conical tank system tuning of Online fuzzy logic controller using Kalman algorithmfor Technology Journal of Applied Researchand

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Availableonlineatwww.sciencedirect.com

Journal of Applied Research and Technology

www.jart.ccadet.unam.mx JournalofAppliedResearchandTechnology15(2017)492–503

Original

Online tuning of fuzzy logic controller using Kalman algorithm for conical tank system

G.M. Tamilselvan

^∗

, P. Aarthy

DepartmentofEIE,BannariAmmanInstituteofTechnology,Sathyamangalam,India Received8September2016;accepted24May2017

Availableonline7November2017

Abstract

Inanon-linearprocesslikeconicaltanksystem,controllingtheliquidlevelwascarriedoutbyproportionalintegralderivative(PID)controller.

Butthenitdoesnotprovideanaccurateresult.Soinordertoobtainaccurateandeffectiveresponse,intelligenceisaddedintothesystembyusing fuzzylogiccontroller(FLC).FLCwhichhelpsinmaintainingtheliquidlevelinaconicaltankhasbeendevelopedandappliedtovariousfields.The resultacquiredusingFLCwillbemoreprecisewhencomparedtoPIDcontroller.ButFLCcannotadaptawiderangeofworkingenvironmentsand alsothereisnosystematicmethodtodesignthemembershipfunctions(MFs)forinputsandoutputsofafuzzysystem.Soanadaptivealgorithm calledKalmanalgorithmwhichemploysfuzzylogicrulesisusedtoadapttheKalmanfiltertoaccommodatechangesinthesystemparameters.

TheKalmanalgorithmwhichemploysfuzzylogicrulesadjustthecontrollerparametersautomaticallyduringtheoperationprocessofasystem andcontrollerisusedtoreducetheerrorinnoisyenvironments.Thistechniqueisappliedinaconicaltanksystem.Simulationsandresultsshow thatthismethodiseffectiveforusingfuzzycontroller.

Keywords: Fuzzylogiccontroller;Proportionalintegralderivativecontroller;Kalmanalgorithm;Matlab

1. Introduction

Inallprocessindustriesmeasurementsoflevel,temperature, pressureandflowparametersareveryvital.Realtimesystems providemanychallengingcontrolproblemsduetotheirdynamic behavior,uncertaintyandtimevaryingparameters,constraints onmanipulatedvariables,deadtimeoninputandmeasurements, interactionbetweenmanipulatedandcontrolledvariablesand unmeasuredfrequentdisturbances.Becauseoftheinherentnon- linearity,mostofthechemicalprocessindustriesareinneedof moderncontroltechniques.Nonlinearsystemslikeconicaltanks findwideapplicationsingasplantsandpetrochemicalindustries.

Theyarepreferredbecauseoftheadvantageslikebetterdisposal ofsolids,easymixingandcompletedrainageofsolventssuchas viscousliquidsinindustries.Inconicaltanknon-linearityexists

∗Correspondingauthor.

E-mail addresses: [email protected] (G.M. Tamilselvan), [email protected](P.Aarthy).

PeerReviewundertheresponsibilityofUniversidadNacionalAutónomade México.

duetoitsvariationincross-sectionalarea.Becauseofthenon- linearity,levelcontrolisachallengingtaskinconicaltankand itsdemandsforimplementationinrealtime.Thenonlinearities alsoexistsduetothesaturation-typeintroducedbymaximumor minimumallowedlevelintanks,valvegeometry,flowdynamics, pumpsandvalves.Themostbasicandpervasivecontrolalgo- rithmusedinthefeedbackcontrolistheproportional,integral andderivative(PID)controlalgorithm.PIDcontrolisawidely usedcontrolstrategytocontrolmostoftheindustrialautoma- tion processesbecauseofitsremarkableefficiency,simplicity ofimplementationandbroadapplicability.Thelonghistoryof itspractical useandproficientworkingdynamicsaresomeof thepivotalreasonsbehindthelargeacceptanceofthePIDcon- trol. APIDcontroller attemptstocorrect theerrorbetweena measuredprocessvariableandadesiredsetpointbycalculat- ing andthenprovidingacorrectiveactionthat canadjustthe processaccordingly.Inthispaper,themodelingofthesystem, calibration ofvarioustransmittersassociated withthe conical tanksystem,tuningofPIDparametersforthelevelcontrolofa conicaltanksetupisconsidered.Theopenlooptestisperformed toobtainprocessreactioncurveandmathematicalmodelofthe

http://dx.doi.org/10.1016/j.jart.2017.05.004

1665-6423/©2017UniversidadNacionalAutónomadeMéxico,CentrodeCienciasAplicadasyDesarrolloTecnológico.Thisisanopenaccessarticleunderthe CCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).

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process.Basedonthemathematicalmodel,gaintuningofthe PIDcontroller is doneusing the Cohen Coon tuningmethod whichisimplementedintherealtimesystemtogetoptimum settlingtimeandrisetime.Fuzzycontrol,anintelligentcontrol methodimitatingthelogicalthinkingofhumanandbeinginde- pendentonan accuratemathematicalmodel ofthe controlled object,canovercomesomeshortcomingsofthetraditionalPID.

