Proceedings of the Institution of

Nonlinearcontrollerofanair-cushionsystemforaswampterrainvehicle:fuzzylogicapproach

AHossain1,2*,ARahman1*,andAKMMohiuddin1DepartmentofMechanicalEngineering,FacultyofEngineering,InternationalIslamicUniversityMalaysia(IIUM),KualaLumpur,Malaysia

DepartmentofMechanicalEngineering,FacultyofEngineering,UniversitiIndustriSelangor(Unisel),KualaSelangor,Malaysia

Themanuscriptwasreceivedon28August2010andwasacceptedafterrevisionforpublicationon27January2011.DOI:10.1177/0954407011400818

21Abstract:Thispaperpresentsthefuzzylogiccontroller(FLC)ofanair-cushionsystemforaswamppeatterrainvehicleanddescribestheprocessbywhichitfunctions.Cushionpres-sureiscontrolledbyanelectronicproportionalcontrolvalveandFLCusingtheoutputsignalofthedistance(height)measuringsensorthatwasattachedtothevehicle.Themainpurposeofthisstudywastodevelopacontrolschemeforanair-cushionsystemandtoinvestigatetherelationshipbetweenvehicleverticalpositionandtheair-cushionsystem,andtoillustratetheimportantroleofthefuzzylogiccontrolsystem.Experimentalvalueswererecordedinthelaboratoryforcontrolsystemtesting,andintheswamppeatterrainfieldforvehicleperfor-manceinvestigation.Inthispaper,afuzzylogicexpertsystem(FLES)model,basedontheMamdaniapproach,wasdevelopedtopredictthechangesinflowrate.ThemeanrelativeerrorofactualandpredictedvaluesfromtheFLESmodelofflowratewasfoundtobeslightlyabovetheacceptablelimit.ThegoodnessoffitofthepredictionvaluesfromtheFLESmodelwasfoundtobecloseto1.0asexpected,andhencedemonstratedthegoodperformanceofthedevelopedsystem.

Keywords:swamppeatterrain,air-cushion,fuzzylogiccontroller,position

1INTRODUCTION

Transportationoperationisanimportantprobleminoff-roadvehiclesusedinagricultureandtravel-lingoverswamppeatterrain;itisconsideredasoneofthemajortransportationissuesinmanypartsoftheworld.Inordertoimprovethetractionperfor-manceofavehicleoperatingonsoftterrainandinwetfields–suchasswamp,sea,andbeach–ahybridvehiclewhichcombinesair-cushiontech-nologywithatracksystemhasbeendevelopedasshowninFig.1[1].However,becauseoftheuncer-taintyofthesoftterrain,thepowerconsumption

*Correspondingauthor:DepartmentofMechanicalEngineering,FacultyofEngineering,InternationalIslamicUniversityMalaysia(IIUM),50728KualaLumpur,Malaysia.

email:altab75@unisel.edu.my(A.Hossain)andarat@iiu.edu.my(A.Rahman)

andcushionpressurecontrolofthisvehiclecreatemajorproblemsforpracticalapplicationswhenthevehiclesareusedforagricultural,oilindustry,andmilitarypurposes.Although,thisvehiclehasbeenshowntobeeffectivewhenmovingonthelow-bearing-capacityswamppeats,someproblemshavebeenincurredduringoperationonswamppeatterrainduetothedifficultiesincontrollingtheair-cushionsystem.Variousdifferentresearchinstitu-tionsfromuniversities,governmentorganizations,andprivatecompanieshaveproposedanddevel-opeddifferenttypesoftrackedvehiclesfortrans-portationoperation,butonlyformoderateterrain[2–4].However,inordertobeabletodriveavehicleoff-road,forexampleinswamppeatterrain,thevehiclesneedlowergroundpressurethanordinaryroadvehicles.Whendrivingonswamppeatterrainthelowergroundpressureisneededtoavoidsink-ingandgettingstuck.Trackedvehiclesprovidelow

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722AHossain,ARahman,andAKMMohiuddin

2METHODOLOGY

2.1TheoreticalmodelofpowerconsumptionTheair-cushiontrackedvehicleispartiallysupportedbytheair-cushion(lifting)systemandisdrivenbythepropulsionsystem.Therefore,thetotalpowerconsumptionPofthevehicleisgivenbyP=Pc+Pd

(1)

Fig.1Photoofthedevelopedvehicle[1]

wherePcisthepowerconsumedbytheair-cushion(inW)whenitpartiallysupportstheweightofthevehiclebodyandPdisthepowerconsumedbythedrivingsystem(inW)whenovercomingthetravel-lingresistanceandmaintainingthenormaldrivingstate.

2.1.1Powerrequiredfortheair-cushionsystemThepowerrequiredfortheair-cushionsystemcanbeexpressedby[13]

󰀂󰀃1=22

ðpcÞ3=2Pc=pcQ=hcLcDc

rwhereQ=hcLcDc

󰀂2pcr

󰀃1=2

(2)

groundpressureandhavethecapabilityofoperat-ingoverawiderangeofunpreparedmoderatepeatterrain[5].However,transportationefficiencyisthemainrequirementforthetrackedvehicleswhenthevehiclesaretravellingoverlow-bearing-capacityswamppeatterrain.Amoderatepeatterrainbear-ingcapacityof12kN/m2isreportedbyRahmanetal.[5];swamppeatterrainwithasurfacematthicknessof70mmandwithabearingcapacityof7kN/m2isreportedbyJamaluddinandSarawak[6].Systematicstudiesoftheprinciplesunderlyingthetransportationdevelopmentofoff-roadvehiclesonlow-bearing-capacityswamppeatterrain,there-fore,haveattractedconsiderableinterestinthesearchtodevelopanintelligentair-cushionsystemforaswampterrainvehicleandtoachievetheasso-ciatedreducedfuelconsumption[7].

