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SimulinkBasicsTutorial

Simulink isagraphicalextension toMATLAB formodelingandsimulationof

systems.One of the main advantages of Simulink is the ability to model a

nonlinearsystem,whichatransferfunctionisunabletodo.Anotheradvantage

ofSimulinkistheabilitytotakeoninitialconditions.Whenatransferfunctionis

built,theinitialconditionsareassumedtobezero.

Contents

StartingSimulink

ModelFiles

BasicElements

SimpleExample

RunningSimulations

BuildingSystems

InSimulink,systemsaredrawnonscreenasblockdiagrams.Manyelementsof

blockdiagramsareavailable, suchas transfer functions, summing junctions,

etc.,aswellasvirtualinputandoutputdevicessuchasfunctiongeneratorsand

oscilloscopes. Simulink is integrated with MATLAB and data can be easily

transferedbetweentheprograms.In thesetutorials,wewillapplySimulink to

theexamplesfromtheMATLABtutorialstomodelthesystems,buildcontrollers,

and simulate the systems. Simulink is supported on Unix, Macintosh, and

WindowsenvironmentsandisincludedinthestudentversionofMATLABfor

personal computers. For more information on Simulink, please visit the

Mathworkslinkatthetopofthepage.

Theideabehindthesetutorialsisthatyoucanviewtheminonewindowwhile

runningSimulink inanotherwindow.Systemmodel filescanbedownloaded

from the tutorialsandopened inSimulink.Youwillmodify andextend these

system while learning to use Simulink for system modeling, control, and

simulation.Donotconfusethewindows, icons,andmenusinthetutorialsfor

youractualSimulinkwindows.Mostimagesinthesetutorialsarenotlivethey

simplydisplaywhatyoushouldseeinyourownSimulinkwindows.AllSimulink

operationsshouldbedoneinyourSimulinkwindows.

SYSTEM

MODELING

ANALYSIS

CONTROL

PID

ROOTLOCUS

FREQUENCY

STATESPACE

DIGITAL

SIMULINK

MODELING

CONTROL

TIPS ABOUT BASICS HARDWARE INDEX NEXT

StartingSimulink

Simulink is started from the MATLAB command prompt by entering the

followingcommand:

simulink

Alternatively,youcanhittheSimulinkbuttonatthetopoftheMATLABwindow

asshownhere:

When itstarts,Simulinkbringsupasinglewindow,entitledSimulinkLibrary

Browserwhichcanbeseenhere.

ModelFiles

InSimulink,amodel isacollectionofblockswhich, ingeneral, representsa

system.Inaddition,todrawingamodelintoablankmodelwindow,previously

savedmodelfilescanbeloadedeitherfromtheFilemenuorfromtheMATLAB

commandprompt.Asanexample,downloadthefollowingmodelfilebyclicking

on the following link and saving the file in the directory you are running

MATLABfrom.

simple.mdl

Openthis file inSimulinkbyentering the followingcommand in theMATLAB

commandwindow.(Alternatively,youcanloadthisfileusingtheOpenoptionin

theFilemenuinSimulink,orbyhittingCtrlOinSimulink).

simple

Thefollowingmodelwindowshouldappear.

A new model can be created by selectingNew from the File menu in any

Simulinkwindow(orbyhittingCtrlN).

BasicElements

TherearetwomajorclassesofitemsinSimulink:blocksandlines.Blocksare

usedtogenerate,modify,combine,output,anddisplaysignals.Linesareused

totransfersignalsfromoneblocktoanother.

Blocks

ThereareseveralgeneralclassesofblockswithintheSimulinklibrary:

Sources:usedtogeneratevarioussignals

Sinks:usedtooutputordisplaysignals

Continuous: continuoustime system elements (transfer functions, state

spacemodels,PIDcontrollers,etc.)

Discrete:linear,discretetimesystemelements(discretetransferfunctions,

discretestatespacemodels,etc.)

Math Operations: contains many common math operations (gain, sum,

product,absolutevalue,etc.)

