecifywhetherafunctionissingle-inputsingle-output(SISO)ormultiple-inputmultiple-output(MIMO).SISOmodelshaveonlyoneinputandoneoutput,whereasMIMOmodelshavetwoormoreinputsoroutputs.YoumakethischoicebyselectingtheappropriateoptionfromthePolymorphicinstancepull-downmenu.

ConfiguringSimulationParameters(ControlDesignandSimulationModule)TheSimulationLoop,showninthefollowingfigure,containstheparametersthatdefinethebehaviorofthesimulation.

Youcanconfigurethesesimulationparametersbyusingthefollowingtwomethods:

UsingtheConfigureSimulationParametersdialogboxWiringvaluestotheInputNode

Youalsocanuseacombinationofthesetwomethodsinthesamesimulationdiagram.However,valuesthatyouprogrammaticallyconfigureoverrideanyequivalentsettingsthatyoumakeintheConfigureSimulationParametersdialogbox.

TipUsetheOutputNodetoviewanyerrorsthatoccurduringtheexecutionoftheSimulationLoop.UsetheGetSimulationParametersfunctiontodisplaytheparametersyouconfigureforthesimulation.

TheSimulationLoopisaversionoftheTimedLoop.Bothloopscaniteratedeterministicallyaccordingtoaperiodandpriorityyoudefine.However,theSimulationLoopalsoexecutesthesimulationdiagramaccordingtotheordinarydifferentialequation(ODE)solveryouchoose.TheinsideoftheSimulationLoopalsohasapaleyellowbackgroundtodistinguishthesimulationdiagramfromtheLabVIEWblockdiagram.

Similartootherloopsandstructures,youcanusetunnelstopassdatainandoutoftheSimulationLoop.

ConfiguringSimulationParametersProgrammaticallyThefollowingfigureshowshowyouconfigureasimulationdiagramprogrammatically.

ThepreviousfigureshowshowthegrayboxesontheInputNodedisplayanyvaluesthatyouconfigureintheConfigureSimulationParametersdialogbox.Valuesthatyouconfigureprogrammaticallydonothavegrayboxes.

UsingSimulationFunctionsandVIs(ControlDesignandSimulationModule)TheLabVIEWControlDesignandSimulationModuleincludesbothfunctionsandVIs.TheSimulationfunctionsaretheelementsthatcompriseasimulationmodel.Usethesefunctionstoperformtaskssuchasdefiningdynamicsystemmodels,generatingandcombininginputsignals,andanalyzinganddisplayingsimulationdata.YoucanconfiguremostSimulationfunctionsusingtheconfigurationdialogboxofthatfunction.AfteryouplaceaSimulationfunctiononthesimulationdiagram,double-clickthatfunctiontolaunchitsconfigurationdialogbox.Youalsocanlaunchthisdialogboxbyright-clickingtheSimulationfunctionandselectingConfigurationfromtheshortcutmenu.Forexample,thefollowingfigureshowstheconfigurationdialogboxfortheSineSignalfunction.

TheParameterssectionlistsalltheparametersthatyoucanconfigure

fortheSineSignalfunction.WhenyouselectaparameterfromtheParameterssection,theParameterInformationsectiondisplaysacontrolyoucanusetosetthevalueofthatparameter.UsetheParametersourcecontroltospecifythesourceoftheparametervalue.IfyouselectConfigurationDialogBox,LabVIEWremovesthatinputfromthesimulationdiagram.Youthenmustsetthevalueforthisparameterintheconfigurationdialogbox.IfyouselectTerminal,LabVIEWdisplaysaninputterminalforthatparameteronthesimulationdiagram,andyoucanwirevaluestothisinputtoconfiguretheSimulationfunction.TheparametersyouspecifyforaSimulationfunctionareuniquetothatfunction.Ifyoucreatemultipleinstancesofthesamefunction,youcansetdifferentparametervaluesforeachinstance.

NoteDiscretesimulationfunctionshaveadditionalparametersyouusetoconfiguretheperiodandskewofthefunction.

InadditiontotheSimulationfunctions,theControlDesignandSimulationModuleincludesVIs.UsetheseVIstoperformtasksindirectlyrelatedtothesimulation,suchastrimmingandlinearizingadynamicsystemmodelordesigningoptimalparametersforadynamicsystemmodel.

DynamicSimulationFunctionsThefollowingSimulationfunctionsaredynamicelementsthatdependontheordinarydifferentialequation(ODE)solveryouspecify.

IntegratorTransferFunctionZero-Pole-GainState-Space

ConfiguringDiscreteSimulationFunctions(ControlDesignandSimulationModule)TheDiscreteLinearSystemsfunctionshaveasampleperiod(s)parameterandasampleskew(s)parameter.Theseparametersarelocatedintheconfigurationdialogboxofthatfunction.Thesampleperiod(s)parametersetsthelengthofthestepsizeofthatfunction.Thesampleskew(s)parameterdelaystheexecutionofthatfunction.ThefollowingfigureshowshowthesetwoparametersaffecttheexecutionofadiscreteSimulationfunction.

Thesampleperiod(s)ofadiscretefunctionmustbeamultipleofthediscretestepsizeofthesimulation.Toconfigurethisoveralldiscretestepsize,double-clicktheInputNodeoftheSimulationLooptolaunchtheConfigureSimulationParametersdialogbox.OntheSimulationParameterspage,youcanentertheDiscreteStepSize(s)orautomaticallyconfigurethediscretestepsizeofthesimulation.

NoteIfyouenteravalueof–1forthesampleperiod(s)parameterofaSimulationfunction,thatfunctioninheritsthesamestepsizeasdefinedintheConfigureSimulationParametersdialogbox.

Generating,Collecting,andDisplayingSimulationData(ControlDesignandSimulationModule)TheLabVIEWControlDesignandSimulationModuleincludesseveralfunctionsyouusetogenerate,collect,anddisplaysimulationdata.Thefollowingsectionsprovideinformationaboutusingthesefunctions.

GeneratingandCombiningSignalsUsetheSignalGenerationfunctionstogeneratemanydifferenttypesofsignals,includingsine,ramp,step,pulse,andchirpsignals.Thesefunctionsareusefulwhenyouwanttoseehowadynamicsystemrespondstoaparticulartypeofinput.Forexample,theStepSignalfunctiongeneratesastepsignal,whichyoucommonlyusetotestcontrollerperformance.EachSignalGenerationfunctionhasconfigurationoptionsyoucanusetofittheneedsofaparticularsituation.UsetheSignalArithmeticfunctionstoadd,subtract,multiply,anddividesignals.

CollectingandIndexingSimulationDataTostoreallorpartofasignalhistoryovertheentiresimulationforlateranalysis,usetheCollectorfunction.Thisfunctionstoresvaluesinanarray,similartotheauto-indexingoutputtunnelofaForLoop.However,whereasLabVIEWindexesForLooparraysbytheloopiteration,theControlDesignandSimulationModuleindexesCollectorarraysbysimulationtime.Therefore,afterthesimulationfinishes,youcanseethevaluesthatcorrespondwithcertainpointsintime.TheoppositeoftheCollectorfunctionistheIndexerfunction,whichtakesanarrayofdataandreturnsthecorrectvaluebasedonthesimulationtime.Forexample,youcandefineanarbitrarysignalasanarrayoftimestampsandvaluesateachtimestamp.YouthenwirethisarraytotheInputinputofanIndexerfunction.Whenyourunthesimulation,thisfunctionreturnsthecorrectarrayvalueatthecorrecttime.Ifyoudonotdefineavalueforaspecifictime,thisfunctionlinearlyinterpolatestheexpectedresultaccordingtoseveraloptionsyoucanspecify.TheIndexerfunctionoperatessimilarlytotheauto-indexinginputtunnelofaForLoop,exceptLabVIEWindexesForLooparraysbyloopiterationinsteadofsimulationtime.