Theair-cushion–terraininteractiontakesplaceinanuncertainandvagueenvironmentduetosoilcon-ditions,andsubmergedandundecomposedmateri-alssuchaswood,stones,stumps,andshrubs,etc.Nomathematicalmodelcandescribesuchacomplexmechanicssystemsatisfactorily[8].Ineffortstocon-trolsuchsystems,thefuzzylogiccontroller(FLC)hasbecomeapopularmodelthatoffersnonlinearcontrolandhastheadvantagethatthefuzzycontrol-lerdoesnotrequireaprecisemathematicalmodel[9–12].Theappropriateandinexactnatureoftheair-cushionsystemforatrackedvehiclehasbeeneffectivelycapturedusingfuzzylogic,whichisalogi-calsystemclosertohumanknowledgeandmachinelanguage.ThispaperdescribestheimplementationofaFLCtocontrolanair-cushionsystembasedonthevehicleverticalpositionfromtheground.Samplingdatacollectedfromtheswampterrainareusedtovalidatethefuzzymodels.

Inequation(2),Qisthevolumeflowrate(inm/s),pcisthecushionpressure(inN/m2),hcistheoreticalcushionclearanceheight(inm),Lcistheair-cushionperimeter(inm),Dcisthedischargecoefficient,andristheairdensity(inkg/m3).

32.1.2Powerrequiredforthedrivingsystem

Forthepropulsionsystem,thepowerconsumptionisfromtotalmotionresistance.Therefore,innormaldrivingcasesforthevehicle,therequiredpowerforthedrivingsystemcanbeexpressedby[8,13,14]

Á

Pd=RtVt=Rc+Rin+RdragVtwhere

󰀂󰀃kpz24

+mmz3Rc=2B23Dht

󰀂󰀃WÀpcAc

ð222+3VtÞRin=

1000gRdrag=pcActanu

À

(3)

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Fuzzylogiccontrollerofanair-cushionsystemforaswampterrainvehicle723

Inequation(3),Rtisthetotalmotionresistance(inN)(whichisthesumofmotionresistanceduetoterraincompactionRc,innerresistanceRin,andthedraggingmotionresistanceRdrag),Vtisthevehi-cletheoreticalspeed(inm/sintheequationforPdandinkm/hintheequationforRin),Bisthetrackwidth(inm),zisthesinkage(inm),mmisthesur-facematstiffness(inN/m3),kpistheunderlyingpeatstiffness(inN/m3),Dhtisthetrackhydraulicdiameter(inm),Wisthetotalweightofthevehicle(inN),pcisthecushionpressure(inN/m2),Acistheair-cushioneffectivearea(inm2),andfistheterraininternalfrictionangle(indegrees).

However,toovercomethetotalmotionresistanceRt,thetractionforce(drivingforce)providedbythetracksofthevehicleFt[1]shouldbeequaltoRt,i.eÀÁ

Ft=Rt=Rc+Rin+Rdragwhere

󰀂󰀃 󰀂󰀃!

Kw1KwiLeÀ1+exp1ÀFt=ðAtc+WttanfÞiLiLKwInequation(4),Ftisthetractionforcedeveloped

atthevehicle’strackgroundcontactpart(inN),Bisthetrackwidth(inm),Listhetrackgroundcontactlength(inm),Atisthetrackgroundcontactarea(inm2),Wtisthevehicleloadsupportedbythetracksystem(inN),cisthecohesiveness(inN/m2),fistheterraininternalfrictionangle(indegrees),Kwisthesheardeformationmodulusoftheterrain(inm),iistheslippageofthevehicle(inpercent),andeistheexponent(exp)term.2.1.3Totalpowerandoptimumstate

Accordingtopreviousstudies[14–16],ithasbeenshownthatloaddistributionratioaffectstotalpowerrequirementandvehicletractiveperfor-mancesignificantly.Whenthevehicleisaffectedbyexternaldisturbances,thischangestheloaddis-tributionratioandtotalpowerrequirement.Itisnotedthatloaddistributionratio(d)shouldbeaslowaspossibleinordertoreducethedraggingmotionresistance.LuoandYu[17]havesuggestedthattheloaddistributionratioshouldbekeptwithintherangeof0.2–0.75inordertomaintainthesemi-trackedair-cushionvehicleinnormaloperatingconditions,i.e.withsatisfactoryperfor-mance.Loaddistributionratioisdefinedasd=

WcWc

=WWt+Wc

(5)(4)

whereWc=pcAcistheweightsupportedbytheair-cushionsystem,Wisthetotalweightofthevehicle,

andWtisthevehicleweightsupportedbythetracksystem(inN).

Combiningequations(1),(2),and(3),thetotalvehiclepowerconsumption,Pisafunctionofpcandhcandcanberewrittenas

P=pcQ+RtVt

\"󰀂󰀃1=2#

ÀÁ2pc

P=pchcLcDc+Rc+Rin+RdragVt

r

\"󰀂󰀃󰀂󰀃1=2

2kz24p

+P=hcLcDcðpcÞ3=2+2Bmmz32r3Dht

#󰀂󰀃

WÀpcAc+ð222+3VtÞ+pcActanuVt

1000gP=f1ðpc,hcÞ+f2ðpcÞ

(6)

Foraparticularsoilcondition,theexistenceofanoptimalloaddistributionratio,whichresultsinminimumtotalpowerconsumptionforthevehicle,couldbedetermined.Soforequation(6),takingthepartialderivativeofPwithrespecttopcandhavingtheresultantequationequaltozero,i.e.∂P

=0∂pc

ThesystemconstraintsasshowninFig.2arehcgÀhi=hc+zz=k1Àhcwherek1=hcgÀhc

Therefore,thefirstderivativeofPinequation(6)withrespecttopccanbeexpressedby󰀂󰀃1=223

ðpcÞ1=2hcLcDc

r2󰀃 󰀂!ÀAc

+ð222+3VtÞ+ActanfVt=0

1000g󰀂󰀃1

pc=f

h2c

(7)

Theoptimalcushionpressurepciscalculated

foragivensoilconditionandvehiclespeed.Foranair-cushiontrackedvehiclewithagivenload,theoptimalair-cushionpressureisrelatedtosoilcon-dition,vehiclespeed,andcushionclearanceheight.

