Tutorial: Introduction to Simulink

UniversityCollegeofSoutheastNorway

http://home.hit.no/~hansha

IntroductiontoSimulinkHans-PetterHalvorsen,2016.11.01

PrefaceSimulink,developedbyTheMathWorks,isacommercialtoolformodeling,simulatingandanalyzingdynamicsystems.Itsprimaryinterfaceisagraphicalblockdiagrammingtoolandacustomizablesetofblocklibraries.ItofferstightintegrationwiththerestoftheMATLABenvironmentandcaneitherdriveMATLABorbescriptedfromit.Simulinkiswidelyusedincontroltheoryanddigitalsignalprocessingforsimulationanddesign.

ThistrainingwillgiveyouthebasicknowledgeofSimulinkandhowyoucanuseittogetherwithMATLAB.

FormoreinformationaboutMATLABandSimulink,seemyBlog:http://home.hit.no/~hansha

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TableofContentsPreface......................................................................................................................................2

TableofContents.....................................................................................................................iii

1 IntroductiontoSimulink....................................................................................................1

2 StartusingSimulink...........................................................................................................2

2.1 BlockLibraries.............................................................................................................3

2.2 CreateanewModel...................................................................................................5

2.3 Wiringtechniques.......................................................................................................6

2.4 Helpwindow...............................................................................................................7

2.5 Configuration..............................................................................................................9

2.6 Examples...................................................................................................................10

3 UsefulFeatures...............................................................................................................19

3.1 Comments/Labels.....................................................................................................19

3.2 AlignandDistributeBlocks.......................................................................................19

3.3 FlipBlocks.................................................................................................................20

3.4 HideNames...............................................................................................................21

4 Data-drivenModelling....................................................................................................22

4.1 Commandwindow....................................................................................................22

4.2 m-file.........................................................................................................................25

4.3 SimulationCommands..............................................................................................26

5 HybridSystems(continuousanddiscrete)......................................................................28

6 Example:Mass-Spring-DamperSystem...........................................................................30

6.1 Model........................................................................................................................30

iv TableofContents

Tutorial: Introduction to Simulink

6.2 Simulink....................................................................................................................31

6.3 m-File........................................................................................................................32

6.4 Results......................................................................................................................32

7 EmbeddedAlgorithms.....................................................................................................35

8 Subsystems......................................................................................................................38

9 ModelExplorer................................................................................................................42

10 Exercises..........................................................................................................................43

1

1 IntroductiontoSimulinkSimulinkisanenvironmentforsimulationandmodel-baseddesignfordynamicandembeddedsystems.Itprovidesaninteractivegraphicalenvironmentandacustomizablesetofblocklibrariesthatletyoudesign,simulate,implement,andtestavarietyoftime-varyingsystems,includingcommunications,controls,signalprocessing,videoprocessing,andimageprocessing.

Simulinkoffers:

• Aquickwayofdevelopyourmodelincontrasttotextbased-programminglanguagesuchase.g.,C.

• Simulinkhasintegratedsolvers.Intextbased-programminglanguagesuchase.g.,Cyouneedtowriteyourownsolver.

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2 StartusingSimulinkYoustartSimulinkfromtheMATLABIDE:

OpenMATLABandselecttheSimulinkiconintheToolbar:

Ortype“simulink”intheCommandwindow,likethis:

Thenthefollowingwindowappears(SimulinkLibraryBrowser):

3 StartusingSimulink


TheSimulinkLibraryBrowseristhelibrarywhereyoufindalltheblocksyoumayuseinSimulink.Simulinksoftwareincludesanextensivelibraryoffunctionscommonlyusedinmodelingasystem.Theseinclude:

• Continuousanddiscretedynamicsblocks,suchasIntegration,Transferfunctions,TransportDelay,etc.

• Mathblocks,suchasSum,Product,Add,etc• Sources,suchasRamp,RandomGenerator,Step,etc

2.1 BlockLibrariesHerearesomecommonusedContinuousBlocks:



HerearesomecommonusedMathOperationsBlocks:

HerearesomecommonusedSignalRoutingBlocks:

HerearesomecommonusedSinksBlocks:

HerearesomecommonusedSourcesBlocks:



InadditiontherearelotsofblockindifferentToolboxes:

2.2 CreateanewModelClicktheNewiconontheToolbarinordertocreateanewSimulinkmodel:

Thefollowingwindowappears:



YoumaynowdragtheblocksyouwanttousefromtheSimulinkLibraryBrowsertothemodelsurface(orright-clickonablockandselect“Addto…”).

