Design Controller.docx

Design Controller.docx

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DesignController

DesignControlSystems

UsingPIDControllerandFuzzyLogicControllerwithMATLAB/SIMULINK

Module:

AdvancedControlTechnology

Tutor:

DrErpingZhou

Number:

0807810

BY:

ZhizhengZhang

DTAE:

3April,2013

TableofContents

1.Abstract3

2.ResultAnalysis4

2.1ExperimentEquipmentandTasks：

4

2.1.1ExperimentEquipment:

4

2.1.2Tasks4

2.2ExperimentProcedure4

2.2.1BackgroundInformation:

4

2.2.2DevelopanEngineeringModel5

2.2.3DesignPIDController7

2.2.4DesignFuzzyLogicController17

3.Conclusion31

Bibliography34

Appendix35

1.Abstract

Therearetwokindsofcontroller,oneisPIDControllerandotheroneisFuzzylogicController.Theworkpresentsinthispapaerwaterlevelandwatertemperaturecontrollerwhichiswidelyusedintheprocessindustry.Thepurposeofthefeedbackcontrolleristoguaranteeadesiredreponseoftheoutput.

ThestudydevotedtocontroldesignmethodusingFuzzyLogicControllerandPIDControllerbasedonlinearcontrolandnon-linearcontrolforwaterlevelandwatertemperaturetoobtainthedesiredoutputwaterlevelandwatertemperatureandtoimplementtheminarealworldenvrionmrnt.

Keywords:

PIDController,FuzzyLogicController,Matlab-7software

2.ResultAnalysis

2.1ExperimentEquipmentandTasks：

2.1.1ExperimentEquipment:

●MATLAB/SIMULINK,ControltoolboxandFuzzyLogictoolbox.

2.1.2Tasks

ThereareFOURmaintasksinvolvedinthisassignment:

●DevelopanEngineeringModel

●DesignaPIDController

●DesignaFuzzyLogicControlSystem

●WorkingwithSIMULINK

2.2ExperimentProcedure

2.2.1BackgroundInformation:

Anelectricheaterisusedtoraisethewatertemperatureinawatertank（asshowninFigure1）.Theinitialconditionsofthesystemare:

●Inletwatertemperature（coldwater）T1isequalto10°C.

●ThewaterflowrateintothetankF0equals5dm3/hr,andthewaterflowrateoutofthetankF1equalsto3dm3/hr.

●TankvolumeVisequalto100dm3.

●Thecross-sectionalareaofthetankAisequalto25dm2.

●WaterdensityandheatcapacitycPare1Kg/dm3and4.19KJ/（Kg°C）.

●InitialheatinputQ0andtanktemperatureT0areequalto500KJ/hrand20°C.

●InitialwaterlevelL0is0.5dm.

Designspecificationsfromtheclientaredescribedfollows:

●Waterlevelandwatertemperaturearemeasuredseparatelybyalevelsensorandatemperaturesensor.

●OutlettemperatureT2mustbeequaltothesetpointtemperature85°C.

●Thewaterlevelmustnotbeover4.0dm.

●Theheaterdevicehasafirstorderdelaywithatimeconstantequalto0.5.

●Thetemperaturemeasurementhasafirstorderdelaywithatimeconstantequalto1.

●Thewaterlevelmeasurementhasafirstorderdelaywithatimeconstantequalto1.

Figure1

Figure1showsthatthere2inputsonthecontrollers.Oneislevelofwateranotheristhetemperaturewhatweneed.Weusethecontrollertocontrollerthelevelofthewaterandthetemperatureofthewatertomakesurethatthenumbermeetwiththedemand.Thecontrollerwillmeasurethelevelofwaterandthetemperatureofwaterbyusingthesignal.Whenthelevelofwaterorthenumberoftemperatureofwaterislowerorhigherthanwesetthelevelorthenumeroftemperature.Thecontrollerwillopentheswitchorclosetheswitchbyusingsingal.That’swhatweneedtobedesignedtoPIDControllerandFuzzyLogicController.

2.2.2DevelopanEngineeringModel

Wehaveknownthetaskweneedtofinishandwegetthebackinfotamtionforthetask.Thefirstthingtodoforapplythecontrolleronthewatertank.Wehavetodeveloptwodifferentialequationsforwatertank’stemperatureandlevel.FortheequationforlevelandtemperatureIrefertoBerkeley-MadonnainChemicalEngineeringDynamicsbyJ.Inghametal.（secondedition,Wiley-VCH,2000）formodellingofthesystem.

WaterTanklevel

Firstly,weassumeamodelofthewatertank,whichconsistsofapump,atank,inflowandoutflowpipesandanoutputvalve.

Waterispumpedintothetankatthetopattherateofthewaterflowincubicmetrespersecond.Waterisflowingoutofthetankthroughtheoutputvalve.（Figure2）

Figure2

Figure2showsthewaterflowintothetankandthewaterflowoutputthetank.Wecanmakesuretheinputandoutputofthewaterlevelsystem:

●Thesysteminputisthevoltageofthemotoroftherotary-pumpV.

●ThesystemoutputisthelevelofthewaterinthetankH.

●TheminimumandmaximumoftheinputvoltageareVmin=0V,Vmax=10V.

●Theheightofthetankis0.5m.