Thecontrollerdesigned usingfuzzy logicimplementshuman reasoningthathasbeenprogrammedintofuzzylogiclanguage (membershipfunctions,rulesandtherulesinterpretation).Fuzzy logicisaformofmanyvalueslogicwhichdealswithreason- ingthatisapproximateratherthanfixedandexact.Compared to traditional binary sets (where variables may take on true orfalse values),fuzzylogicvariablesmayhaveatruthvalue that rangesindegreebetween0 and1. Fuzzylogic hasbeen extendedtohandletheconceptofpartialtruth,wherethetruth valuesmayrangebetweencompletelytrueandcompletelyfalse.

Fuzzylogichasbeenappliedtomanyfieldsfromcontrolthe- oryto artificial intelligence. Fuzzylogic has rapidly become oneofthemostsuccessfultechnologiesfordevelopingsophis- ticatedcontrolsystems.Itisinterestingtonotethatthesuccess offuzzylogiccontrolislargelyduetotheawarenesstoitsmany industrialapplications.Butthefuzzyalgorithmcannotadaptfor largerangeofworkingenvironments.SoKalmanalgorithmis used.

Somerelatedresearches study thisproblemof tuningPID controllers.Modelsenablepredictionsabouthowaprocesswill changewhenperturbedormodified.Manydifferentapproaches havebeenproposedforusinglocalmodelstoapproximatenon- linearsystems.

Ahn andTruong (2009) presented a novel online method usingarobustextendedKalmanfiltertooptimize aMamdani fuzzyPIDcontroller.TherobustextendedKalmanfilter(REKF) isusedtoadjustthecontrollerparametersautomaticallyduring theoperationprocessofanysystemapplyingthecontrollerto minimizethecontrolerror.

Alleyne,Lui, andWright (1998) presented anewkind of hydraulicloadsimulatorfor conductingperformanceandsta- bilitytestsforcontrolforcesofhydraulichybridsystems.Inthe dynamicloadingprocess,disturbancemakesthecontrolperfor- mance(suchasstability,frequencyresponse,loadingsensitivity, etc.)decreaseorturnbad.Inordertoimprovethecontrolper- formance of aloadingsystemandto eliminateor reducethe disturbance,an onlineself-tuningfuzzyproportional-integral- derivative(PID)controllerisdesigned.

Sakthivel,Anandhi, and Natarajan (2011) designed a real timefuzzylogiccontrollerbasedonMamdanitypemodelfor controllingtheliquidlevelinasphericaltank.Sincetheprocess isnon-linear,themodelisdesignedatthreedifferentoperating regions(atlevel30cm,45cm,and60cm).Theprocessmodel isexperimentallydeterminedfromstepresponseanalysisandis interfacedtosphericaltankinrealtimeusingVAMT-01module throughMATLAB.

Cheng,Zhong,Li,andXu(1996)designedahigh-accuracy and high-resolution fuzzy controller to stabilize a double- invertedpendulumatanupright positionsuccessfully.Anew ideaofdealingwithmultivariatesystemsisdescribed.

Fukami,Mizumoto,andTanaka(1980)proposedamethod whichinvolvesaninferenceruleandaconditionalproposition whichcontainsfuzzyconcepts.Andalso pointedoutthat the consequenceinferredbytheirmethodsdoesnotalwaysfitour intuitions andsuggested the improvedmethods whichfit our intuitionsunderseveralcriteria.

Garcia-Benitez,Yurkovich,andPassino(1993)proposeda two level hierarchicalcontrol strategy to achievean accurate endpoint position of a planar two-link flexible manipulator.

Theupper levelconsistsof afeedforwardrule-basedsupervi- sorycontrollerthatincorporatesfuzzylogic,whereasthelower level consists of conventional controllers that combine shaft position-endpoint accelerationfeedbackfordisturbancerejec- tion properties and shaping of the (joint) actuator inputs to minimize the energy transferredtothe flexiblemodes during commandedmovements.

Guo,Zhou,andCui(2004)introducedahybridfuzzycontrol systemofthefurnace.Appliedthefuzzycontrolstrategytoshort period prediction of the furnace temperature and Combining fuzzycontrol withPIDcontrol,theheavy oilfluxisachieved byusingtheon-lineself-adjustingcapabilityoftheharmonious factor.Andtheself-optimizationfuzzycontroloftheratioofair tofuelbecomesrealized.

JwoandWang(2007)usedthetraditionalapproachforselect- ingthesofteningfactorsheavilyreliesonpersonalexperience orcomputersimulation.Inordertoresolvethisshortcoming,a novelschemecalledtheadaptivefuzzystrongtrackingKalman filter(AFSTKF)iscarriedout.

Kobayashi,Cheok,andWatanabe(1995)describedafuzzy rule-basedKalmanfilteringtechniquewhichemploysanaddi- tional accelerometer to complement the wheel-based speed sensor,andproduceanaccurateestimationofthetruespeedof avehicle.TheKalmanfiltersareusedtodealwiththenoiseand uncertainties inthe speedandaccelerationmodels,andfuzzy logictotunethecovariancesandresettheinitializationof the filter accordingtoslipconditions detectedandmeasurement- estimationcondition.