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724AHossain,ARahman,andAKMMohiuddin

Fig.2Vehicletracksystemwithinitialinflatedair-cushion

Allthesefactorsaffectpowerconsumptionandoperationperformances.Sincetheloaddistributionfromthevehicletotheair-cushionsystemchangesduetoexternaldisturbances,thecushionclearanceheight(hc)ofthevehicleandtherequiredpowerfortheair-cushiontrackedvehiclechanges,andhenceair-cushionpressure(pc)alsochanges,asshowninFig.2.InFig.2,Tisthedrivingtorque(inNm),Rrsistheradiusofsprocket(inm),hiistheinitialinflatedair-cushionheight(inm),hcisthecushionclearanceheight(inm),hcgistheheightofvehiclecentreofgravity(CG)(inm),zisthevehiclesinkage(inm),Wisthetotalweightofthevehicle(inN),pcistheair-cushionpressure(inN/m2),andk1isaconstant.

Bysolvingequation(7),theminimumpowerconsumptioncanthusbedetermined,whichcanbeexpressedasanoptimalpoint(Pm,pcm,Qm,hcm),wherepcm,Qmandhcm,respectively,aretheopti-mumvaluesofcushionpressure,volumeflowrate,andtheoreticalcushionclearanceheightwithmini-mumpowerconsumptionPm.Becauseoftheprac-ticaldifficultiesofcontinuousmeasurementofswampterrainparametersinoperation,aFLCisdevelopedwhichcanrecognizecurrentterrainconditionsinoperationon-line.2.2Controlsystemdevelopment

2.2.1VehicleverticalpositioncontrolsystemThecontrolobjectiveoftheair-cushionpressuresystemmanagementistoregulatevolumeflowratethroughthechangeinvalvepositionbyusingafuzzylogicexpertsystem(FLES).Figure3illus-tratesthebasicschemeforvehicleverticalposition(i.e.height,h)controlduringsinkingduetothelow-bearing-capacityswamppeatterrain.Inthisfigure,twoelectronicproportionalvalvescontroltheinletandoutletflowratesoftheairrespectively.Adistancesensorismountedatthevehiclechassisframetomeasurethevehicleverticalposition(correspondingheightandhencesinkageare

Proc.IMechEVol.225PartD:J.AutomobileEngineering

measured).Figure3showsthecontrolsystemwhichincorporatesanaircompressorwithaccumu-lator,anair-cushionchamber,adistancesensor,amicrocontroller,andabatterypack.

ReferringtoFig.3,theoperationofthevehicleverticalpositioncontrolsystemcanbedescribedinthefollowingmanner.Theaimofthesystemisthatthevehicleverticalpositionismaintainedatadesired(reference)positionsothatthevehicleobtainssufficienttractioncontrol.Inordertoaccomplishthistask,itisrequiredthattheerrorbetweentheactualpositionandthedesiredposi-tionisequaltozero,andthedifferentialpositionrateshouldalsobeequaltozero.Anappropriatecontrolschemehasbeendevelopedforthiscontrolsystem;thefundamentalgoalistoemploytheFLEStosetthefuzzyrulesandtoactuatetheelectronicproportionalvalveinordertoobtainappropriatevalvecontrolactions.

2.2.2PrincipleofthecontrolsystemstructureAposition(height)controlsystemwithaFLCisdesignedtorealizethevehicleverticalposition(h)targetsandthusminimizethetotalpowercon-sumptionbasedonthevehiclesinkage.Thecontrollercanovercomethedisadvantageofconventionalproportional–integral–derivative(PID)control,i.e.theunadjustableparametersetting.TheFLChastheadvantageofthefuzzycontrollerbeingsimpleandrobust,andnotrequiringanexactmathematicalmodel[18,19].Inthevehiclecontrolsystem,positionhisselectedasthecontrolledvari-ableandairflowrateQisselectedastheregulatedvariable,asshowninFig.4.Basedonthedifferencebetweenthemeasuredvalue(h)andthereferencevalue(hr),thepositioniscontrolledbyaregulatedvariable,i.e.flowrateQ.Thereferencepositionhriscalculatedbasedonthemaximumallowablesink-ageandisthencomparedwiththemeasuredposi-tionvalues.Hence,theresultantdeviatione,i.e.positionerror(PE)anddifferentialpositionde/dtorrateofpositionerror(RPE)ofhrarecontinuouslymeasuredinoperation.2.2.3ImplementationofFLES

ForimplementationoffuzzyvaluesintothesystembyusingFLES,positionerror(e)andrateofposi-tionerror(de/dt)areusedasinputparametersandflowrate(Q)isusedastheoutputparameter.PEandRPE,respectively,arefuzzyvariablesofeandde/dt.Forfuzzificationofthesefactors,thelinguis-ticvariableslargenegativeerror(LNE),smallnega-tiveerror(SNE),zeroerror(ZE),smallpositiveerror