Example:

Inthisexampleweplace(draganddrop)toblocks,aSineWaveandaScope,onthemodelsurface:

2.3 WiringtechniquesUsethemousetowiretheinputsandoutputsofthedifferentblocks.Inputsarelocatedontheleftsideoftheblocks,whileoutputsarelocatedontherightsideoftheblocks.



Whenholdingthemouseoveraninputoranoutputthemousechangestothefollowingsymbol.

Usethemouse,whileholdingtheleftbuttondown,todragwiresfromtheinputtotheoutput.

AutomaticBlockConnection:

Anotherwiringtechniqueistoselectthesourceblock,thenholddowntheCtrlkeywhileleft-clickingonthedestinationblock.

Trythedifferenttechniquesontheexampleabove.

Connectionfromawiretoanotherblock

Ifwireaconnectionfromawiretoanotherblock,liketheexamplebelow,youneedtoholddowntheCtrlkeywhileleft-clickingonthewireandthentotheinputofthedesiredblock.

2.4 HelpwindowInordertoseedetailedinformationaboutthedifferentblocks,usethebuilt-inHelpsystem.



AllstandardblocksinSimulinkhavedetailedHelp.ClicktheHelpbuttonintheBlockParameterwindowforthespecificblockinordertogetdetailedhelpforthatblock.

TheHelpWindowthenappearswithdetailedinformationabouttheselectedblock:



2.5 ConfigurationTherearelotsofparametersyoumaywanttoconfigureregardingyoursimulation.Select“ConfigurationParameters…”intheSimulationmenu.

Thefollowingwindowappears:



Hereyousetimportantparameterssuchas:

• StartandStoptimeforthesimulation• WhatkindofSolvertobeused(ode45,ode23etc.)• Fixed-step/Variable-step

Note!EachofthecontrolsontheConfigurationParametersdialogboxcorrespondstoaconfigurationparameterthatyoucansetviathe“sim”and“simset”commands.Youwilllearnmoreaboutthesecommandslater.

Solversarenumericalintegrationalgorithmsthatcomputethesystemdynamicsovertimeusinginformationcontainedinthemodel.Simulinkprovidessolverstosupportthesimulationofabroadrangeofsystems,includingcontinuous-time(analog),discrete-time(digital),hybrid(mixed-signal),andmultiratesystemsofanysize.

2.6 ExamplesBelowwewillgothroughsomeexamplesinordertoillustratehowtocreateblockdiagramsandrelatedfunctionality.

Example:Integratorwithinitialvalue

Createthefollowingmodel(anintegrator)andrunthesimulation:



Step1:Placetheblocksonthemodelsurface

Thisexampleusethefollowingblocks:

Step2:Configuration

Double-clickontheIntegratorblock.TheParameterwindowfortheIntegratorblockappears:



Select“Initialconditionsource=external”.TheIntegratorblocknowlookslikethis:

Double-clickontheConstantblock.TheParameterwindowfortheConstantblockappears:



IntheConstantvaluefieldwetypeintheinitialvaluefortheintegrator,e.g.,typethevalue1.

Step3:Wiring

Usethemousetowiretheinputsandoutputsofthedifferentblocks.

Whenholdingthemouseoveraninputoranoutputthemousechangetothefollowingsymbol.

DrawawirebetweentheoutputontheConstantblocktothelowerinputintheIntegratorblock,likethis:

Youcouldalsodolikethis:

Wiretherestoftheblockstogetherandyouwillgetthefollowingdiagram:



Step4:Simulation

Startthesimulationbyclickingthe“StartSimulation”iconintheToolbar:

Step5:TheResults

Double-clickintheScopeblockinordertoseethesimulatedresult:



Example:SineWave

Createtheblockdiagramasshownbelow:

SetthefollowingparameterfortheIntegratorblock:

Theresultshouldbelikethis:



Example:Usingvectors

Createthefollowingblockdiagram:

FortheGainblock,typethefollowingparameters:



Asyousee,wecanusestandardMATLABsyntaxtocreateavector.