Ports&Subsystems:containsusefulblockstobuildasystem

Blocks have zero to several input terminals and zero to several output

terminals. Unused input terminals are indicated by a small open triangle.

Unusedoutput terminalsare indicatedbyasmall triangularpoint.Theblock

shownbelowhasanunusedinput terminalonthe leftandanunusedoutput

terminalontheright.

Lines

Linestransmitsignalsinthedirectionindicatedbythearrow.Linesmustalways

transmitsignals from theoutput terminalofoneblock to the input terminalof

anotherblock.Onexceptiontothisisalinecantapoffofanotherline,splitting

the signal to each of two destination blocks, as shown below (click here to

downloadthemodelfilecalledsplit.mdl).

Lines can never inject a signal into another line lines must be combined

throughtheuseofablocksuchasasummingjunction.

A signal can be either a scalar signal or a vector signal. For SingleInput,

SingleOutput (SISO) systems, scalar signals are generally used. For Multi

Input,MultiOutput(MIMO)systems,vectorsignalsareoftenused,consistingof

twoormorescalarsignals.Thelinesusedtotransmitscalarandvectorsignals

areidentical.Thetypeofsignalcarriedbyalineisdeterminedbytheblockson

eitherendoftheline.

SimpleExample

(1)

Thesimplemodelconsistsofthreeblocks:Step,TransferFunction,andScope.

The Step is aSource block from which a step input signal originates. This

signalistransferredthroughtheline inthedirectionindicatedbythearrowto

theTransferFunctionContinuousblock.TheTransferFunctionblockmodifies

itsinputsignalandoutputsanewsignalonalinetotheScope.TheScopeisa

Sinkblockusedtodisplayasignalmuchlikeanoscilloscope.

TherearemanymoretypesofblocksavailableinSimulink,someofwhichwill

bediscussedlater.Rightnow,wewillexaminejustthethreewehaveusedin

thesimplemodel.

ModifyingBlocks

Ablockcanbemodifiedbydoubleclickingonit.Forexample, ifyoudouble

click on the TransferFunction block in the Simple model, you will see the

followingdialogbox.

Thisdialogboxcontains fields for thenumeratorand thedenominatorof the

block'stransferfunction.Byenteringavectorcontainingthecoefficientsofthe

desirednumeratorordenominatorpolynomial,thedesiredtransferfunctioncan

beentered.Forexample,tochangethedenominatorto

(1)

enterthefollowingintothedenominatorfield

[124]

andhittheclosebutton,themodelwindowwillchangetothefollowing,

whichreflectsthechangeinthedenominatorofthetransferfunction.

TheStep block can also be doubleclicked, bringing up the following dialog

box.

Thedefaultparametersinthisdialogboxgenerateastepfunctionoccurringat

time=1sec,fromaninitiallevelofzerotoalevelof1(inotherwords,aunit

time=1sec,fromaninitiallevelofzerotoalevelof1(inotherwords,aunit

step at t = 1). Each of these parameters can be changed.Close this dialog

beforecontinuing.

ThemostcomplicatedofthesethreeblocksintheScopeblock.Doubleclicking

onthisbringsupablankoscilloscopescreen.

Whenasimulationisperformed,thesignalwhichfeedsintothescopewillbe

displayedinthiswindow.Detailedoperationofthescopewillnotbecoveredin

this tutorial. The only function we will use is the autoscale button, which

appearsasapairofbinocularsintheupperportionofthewindow.

RunningSimulations

Torunasimulation,wewillworkwiththefollowingmodelfile:

simple2.mdl

DownloadandopenthisfileinSimulinkfollowingthepreviousinstructionsfor

thisfile.Youshouldseethefollowingmodelwindow.

Before running a simulation of this system, first open the scope window by

doubleclickingonthescopeblock.Then,tostartthesimulation,eitherselect

StartfromtheSimulationmenu,clickthePlaybuttonatthetopofthescreen,or

hitCtrlT.

Thesimulationshouldrunveryquicklyandthescopewindowwillappearas

shownbelow.

Notethatthesimulationoutput(showninyellow)isataverylowlevelrelative

totheaxesofthescope.Tofixthis,hittheautoscalebutton(binoculars),which

willrescaletheaxesasshownbelow.