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Fuzzylogiccontrollerofanair-cushionsystemforaswampterrainvehicle725

withtheaidofthefollowingfunctions.Thesefor-mulaearedeterminedbyusingmeasurementvaluesPEði1Þ=

&i1;0;i2;0;

À6'

(8)

'

RPEði2Þ=

&

&

À1:5(9)

Fig.3Vehicleverticalpositioncontrolsystem

Qðo1Þ=

o1;0;

'

(10)

Fig.4Blockdiagramofthecontrolsystem

(SPE),andlargepositiveerror(LPE)areusedastheinputparametersforthepositionerror(PE);largenegativerateoferror(LNRE),smallnegativerateoferror(SNRE),zerorateoferror(ZRE),smallpositiverateoferror(SPRE),andlargepositiverateoferror(LPRE)areusedastheinputparametersfortherateofpositionerror(RPE).Similarly,thelinguisticvari-ableslargenegativeopen(LNO),smallnegativeopen(SNO),leavealone(LA),smallpositiveopen(SPO),andlargepositiveopen(LPO)areusedasoutputparametersfortheflowrate(Q).ThelogicalANDisimplementedwiththeminimumoperator,theaggregationmethodismaximum,andthecentreofgravitydefuzzificationmethodisusedbecausetheseoperatorsassurealinearinterpola-tionoftheoutputbetweentherules[20].Themem-bershipfunctionsmostfrequentlyusedinthecontrolhypothesisaretriangular,trapezoidal,Gaussian,Z-,S-,andbell-shapedforms[21].Basedontheexpertandtheapplication,manydifferentchoicesofmembershipfunctionsarepossible.However,thetriangularshapemembershipfunc-tionsareusedinthisstudyforbothinputandoutputvariablesbecauseoftheiraccuracy[22].Theunitsoftheusedfactorsare:PE(cm),RPE(cm/s)andQ(%).Forthetwoinputsandoneoutput,afuzzyassociatedmemoryordecisionisformedasregulationrules.Atotalof25rulesareformed;thepartsoftherulesareshowninTable1.

ThefirstblockinsidetheFLESisfuzzification,whichconvertseachpieceofinputdatatodegreesofmembershipinoneorseveralmembershipfunc-tions.Fuzzificationofthepositionerror(PE),rateofpositionerror(RPE),andflowrate(Q)iscarriedout

Inequations(8)to(10),i1isthefirstinputvari-able(PE),i2isthesecondinputvariable(RPE),ando1isthefirstoutputvariable(Q).Prototypetriangu-larfuzzysetsforthefuzzyvariables,namelyposi-tionerror(PE),rateofpositionerror(RPE),andflowrate(Q)aresetupusingMATLABFUZZYToolbox.ThemembershipvaluesobtainedfromtheaboveformulaeareshowninFigs5to7.ThedegreeofPEismeasuredincmfrom26to6,RPEismeasuredincm/sfrom21.5to1.5,andQismeasuredinpercentfrom2100to100.Withintheframeworkofthepresentstudy,thefollowingrulesareusedtocreatetheinputandoutputmember-shipfunctions.

Ivanovetal.[21]hasreportedthatifthereisminimalinformationforaparticularvariableandthisvariableisaresponsiveindicator,therangeofvaluesisdividedintonumerousidenticaltriangularmembershipfunctions

8

0;>>>0;

x\\c1

;;

c19

>>>=

mtriangleðx,c1,c2,c3Þ=

c2Àc1

c3Àx>>c>3Àc2

c2>>;

x.c3

(11)

Inthiscase,theedgeofthevariable’sintervalmayberepresentedwithlinearZ-andS-shapedfunctionsdescribedrespectivelyas

8><1;:

x;

9

>=

(12)

mZðx,c1,c2Þ=

c2Àx

c>2Àc1

0;

c1\\x\\c2

>;

x˜c2x9>=

mSðx,c1,c2Þ=

8

><0;:

xÀc1c>2Àc1

;

1;

c1>;

x˜c2

(13)

Inequations(11)to(13),xistheinputandoutputvariable,andc1,c2,andc3arethecoeffi-cientsofmembershipfunctionsforthedescribed

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Table1Inferencerulesofcontrollerparameters

Rules

PE

1–6–10–14–25

LNE–SNE–SNE–ZE–LPE

Inputvariables

RPELNRE–

LNRE–LPRE–SPRE–LPRE

OutputvariableQLNO–SNO–SNO–LA–LPO

mLPEði1Þ=

8><0;:

1;

i1<3

i1À3

;>33>;

i1.6i1<3

9>=

9>=

(17)

mLPEði1Þ=

8

><0;:

1;

i1À3

;>33>;

i1.6

(18)

Fig.5Prototypemembershipfunctionsofinputvari-ablePE

inputandoutputvariables.ThecoefficientsofmembershipfunctionsfortheinputandoutputvariablesaregiveninTables2to4.

Inordertoillustratethefuzzificationprocess,lin-guisticexpressionsandmembershipfunctionsofpositionerror(PE)obtainedfromthedevelopedrulesandpreviousformulaearepresentedanalyti-cally.Thenotationi1indicatesthesysteminput(forthiscasePE)andithasitsmembershipfunctionvaluesthatcanbecomputedforallfuzzysetsasfollows

9

i1\\À6>=

À3Ài1mLNEði1Þ=3;À6>;:

0;i1.À3

8><1;

8iÀðÀ6Þ

1><3;

0Ài1mSNEði1Þ=;>:30;

9

À6=À3

;

i1.0

Similarly,thelinguisticexpressionsandmem-bershipfunctionsofotherparameterscanbecalculated.