Ifyouwanttoseethesignaldimensions,select“SignalDimensions”and“WideNonscalarLines”asshownhere:

Theblockdiagramshouldnowlooklikethis:



Thethicklinesindicatevectors,whilethenumber(8)isthesizeofthevector.

Let’schangetheSaturationblock:

AsyouseeyoumayusestandardMATLABfunctionsandsyntax.

RunthesimulationandseetheresultsintheScopeblock.

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3 UsefulFeaturesYoushouldknowaboutthesefeaturesinSimulinkinordertotakefulladvantageofSimulink.

3.1 Comments/LabelsDouble-clickonyoursurfaceinordertowriteLabelsorCommentsinyourmodelblockdiagram.

3.2 AlignandDistributeBlocksYoumayalignyourblocks:

20 UsefulFeatures


3.3 FlipBlocksNormallytheinputsareontheleftandtheoutputsontheright,butinsomecasesitisconvenienttohavetheinputsontherightandoutputontheleftside.

Inorderto“flip”theinputandoutputsright-clickontheblockandselect“FlipBlock”.

21 UsefulFeatures


3.4 HideNamesHidedefaultlabelsthatappearonthediagram,suchasConstant1,Integrator1,etc.

Select“HideNames”onthe“Format”menu:

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4 Data-drivenModellingYoumayuseSimulinktogetherwithMATLABinordertospecifydataandparameterstoyourSimulinkmodel.YoumayspecifycommandsintheMATLABCommandWindoworascommandsinanm-file.Thisiscalleddata-drivenmodeling.

4.1 Commandwindow

Example:

Note!Inordertoget3inputsontheScopeblock:

Double-clickontheScopeandselecttheParametersiconintheToolbar:

ThenselectNumberofAxes=3:

23 Data-drivenModelling


Configurethezero-orderholdblockslikethis:

WritethefollowingintheCommandwindowinMATLAB:



RuntheSimulinkmodelfromtheSimulink:

Wethengetthefollowingresults:



4.2 m-fileItisgoodpracticetobuildyourinSimulinkandconfigureandrunthesimulationfromaMATLABm-file.

ATypicalm-filecouldlooklikethis:



Youusethesimsetcommandtoconfigureyoursimulationparametersandthesimcommandtorunthesimulation.

Thevariablesyourefertointhem-fileissetintheConstantvaluefieldintheParameterwindowforeachblock.

4.3 SimulationCommands



Themostusedcommandis:

• simset• sim

UsethesecommandsifyouconfigureandrunyourSimulinkmodelfromam-file.

Example:

%Simulator Settings t_stop=100; %[s] T_s=t_stop/1000; %[s] options=simset('solver', 'ode5', 'fixedstep', T_s); %Starting simulation sim('mass_spring_damper', t_stop, options);

28

5 HybridSystems(continuousanddiscrete)

Youmaymixcontinuousblocksanddiscreteblocksinthesamesystem,so-calledHybridsystems.

Example:HybridSystem

Createthefollowingblockdiagram:

29 HybridSystems(continuousanddiscrete)


TheBlockdiagramnowlookslikethis:

Theblackcoloristhecontinuoussystemwhilethecoloredpart(redandgreen)isthediscretepartofthesystem.

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6 Example:Mass-Spring-DamperSystem

6.1 ModelInthisexamplewewillcreateamass-spring-dampermodelinSimulinkandconfigureandrunthesimulationfromaMATLABm-file.

Inthisexerciseyouwillconstructasimulationdiagramthatrepresentsthebehaviorofadynamicsystem.Youwillsimulateaspring-massdampersystem.

𝐹(𝑡) − 𝑐𝑥(𝑡) − 𝑘𝑥(𝑡) = 𝑚𝑥(𝑡)

wheretisthesimulationtime,F(t)isanexternalforceappliedtothesystem,cisthedampingconstantofthespring,kisthestiffnessofthespring,misamass,andx(t)isthepositionofthemass. 𝑥 isthefirstderivativeoftheposition,whichequalsthevelocityofthemass. 𝑥 isthesecondderivativeoftheposition,whichequalstheaccelerationofthemass.

Thefollowingfigureshowsthisdynamicsystem.