DisplayingSimulationDataTheSimTimeWaveformfunctionandBufferXYGraphfunctionoperatesimilarlytotheLabVIEWWaveformChartandXYGraphobjects.However,whereasLabVIEWdisplaystheloopiterationonthex-axisoftheseobjects,theSimulationversionsofthesefunctionsproperlydisplaysimulationtimeonthex-axis.Thisdistinctionisimportantwhenyouareusingavariablestep-sizeordinarydifferentialequation(ODE)solver.Inthissituation,thesimulationmightnotreturnavalueateveryloopiteration,duetochangesinthestepsize.However,theLabVIEWWaveformChartstillplotsavalueeveryloopiteration.TheSimTimeWaveformfunctioncorrectsthisbehaviorandproperlydisplaysunevenly-spacedvaluesonthex-axis.ThefollowingfigureshowshowaSimTimeWaveformChartandaLabVIEWWaveformChartdisplaytheoutputofthePulseSignalfunctionwhensimulatedfor30secondsusingavariablestep-sizeODEsolver.

NoticetheirregularitiesintheLabVIEWWaveformChartwhencomparedtotheSimTimeWaveformChart.

NoteWhenyouplaceaSimTimeWaveformfunctionorBufferXYGraphfunctiononthesimulationdiagram,LabVIEWautomaticallycreatesachartorgraphobjectconnectedtothefunctionoutput.

StoringPrecalculatedDatainLookupTablesLookuptablesareusefulfordefiningsetsofexperimentaldata,suchastheresultofafunction,andthenretrievingthatdatawithoutcalculatingthefunction.Ifyoustorethedatainalookuptable,thesimulationdoesnothavetocomputethefunctioneverytimestep.Instead,youcallthelookuptabletoobtaintheappropriatevalue.Inthissituation,youimprovecomputationperformancebyreducingtheneedtocalculatefunctionsateachiterationoftheSimulationLoop.Alookuptableconsistsoftwodatasets:asetoftablevaluesandacorrespondingsetofdatavalues.Whenyouspecifyaninputvalue,thelookuptablematchesthatinputvaluetoatablevalueandreturnstheappropriatedatavalue.Forexample,consideralookuptablewithtablevaluesof[015]anddatavaluesof[428].Ifyouspecifyaninputvalueof0,thelookuptablereturns4.Ifyouspecifyaninputvalueof5,thelookuptablereturns8.Youalsocanconfigurehowthelookuptableoperatesifyouspecifyaninputvaluethatdoesnotexistasatablevalue.Forexample,youcanconfigurealookuptabletointerpolateorextrapolatetheappropriatedatavaluefromtheavailabletablevalues.UsetheMethodparameteroftheLookupTablesfunctionstodefinethisbehavior.Thisexampleusesaone-dimensionallookuptable;however,theControlDesignandSimulationModulealsoincludesfunctionsthatimplementtwo-andthree-dimensionallookuptables.

TransferringDataBetweenSimulationLoopIterationsUsetheMemoryfunctiontotransferthevalueofasignalfromoneiterationoftheSimulationLooptothenext.ThisfunctionbehavessimilarlytoashiftregisteryoucanplaceonaWhileLoop.ThisfunctionispolymorphicandacceptsanydatatypeyouwiretotheInitialValueinput.Toimplementafixed-timedelay,usetheDiscreteUnitDelayfunction.

ChangingFunctionIconStyles(ControlDesignandSimulationModule)YoucanchangetheiconstyleofaSimulationfunctiononthesimulationdiagram.Right-clickaSimulationfunctionandselectIconStylefromtheshortcutmenutodisplaythefollowingoptions:

Static—DisplaystheSimulationfunctionasastandardVI.Dynamic—DisplaystheSimulationfunctionasanobjectthatyoucanresize.Dynamiciconsalsodisplayapreviewoftheircontents.Forexample,aSineSignalfunctionwithadynamicicondisplaysasinewavewiththefrequency,amplitude,andphasethatyouconfigure.TextOnly—DisplaystheSimulationfunctionasalistofparametervalues.Express—DisplaystheSimulationfunctionwithalistofparametersbelowtheicon.Youcanresizetheparameterlisttodisplaymoreinputsandoutputs.Thisiconstylealsoshowsparametervaluesdirectlyonthesimulationdiagram.

DeterminingFeedthroughBehaviorandDefiningFeedbackCycles(ControlDesignandSimulationModule)TherelationshipbetweenafunctioninputandoutputdefinesthefeedthroughbehaviorofthatI/Opair.AnI/Opaircanhaveindirect,direct,orparameter-dependentfeedthroughbehavior.IfanI/Opairhasindirectfeedthroughbehavior,youcancreateafeedbackcyclebetweenthatinputandoutput.AnI/Opairwithdirectfeedthroughbehaviordoesnotallowafeedbackcycle.Thefollowingsectionsprovidemoreinformationaboutthesebehaviors.

IndirectFeedthroughandFeedbackCyclesWhereasLabVIEWVIsexecuteonlyafterreceivingthevalueofallinputstothatVI,manySimulationfunctionscanexecutewithoutreceivingthevalueofcertaininputs.ConsideraSimulationfunctionwithinputuandoutputy.Atanytimestep,ifthefunctiondoesnotrequirethevalueofutocomputethevalueofy,uhasindirectfeedthroughtoy.Whenindirectfeedthroughexistsbetweenuandy,youcancreateafeedbackcyclebetweentheseparameters.Inafeedbackcycle,thevalueofyattimetreliesonthevalueofuattimet–dt,t–dt2,andsoon.

Forexample,theinputparameteroftheIntegratorfunctionhasindirectfeedthroughtotheoutputparameter.Youcancreateafeedbackcyclebetweenthisinputandoutput.Thefollowingfigureshowsthisbehavior:

YoucanuseoneormoreSimulationfunctionsandotherLabVIEWfunctionsinafeedbackcycleaslongasatleastoneSimulationfunctioninthefeedbackcyclehasindirectfeedthroughbehavior.Theindirectfeedthroughfunctioncanstartthedataflowbyexecutingthefunctionoutputatthecurrentstepbeforereceivinganinputfromthecycleatthecurrentstep.Therefore,theinputatthecurrentstepandtheoutputatthecurrentstepmustnotdependoneachotherdirectlyinatleastonefunctioninthecycle.ThefollowingSimulationfunctionshaveatleastoneI/Opairwithindirectfeedthrough.

DiscreteKalmanFilterDiscreteObserver

DiscreteStochasticState-SpaceDiscreteUnitDelayIntegratorMemoryTransportDelay

DirectFeedthroughIfafunctionoutputyrequiresaninputuinordertoexecute,uhasdirectfeedthroughtoy.Youcannotcreateafeedbackcyclebetweeninputsandoutputswithdirectfeedthrough.Forexample,theinitialconditionparameteroftheIntegratorfunctionhasdirectfeedthroughbehaviortotheoutputparameter.Thisfunctionrequiresavaluefortheinitialconditionparameterinordertocalculatetheoutputparameter.Otherfunctions,suchasFriction,requirethevaluesofallinputsinordertoexecute.Ifyouattempttocreateafeedbackcyclebetweenaninputandoutputwithdirectfeedthrough,thewireappearsbroken.Thefollowingfigureshowsthisbehavior:

Noticethedifferencebetweenthepreviousfigureandthefigureshowingthefeedbackcycle.