Theinferenceprocessgenerallyinvolvestwosteps:(1)thelinguisticsvariablesofalltherulesarecomparedtothecontrollerinputstodeterminewhichrulesapplytothecurrentsituation;and(2)theconclusions(whatcontrolactionstotake)aredeterminedbyusingtherulesatthecurrenttime.Inthisstage,truthdegrees(m)oftherulesaredeterminedforeachrulebyaidoftheminimum,andthenbytakingthemaximumamongthework-ingrules.

Inordertocomprehendfuzzification,anexampleisconsidered.ForcrispinputPE(i1)=23.15cm,andRPE(i2)=20.46cm/s,therules2,3,7,and8arefired.Thefiringstrength(truthvalues)aofthefourrulesareobtainedas

a2=minfmLNEðPEÞ,mSNREðRPEÞg=minð0:05,0:61Þ=0:05

a3=minfmLNEðPEÞ,mZREðRPEÞg=minð0:05,0:39Þ=0:05

a7=minfmSNEðPEÞ,mSNREðRPEÞg=minð0:95,0:61Þ=0:61a8=minfmSNEðPEÞ,mZREðRPEÞg=minð0:95,0:39Þ=0:39

(14)

(15)

98iÀðÀ3Þ

1>=<3;À3

3Ài1mZEði1Þ=03;>;:

0;i1.3

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(16)

Therefore,membershipfunctionsfortheconclu-sionreachedbyrules2,3,7,and8areobtainedas

follows

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Fuzzylogiccontrollerofanair-cushionsystemforaswampterrainvehicle727

Fig.6Prototypemembershipfunctionsofinputvari-ableRPE

Fig.7Prototypemembershipfunctionsofoutputvari-ableQ

Table2Coefficientsofmembershipfunctionsforthefuzzyinferencesystem(FIS)parameterofPE

Linguisticvariables

Type

c1LargenegativeerrorSmallnegativeerrorZeroerror

Z-shapedTriangularTriangular

262623

Coefficients(cm)

c223230

c3–03(continued)

Table3CoefficientsofmembershipfunctionsforFISparameterofRPE

Linguisticvariables

Type

c1LargenegativerateoferrorSmallnegativerateoferrorZerorateoferror

SmallpositiverateoferrorLargepositiverateoferror

Z-shapedTriangularTriangularTriangularS-shaped

21.521.520.7500.75

Coefficients(cm/s)

c220.7520.7500.751.5

c3–00.751.5–

m2ðQÞ=minf0:05,mLNOðQÞgm3ðQÞ=minf0:05,mLNOðQÞgm7ðQÞ=minf0:61,mSNOðQÞgm8ðQÞ=minf0:39,mSNOðQÞg

wherebiisthepositionofthesingletonintheithuniverse,andm(i)isequaltothefiringstrengthoftruthvaluesofrulei.

2.2.4Controlsurfaceofthefuzzyinferringsystem

RajasekaranandVijayalakshmiPai[23]havereportedthatinmanyconditions,forasystemwhoseoutputisfuzzy,itcanbesimplertoreceiveacrispdecisioniftheoutputisrepresentedasasinglescalarquantity.Thisconversionofafuzzysettoasinglecrispoutputinordertotakeactioniscalleddefuzzifi-cation.Inthisstage,theoutputmembershipvaluesaremultipliedbytheircorrespondingsingletonvaluesandthenaredividedbythesumofmembershipvaluestocomputeQcrispasfollows[18,19]P

ibimðiÞ

Qcrisp=PimðiÞ

(19)

UsingMATLAB,thefuzzycontrolsurfaceisdevelopedasshowninFig.8.ItmayserveasavisualdepictionofhowFLESoperatesdynamicallyovertime.Thisisthemeshplotoftheexamplerelationshipbetweenpositionerror(PE)andrateofpositionerror(RPE)ontheinputsideandcontrolleroutputflowrate(Q)ontheoutputside.ThiscontrolsurfacedisplaystherangeofpossibledefuzzifiedvaluesforallpossibleinputsofPEandRPE.ThesurfaceplotshowninFig.8depictstheimpactsofPEandRPEparametersonQ.Itshowsthatasthevehiclepositionerrorandrateofpositionerrorincreasepositively,thereisaconcomitantincreaseinflowratethroughthe

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Table4CoefficientsofmembershipfunctionsforFISparameterofQ

Linguisticvariables

Type

c1LargenegativeopenSmallnegativeopenLeavealone

SmallpositiveopenLargepositiveopen

Z-shapedTriangularTriangularTriangularS-shaped

21002100250050

Coefficients(%)

c2250250050100

c3–050100–

changeinvalvepositionasexpected.Theflowratereachestheapexwhenthepositionerrorandrateofpositionerrorbothreachtheirrespectivemaximumlevels.Theplotisusedtochecktherulesandthemembershipfunctionsandtoseeiftheyareappro-priateandwhethermodificationsarenecessarytoimprovetheoutput.Whenasatisfactorysystemisachieved,thefuzzyprogramisconvertedtomachinelanguageanddownloadedintoamicroprocessorcon-troller.Themicroprocessorthenrunsthemachinebasedonthefuzzyprogram.Althoughtheprocessseemstobelong,itactuallyisrelativelyeasytoexe-cute,anditaddsintelligencetoamachine.