Adifferentialequationfortheheightofwaterinthetank,H,isgivenby（）

Equationforwaterlevel

TheVolisthevolumeofwaterinthetank,Aisthecross-sectionalareaofthetank,bisaconstantrelatedtotheflowrateintothetank,andaisaconstantrelatedtotheflowrateoutofthetank.Theequationdescribestheheightofwater,H,asafunctionoftime,duetothedifferencebetweenflowratesintoandoutofthetank.

WecannoticethatTheequationcontainsonestate,H,oneinput,V,andoneoutput,H.Itisnonlinearduetoitsdependenceonthesquare-rootofH.Linearizingthemodelsimplifiestheanalysisofthismodel.

NowweusetheequationtobuildSimulinkModelforthecontrolofthewaterlevelinthetank.

Figure3isthesybsystemofthewaterleveltank,InitialwaterlevelL0=0.5dm.ThewaterflowrateintothetankF0equals5dm3/hr,andthewaterflowrateoutofthetankF1equalsto3dm3/hr.Thecross-sectionalareaofthetankAisequalto25dm2.

Figure3

Wehavethesubsystemofwaterleveltank.ThePIDControllerneedtobedesignedtosimulinkmodelandwetunningthreetermsforthesystem.

2.2.3DesignPIDController

PIDstandsfor:

P（Proportional）

I（Integral）

D（Derivative）

History

ThefirstapplicationofPIDcontrollerwasin1922byMinorskyonshipsteering.

Minorsky（1922）“Directionalstabilityofautomaticallysteeredbodies”,J.Am.Soc.NavalEng.,34,p.284.

Thiswasthefirstmathematicaltreatmentofthetypeofcontrollerthatisnowusedtocontrolalmostallindustrialprocesses.

Thecurrentsituation

Despitetheabundanceofsophisticatedtools,includingadvancedcontrollerdesigntechniques,PIDcontrollersarestillthemostwidelyusedcontrollerstructureinmodernindustry,controllingmorethat95%ofclosed-loopindustrialprocesses.

DifferentPIDcontrollersdifferinthewayhowtheirparametersbetuned,manually,orautomatically.

2.PIDstructure

Figure4showsthePIDstructure:

reference,set-point（SP）

output,measuredsignaltoberegulated

controlerror

aorderdelaywithatime

Figure4

Figure5showsPIDController:

Figure5

GeneralTipsforDesigningaPIDController

Figure6

Figure6showstheroleofProportional.AddaProportionalcontroltoimprovetherisetimeandcontrolsignalProportionaltocontrolerror.

I-part（Intrgrator）isshownonFigure7:

surfaceundere（t）sofar

becomesasbigasconstanterrore0intimeTi

usedtoeliminateremainingerror

Figure7

Figure8isD-part（derivator）usedtodamposcillations

Figure8

WehaveknowtheroleofP,I,DonPIDcontroller.WearedesigningaPIDcontrollerforagivensystem,followthestepsshownbelowtoobtainadesiredresponse.

1Obtainanopen-loopresponseanddeterminewhatneedstobeimproved

2Addaproportionalcontroltoimprovetherisetime

3Addaderivativecontroltoimprovetheovershoot

4Addanintegralcontroltoeliminatethesteady-stateerror

5AdjusteachofKp,Ki,andKduntilyouobtainadesiredoverallresponse.

FromFigure6-8TheCharacteristicsofP,I,andDControllerscanbemadeaconclusionby:

Aproportionalcontroller（

）willhavetheeffectofreducingtherisetimeandwillreducebutnevereliminatethesteady-stateerror.Anintegralcontrol（

）willhavetheeffectofeliminatingthesteady-stateerrorforaconstantorstepinput,butitmaymakethetransientresponseslower.Aderivativecontrol（

）willhavetheeffectofincreasingthestabilityofthesystem,reducingtheovershoot,andimprovingthetransientresponse.

APIDControllerisdesignedforwaterleveltankFigure9

Figure9

ThedesignofPIDControllerismeetwithwhatthementionedbefore,Thenumber3istheaimatthedesignofPIDContorller,

isthewaterlevelmeasurementhasafirstorderdelaywithatimeconstantequalto1.Subsystemisthedesignofequationofwaterleveltank.DoubleclickthediagramofPIDController.TheFigure10showstheFunctionBlockParameters:

PIDControllerFiguer10.ThePIDControllerisbeselecttedforthedemandofclients:

Thewaterlevelmustnotbeover4.0dm.

Figure10

ClicktheTune,MatlabwillautomatictunethePIDController.Wejustmovetorightorlefttogetwhatweneed.ItistheadvatageofPIDDontrollerFigure11

Figure11

Whenthegoodresponseisgotbyautomatictune.Weclickrunthesimulinkmodelandclickscope

TheFigure12showtheresultofsimulinkmodle:

Thewaterlevelmustnotbeover4.0dm.

Figure12

Theresultofsimulinkmodleismeetwithclientneedthatthewaterlevelmustnotbeover4.0dm.Thesystemneed28hourstogetthelevel3Figure13

Figure13

ThedesignofPIDControllerforwaterleveltankisfinished,Ithasmetwiththeclient’sdemandandagoodresponseisgot.

DesignPIDControllerfortemperature

ThewayofdesignPIDControllerfortemperatureissimilarwithwaterlevel.TheequationoftemeraturereferstoBerkeley-MadonnainChemicalEngineeringDynamicsbyJ.Inghametal.（secondedition,Wiley-VCH,2000）formodellingofthesystem.

Wegettwoequactionfottemperature.Weshouldset