Parameter-DependentFeedthroughSeveralfunctionshavefeedthroughbehaviorthatdependsonhowyouconfiguretheparametersofthatfunction.Forexample,considertheTransferFunctionfunction.Thefeedthroughbehaviorofthisfunctiondependsontheorderofthenumeratoranddenominatorpolynomialequationsyouspecify.ThefollowingSimulationfunctionshaveatleastoneI/Opairwithparameter-dependentfeedthrough.

TransferFunctionZero-Pole-GainState-SpaceDiscreteFilterDiscreteIntegratorDiscreteTransferFunctionDiscreteZero-Pole-GainDiscreteState-Space

Ifyouusetheconfigurationdialogboxtodefinetheparametersofthesefunctions,suchasthenumeratoranddenominatorofatransferfunction,LabVIEWautomaticallydeterminestheappropriatefeedthroughbehavioranddisplaysthischoiceintheFeedthroughpull-downmenu.However,ifyouuseblockdiagramterminalstodefinetheparametersofthesefunctions,youmustsetthefeedthroughbehaviormanually.AllSimulationfunctionsnotmentionedinthissectionorintheIndirectFeedthroughandFeedbackCyclessectionhavedirectfeedthrough.

PlacingLabVIEWVIs,Functions,andStructuresontheSimulationDiagram(ControlDesignandSimulationModule)YoucanuseamajorityofLabVIEWVIsandfunctionstodescribeadynamicsystemmodel.However,youcannotplacecertainstructures,suchastheWhileLoop,ForLoop,orEventstructure,directlyonthesimulationdiagram.Instead,youcanplacethesestructuresinasubVI,whichyouthenplaceonthesimulationdiagram.Bydefault,theControlDesignandSimulationModuleexecutesVIsandExpressVIsascontinuousfunctions.YoucanchangethisbehaviorbyusingtheSubVINodeSetupdialogbox.Tolaunchthisdialogbox,right-clicktheobjectandselectSubVINodeSetupfromtheshortcutmenu.YoucanconfigureaVItoexecuteatonlymajortimestepsoftheODEsolver,atbothmajorandminortimestepsoftheODEsolver,asadiscretefunction,oratinitializationofthesimulationdiagram.

UsingCaseStructuresontheSimulationDiagramYoucanplaceaCasestructuredirectlyonthesimulationdiagram.Thevalueyouwiretotheselectorterminaldetermineswhichmodeltoevaluate.Ifaninput-outputpaironanysubdiagramofthecasestructurecontainsdirectfeedthrough,youcannotcreateafeedbackcyclebetweenthatinputandoutput.NationalInstrumentsrecommendsyouuseafixedstep-sizeordinarydifferentialequation(ODE)solverwhenusingaCasestructureonthesimulationdiagram.

NoteYoucannotplacefrontpanelterminalsinsideaCasestructureonasimulationdiagram.

How-ToThisbookcontainsstep-by-stepinstructionsandotherinformationthatmightbeusefulasyouusetheLabVIEWControlDesignandSimulationModule.RefertotheConceptsbooktolearnaboutrelatedconcepts.

(Windows)Toviewrelatedtopics,clicktheLocatebutton,shownatleft,inthetoolbaratthetopofthiswindow.TheLabVIEWHelphighlightsthistopicintheContentstabsoyoucannavigatetherelatedtopics.

ModularizingtheSimulationDiagram(ControlDesignandSimulationModule)TheLabVIEWControlDesignandSimulationModulesupportssimulationsubsystems,whichyouusetomodularizeandencapsulateportionsofthesimulationdiagram.YoucreatesimulationsubsystemssimilarlytocreatingsubVIs.

(Windows)Toviewrelatedtopics,clicktheLocatebutton,shownatleft,inthetoolbaratthetopofthiswindow.TheLabVIEWHelphighlightsthistopicintheContentstabsoyoucannavigatetherelatedtopics.

TypesofSimulationSubsystems(ControlDesignandSimulationModule)Simulationsubsystemsprovideawaytomodularizesimulationdiagramcode.Bycombiningseveralfunctionsintoasubsystem,youreducetheamountofspaceneededonthesimulationdiagram,makingthesimulationeasiertonavigatevisually.Simulationsubsystemsalsoareusefulforvalidating,distributing,andreusingportionsofthesimulationdiagram.YoucanusemanySimulationVIsandfunctionsonlyonasimulationdiagram,suchaswithinaSimulationLoop.Becausesimulationsubsystemsmodularizesimulationdiagramcode,youcanusetheSimulationVIsandfunctionsinsimulationsubsystemsaswell.TheentireblockdiagramofasimulationsubsystemispaleyellowliketheinsideofaSimulationLoop.WhenyouuseSimulationVIsandfunctionsinasimulationsubsystem,youplacetheVIsandfunctionsdirectlyonthesubsystemblockdiagramratherthanwithinaSimulationLoop.Youcanrunsimulationsubsystemsasstand-aloneVIs,withinaSimulationLooporanothersimulationsubsystem,oronablockdiagramoutsideaSimulationLoop.

RunningaSubsystemasaStand-AloneVIWhenyourunasimulationsubsystemasastand-aloneVI,youconfigurethesimulationparametersbyselectingOperate»ConfigureSimulationParameterstolaunchtheConfigureSimulationParametersdialogbox.YoualsocanconfiguretheexecutionandappearanceofthesubsystembyselectingFile»VIProperties.Whenrunningasimulationsubsystemasastand-aloneVI,youcanusestandardLabVIEWdebuggingtechniques,suchasexecutionhighlighting,breakpoints,probes,andsingle-stepping.YoucannotusethesetechniquesonasubsystemthatiswithinanotherSimulationLoop.Youalsocannotstepintothesubsystem.However,youcansetabreakpointontheentiresubsystembyright-clickingthesubsystemandselectingBreakpoint»SetBreakpointfromtheshortcutmenu.Youalsocanuseaprobeoracustomprobetomonitorthesubsystemoutput.ThefollowingfigureshowsthesimulationdiagramofasimulationsubsystemNewton.vi,whichobtainsthepositionofamassbyusingNewton'sSecondLawofMotion.

Inthepreviousfigure,thissubsystemhasfrontpanelcontrolsandindicators,soyoucanrunthissubsystembyclickingtheRunbutton.BecauseNewton.vidoesnothaveaSimulationLoop,youconfigurethe

parametersofthissubsystembyselectingOperate»ConfigureSimulationParameters.

RunningaSubsysteminaSimulationLoopIfyourunasimulationsubsysteminsideaSimulationLoop,thesimulationsubsysteminheritstheparametersfromtheSimulationLoop.ThefollowingfigureshowsNewton.viincludedwithintheSimulationLoopofanothersimulationdiagram.

Inthepreviousfigure,theparametersoftheSimulationLoopoverrideanyparametersyouconfiguredspecificallyforNewton.vi.

NoteYoucreatethissubsystemandthisVIintheGettingStartedwithSimulationtutorial.

RunningaSubsystemOutsideaSimulationLoopIfyourunasimulationsubsystemonablockdiagramoutsideaSimulationLoop,thesimulationsubsystemexecutesonestepoftheordinarydifferentialequation(ODE)solvereachtimethesimulationsubsystemiscalled.Forexample,ifyouplacethesimulationsubsysteminaTimedLoop,onestepoftheODEsolverexecutesateachiterationoftheloop.Youcanuseonlyfixedstep-sizeODEsolversforasimulationsubsystemoutsideaSimulationLoop.SpecifythetimestepusingtheStepSize(s)configurationoptionofthesubsystem.