Inaddition,thepredictiveabilityofthedevel-opedsystemhasbeeninvestigatedaccordingtomathematicalandstatisticalmethods.Inordertoestablishthis,therelativeerror(e)ofastructureiscalculatedas[15,16,20]

󰀊n󰀊X󰀊yÀy󰀊100%^󰀊󰀊e=(20)󰀊y󰀊ni=1Thegoodnessoffit(h)ofthepredictedsystemiscalculatedby

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiunPu^Þ2ðyÀyuu

(21)h=u1Àni=1

Pt2

ðyÀymeanÞ

i=1

Fig.8Controlsurfaceofthefuzzyinferringsystem

Simulinkhastwoinputs:PEandRPErespectively,andoneoutput,Q.Figure9showsthefinalizedFLCwithallthesourcesandsinksconnectedtoit.Sincetheloaddistributionaffectsthetotalpowerconsumptionsignificantly,soposition(h)ofthevehicleisusedasacontrolledvariableinthecontrolsystemoftheair-cushiontrackedvehicle.UsingMATLABSimulink,theFLCshowstheoutputresultofflowrate(Q)as228.25basedontwoinputsofpositionerror(PE)andrateofpositionerror(RPE)as21.717and0.3997,respectively,whichcanbeobservedusingthreedisplayresultsofthecontrolsystem.Itisnoticedthattheinletvalveneedstobeopen28.25percentwiththeoutletvalveintheclosedposition.

3.2Investigationofcontrolsystemperformance

bylaboratorytestingThecontrolsystemattachedtothevehiclewasequippedwithadistancesensor,pressuresensor,microcontroller,andelectronicproportionalcon-trolvalveasshowninFig.10.Theair-cushionsystemperformancetestingwasconductedintheAutomotiveLaboratoryoftheInternationalIslamicUniversityMalaysia(IIUM)withaloadingconditionof1.96kN.Duringthecontrolsystemtesting,thedistancesensorwasplacedonthefrontofthevehi-cletotestthecontrolsystemfunction.Anobstaclewasplacedinfrontofthedistancesensorandthecontrolsystemwastestedbymovingtheobstacle

wherenisthenumberofinterpretations,yisthe

^isthepredictedvalue,andymeanmeasuredvalue,y

isthemeanofthemeasuredvalue.Therelativeerrorprovidesthedifferencebetweenthepredictedandmeasuredvaluesanditisnecessarytoattainzero.Thegoodnessoffitalsoprovidestheabilityofthedevelopedsystemanditshighestvalueis1.3

RESULTSANDDISCUSSION

3.1SimulationresultsofthecontrolsystemAnFLCwasdesignedtosimulatetheFLESonceithadbeenverifiedwiththeruleviewer.TheFLCblockin

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Fig.9BlockdiagramofFLCsimulation

Fig.11Correlationbetweenactualandpredictedval-uesofflowrate

3.3Variationofloaddistributionand

totalpowerconsumption

Thecurrentstudyisfocusedonloaddistributionfromthevehicletotheair-cushionsystem,withtheaimofreducingtotalpowerconsumption;therefore,thepri-maryinvestigationisconcernedwiththeeffectofloaddistributiononthetotalpowerconsumption.TerrainpropertiesandvehicleparametersarepresentedinTable5.Figure12showsthevariationoftheloaddis-tributionandtotalpowerconsumption.Itcanbeseenthattheloaddistributionratio(d)affectsthetotalpowerconsumptionsignificantlyasitincreaseslinearlywiththeincreaseintheloaddistributionratio.Foraparticularterrainsituation,anoptimalloaddistribu-tionratioexistswhichresultsinminimumpowercon-sumption.However,forthepresentstudy,anoptimalloaddistributionratioof0.20isobtainedwhichresultsinoptimumtotalpowerconsumptionof3.5kW.Inaddition,whendexceedsabout0.4,thetotalpowerconsumptionwillincreasesignificantly.Obviously,indifferentoperatingconditions,thereisminimaltheo-reticalpowerconsumptionwithrespecttod.3.4Vehicleperformanceinvestigationby

fieldtesting

Thefieldtestwascarriedoutonaterrainoflength50m,whichissimilartotheswamppeatattheFacultyofEngineering,IIUM.Theterrainusedintestingissoftwithshortgrassandasmallamountofwatertomakeitsimilartoswamppeat.Figures13(a)and(b)showthetypicalvariationoftractionforceoftheair-cushiontrackedvehiclewithoutthecontrolsystemforthetwovehicleload-ingconditionsof1.96kNand2.45kNrespectively.Themeanvaluesoftractionare0.62kNand1.06kNforthevehicleweightsof1.96kNand2.45kN

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Fig.10Vehiclecontrolsystemtestinginthelabora-tory.Numbersindicate:1,hoseconnectiontothecompressorandair-cushion;2,tracksystem;3,air-cushion;4,microcontroller;5,valve;6,ACtoDCconverter;7,distancemea-suringsensor;8,obstacle;9,computerdatarecording

andrecordingthecorrespondingdata.TheresultsofthedevelopedFLESwerecomparedwiththeexperimentalresults.Themeanmeasuredandpre-dictedvalues(fromFLES)offlowrateQare77.78and70.29percentrespectively.Thecorrelationbetweenactual(measured)andpredictedvalues(fromtheFLESmodel)ofairflowrateisshowninFig.11.Thecorrelationcoefficientwas0.971,whichissignificantinoperation.Furthermore,forflow-rate,themeanrelativeerroroftheactualvalueandpredictedvaluesfromtheFLESmodelwas10.93percent,whichisalmostequaltotheacceptablelimitof10percent[22].ThegoodnessoffitofthevaluespredictedfromtheFLESmodelwas0.91whichiscloseto1.0asexpected.