Kwon (2006) suggested arobust Kalman filtering method ofadoptingaperturbationestimationprocesswhichistorecon- structtotaluncertaintywithrespecttothenominalstateequation ofaphysicalsystem.Thepredictorandcorrectorofthediscrete Kalmanfilterarereformulatedwiththeperturbationestimator.

Insuccession,thestateandperturbationestimationerrordynam- icsandthecovariancepropagationequationsarederived.Inthe sequel,therecursivealgorithmofcombineddiscreteKalmanfil- terandperturbationestimatorisobtained.Theproposedrobust Kalmanfilterhasthepropertyofintegratinginnovationsandthe adaptivecapabilityofthetime-varyinguncertainties.Anexam- ple of application to amobilerobot isshown tovalidate the performanceoftheproposedscheme.

Wang andYuan(2012)developedaself-tuningfuzzy PID controlmethodofgratecoolerpressurebasedonKalmanfilter toovercomethefrequentvaryingworkingconditionandworse signal-to-noiseradioofpressuresignals.Basedondynamicsim- ulationandcharacteristicsanalysisoftheclinkercoolingsystem, thesystemvariablesweredetermined,thenthecontrolmodelof gratecoolerwasobtainedbysystemidentification.

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Gaeid(2013),designed an appropriate Kalman filter (KF) withoptimalgainaswellasthetwodegreeoffreedomcompen- satorfortheDCmotorandverifiedthestabilityoftheproposed algorithmandthenoisesensitivity.

Muniandy, Samin, and Jamaluddin (2015) explains how the derivative kick problem arises due to the nature of the PID controller as well as the conventional fuzzy PID controller in association with an AARB. The authors proposed two types of controllers: self-tuning fuzzy proportional- integral–proportional-derivative(STFPI–PD)andPI–PD-type fuzzycontroller.

The Kalman filterprovides an effective meansof estimat- ingthestateofasystemfromnoisymeasurements,giventhat the system parametersare completely specified.The innovations sequencefor aproperlyspecified Kalman filter will be azero-mean white noiseprocess.However,when the system parameterschangewithtime,theKalmanfilterhastobeadapted to compensate for the changes. Traditionally, this has been accomplishedbyusingnonlinearfiltering,parallelKalmanfil- teringandcovariancematchingtechniques.Thesemethodshave producedgoodresultsattheexpenseoflargeamountsofcompu- tationaltime.Anadaptivealgorithmwhichemploysfuzzylogic rulesisusedtoadapttheKalmanfiltertoaccommodatechanges inthesystemparameters.Theadaptivealgorithmexaminesthe innovationssequenceandmakestheappropriatechangesinthe Kalmanfiltermodel.

2. Conicaltanksetup

Therealtimesystemconsistsofoneinput(inflow)andone output(levelofthetank).Theinflowistakenfromareservoir tankthroughacentrifugalpumpwithsinglephasemotor.The inletpipehasaRota meter, Electromagnetictypeflow meter called as flow transmitter (FT1), air-to-open type pneumatic control valve (CV) anda hand valve tomonitor andcontrol theflowrate.Theoutlethasahandvalve,Electromagnetictype flowmetercalledasflowtransmitter(FT2)andair-to-opentype pneumaticCV.ThetanklevelismeasuredusingaDPT,called asleveltransmitter(LT).Thelevel inthetankisdirectlypro- portionaltothepressurecreatedbyliquidinit.LTmeasuresthe level bymeasuringpressureatbottom ofthe tankwithrefer- encetotheatmosphereandcovertsinto anelectricalquantity (4–20mA).TheLTisenergizedwith24VDCsourceandlower rangevalue(LRV)andupperrangevalue(URV)aresetusinga highwayaddressableremotetransducer(HART)communicator.

ThelayoutoftheconicaltanksetupisshowninFig.1.

Thesystemisinterfacedtothecomputer through NIUSB 6211dataacquisitioncard(NIDAQ)anditcanhandleamaxi- mumof10V,sotheDPToutputs(4–20mA)areconvertedinto 2–10Vusinga500resistancesandscaledupusingLabView.

Thecontrollersignals(0–10V)fromcomputerviaNIDAQare converted into 4–20mA using a voltageto current convertor andgiventocurrenttopressure(E/P)convertor.Thepneumatic linefrom thecompressorisconnectedtoanairregulatorand itsoutputisgivenasconstantinputs(20psi)fortwodifferent

E/Pconverters.TheCVsareoperatedbasedonthepneumatic outputsfromE/Ps.

3. EstimationoftransferfunctionandPIDgain 3.1. Transferfunctionforthesystem

The openloopresponseis plottedandthe valuesobtained fromtheplotlikepercentagechangeinlevel(Q%),delaytime (td),thetimetakenbythelevelareusedforgettingmathematical model oftheconicaltank.Themodel offirstorderprocessis asinEq.(1).Thefirstorderprocesswithtimedelay(FOPTD) modelis,

G(s)=Kpe^−td^s

τs+1 (1)

Timeconstantτ=960s.