TipIfyoucreateanapplicationwithasimulationsubsysteminsideaTimedLoopandthendeploytheapplicationtoareal-timetarget,settheStepSize(s)ofthesubsystemequaltotheperiodoftheTimedLoop.

WhenyouplaceasimulationsubsystemonablockdiagramoutsideaSimulationLoop,theiconofthesimulationsubsystemappearsintheExpressstylebydefault.Youcanwirevaluestotheparametersofthesimulationsubsystemtoconfigurethesimulationsubsystemprogrammatically.

NoteTheStaticandDynamiciconstylesaredisabledforsubsystemsoutsideaSimulationLoop.

Youalsocanconfiguretheparametersofthesimulationsubsysteminteractively.Double-clickthesimulationsubsystemtolaunchtheconfigurationdialogboxofthatsimulationsubsystem.Inthisconfigurationdialogbox,youcanconfigurethespecificparametersofthesimulationsubsystemaswellasthefollowinggeneralsimulationparameters:

InitialTime(s)—SpecifiesthetimeatwhichtostarttheODEsolver.ODESolver—SpecifiesthetypeofODEsolverthesimulationuses.Nan/InfCheck—SpecifiesthatyouwanttheControlDesignandSimulationModuletocheckthesimulationvaluesfornotanumber(NaN)andinfinite(Inf)values.TheControlDesignandSimulationModulereturnsanerrorifitencountersaNaNorInfvalue.

StepSize(s)—Specifiestheinterval,inseconds,betweenthetimesatwhichtheODEsolverevaluatesthemodelandupdatesthemodeloutput.DiscreteStepSize(s)—Specifiesthebasetimestepsize,inseconds,forthesimulation.AutoDiscreteTime—AutomaticallycalculatestheDiscreteStepSize(s).

TheseparametersareidenticaltoparametersyoucanconfigureintheConfigureSimulationParametersdialogboxofaSimulationLoop.Intheconfigurationdialogboxofasimulationsubsystem,theseparametersappearassub-itemsoftheSimulationParametersitemintheParameterstree.Ifthesimulationsubsystemalreadycontainsaparameterwiththesamenameasoneofthegeneralsimulationparameterslistedabove,LabVIEWappendsthegeneralsimulationparameternamewithanunderscore.ThefollowingfigureshowsNewton.vionablockdiagramoutsideaSimulationLoop.

Inthepreviousfigure,theTimedLoopdetermineswhenNewton.viexecutesthenextstepoftheODEsolver.BecauseNewton.viisoutsideaSimulationLoop,youcanconfigurethesimulationparameters,includingtheODEsolvertouse,bydouble-clickingthesimulationsubsystem.IfyourunasimulationsubsystemoutsideaSimulationLoop,youcanreinitializethesimulationsubsystembysettingtheInitializeinputofthesimulationsubsystemtoTRUE.ThisinputrestartstheODEsolverfromthespecifiedInitialTime(s).TheInitializeinputisavailableforasimulationsubsystemonlywhenthesubsystemisnotinsideaSimulationLooporanothersimulationsubsystem.

PolymorphicSubsystemsIfyoucreateoneormoresubsystemsthatperformthesameoperationondifferentdatatypes,youcanpackagethosesubsystemstogethertocreateapolymorphicsubsystem.ApolymorphicsubsystemisasingleVIthatpointstooneormoresubsystems,calledinstances.Eachinstanceacceptsadifferentdatatypeforasingleinputoroutputterminal.LabVIEWautomaticallyselectsthecorrectinstancebasedontheinputdatatype.Forexample,onesubsystemcouldoperateonadouble-precisionfloatingpointnumber,whileanothersubsystemperformsthesameoperationona16-bitinteger.Insteadofplacingbothsubsystemsonthesimulationdiagram,youcancreateapolymorphicsubsystemthatautomaticallychoosesthecorrectinstance.Forapolymorphicsubsystemtowork,eachinstanceofthepolymorphicsubsystemmustbeasimulationsubsystem.YoucannotcreateapolymorphicsubsystemwithbothVIsandsubsystemsasinstances.Also,eachsubsystemmusthaveanidenticalconnectorpanepattern.Additionally,thenamesofcorrespondinginputparametersforeachinstancemustbeidentical.

TrimmingandLinearizingNonlinearModels(ControlDesignandSimulationModule)Manyreal-worlddynamicsystemmodelsarenonlinear.Ifyouwanttodesignacontrollerforanonlinearmodel,youmustfirstlinearizethatmodel.Linearizinganonlinearmodelinvolvesapproximatingthebehaviorofthatmodelaroundanoperatingpoint.Theoperatingpointisthesetoftheinputsandstatesofthemodel.Whenyoulinearizeamodel,theresultisalineartime-invariant(LTI)state-spacemodel.

NoteYoucandesignacontrollerforLTImodelsusingtheControlDesignVIsandfunctions.

Trimmingamodelinvolvessearchingforvaluesofmodelinputsandstatesthatsatisfyanyconditionsyouspecify.Forexample,youcanspecifythatthemodeloutputsorstatederivativesmusthaveacertainvalue.Trimmingthemodelusingtheseconditionsreturnsthevaluesoftheinputsandstatesthat,whengiventothemodel,producetheoutputsandstatederivativesyouspecified.Youalsocantrimamodeltodetermineanoperatingpointaboutwhichyoulinearizethemodel.TheLabVIEWControlDesignandSimulationModuleprovidesseveralmethodsfortrimmingandlinearizingmodels.Youcaninteractivelytrimandlinearizeamodel.Youalsocanprogrammaticallytrimandprogrammaticallylinearizeamodel.

NoteTheabovemethodsoperateoncontinuoussimulationsubsystems.Therefore,youmustcreateasimulationsubsystemthatrepresentsthemodelbeforetrimmingorlinearizingthatmodel.

(Windows)Toviewrelatedtopics,clicktheLocatebutton,shownatleft,inthetoolbaratthetopofthiswindow.TheLabVIEWHelphighlightsthistopicintheContentstabsoyoucannavigatetherelatedtopics.

ExecutingSimulationsinRealTime(ControlDesignandSimulationModule)YoucanusetheLabVIEWControlDesignandSimulationModulewiththeLabVIEWReal-TimeModuleandvariousNationalInstrumentsreal-time(RT)targetstoimplementsimulationsandcontrollersinrealtimewithreal-worldinputsandoutputs.Forexample,youcancombinethissoftwareandhardwaretodesignandimplementarapidcontrolprototype(RCP)orhardware-in-the-loop(HIL)configuration.YouconfigurethetimingSimulationLoopaccordingtotheneedsofthesimulation.TheControlDesignandSimulationModulecanexecuteVIsonhardwaretargetsrunningthereal-timeoperatingsystem(RTOS)oftheArdencePharLapEmbeddedToolSuite(ETS)orWindRiverVxWorks.

NoteTheControlDesignandSimulationModulesupportsonlyETSandVxWorkstargetswithatleast32MBofRAM.

TheReal-TimeModuleincludestheGettingStartedwiththeLabVIEWReal-TimeModulemanual,whichintroducestheconceptsnecessarytocreatereal-timeapplications.TheReal-TimeModuledocumentationalsoincludestopicsaboutorganizingandmanagingprojects,creatingdeterministicapplications,andsharingdataindeterministicapplications.

(Windows)Toviewrelatedtopics,clicktheLocatebutton,shownatleft,inthetoolbaratthetopofthiswindow.TheLabVIEWHelphighlightsthistopicintheContentstabsoyoucannavigatetherelatedtopics.