[Figure:Wikipedia]

Thegoalistoviewthepositionx(t)ofthemassmwithrespecttotimet.Youcancalculatethepositionbyintegratingthevelocityofthemass.Youcancalculatethevelocitybyintegratingtheaccelerationofthemass.Ifyouknowtheforceandmass,youcancalculatethisaccelerationbyusingNewton'sSecondLawofMotion,givenbythefollowingequation:



Force=Mass×Acceleration

Therefore,

Acceleration=Force/Mass

Substitutingtermsfromthedifferentialequationaboveyieldsthefollowingequation:

𝑥 =1𝑚 (𝐹 − 𝑐𝑥 − 𝑘𝑥)

Youwillconstructasimulationdiagramthatiteratesthefollowingstepsoveraperiodoftime.

6.2 SimulinkCreatetheblockdiagramforthemass-spring-dampermodelabove.

Insteadofhard-codingthemodelparametersintheblocksyoushouldrefertothemasvariablessetinanm-file.

Thesevariablesshouldbeconfigured:

• x_init• dxdt_init• m=• c=• k• t_step_F



• F_O• F_1

6.3 m-FileThefollowingvariablesshouldthenbesetinthem-file:

x_init=4; %[m]. Initial position. dxdt_init=0; %[m/s]. Initial Speed. m=20; %[kg] c=4; %[N/(m/s)] k=2; %[N/m] t_step_F=50; %[s] F_O=0; %[N] F_1=4; %[N]

6.4 ResultsTheBlockDiagramshouldlooksomethinglikethis:

Them-Fileshouldlooksomethinglikethis:



Graphs:

ForceF

Position 𝑥 andspeed 𝑥:

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7 EmbeddedAlgorithmsThischapterexplainshowyouincorporateanexistingMATLABfunctionintoyourSimulinkmodel.

MakesureyourMATLABfunctioniscompiledasanembeddedMATLABfunctionusingthe#emldirective,e.g.:

36 EmbeddedAlgorithms


DragintheEmbeddedMATLABfunction:

Double-clickontheEmbeddedMATLABfunctiongiveusthestandardtemplateforanembeddedfunction:

ModifythetemplatesoitcallsyourMATLABfunction:

37 EmbeddedAlgorithms


Wirethesystemlikethis:

RuntheSimulation:

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8 SubsystemsYoucreatesubsystemstocreatehierarchicalsystemsandhidedetailsinthemodel.

Selectthepartofyoursystemfromwhichyouwanttocreateasubsystem,right-clickandselect“CreateSubsystem”.

Example:

Right-clickandselect“CreateSubsystem”:

39 Subsystems


Ifwedouble-clickonthesubsystemweseetheblocksinthesubsystem:

Right-clickontheblockandselect“EditMask”inordertoopentheMaskEditor:

40 Subsystems


TheMaskEditorallowsyoutochangehowthesubsystemshouldlook,e.g.,thesubsystemicon.

SetParametersforthesubsystem:

DoubleclickonthesubsystemnowgivestheParameterwindowforthesubsystem:

41 Subsystems


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9 ModelExplorerTheModelExplorerallowsyoutoquicklylocate,view,andchangeelementsofaSimulinkmodelorStateflowchart.

TodisplaytheModelExplorer,selectModelExplorerfromtheSimulinkViewmenu.

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10 ExercisesInthischapterweprovidemoreexercises.

Exercise:

Buildthefollowingblockdiagram:

Inthisexercisewewillmodelarubberballthatisthrownintheairwithaninitialvelocityof15m/sfromaheightof10m.Wewillmodelthedynamicsoftheballasitbounces,undertheinfluenceofgravity.Wewillassumethat20%oftheenergyislostoneachbounce.(Thatis,aftereachimpact,theballwilltravelat80%ofitspriorvelocity,butintheoppositedirection.)

Wecanmodelthisexamplebyintegratingg(g=-9.81m/s^2)overtimewiththeinitialconditionsetto15m/s.Weresettheintegratoreachtimethepositionreacheszerometersandsetthenewinitialconditionto-80%oftheimpactvelocity.Positionismodeledbyintegratingthevelocityovertimewiththeinitialconditionsetto10m/s.

Theresultshouldbe:

44 Subsystems


Watchthisvideotoseetheresult:http://www.mathworks.com/products/demos/simulink/Simulink_Key_Features/videos/building.html

Hans-PetterHalvorsen,M.Sc.

E-mail:[email protected]

Blog:http://home.hit.no/~hansha/

UniversityCollegeofSoutheastNorway

www.usn.no

Tutorial: Introduction to Simulink

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