K_p= %changeinoutput

%changeininput =Q

P =64.08

G(s)=64.08e^−11s

960s+1 (2)

Eq.(2)indicatedaboveistheobtainedmathematicalmodel fortheentireoperatingrangeoftheconicaltanksystem.

3.2. PIDgainsforthesystem

Theproportionalgain,integralgainandderivativegainsfor thesystemisasinEqs.(3)–(5).

Proportionalgain, Kc= 1 K

τ τ_d

4 3 + τ_d

4τd

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Integralgain, τ_I =τ_d32+6(τd/τ)

13+8(τd/τ) (4)

Derivativegain, τ_D=τ_d 4

11+2(τd/τ) (5)

4. Fuzzycontroller

Fuzzycontrol has beenwidelyused inindustrial controls, particularlyinsituationswhereconventionalcontroldesigntech- niqueshavebeendifficulttoapply.Numberoffuzzyrulesisvery important forreal timefuzzy controlapplications.Thispaper proposesanovelapproachcalledblockbasedfuzzycontrollers.

Thisstudyismotivatedbytheincreasingneedintheindustryto designhighlyreliable,efficientandlowcomplexitycontrollers.

Theproposedblockbasedfuzzycontrollerisconstructedby severalfuzzycontrollerswithlessfuzzyrulestocarryoutcon- troltasks.Thefuzzylogiccontrollerinvolvesfourmainstages:

Fuzzification,rulebase,inferencemechanismanddefuzzifica- tion. Forthesystems wherethe physicalmodelingisdifficult andinformationregardingthemodelisinadequateforapplying anycontrolaction,Fuzzylogicactionsareappliedoverit.Fuzzy logicsystemsarebasedonlogicalreasoningalongwithability tofuzzifyanysystemwhichhelpsineasyimplementation.In

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Fig.1.Layoutofconicaltanksystem.

manyindustrialprocesses,fuzzylogiccontrollersareuseddue towhichtakesthecontrolactionlikehumanandthecontrolling processissimpleonceitisdesigned.MainlyFLC areimple- mented on non-linear systems whichyield for better results.

Fordesigningthecontrollernumberofparametersneedstobe selectedandthenMembershipFunctionandrulesareselected basedonheuristicknowledge.Therearetwoinputstothefuzzy controllers:absoluteerror|e(t)|andabsolutederivativeoferror

|de(t)|.The rangesoftheseinputsarefrom 0to1,whichare obtainedfromtheabsolutevaluesofsystemerroranditsderiva- tivethrough scalefactorschosen fromthe specificationofthe nonlinearsystem.Foreachinputvariable,trianglemembership functions(MFs)arerequestedtouse.

Inpractice,fuzzycontrolisappliedusinglocalinferences.

Thatmeans eachrule isinferred,andtheresultsof theinfer- encesofindividualrulesarethenaggregated.Themostcommon inferencemethodsare:themax–minmethod,themax–product methodand the sum–productmethod, wherethe aggregation operatorisdenotedbyeithermaxorsum,andthefuzzyimpli- cationoperatorisdenotedbyeitherminorprod.Fig.2showsthe basicfuzzystructure.Especiallythemax–mincalculusoffuzzy relations offers acomputationallynice andexpressivesetting forconstraintpropagation.Finally,adefuzzificationmethodis neededtoobtainacrispoutputfromtheaggregatedfuzzyresult.

Data base (Known states and derived information)

(Quantitative knowledge and heuristics)

Inference (composition)

Plant Quantizer

Reference input

∆ Error Error

Error

Fuzzy rule base

Defuzzification Fuzzification

Fig.2.StructureoftypicalFLC.

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Popular defuzzificationmethods include maximum matching and centroid defuzzification. The centroid defuzzification is widelyusedforfuzzycontrolproblemswhereacrispoutputis needed,andmaximummatchingisoftenusedforpatternmatch- ingproblemswhereweneedtoknowtheoutputclass.Hence, inthisstudy,thefuzzyreasoningresultsofoutputsaregained fromaggregationoperationoffuzzysetsofinputsanddesigned fuzzyrules,wheremax–minaggregationmethodandcentroid defuzzificationmethodareused.

4.1. FISeditor

Twoinputsaredefinedfor thefuzzycontroller.Oneisthe leveloftheliquidinthetankdenotedas“level”andtheother oneis the rate of change of liquid level inthe tankdenoted as “rate”. Both of these inputsare applied tothe rule editor.

AccordingtotheruleswrittenintheruleEditorthecontroller takestheactionandgovernstheopeningofthevalvewhichis theoutputofthecontrollerandisdenotedby“valve”.TheFIS editorisshowninFig.3.

4.2. Membershipfunctioneditor

Themembershipfunctioneditorsharessomefeatureswith theFISeditor.Infact,allofthefivebasicGUItoolshavesim- ilarmenuoptions,statuslinesandhelpandclosebuttons.The

Fig.3.FISeditor.

membershipeditorshowninFig.4isthetoolthatletsyoudis- playandeditsallofthemembershipfunctionsassociatedwith alloftheinputandoutputvariablesfortheentirefuzzyinfer- ence system.Whenyouopenthe membershipfunctioneditor toworkonafuzzyinferencesystemthatdoesnotalreadyexist intheworkspace,therearenotyetanymembershipfunctions associatedwiththevariablesthatyouhavejustdefinedbythe FISeditor.Themembershipeditingisdoneforeveryinputand output variables. Forthe first inputvariable namederror, the

Fig.4.(a)Membershipeditingofthefirstinputvariable.(b)Membershipeditingofthesecondinputvariable.(c)Membershipeditingofthefirstoutputvariable.