Offline,RCP,andHILConfigurations(ControlDesignandSimulationModule)Thefollowingsectionsprovideanoverviewoftheprocessyoumightusetosimulateadynamicsystem.Thefollowingsectionsalsodescribeexamplesofofflinesimulations,rapidcontrolprototyping(RCP)configurations,andhardware-in-the-loop(HIL)configurations.

OfflineSimulationAnofflinesimulationisonethatisnotconnectedtoanyhardware.YouusetheLabVIEWControlDesignandSimulationModuletosimulateallpartsofthedynamicsystem,includingthecontroller,thesystemyouwanttocontrol,andanyinputsoroutputs.Thefollowingfigurerepresentsasimulationofanofflinecontrolsystem.

IfyouarerunninganofflinesimulationonaWindowscomputer,NationalInstrumentsrecommendsyouplaceacheckmarkintheSynchronizeLooptoTimingSourcecheckboxontheTimingParameterspageoftheConfigureSimulationParametersdialogboxforoptimalperformance.

RapidControlPrototypeConfigurationAnRCPconfigurationreplacesthesimulatedsystemwithanactualsystem.Usethisconfigurationtotestmultiplecontrolleralgorithmswithoutbuildingthecontrolleragaineverytimeyoumakeachange.Inthissituation,thesimulatedcontrollerisconnectedtohardwareactuatorsandhardwaresensors.ToconvertanofflinesimulationtoanRCPconfiguration,removethesystemmodelfromthesimulation.Replacethesysteminputwithanoutputfromahardwaredevice,andreplacethesystemoutputwithaninputfromahardwaredevice.ThefollowingfigurerepresentsanRCPconfiguration.

Inthepreviousfigure,thesimulatedcontrollerusesNationalInstrumentsreal-timehardware,suchasaDAQdevice,tosenddatatothehardwaresystem.

Hardware-in-the-LoopConfigurationAHILconfigurationinvolvestheactualcontrollerprovidinginputtoasimulatedsystem.Usethisconfigurationtotestacontrolleronasystemwithoutactuallyhavingthatsystemavailable.Forexample,ifyouweretestinganenginecontrolunit(ECU)foracar,youcouldtesttheECUwithouthavingtobuildthecarmultipletimes.HILconfigurationsalsoareusefulfortestingcontrollersunderextremeconditionsthatyoucannotreplicateconvenientlyinalaboratory.ToconvertanofflinesimulationtoaHILconfiguration,removethecontrollermodelfromthesimulation.Replacethecontrollerinputwithanoutputfromahardwaredevice,andreplacethecontrolleroutputwithaninputfromahardwaredevice.TheresultissimilartotheRCPconfiguration,exceptwiththecontrollermodel,notthesystemmodel,replacedwithphysicalhardwareinputsandoutputs.ThefollowingfigureshowsaHILconfigurationoftheexampleinthepreviousfigure.

Inthepreviousfigure,thecontrollerusesNationalInstrumentsreal-timehardware,suchasaDAQdevice,tosenddatatothesimulatedsystem.

DeterministicODESolvers(ControlDesignandSimulationModule)Runningasimulationorcontrollerinrealtimemeansthatthesimulationtimemustequalthewall-clocktimeateachpointthatthesimulationorcontrollerinteractswiththerealworld.Generally,thesephysicalinteractionpointscorrespondtothesamplingpointsoftheinputandoutputhardware.Therefore,ateachsamplingtime,thesimulationtimemustequalthewall-clocktime.Tomeetthereal-timedeadline,youcanconfiguretheLabVIEWControlDesignandSimulationModuletoexecutedeterministicallybyplacingastrictupperboundontheexecutiontimeoftheSimulationLoop.NationalInstrumentsalsorecommendsyouconfiguretheSimulationLooptouseafixedstep-sizeordinarydifferentialequation(ODE)solver.TheseODEsolversaredeterministic,whichensuresthatblockdiagramcoderunningateachtimestepmeetsthedeadlinesimposedbythetimingofthehardwareinputsandoutputs.TheControlDesignandSimulationModuleincludesthefollowingdeterministicODEsolvers:

Runge-Kutta1RungeKutta2Runge-Kutta3Runge-Kutta4DiscreteStatesOnly

Variablestep-sizeODEsolversarenotappropriateforreal-timeapplicationsbecausethesesolversadjustthestepsizebasedontheestimatederrorofthesolution.Thisadjustmentrequiresadditionalcomputationalresources,whichcaninterferewiththetimingrequirementsofareal-timeapplication.

ConsiderationsforETSTargets(ControlDesignandSimulationModule)IfyouareexecutingasimulationonanArdencePharLapEmbeddedToolSuite(ETS)target,NationalInstrumentsrecommendsyoulettheLabVIEWControlDesignandSimulationModulecalculatethenecessaryvalueofthesimulationperiod.Toautomaticallycalculatetheperiod,placeacheckmarkintheAutoPeriodcheckbox,whichislocatedontheTimingParameterspageoftheConfigureSimulationParametersdialogbox.Whenyoufollowthisprocedure,othertaskscantocontinuetoexecutewhenthesimulationisnotscheduledtoexecute.

LabVIEWProjectsandSharedVariables(ControlDesignandSimulationModule)Toexecuteasimulationonareal-time(RT)target,youmustcreateaproject.AprojectprovidesawaytomanageVIs,RTtargets,dependencies,buildspecifications,andotherfilesrelatedtotheproject.UsetheProjectExplorerwindow,availablebyselectingFile»NewProject,tomanagethecontentsofaproject.Anothercomponentofareal-timesimulationisthesharedvariable.YoucreatesharedvariablestosimplifytheprocessofsharinglivedatabetweentheWindowscomputerandtheRTtarget.FormoreinformationabouttheLabVIEWprojectandthesharedvariable,includingtutorialsthatintroduceyoutotheseconcepts,refertotheGettingStartedwiththeLabVIEWReal-TimeModuledocument,locatedinthelabview\manualsdirectory.IfyouhavenotinstalledtheLabVIEWReal-TimeModule,youcanaccessthisdocumentatni.com/manuals.

OptimizingDesignParameters(ControlDesignandSimulationModule)Oneimportantapplicationofsimulatingdynamicsystemmodelsisusingthesimulationtodetermineparametervaluesthatmaximizesomemeasureofperformance.TheLabVIEWControlDesignandSimulationModuleincludestheSIMOptimalDesignVI,whichyoucanusetoobtainparametersthatminimizeacostfunctionwhilesatisfyingconstraintsonadynamicsystem.YoucanusethisVIwithbothlinearandnonlinearsystems,althoughtheControlDesignandSimulationModuleincludespre-definedoptionsforonlylinearsystems.Designproblemscanrangefromdesigningphysicalelements,suchassprings,todesigningmoreabstractelementssuchascontrollersordigitalfilters.Correspondingly,performancespecificationsmightrangefromsimplemechanicallimitsonoutputstomoresophisticatedrequirementssuchasfrequencydomainnormsforcontrolledsystems.Forexample,whendesigningasuspensionsystemforacar,youmustselectastiffnessconstantforaspringandadampingconstantforadissipativeelement.Thegoalistofindaparametersetthatprovidesmaximumcomfort.Thisoptimalparametersetcorrespondstoaperformancemeasure,suchastheaveragedeviationofthepassengerfromadesiredheightasthecartravelsdowntheroad.Youuseparameterdesigntodeterminethisoptimalparametersetwhiletakingintoaccountthedynamicsofthesystemandtheexpectedoperatingconditionsanddisturbances.Youcanuseseveraltechniquestodeterminethisparameterset.Forsomeproblems,youmightbeabletocomputetheoptimumanalytically.However,analyticalsolutionstypicallyaredifficultorimpossibletocompute.Insuchcases,youcanusenumericaloptimizationinstead.ApowerfulandgeneralpurposenumericaloptimizationalgorithmisSequentialQuadraticProgramming(SQP).TheSIMOptimalDesignVIusesthisalgorithm.ThisVIprovidesdomain-specificfunctionsyoucanusetoperformparameteroptimizationfordesignpurposes.Specifically,youcanusethisVItodetermineoptimalparametersfromfinite-horizontime-domaindynamicssimulations.Thefollowingexpressionsdefinethenonlinearoptimizationproblem.min(J(p))

hl≤H(p)≤hupl≤p≤puwherepisaparametervalue,J(p)isacostfunction,andH(p)isasetofconstraints.TheobjectiveoftheSQPalgorithmistominimizeJ(p)andsatisfytheconstraintsdefinedbyhl≤H(p)≤huwhilekeepingpwithinspecifiedminimumandmaximumvalues.DesigningasystemusingtheSQPalgorithminvolvesthefollowingsteps:

1. Constructingthedynamicsystemmodelandspecifyingthecomponentofthatmodelforwhichyouwanttofindoptimalparametervalues.

2. Definingaperformancemeasure,alsoknownasacostfunction,youwanttominimize.

3. Defininganyconstraintsonthedynamicsystemthatanyfeasibleparametervaluesmustsatisfy.

4. Definingminimumandmaximumvaluesforeachparameter.5. Definingasetofinitialparametervaluesandaninitialparameters

mesh,whichgeneratesadditionalsetsofinitialparametervalues.6. ExecutingtheSQPalgorithm,usingtheinformationyouspecified

insteps1through5,byrunningtheSIMOptimalDesignVI.Thecostfunction,inequalityconstraints,andcomponenttooptimizemakeuptheProblemSpecificationparameteroftheSIMOptimalDesignVI.Foreachoption,youcanchoosefrompre-definedtypesorspecifyacustomizedversion.

NoteTheControlDesignandSimulationModuleincludesacasestudythatdeterminestheoptimalparametersforaproportional-integral-derivative(PID)controller.

ConstructingtheDynamicSystemModel(ControlDesignandSimulationModule)Bydefault,theSIMOptimalDesignVIcomputesoptimaldesignparametersforaproportional-integral-derivative(PID)controllerplacedinaclosed-loopdynamicsystem.Thefollowingfigureshowsthiscontrollerandthedynamicsystemstructure.

F1,F2,C,G1,G2,andSconsistoftransferfunctionsandassociatedinformation,suchasdelaysandsamplingtime.YoucanusetheSIMConstructDefaultSystemVItoconstructthesetransferfunctionsandspecifyreferenceinputsignalsr,ru,andry.ThisVIreturnsthenecessarydynamicsysteminformationintheSystemDataoutput,whichyouthencanwiretotheSystemDatainputoftheSIMOptimalDesignVI.TheSIMOptimalDesignVIthenexcitesthesystemusingthedefinedinputsandobtainsthetimeresponse.UsetheSystemresponsetypeparameteroftheSIMOptimalDesignVItospecifyifyouwantthisVItoreturnoptimalparametervaluesforC,F1,orF2.Bydefault,CisaparallelPIDcontrollerdefinedbythefollowingequation:

where =0.01,Uisthecontrolaction,sistheLaplacevariable,andKP,KI,andKDaretheproportional,integral,andderivativegains,respectively.YoualsocandefineacustomtypeofsystemresponsedatayouwanttooptimizebyusingVItemplates.Toaccessthesetemplates,select

File»NewtolaunchtheNewdialogbox.ThenselectVI»FromTemplate»Simulation»OptimalDesignfromtheCreateNewtree.Double-clickSystemResponse(ModifyControllerOnly)tomodifyonlythestructureofthecontroller.Double-clickSystemResponse(General)todefineanewdynamicsystemstructure.Ifyoudefineanewdynamicsystemstructure,theblockdiagramcodeyouwritemustgeneratetheoutputvectoryandthetimevectorTime.Thecodealsomustgeneratethecontrolactionvectoruunlesstheoptimizationproblemdoesnotrequireacontrolaction.Forexample,ifyouusetheSIMOptimalDesignVItodesignthephysicalparametersofamechanism,youdonotneedtospecifyacontrolaction.Inthissituation,ensurethecostfunctionandinequalityconstraintsyouspecifydonottakeacontrolactionintoaccount.

DefiningaCostFunction(ControlDesignandSimulationModule)Acostfunctionistheperformancemeasureyouwanttominimize.Examplesofcostincludetotalpowerconsumption,integratederror,anddeviationfromareferencevalueofasignal.Thecostfunctionisafunctionalequation,whichmapsasetofpointsinatimeseriestoasinglescalarvalue.Thisscalarvalueisthecost.UsetheCosttypeparameteroftheSIMOptimalDesignVItospecifythetypeofcostfunctionyouwantthisVItominimize.TheLabVIEWControlDesignandSimulationModuleincludesthefollowingtypesofcostfunctions:

IE—Acostfunctionthatintegratestheerror.IAE—Acostfunctionthatintegratestheabsolutevalueoftheerror.ISE—Acostfunctionthatintegratesthesquareoftheerror.ITAE—Acostfunctionthatintegratesthetimemultipliedbytheabsolutevalueoftheerror.ITE—Acostfunctionthatintegratesthetimemultipliedbytheerror.ITSE—Acostfunctionthatintegratesthetimemultipliedbythesquareoftheerror.ISTE—Acostfunctionthatintegratesthesquareofthetimemultipliedbythesquareoftheerror.LQ—Alinearquadraticcostfunction.SumofVariances—Acostfunctionbasedonthevarianceoftheerrormultipliedbythevarianceofthecontrolaction.

YoualsocandefineacustomcostfunctionusingaVItemplate.Toloadthistemplate,intheNewdialogbox,selectVI»FromTemplate»Simulation»OptimalDesign»ComputeCostfromtheCreateNewtree.Theblockdiagramofthistemplatecontainsseveralparametersincludingthecontrolactionu,thedynamicsystemoutputy,anarrayofinputsignals,andatimeseriesvector.Youalsocanspecifyanyweightsonanypartofthecostfunction.

Afteryoudefinetheseparameters,youcanwriteLabVIEWblockdiagramcodetomanipulatetheparametersaccordingtothecostfunction.Forexample,thefollowingequationdefinestheIEcostfunction.

wheree(t)isthemeasurederror,Nisthetotalnumberofsamplesinthetimeresponse,nisthecurrenttimeresponsesample,andiistheindexofthecurrentoutput.YoucanviewtheVIthatimplementsthiscostfunctioninthelabview\vi.lib\Simulation\OptimizationBasedDesign\Costdirectory.

NoteIfyoucreateacostfunctionVIthatdoesnottakethecontrolactionintoaccount,donotdeletetheuparameterfromtheblockdiagram.DeletingthisparameterbreakstheconnectorpanestructureonwhichtheSIMOptimalDesignVIdepends.Instead,leavetheparameterunwired.

AfteryousavethecustomcostfunctionasaVI,youmustspecifythelocationofthecustomfunctionintheProblemSpecificationparameteroftheSIMOptimalDesignVI.SelectUserdefinedfortheCosttypeparameterandspecifythepathtotheVIintheFilepathuserdefinedcustomcostcalculationpathcontrol.