Notethatthestepresponsedoesnotbeginuntilt=1.Thiscanbechangedby

doubleclickingonthestepblock.Now,wewillchangetheparametersof the

systemandsimulatethesystemagain.DoubleclickontheTransferFunction

blockinthemodelwindowandchangethedenominatorto:

[120400]

Rerunthesimulation(hitCtrlT)andyoushouldseewhatappearsasa flat

line in the scopewindow.Hit theautoscale button, and you should see the

followinginthescopewindow.

Noticethattheautoscalebuttononlychangestheverticalaxis.Sincethenew

transferfunctionhasaveryfastresponse,itcompressedintoaverynarrowpart

ofthescopewindow.Thisisnotreallyaproblemwiththescope,butwiththe

simulation itself. Simulink simulated the system for a full ten seconds even

thoughthesystemhadreachedsteadystateshortlyafteronesecond.

Tocorrect this,youneedtochangetheparametersof thesimulation itself. In

the model window, select Configuration Parameters from the Simulation

menu.Youwillseethefollowingdialogbox.

Therearemanysimulationparameteroptionswewillonlybeconcernedwith

thestartandstoptimes,whichtellSimulinkoverwhattimeperiodtoperformthe

simulation.ChnageStarttimefrom0.0to0.8(sincethestepdoesn'toccuruntil

t=1.0).ChangeStoptimefrom10.0to2.0,whichshouldbeonlyshortlyafter

thesystemsettles.Closethedialogboxandrerunthesimulation.After hitting

theautoscalebutton,thescopewindowshouldprovideamuchbetterdisplay

ofthestepresponseasshownbelow.

BuildingSystems

In this section, you will learn how to build systems in Simulink using the

building blocks in Simulink's Block Libraries. You will build the following

system.

Ifyouwouldliketodownloadthecompletedmodel,clickhere.

First,youwillgatherallofthenecessaryblocksfromtheblocklibraries.Then

you will modify the blocks so they correspond to the blocks in the desired

model. Finally, you will connect the blocks with lines to form the complete

system.Afterthis,youwillsimulatethecompletesystemtoverifythatitworks.

GatheringBlocks

Followthestepsbelowtocollectthenecessaryblocks:

Createanewmodel(NewfromtheFilemenuorhitCtrlN).Youwillgeta

blankmodelwindow.

ClickontheSourceslistinginthemainSimulinkwindow.

ThiswillbringuptheSourcesblocklibrary.Sourcesareusedtogenerate

signals.

Drag theStep block from theSources window into the left side of your

modelwindow.

ClickontheMathOperationslistinginthemainSimulinkwindow.

Fromthislibrary,dragaSumandGainblock into themodelwindowand

placethemtotherightoftheStepblockinthatorder.

ClickontheContinuouslistinginthemainSimulinkwindow.

First,fromthislibrary,dragaPIDControllerblock into themodelwindow

andplaceittotherightoftheGainblock.

From the same library, drag a Transfer Function block into the model

windowandplaceittotherightofthePIDControllerblock.

ClickontheSinkslistinginthemainSimulinkwindow.

DragtheScopeblockintotherightsideofthemodelwindow.

ModifyBlocks

Followthesestepstoproperlymodifytheblocksinyourmodel.

DoubleclickontheSumblock.Sinceyouwillwantthesecondinputtobe

subtracted,enter+intothelistofsignsfield.Closethedialogbox.

DoubleclicktheGainblock.Changethegainto2.5andclosethedialog

box.

DoubleclickthePIDControllerblockandchangetheProportionalgainto

1andtheIntegralgainto2.Closethedialogbox.

Doubleclick the Transfer Function block. Leave the numerator [1], but

changethedenominatorto[124].Closethedialogbox.Themodelshould

appearas:

ChangethenameofthePIDControllerblock toPIController by double

clickingonthewordPIDController.

Similarly,changethenameoftheTransferFunctionblocktoPlant.Now,all

theblocksareenteredproperly.Yourmodelshouldappearas:

ConnectingBlockswithLines

Nowthattheblocksareproperlylaidout,youwillnowconnectthemtogether.