(d)Membershipeditingofthesecondoutputvariable.

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Table1 Ruletable.

Error RCE

HN MN SN ZERO SP MP HP

HN Kp=dec

Ki=dec

Kp=dec Ki=med

Kp=dec Ki=inc

Kp=dec Ki=dec

Kp=dec Ki=inc

Kp=dec Ki=med

Kp=dec Ki=dec

MN Kp=med

Ki=med

Kp=med Ki=med

Kp=med Ki=inc

Kp=dec Ki=inc

SN Kp=dec

Ki=dec

Kp=dec Ki=med

Kp=dec Ki=inc

Kp=dec Ki=med

Kp=dec Ki=inc

Kp=dec Ki=med

Kp=dec Ki=inc

ZERO Kp=med

Ki=dec

Kp=med Ki=med

Kp=med Ki=inc

Kp=med Ki=med

Kp=med Ki=inc

Kp=med Ki=med

SP Kp=dec

Ki=dec

Kp=inc Ki=inc

Kp=med Ki=med

Kp=dec Ki=dec

MP Kp=med

Ki=dec

Kp=inc Ki=inc

Kp=inc Ki=dec

Kp=inc Ki=inc

Kp=med Ki=med

Kp=inc Ki=med

HP Kp=inc

Ki=dec

Kp=inc Ki=med

Kp=inc Ki=inc

Kp=med Ki=med

Kp=inc Ki=med

Kp=inc Ki=inc inc,increase;dec,decrease;med,medium.

rangefortheinputvariableisfrom−7to+51.Themembership editingforthesecondinputvariablenamedrcerangesfrom−15 to+15.Similarlythemembershipeditingcarriedoutforthefirst outputvariablerangesfrom0to2forthefirstoutputvariable namedKp.ThesecondoutputvariablenamedKirangeisfrom 0to0.6.Forthelevelcontrolofconicaltankprocess,inputand outputmembershipfunctionsaredesignedasshowninFig.4 andbothinputsandoutputsconsistofsevenfunctions.Theout- putvariablesfromFLCKpandKiwillbeusedtotunethePID controllerforbetterperformance.

4.3. Ruleviewer

Theruleviewerallowsyoutointerprettheentirefuzzyinfer- enceprocessatonce.Therulevieweralsoshowshowtheshape ofcertainmembership functionsinfluencesthe overallresult.

Sinceitplotseverypartofeveryrule,itcanbecomeunwieldy forparticularlylargesystems,butforarelativelysmallnumber ofinputsandoutputsitperformswell(dependingonhowmuch screenspaceyoudevotetoit)withupto49rules.Theruleviewer showsonecalculationatatimeandingreatdetail.Inthissense, itpresentsasortofmicroviewofthefuzzyinferencesystem.

Toobservetheentireoutputsurfaceofthesystemandtheentire spanoftheoutputset,basedontheentirespanoftheinputset, byopenupthesurfaceviewer.Therulesformedareshownin Table1.

Obtained FLC simulation results are plotted against with that ofconventional controller PIDcontroller for comparison purposes.Thesimulation resultsare obtainedusing a49rule FLC.Rulesshownintheruleeditorprovidethecontrolstrategy.

Heretheserulesareimplementedintheabovecontrolsystem.

Forcomparisonpurposes, simulationplots include aconven- tional PID controller and the fuzzy algorithm. As expected, FLC provides goodperformance interms of oscillations and overshootintheabsenceofapredictionmechanism.TheFLC

algorithm adapts quicklyto longer time delays and provides astableresponse whilethePIDcontrollers,drivesthesystem unstable due to mismatch error generated by the inaccurate timedelay parameterusedinthe plantmodel.From thesim- ulations inthepresence ofunknown orpossiblyvaryingtime delay, the proposedFLC showsa significantimprovement in maintainingperformanceandpreservingstabilityoverstandard PIDmethod.To strictlylimit theovershoot using Fuzzycon- trol can achievegreater control effect. Fig. 5 shows the rule viewer.

Inthispaper,liquidlevelistakenandMATLABisusedto designafuzzycontrol.Thenweanalyzethecontroleffectand compareitwithPIDcontrol.Especiallyitcangivemoreatten- tiontovariousparameterssuchasthetimeofresponse,theerror ofsteadyingandovershoot.Comparisonof thecontrolresults fromthesetwosystemsindicatedthatthefuzzylogiccontroller significantlyreduced steadystate error.Thesurfaceviewer is showninFig.6

.