DefiningInequalityConstraints(ControlDesignandSimulationModule)Inequalityconstraintsrepresenttrade-offsimplicitintheproblemspecification.Forexample,youmightbeabletoremoveerrorsinacontrolloopbyapplyingaverylargecontrolaction.However,thenecessarycontrolactionmightbeimpossibletoachieveintherealworld.IfyouspecifyconstraintsonthecontrolactionbeforeexecutingtheSequentialQuadraticProgramming(SQP)algorithm,youcaneliminateoptimalvaluesthatrequireanunfeasiblecontrolaction.

NoteConstraintsaddagreatdealofcomplexitytotheoptimizationproblem.Ifpossible,minimizethenumberofconstraintsbeforeexecutingtheSQPalgorithm.Onestrategytominimizethenumberofconstraintsinvolvesfirstfindingoptimalvalueswithnoconstraints,thengraduallyaddingconstraintsanddeterminingtheleastamountofconstraintsrequiredforthedynamicsystem.

Becausetheoptimizationproblemisbasedonafinite-horizontime-domainsimulation,youspecifytheinequalityconstraintsasenvelopesthatboundthetimeresponseofthecontrolactionandtheoutput.Youalsocanplaceinequalityconstraintenvelopesontherateofchangeofthecontrolactionandtherateofchangeoftheoutput.Theseenvelopesarepiecewiselinearcurvesthatspecifytheupperandlowerlimitsonasignalduringthesimulation.TheSIMOptimalDesignVIthencalculatesH(p)astheminimumandmaximumdistanceofthetimeseriespointsfromtheseenvelopes.UsetheInequalityConstraintsparameteroftheSIMOptimalDesignVItodefinetheseenvelopes.Thisparameterspecifiestheupperandlowerconstraintenvelopesonthefollowingfourareasofthedynamicsystem:thecontrolaction,theoutput,therateofchangeofthecontrolaction,andtherateofchangeoftheoutput.

NoteYoucanusetheGraphicallySpecifyInequalityConstraintsVI,locatedinthelabview\examples\ControlandSimulation\Simulation\OptimalControlDesign\GraphicallySpecifyInequalityConstraintsdirectory,todrawtheupperandlowerenvelopes.ThisVIreturnsasetofpointsyouthencanwiretothe

InequalityConstraintsparameter.

Forexample,consideranoutputyi(t)constrainedbyenvelopes,asshowninthefollowingfigure.

A,B,C,andDarepointsthatdefinetheupperenvelopeUEi(t),andE,F,G,andHarepointsthatdefinethelowerenvelopeLEi(t).TheSIMOptimalDesignVIthenconstrainsyi(t)tothefollowingrelationship:

LEi(t)<yi(t)<UEi(t)

ThisVIencodesthisconstraintbycomputingtheclearancebetweentheoutputandeachenvelope.TheupperclearanceUCiisdefinedasmax(UEi(t)–yi(t)).ThelowerclearanceLCiisdefinedasmax(yi(t)–LEi(t)).Theseclearancesclarifythattheconstraintsmustbepositive,asthefollowingrelationshipsshow:–ε<UCi<∞

–ε<LCi<∞

whereε=1E–21.Youalsocanplaceconstraintsontherateofchangeofcontrolactionsandoutputs.Ifatleastfivepointsareavailable,thisVIcomputestheseratesofchangeusingthefollowingequation:

wheretisthesimulationtime,histhespacebetweentimesteps,andf(t)

isanoutputorcontrolactionsignal.Atboundaries,oriffewerthanfivepointsareavailable,thisVIusesthefollowingequationsinstead:

or

YoucanuseaVItemplatetospecifycustomcalculationsforimplementingtheinequalityconstraints.Toloadthistemplate,intheNewdialogbox,selectVI»FromTemplate»Simulation»OptimalDesign»ComputeInequalityConstraintsfromtheCreateNewtree.Toseeanexampleofhowtodefineandmanipulatetheseparameters,opentheSIMoptComputeInequalityConstraints(Default)VI,locatedinthelabview\vi.lib\Simulation\OptimizationBasedDesign\Constraintsdirectory.ThisVIimplementstheinequalityconstraintsthepreviousequationsspecified.AfteryousavethecustominequalityconstraintcalculationsasaVI,youmustspecifythelocationofthecustomfunctionintheProblemSpecificationparameteroftheSIMOptimalDesignVI.SelectUserdefinedfortheInequalityconstraintstypeparameterandspecifythepathtotheVIintheFilepathuserdefinedinequalityconstraintspathcontrol.

DefiningParameterBounds(ControlDesignandSimulationModule)Parameterboundsareconstraintsonparametervaluesbeingoptimized.Forexample,whilesearchingforthebestvalueofaspringconstant,youmightknowthatspringsareavailableonlywithcertainphysicalproperties.Inthiscase,youcanspecifythattheparameterkmuststaywithinminimumandmaximumvalues.ParameterboundsareimportantbecausetheseboundsdefinetheparameterspaceinwhichtheSequentialQuadraticProgramming(SQP)algorithmsearchesforoptimalvalues.UsetheParameterBoundsparameteroftheSIMOptimalDesignVItospecifyminimumandmaximumvaluesforeachparameter.

DefiningInitialParameterValuesandaMesh(ControlDesignandSimulationModule)Afteryoudefinetheparameterspaceusingtheminimumandmaximumvaluesofeachparameter,youmustspecifytheinitialvaluesofeachparameter.TheseinitialparametervaluesdeterminewheretheSequentialQuadraticProgramming(SQP)algorithmbeginsthesearchforoptimalvalues.However,ifyouchooseonlyasingleinitialsetofinitialvalues,theSQPalgorithmmightreturnlocaloptimalvalues.Localoptimalvaluesarevaluesthatminimizethecostfunctionwithinonlyasubsetofparameterspace.LocaloptimalvaluesarenotthetruesolutiontotheSQPalgorithmbecausethetrueoptimalvaluesmightexistoutsidetheparameterspacethealgorithmsearched.Tomitigatethisproblem,youcanexecutetheSQPalgorithmseveraltimes,usingadifferentsetofinitialparametervalueseachtime.Ifyouusealargeenoughrangeofinitialparametervalueswithinthegivenparameterspace,youcanberelativelyconfidentthattheSQPalgorithmfindstheglobaloptimalvalues.Youcanimplementthisstrategybydefininganinitialparametersmesh.Theinitialparametersmeshdefinesthedistributionpatternofthesesetsofinitialvaluesandthetotalnumberofinitialvaluesetstogenerate.Youcanchoosefromfourpatternsdependingontheneedsoftheproblem:Uniformgrid,Uniformrandom,Quasirandom,andRandomwalk.Eachpatternhasuniquecharacteristicsandstrengths.Forexample,thesimplestpossibleoptionistheuniformgrid,whichgeneratesaspecifiednumberofequally-spacedlocationsintheparameterspace.However,theuniformrandomandquasirandomoptionsoftenprovidebettercoverageoftheparameterspacewhileusingafewernumberofpointsthantheuniformgridoption.Therandomwalkoptionbiasesthesearchtoexploreclosetotheinitialvaluesbuteventuallyexploresalargerregionofparameterspace.Thisoptionisusefulifyouthinkaparticularparameterspacecontainstheoptimalvaluesandyouwanttofocusonacertainregionofthatspace,suchasthecenter.UsetheInitialParametersparameteroftheSIMOptimalDesignVItospecifyinitialparametervalues.UsetheInitialParametersMeshparameterofthisVItodefineaninitialparametersmesh.