730AHossain,ARahman,andAKMMohiuddin

Fig.12Variationoftheloaddistributionandtotal

powerconsumption

respectively;i.e.whenthevehicleloadingcondi-tionsareincreasedfrom1.96kNto2.45kN,themeanvalueofthevehicletractionincreasesby71percent.Thissignificanttractionincreaseisprincipallyduetotheloadingsituationofthevehi-cleasthecohesivenessofthefieldisapproximatelyinvariablefortheentireterrainlength.Furthermore,thistrendcouldbeduetothehydrodynamiceffectoftheterrainasthereisnodrainagesysteminthefield[13].However,fromtheexperiments,itwasobservedthattheair-cushiontrackedvehiclegotstuckoncetheair-cushionwasincontactwiththeterrain.Byusingthepropeller’sadditionalthrustthevehiclecouldbeoperatedwithoutgettingstuck.Itappearsthatifthecushionsystemisincontactwiththeterrainallthetime,morepowerisneededtooperatethepropeller.Itwasalsonoticedthattheair-cushionsystemwasincontactwiththeterrainonceithadbeeninflated.Therefore,inthisstudy,anintelligentsystemhasbeendevelopedtooperatetheair-cushionsystemandtoovercometheabove-mentionedproblem.

Unlikeconventionalvehiclesoperatingonhardsurfaceconditions,theintelligentair-cushiontrackedvehicle(IACTV)wasdevelopedwithaspe-cialconfigurationforitsauto-adjustedair-cushion

protectingmechanism,withmoreflexibilitytosat-isfythedemandsofworkinginsevereconditions.Sincepowerconsumptionisthemainissueworld-wide,loaddistributionfromthevehicletotheair-cushionsystemshouldbedeterminedproperly[17];ifthisisnotdone,thevehicle’sfullpotentialmaynotbereachedandexcessivepowerconsumptioncouldresult.

ThetestingofvehicleperformancewhenusingthedevelopedfuzzylogiccontrolsystemwascarriedoutonsoftterrainattheFacultyofEngineering,IIUM.Thevehiclewastestedundercontrolledcon-ditionswiththecohesivenessofthefieldconsideredasapproximatelyconstantfortheentirelengthtrav-elled.Thevehiclewastestedatatravellingspeedof10km/hwithloadingconditionsof1.96kNand2.45kN,andwiththeintelligentair-cushionsystemactivated.Thevehicletravellingdistanceduringtest-ingwasconsideredtobe50m.VehiclefieldtestingwascarriedouttomeasurethevehiclesinkageandtractionforceinordertoevaluatethevehicletractiveperformanceandtovalidatethesustainabilityofthedevelopedmathematicalmodelsandFLES.Vehiclesinkageismeasuredusingadistancesensorinstalledonthefrontofthechassisframe,atthecentrepointbetweenthetwofrontroadwheels.TheoutputtorqueoftheDCmotorwasmeasuredusingadigitalmultimeterandwasconvertedintotractionforce,tractiveefficiency,andtotalpowerrequirement.SamplingdatacollectedfromthefieldtestwereusedtovalidatetheFLESmodels.ThemeasuredtractiveperformancedatawereusedtoprepareanExcelspreadsheetandthevaluesoftractionforcewerecalculated.Figures14(a)and(b)showthetypicalvariationintractionforceoftheair-cushiontrackedvehicleusingthecontrolsystem,forthesamevehi-cleloadingconditions.Themeantractionvaluesare0.94and1.43kNforvehicleweightsof1.96and2.45kNrespectively;i.e.increasingthevehicleload-ingconditionsfrom1.96kNto2.45kNincreasedthemeanvehicletractionvalueby52percent.Thissig-nificantincreaseintractionisprincipallyduetotheloadingsituationofthevehicleasthecohesiveness

Table5Terrainandvehicledesignparameters

Parameters

Totalvehicleload

LengthoftrackgroundcontactWidthoftrackgroundcontactLengthoftheair-cushionWidthoftheair-cushionAircushioneffectiveareaVehicletheoreticalvelocitySurfacematstiffnessUnderlyingpeatstiffness

NotationWLBLacBacAcVtmmkpValue19620.530.130.480.300.1442.7813590171540

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Fig.13Variationoftractionforceforthevehicle

withoutthecontrolsystem.Vehicleweightof(a)1.96kNand(b)2.45kN

Fig.14Variationoftractionforceforthevehiclewith

thecontrolsystemVehicleweightof(a)1.96kNand(b)2.45kN

ofthefieldisapproximatelyinvariablefortheentireterrainlength.Furthermore,themeanvaluesoftrac-tionforceforthevehiclewiththecontrolsystemare51.6and34.9percenthigherthanthetractionforcevaluesforthevehiclewithoutthecontrolsystem,forthesamevehicleloadingconditionsof1.96and2.45kNrespectively.Finallyitcanbeconcludedthatthetractionforceincreasesmorewiththeadditionofthecontrolsystemtothevehicle.ItcanbestatedthattheIACTVhas,overall,thebestperformance,givingabout51.6percentincreaseintractionforceascomparedwiththevehiclewithouttheintelligentsystemandtheIACTVgivesthebestdrivingopera-tion.Figure15showsfieldtestingofthevehicleontheswampterrain.

3.5Powerconsumptionpredictionand

validation

Thevalidationofthemathematicalmodeldevel-opedinthisstudyhasbeencarriedoutbycompar-ingthemeasured(actual)andpredictedpowerconsumptionofthevehicle.PredictionofpowerconsumptionhasbeendonebyusingtheFLES

Fig.15Vehiclefieldtesting.Numbersindicate:1,

microcontroller;2,battery;3,inletvalve;4,outletvalve;5,connector;6,hosepipecon-nectedtoair-cushion;7,distancesensor;8,vehicleglasscover;9,counterbalanceweight;10,controlboard;11,pressuresensor;12,converter

modelbasedonvehiclesinkage(VS)andvehicleweight(VW).Themeansofthemeasuredand

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732AHossain,ARahman,andAKMMohiuddin

Table6Weightsandbiasesbetweeninputlayerand

hiddenlayerforPC

i

C112345

3.415425.718425.954921.594524.1258

Ei=C1CH+C2CP+C3C25.22592.395721.44223.346225.0255

C326.31013.046921.500025.769625.7378

Themainconclusionsdrawnfromthisstudyareasfollows.