5. TheKalmanalgorithm

Theneedforaccuratestateestimatesoftenarisesincontrol systems applications.The performanceof astate estimatoris usuallyjudgedbytwocriteria.First,theestimatorneedstobe accurate.Therefore,themeanerrorshouldbeassmallaspossi- ble,ideallyzero.Theestimatoralsoneedstoprovideaprecise estimateof thecurrent state.Therefore,the covarianceof the errorshouldbesmall.Theoptimalestimatebasedontheerror variancecriterioniscalledtheminimumvarianceestimate.The Kalmanfilterprovidesaneffectivemeansofsolvingthemini- mumvarianceestimationproblemforalinearsystemwithnoisy measurements linearlyrelatedto the states. Alinear discrete systemcanbedescribedbythefollowingsetofequations.

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Fig.5.Ruleviewer.

Fig.6.Surfaceviewer.

Systemmodel

x(k+1)=Ax(k)+Ww(k) (6)

wherew(k)isazeromeanwhiteprocessnoisewithcovariance Rw.

Measurementmodel

y(k)=Cx(k)+v(k) (7)

wherev(k)isazeromeanwhiteprocessnoisewithcovariance Rv.

The Kalman filter algorithm canbe viewedas a predictor correctoralgorithmasshowninFig.7.

Measurement Innovations sequence

Kalman gain

Correction

K K+1

Prediction Initial conditions

Fig.7.BlockdiagramofKalmanfilteralgorithm.

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Table2

PropertiesofproperlyspecifiedKalmanfilter.

1 Innovationssequenceiszero-mean.

2 Innovationssequenceiswhite.

3 Innovationssequenceisuncorrelatedintime.

4 Innovationssequencelieswithintheconfidenceinterval constructedfromReoftheKalmanfilteralgorithm.The innovationssequencewillhaveanormaldistribution.Therefore, lessthanfivepercentoftheinnovationswillbeoutsidetwo estimatedstandarddeviations.Theconfidenceintervalisthen constructedusingthefollowingequations.

Upperlimit=2.0sqrt(Re) Lowerlimit=−2.0sqrt(Re)

5 Theactualvarianceoftheinnovationssequencewillbereasonably closetotheestimatedvariance,Re.

6 Theerrorestimationlieswithintheconfidencelimitsconstructed fromtheestimatederrorcovariance,p,˜ oftheKalmanfilter algorithm.Theestimationerrorwillhaveanormaldistribution.

Therefore,lessthanfivepercentoftheestimatederrorswillbe outsidetwoestimatedstandarddeviations.Theconfidencelimits willbeconstructedusingthefollowingequations.

Upperlimit=2.0sqrt(p)˜ Lowerlimit=−2.0sqrt(p)˜

7 Theactualerrorvarianceisclosetotheestimatedvariance.

TheKalman filteralgorithm showninFig.7 assumesthat thesystemstatetransitionmatrix,measurementmodelandthe covariance’softheplantandmeasurementnoiseareknown.This israrelythecaseintherealworld.AproperlyspecifiedKalman filterwillhavethepropertiesgiveninTable2.Adaptivefiltering isanonlineprocessoftryingtoidentifyunknownsystemparam- etersbasedonthemeasurementsandinnovationssequenceas theyoccurin realtime. The innovations sequenceof aprop- erlyspecifiedKalmanfiltershouldbeapurelyrandomprocess.

Severaltechniqueshavebeensuggestedfordealingwithfilter- ingproblemswhenthesystemcontainsunknownparameters.

Nonlinearfilteringhasbeen successfullyapplied tothe prob- lemofsystemidentification(i.e.statetransitionmatrixand/or measurementmodelcontainunknowns).

AsshowninFig.8,theproposedmethodusesthestandard Kalmanfilterequationsandadaptsthesystemparametersbased ontheinnovationssequence.Thefuzzylogicadaptivealgorithm examinesthe innovationssequenceanddetermineswhat type ofchange inmodel parametersisnecessarytoinsurethatthe sequenceisazeromeanwhiteprocess.Acertainamountofa prioriinformationaboutthesystemisnecessaryinconstructing thecontrolrulesforadaptingthefilterparameters.

6. SimulinkmodeloffuzzyandPIDcontroller

SimulinkisaMatlabtoolboxdesignedforthedynamicsimu- lationoflinearandnonlinearsystemsaswellascontinuousand discrete-timesystems.It canalsodisplayinformationgraphi- cally.Matlabisaninteractivepackagefornumericalanalysis, matrix computation, control system design, and linear system analysis and design available on most CAEN platforms

Initial conditions

Prediction

Measurement K K+1 Innovations sequence

Correction Gain Fuzzy logic adaptive

algorithm

Fig.8.BlockdiagramoffuzzylogicadaptiveKalmanalgorithm.

(Macintosh,PCs,Sun,andHewlett-Packard).Inadditiontothe standardfunctionsprovidedbyMatlab,thereexistalargesetof toolboxes,orcollectionsoffunctionsandprocedures,available aspartoftheMatlabpackage.Fig.9showstheSimulinkmodel forfuzzyandPIDcontroller.

7. SimulinkmodeloffuzzywithKalmanalgorithm The Simulink model of the Kalman algorithm along with fuzzycontrollerandplantisasshowninFig.10.