Followthesesteps.

DragthemousefromtheoutputterminaloftheStepblockto thepositive

inputoftheSuminput.AnotheroptionistoclickontheStepblockandthen

CtrlClickontheSumblocktoconnectthetwotogther.Youshouldseethe

following.

Theresultinglineshouldhaveafilledarrowhead.Ifthearrowheadisopen

andred,asshownbelow,itmeansitisnotconnectedtoanything.

You can continue the partial line you just drew by treating the open

arrowheadasanoutputterminalanddrawingjustasbefore.Alternatively,

ifyouwanttoredrawtheline,orifthelineconnectedtothewrongterminal,

you should delete the line and redraw it. To delete a line (or any other

object),simplyclickonittoselectit,andhitthedeletekey.

DrawalineconnectingtheSumblockoutputtotheGaininput.Alsodrawa

linefromtheGaintothePIController,alinefromthePIController to the

Plant,anda line from thePlant to theScope.You shouldnowhave the

following.

The line remaining to be drawn is the feedback signal connecting the

output of thePlant to the negative input of theSum block. This line is

differentintwoways.First,sincethislineloopsaroundanddoesnotsimply

followtheshortest(rightangled)routesoitneedstobedrawninseveral

stages.Second,thereisnooutputterminaltostartfrom,sothelinehasto

tapoffofanexistingline.

Draga lineoff thenegativeportionof theSum block straight down and

releasethemousesothelineisincomplete.Fromtheendpointofthisline,

click anddrag to the linebetween thePlant and theScope. The model

shouldnowappearasfollows.

Finally,labelswillbeplacedinthemodeltoidentifythesignals.Toplacea

labelanywhereinthemodel,doubleclickatthepointyouwantthelabelto

be.StartbydoubleclickingabovethelineleadingfromtheStepblock.You

willgetablanktextboxwithaneditingcursorasshownbelow.

Typeanr in thisbox, labelingthereferencesignalandclickoutside it to

endediting.

Labeltheerror(e)signal,thecontrol(u)signal,andtheoutput(y)signalin

thesamemanner.Yourfinalmodelshouldappearas:

Tosaveyourmodel,selectSaveAsintheFilemenuandtypeinanydesired

modelname.Thecompletedmodelcanbefoundhere.

Simulation

Nowthatthemodeliscomplete,youcansimulatethemodel.SelectStartfrom

theSimulationmenutorunthesimulation.Doubleclickonthe_Scope_block

toviewitsoutput.Hittheautoscalebutton(binoculars)andyoushouldseethe

following:

TakingVariablesfromMATLAB

Insomecases,parameters,suchasgain,maybecalculatedinMATLABtobe

used inaSimulinkmodel. If this is the case, it is not necessary to enter the

resultoftheMATLABcalculationdirectlyintoSimulink.Forexample,suppose

wecalculatedthegaininMATLABinthevariableK.Emulatethisbyentering

thefollowingcommandattheMATLABcommandprompt.

K=2.5

This variable cannowbeused in theSimulinkGain block. In your Simulink

model,doubleclickontheGainblockandenterthefollowingtheGainfield.

K

Close thisdialogbox.Noticenow that theGain block in theSimulinkmodel

showsthevariableKratherthananumber.

Now, you can rerun the simulation and view the output on the Scope. The

resultshouldbethesameasbefore.

Now, ifanycalculationsaredone inMATLABtochangeanyof thevariables

usedintheSimulinkmodel,thesimulationwillusethenewvaluesthenexttime

itisrun.Totrythis,inMATLAB,changethegain,K,byenteringthefollowingat

itisrun.Totrythis,inMATLAB,changethegain,K,byenteringthefollowingat

thecommandprompt.

K=5

Start theSimulink simulation again, bring up theScopewindow, and hit the

autoscale button. You will see the following output which reflects the new,

highergain.

Besides variables and signals, even entire systems can be exchanged

betweenMATLABandSimulink.

PublishedwithMATLAB7.14

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