1.Takingthevehicleposition(height)inrelation

tothegroundasthecontrolvariable,acontrolschemeisproposedanditsfeasibilityisexam-inedbysimulations.

2.Experimentalresultsshowedthatthefuzzylogic

controllerdevelopedcankeepthevehicleoper-atingsteadilybyadjustingcushionpressureandbymaintainingsufficienttraction.

3.Themeanrelativeerroroftheactualflowrate

valuesandthevaluespredictedfromtheFLESmodelwas10.93percentwhichisalmostequaltotheacceptablelimit;thegoodnessoffitvaluewascloseto1.0asexpected.

4.Foraparticularswampterraincondition,anopti-malloaddistributionratioof0.20wasobtainedwhichresultedinoptimumtotalpowerconsump-tionof3.5kW.

5.Theintelligentair-cushiontrackedvehiclehad,

overall,thebestperformance,givinga51.6percentincreaseintractionforceascomparedwiththevehiclewithouttheintelligentsystem.

predicted(fromtheFLES)valueswere4.206and4.224kWrespectively.Thecorrelationcoefficientoftotalpowerconsumptionwas0.961.Themeanrela-tiveerroroftheactualvaluesandvaluespredictedfromtheFLESmodelwas10.3percentwhichisalmostequaltotheacceptablelimitof10percent[22].ThegoodnessoffitofthevaluespredictedfromtheFLESmodelwas0.9whichiscloseto1.0asexpected.Furthermore,thedevelopedFLEShasbeenjustifiedwiththepowerconsumptionresultsobtainedbyusinganartificialneuralnet-work(ANN)controlmodel.Cushionclearanceheight(CH)andcushionpressure(CP)areusedintheinputlayerwhilepowerconsumption(PC)isusedintheoutputlayer.ThedetailedprocedureandcomparisonoftheANNandthefuzzylogiccontrolsystemcanbefoundinapreviouslypub-lishedarticle[14].Theoutputobtainedfromtheweightsisgivenas

PC=

1

1+eÀ(0:2439F1+0:61F2+2:1031F3+5:1129F4À1:9788F5À2:3312)5FUTUREWORK

(22)

whereFi=

11+eÀEi

Inthispaper,accordingtoevaluationcriteriaofpre-dictedperformance,thedevelopedFLESmodelhasbeenfoundtobevalid.Therefore,thedevelopedmodelcanbeusedasareferenceforfurtherair-cush-ion–terraininteractionstudies.Thissystemcanbedevelopedfurtherbyincreasingtheknowledgebaserulesandbytheadditionofanadaptiveneuro-fuzzyintegratedcontrolapproachtocreateahybridintelli-gentsystem.

EiistheweightedsumoftheinputandcanbeobtainedusingTable6.Basedontheoptimalloaddistributionratioof0.2,totalpowerconsumptionisfoundas3.42kWbyusingANNwhichjustifiesthedevelopedfuzzylogicsystem.Thedetailedexpla-nationandcomparisonofpowerconsumptionbetweenthefuzzylogiccontrollerandtheneuralnetworkcontrolleraregiveninreference[14].4

CONCLUSIONS

ACKNOWLEDGEMENT

TheauthorsaregratefulforthefinancialassistanceprovidedbytheInternationalIslamicUniversityMalaysia(IIUM)forthisproject.ÓAuthors2011REFERENCES

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APPENDIXNotation

AcAtbiBBaccciCiDcDhte_ee1EiFiFtghhchcghcmhihri

air-cushioneffectiveareatrackgroundcontactareapositionofsingletonwidthofthetrack

widthoftheair-cushionterraincohesivenesscoefficientsofvariables

coefficientsofinputandhiddenlayersdischargecoefficienttrackhydraulicdiameterpositionerror

rateofpositionerrorexponential

weightedsumofinputvariablescoefficientsTractionforce

gravitationalaccelerationvehicleverticalpositioncushionclearanceheight

heightofvehiclecentreofgravityoptimumcushionclearanceheightinitialinflatedair-cushionheightreferencevehicleverticalpositionslippageofthevehicle

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734AHossain,ARahman,andAKMMohiuddin

i1/2kpk1KwLLacLcmmno1pcpcmPPcPdPmQQmRcRdragRininputvariables

underlyingpeatstiffnessconstant

sheardeformationmodulustrackgroundcontactlengthlengthoftheair-cushionair-cushionperimetersurfacematstiffness

numberofinterpretationsoutputvariablecushionpressure

optimumcushionpressuretotalpowerconsumption

powerconsumedbyair-cushionsystempowerconsumedbydrivingsystemminimumpowerconsumptionvolumeflowrate

optimumvolumeflowrate

terraincompactionmotionresistancedraggingmotionresistanceinnermotionresistance

RrsRtTVtWWcWtxy^yyzadehmrf

radiusofsprocket

totalmotionresistancetorqueofthesprocketvehicletheoreticalspeedtotalweightofthevehicle

vehicleweightsupportedbyair-cushionvehicleweightsupportedbythetrackabscissa(input/outputvariables)measuredvaluepredictedvalue

meanofmeasuredvaluevehiclesinkage

firingstrengthortruthvaluesloaddistributionratiorelativeerrorgoodnessoffitmembershipvalueairdensity

terraininternalfrictionangle

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