8. Resultsanddiscussion

TheresponseobtainedfromtheplantmodelbyusingFLC andPIDcontrollerisas showninFig.11.Fromtheresponse, it can be clearly seen that the response obtained from the fuzzycontrollerismoreaccurateandprecise whencompared toconventionalcontroller.Parameterslikeresponsetime,peak overshoot,settlingtimearefast,lessandaccuratecomparedto PIDcontroller.

Inthisresearchwork,theliquidlevelistakenandMATLABis usedtodesignafuzzycontrol.Thenweanalyzethecontroleffect andcompareit withPIDcontrol.Especiallyit cangivemore attention tovarious parameterssuch as the timeof response, theerrorofsteadyingandovershoot.Comparisonofthecontrol resultsfromthesetwosystemsindicatedthatthefuzzylogiccon- trollersignificantlyreducedsteadystateerror.Eventhoughthe responseofthefuzzinessismoreaccurateandprecisethanPID, theplantisstillsensibletoexternalnoise.In ordertoremove thatnoiseandmakethesystemchangeitsparametersaccord- ingly,Kalmanalgorithmisusedhere.Kalmanalgorithmisused

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Math function

Integrator Display

Scope2

Scope Scope1

Scope3

Scope4 Integrator1

Math function1

Step PID controller Transfer fon

Transfer fon1 Product

Display1 Product1

Derivative du/dt

Fuzzy logic controller with ruleviewer

X

X Transfer

delay

Transfer delay1 64.08

64.08 980s+1

980s+1 +

++ +

-

PID(s)

1 s

1 s u²

u²

Fig.9.FuzzyandPIDsimulinkmodel.

100-99z^-1

100z-99 0-2z+0.8

Discrete filter

Fuzzy logic controller with ruleviewer

Discrete transfer fon

Transport delay

Scope Step

+- 1+-0.8z^-20.2z^-3

Fig.10.SimulinkmodelofKalmanalgorithmwithfuzzycontroller.

becauseofitsabilitytoprovidethequalityoftheestimateandits relativelylowcomplexity.TheresultobtainedbyusingKalman filterisasshowninFig.12

.

Figs. 13 and 14 show the front panel and block diagram panel ofaLabView simulatorof alevelestimator.Thefuzzy model is developed using Matlab simulink. On the Simulink Model toolbar, NORMALsimulation ischangedas EXTER- NALsimulation.Thesimulationconfigurationparametersare changed.Thenthemodelisbuilt.InLabViewnewVIisbuilt withthe desiredindicators andcontrols.Thesimulink model

80

20

10

0 100 150 200 250 300 350 400 450 500

Time offset: 0

PID FUZZY

50 0 30 40 50 60 70

Fig.11.ResponseoffuzzyandPIDcontroller.

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Fig.12.ResponseoffuzzyusingKalmanalgorithm.

andLabviewVI aresaved insamelocation. In SIT Connec- tion manager the correct Simulinkparameter is selected that goesalongwiththeLABVIEWLABELandTYPE.Thenthe NIDAQandmappingsareconfigured.Thisiswheretheinput andoutputchannelsareselected.Selectaninputoroutputfrom DAQCHANNELSthat isbeing used.Selectthe correspond- ingSimulinkinput/outputfromMODELINPUTS/OUTPUTS.

Whenbothboxescontainahighlighteditem,selectADD.This willmaptheinput/output.Makesurethatalldesiredindicators are present.Connect awirefrom the SIGNALSinput of the blocktothewirethatgoesintothedesiredindicator.Nowthe programcanbeexecuted.

Fig.15 showsthe real timeexperimental setupof a coni- caltankprocess.Thelevelprocessstationwasusedtoconduct theexperiments andcollectthe data.The computer acts as a controller.Itconsistsofthesoftware usedtocontrol thelevel processstation.Thesetupconsistsofaprocesstank,reservoir tank,controlvalve,ItoPconverter,levelsensorandpneumatic

signalsfromthe compressor.Whenthesetupisswitchedon, levelsensor sensestheactuallevelvaluesinitiallythensignal isconvertedtocurrentsignalintherange4–20mA.Thissignal isthengiventocomputerthroughdataacquisitioncord.Based onthevaluesenteredinthecontrollersettingsandthesetpoint thecomputerwilltakecontrolactionandthesignalsentbythe computer istaken tothe stationagain through thecord. This signalisthenconvertedtopressuresignalusingItoPconverter.

Thenthepressuresignalactsonacontrolvaluewhichcontrols theflowofwaterintothetanktherebycontrollingthelevel.

Theservoresponseobtainedfromtherealtimeconicaltank Taexperimental setupis showninFig. 16.The results show the comparison of servo response by the FLC andPID con- trollerwithsetpoint.Fromtheresponse,itisapparentthatthe fuzzycontrollerprovides betterresultswhencomparedtothe conventionalPIDcontroller.