ExecutingtheSQPAlgorithm(ControlDesignandSimulationModule)TheSIMOptimalDesignVIusesaninternalsimulationdiagramtoobtainthefinite-horizontime-domainresponseofthedynamicsystemmodel.UsetheSolverParametersparameterofthisVItoconfigurethesimulation.YoualsocanconfiguretheSequentialQuadraticProgramming(SQP)algorithmusingthebeginningstate,cnosettings,andstoppingcriteriaparameters.ThisVIreturnsthefollowinginformation:

Signals—Thefinite-horizontime-responsedatafortheoutputandcontrolactionofthedynamicsystem,evaluatedateachpointspecifiedintheOptimalparametersarray.Designparameters—Thesetofparametervaluesthatminimizethespecifiedcostfunction.Thesevaluesaretheoptimalparametervalues.Designcost—TheresultofthespecifiedcostfunctionifyouapplythevaluesfromtheDesignparametersarray.Optimalparameters—Alistofpossibleoptimalparametervalues.EachcolumnofthisarraycorrespondstooneparameteryouspecifiedintheParameterBoundsarray.EachrowofthisarraycorrespondstooneexecutionoftheSQPalgorithm.Optimalcosts—TheresultsofthespecifiedcostfunctionthatcorrespondtoeachrowoftheOptimalparametersarray.

TheSQPalgorithmtakesaslongtoexecuteastheproductofthenumberoffunctionevaluationsandtheruntimeofthesimulation.Ifyouspecifyonlyonesetofinitialparametervalues,thealgorithmmustsolve,onaverage,between30and200functions.ThefrontpaneloftheSIMOptimalDesignVIincludesaCurrentDatapagethatyoucanusetomonitortheprogressofthealgorithmastheVIruns.ThispageupdateseachtimetheSQPalgorithmexecutesfromonesetofinitialparametervalues.TheOptimalDesignParameterspageofthisVIalsoincludestheBestParameters(InfeasibleConstraints)andBestcost(Infeasibleconstraints)parameters.Theseparametersreturnoptimalparametervaluesandtheassociatedcostfunctionresultwithnoconstraints.This

informationcanbeusefulwhenrevisingtheconstraintenvelopes.IfthedynamicsystemhasconstraintsandtheSQPalgorithmdoesnotreturnfeasibleoptimalvalues,tryensuringthatthespecifiedcostfunctionremainsconstantwhenparametervaluesareoutsidethefeasiblerange.Thismethodhelpsyousetreasonableparameterbounds.Additionally,reducingsystemdiscontinuitieshelpstheSQPalgorithmexecuteprecisely.Youcanuseseveralmethodstoreducediscontinuities,forexample,avoidingsaturationeffectsandratelimitersinthesystemmodel.

UsingtheSimulationModelConverter(ControlDesignandSimulationModule)YoucanusetheSimulationModelConvertertoconverta.mdlfile,developedinTheMathWorks,Inc.Simulink®simulationenvironment,intoaLabVIEWVIthatconsistsofasimulationdiagramcontainingLabVIEWfunctions,wires,andsimulationsubsystemscorrespondingtothecontentsofthe.mdlfile.Aspartoftheconversionprocess,theSimulationModelConverterusestheMathWorks,Inc.MATLAB®applicationsoftwareandtheSimulinkapplicationsoftwaretocompilethe.mdlfileandexecuteany.mfilesthatyouspecifyinthedialogbox.IftheMATLABsoftwareortheSimulinksoftwareisnotinstalledonthesamecomputerastheLabVIEWControlDesignandSimulationModule,theresultsoftheconversionmightbelessaccurate.

NoteTheSimulationModelConvertercannotconvertdiagramsdevelopedwithTheMathWorks,Inc.Stateflow®applicationsoftwareorotherSimulinkblocksets.

(Windows)Toviewrelatedtopics,clicktheLocatebutton,shownatleft,inthetoolbaratthetopofthiswindow.TheLabVIEWHelphighlightsthistopicintheContentstabsoyoucannavigatetherelatedtopics.

CommonWarnings(ControlDesignandSimulationModule)IftheSimulationModelConvertercannotfindavalueforaparameterinthe.mdlfileitisconverting,LabVIEWdisplaysawarning.Inthesecases,theSimulationModelConverterusesthedefaultvalueoftheparameterinthecorrespondingLabVIEWfunction.

NoteInsomecases,theSimulationModelConvertercannotfindavalueforaparameterbecausetheparametercontainsanexpressioninsteadofaconstantvalue.IftheMathWorks,Inc.MATLAB®softwareisinstalledonthecomputer,theSimulationModelConverterattemptstoevaluatetheMATLABsoftwareexpressionsinthe.mdlfilepriortoconvertingthefile.IftheSimulationModelConvertersuccessfullyevaluatestheexpression,theSimulationModelConverterusestheresultofthatevaluationastheparametervalueanddoesnotproduceawarning.

TheSimulationModelConvertercannotfullyconvertallfunctionsofeverymodeltoLabVIEWblockdiagramcode.IftheSimulationModelConverterencountersablockitcannotconvert,youreceiveawarning.Inthesecases,theSimulationModelConvertercreatesaplaceholdersimulationsubsystem.YoumustcreateasimulationsubsystemusingaLabVIEWVItoaccomplishthesamefunctionalityastheblocktoreplacethisplaceholdersimulationsubsystem.BecauseLabVIEWisstrictaboutdatatypes,theconvertedsimulationsubsystemmighthavebrokenwires.Inthiscase,addblockdiagramcodetoconvertbetweenconverteddatatypes.

UnsupportedBlocks(ControlDesignandSimulationModule)TheSimulationModelConverterdialogboxcannotconvertthefollowingblocksusedinTheMathWorks,IncSimulink®applicationsoftware.Inthesecases,theSimulationModelConvertercreatesaplaceholdersimulationsubsystem.YoumustcreateasimulationsubsystemusingaLabVIEWVItoaccomplishthesamefunctionalityastheblocktoreplacethisplaceholdersimulationsubsystem.

AlgebraicConstraintAtomicSubsystemBand-LimitedWhiteNoiseConfigurableSubsystemEnabledEnabledandTriggeredForSubsystemFromWorkspaceFunction-CallFunction-CallGeneratorIfIfActionSubsystemInterpolation(n-D)usingPreLook-UpLook-UpTable(n-D)MemoryMergeModelInfoPreLook-UpIndexSearchProbeRandomNumberRateTransitionRepeatingSequenceS-FunctionS-FunctionBuilderSwitchCaseActionSubsystem

SwitchCaseToWorkspaceTriggeredWhileIteratorSubsystem

AdditionalImportantInformation(ControlDesignandSimulationModule)TrademarksPatents

TrademarksNationalInstruments,NI,ni.com,andLabVIEWaretrademarksofNationalInstrumentsCorporation.RefertotheTermsofUsesectiononni.com/legalformoreinformationaboutNationalInstrumentstrademarks.MATLAB®,Stateflow®,andSimulink®areregisteredtrademarksofTheMathWorks,Inc.Otherproductandcompanynamesmentionedhereinaretrademarksortradenamesoftheirrespectivecompanies.MembersoftheNationalInstrumentsAlliancePartnerProgramarebusinessentitiesindependentfromNationalInstrumentsandhavenoagency,partnership,orjoint-venturerelationshipwithNationalInstruments.

PatentsForpatentscoveringNationalInstrumentsproducts,refertotheappropriatelocation:Help»Patentsinyoursoftware,thepatents.txtfileonyourmedia,orni.com/patents.Youareonlypermittedtousethisproductinaccordancewiththeaccompanyinglicenseagreement.AllrightsnotexpresslygrantedtoyouinthelicenseagreementaccompanyingtheproductarereservedtoNI.Further,andwithoutlimitingtheforgoing,nolicenseoranyrightofanykind(whetherbyexpresslicense,impliedlicense,thedoctrineofexhaustionorotherwise)isgrantedunderanyNIpatents.