9. Conclusions

Unlike some fuzzy controllers with hundreds or even thousands of rules running on dedicated computer systems a uniqueFLCusingasmallnumberofrulesandstraightforward implementation is proposed to solve a class of level control problemswithunknowndynamicsorvariabletimedelayscom- monly foundinindustry.Additionally theFLC canbe easily programmed into many currentlyavailable industrial process controllers.TheFLCsimulatedonalevelcontrolproblemwith promisingresultscanbeappliedtoanentirelydifferentindus- trial level controllingapparatus. The result shows significant improvementinmaintainingperformanceoverthewidelyused PIDdesignmethodintermsofoscillationsproducedandover- shoot. As seenfrom the graph the rise time in case of PID controllerisless,butoscillationsproducedandovershootand settling time is more. But in case of fuzzy logic controller,

Fig.13.LabViewimplementationofKalmanfilter.

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Fig.14.BlockdiagrampanelviewofLabViewsimulatorforlevelestimator.

Fig.15.Conicaltankexperimentalsetup.

0

0 200 300 400

Set point Fuzzy

PID

Process time in seconds

Tank level in mm

100 20

40 60 80 100 120 140 160 180 200

Fig.16.Servoresponseofconicaltanksystem.

oscillations and overshoot and settlingtime are low, so FLC canbeappliedwhereoscillationscannotbetoleratedinthepro- cess.TheFLCalsoexhibitsrobustperformanceforplantswith significantvariationindynamics.HereFLCandPIDbothare appliedtothesameexactingmodeledlevelcontrolsystemand simulationresultsareobtained.PIDwouldnothavetakencare oftheunknowndynamicsorvariabletimedelaysinthesystem, ifthetechniquesbeenappliedtoasystemwhoseexactsystem dynamicswerenotknown,Fuzzylogicprovideacompletelydif- ferent,unconventionalwaytoapproachacontrolproblem.This methodfocusesonwhatthesystemshoulddoratherthantrying

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tounderstandhowitworks.Onecanconcentrateonsolvingthe problemrathertryingtomodel the systemmathematically,if thatis evenpossible.Thisalmost invariablyleadstoquicker, cheapersolutions.AndalsousingKalmanfilterprovidesmore preciseresultssothatcontrollerwithKalmanalgorithmcanbe usedinnoisyenvironments.Thisresearchworkcanbeextended byusingtherobustextendedKalmanfiltertoeffectivelyusethe controllerinnoisyenvironments.

Conﬂictofinterest

Theauthorshavenoconflictsofinteresttodeclare.

References

Ahn,K.K.,& Truong,D.Q.(2009). OnlinetuningfuzzyPID controller usingrobustextendedKalmanfilter.JournalofProcess Control,19(6), 1011–1023.

Alleyne,A.,Liu,R.,&Wright,H.(1998).Onthelimitationsofforcetracking controlforhydraulicactivesuspensions.InAmericancontrolconference, 1998.Proceedingsofthe1998(Vol.1,pp.43–47),IEEE.

Cheng,F.,Zhong,G.,Li,Y.,&Xu,Z.(1996).Fuzzycontrolofadouble-inverted pendulum.FuzzySetsandSystems,79(3),315–321.

Fukami,S.,Mizumoto,M.,&Tanaka,K.(1980).Someconsiderationsonfuzzy conditionalinference.FuzzySetsandSystems,4(3),243–273.

Gaeid, K. S. (2013). Optimal gain Kalman filter design with Dc motor speedcontrolledparameters.JournalofAsianScientiﬁcResearch,3(12), 1157–1172.

Garcia-Benitez,E.,Yurkovich,S.,&Passino,K.M.(1993).Rule-basedsuper- visorycontrolofatwo-linkflexiblemanipulator.JournalofIntelligent&

RoboticSystems,7(2),195–213.

Guo,J.,Zhou,J.,&Cui,T.(2004).Theapplicationofthehybridfuzzycontrol ofthefurnace.TheInformationofMicrocomputer,21,106–109.

Jwo,D.J.,&Wang,S.H.(2007).Adaptivefuzzystrongtrackingextended Kalman filtering for GPS navigation. IEEE Sensors Journal, 7(5), 778–789.

Kobayashi,K.,Cheok,K.C.,&Watanabe,K.(1995).Estimationofabsolute vehiclespeedusingfuzzylogicrule-basedKalmanfilter.InProceedingsof theAmericancontrolconference(Vol.5,pp.3086–3090),IEEE.

Kwon,S.J.(2006).RobustKalmanfilteringwithperturbationestimationprocess foruncertainsystems.IEEEProceedings–ControlTheoryandApplications, 153(5),600–606.

Sakthivel,G.,Anandhi, T. S.,& Natarajan, S.P. (2011).Design offuzzy logiccontrollerforasphericaltanksystemanditsrealtimeimplementa- tion.InternationalJournalofEngineeringResearchandApplications,1(3), 934–940.

Muniandy,V.,Samin,P.M.,&Jamaluddin,H.(2015).Applicationofaself- tuningfuzzyPI–PDcontrollerinanactiveanti-rollbarsystemforapassenger car.VehicleSystemDynamics,53(11),1641–1666.

Wang,Z.,& Yuan,M.(2012).Aself-tuningfuzzyPID controlmethodof gratecoolerpressurebasedonKalmanfilter.InInternationalconference oncomputerscienceandinformationprocessing(CSIP),(pp.257–260), IEEEhttp://dx.doi.org/10.1109/CSIP.2012.6308843