NewRealtimeAlgorithmForControlAllocationofInWheelmotorvehicle轮毂电机电动汽车转矩分配算法解读.docx

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NewRealtimeAlgorithmForControlAllocationofInWheelmotorvehicle轮毂电机电动汽车转矩分配算法解读.docx

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NewRealtimeAlgorithmForControlAllocationofInWheelmotorvehicle轮毂电机电动汽车转矩分配算法解读.docx

NewRealtimeAlgorithmForControlAllocationofInWheelmotorvehicle轮毂电机电动汽车转矩分配算法解读

F2014-EPT-068

ANewReal-timeAlgorithmForControlAllocationofIn-Wheel-MotorElectricalVehicle

Zhengyi,He;Quanhui,Du;Hao,Zhang

ChinaAutomotiveEngineeringResearchInstitute,P.R.China

KEYWORDS–In-wheelmotorelectricvehicle,Controlallocation,Real-timealgorithm

ABSTRACT–

Themaingoalofthispaperistodevelopageometrybasedalgorithmtosolvethecontrolallocationproblemforelectricvehicleusingin-wheelmotors.Theproposedmethoddonotrequireiterativecomputations,hencethecomputationeffortcanbegreatlyreducedandcanbeusedinreal-timeapplication.Thetheoreticalbasisanddetailsofthealgorithmarediscussedthispaper.Itisalsoshownthattheproposedmethodalsocanbeusedinseveralotherfour-wheeldrivevehicles.Theeffectivenessoftheproposedcontrolallocationalgorithmhasbeenvalidatedbythesoftwaretests.

1.Introduction

Astofour-wheelindependentdrivevehicle（4WD）usingfourin-wheelmotors,thefourmotorscanbeusedastheactuatorstogeneratethedesiredtractionandactiveyaw-moment.Thisariseanewproblemcalledcontrolallocationproblem.Controlallocationdealswiththeproblemofdistributingtheyawmomentcommandanddesiredtractionforcecommandtoseveralactuators（fourin-wheel-motors）,whiletheoutputofactuators（fourin-wheel-motors）satisfyingthegivenconstraints.

Itisnoticedthatthepreviouspublishedpapers[1-6]oncontrolallocationproblemareallfocusondiscussingthemethodswhichrequiremanyiterationtimes,suchasinterior-pointalgorithms,lowcomputationalefficiencyisthemajorproblemforthosecontrolallocationalgorithms.

Ingeneral,thecontrolallocationproblemcanbeformulatedaslinearprogrammingproblem.However,whenthenumberofvariablesinalinearprogrammingproblemisgreatthanthreeormore,itisdifficulttousegeometrymethodtocalculatethefeasiblesolutions.Inthispaper,wedevelopageometrybasedmethodtogetthefeasiblesolutionswhilethecontrolallocationhasfourvariables.

Themajorcontributionofthispaperisthatweusegeometrymethodtodevelopreal-timealgorithmforcontrolallocationproblem,whichdoesnotrequireiterationcomputation.Astotheproposedmethod,thereisnoproblemontheperformanceofconvergencerateandcomputationalefficiency.

2.DetailsofTheProposedMethod

2.1TheControlAllocationProblem

Thecontrolallocationproblemoffour-wheelindependentdrivevehicle（4WD）usingfourin-wheelmotors,canbedescribedbyTable1.F_Pedaldenotesthedesiredforcecomputedfromaccelerationpedalposition,Ffldenotesdesiredfront-leftmotoroutputforce,etc.Ffl_B_maxdenotesfront-leftmotormaximumbrakingtorque,etc.

kisdefinedasthefrontforcedividedbytotalforce,Mdefinedasthedesiredyawmomenttorque.

Table1.thecontrolallocationproblemoffour-wheel-drivevehicle

ProblemA

ProblemB

Costfunction

Min|ΔF|,

Min|ΔM|.

Min|ΔF|,

Min|ΔM|.

Inputvariables.

F_Pedal,k,M

AuxiliaryrelaxationvariablesΔF,ΔM

ΔF=F_Pedal_Modi-F_Pedal,

ΔM=M_Modi–M.

ΔF=F_Pedal_Modi-F_Pedal,

ΔM=M_Modi–M.

Outputvariables.

solutionofFfl,Ffr,Frl,Frr

solutionofFf,Fr,Df,Dr

Outputvariables.

F_Pedal_Modi,M_Modi

Equationconstraints

（1）

Frr+Ffl+Frl+Ffr=F_Pedal+ΔF,

（Ffr-Ffl）Lf+（Frr-Frl）Lr=M+ΔM.

Ff+Fr=F_Pedal+ΔF,（1.1）

DfLf+DrLr=M+ΔM.（1.2）

Inequalityconstraints

（2）.

Ffl_B_max

Ffr_B_max

Frl_B_max

Frr_B_max

Ffl_B_max

Ffr_B_max

Frl_B_max

Frr_B_max

IfwedefinenewvariablesFf,Fr,Df,Dras

Ffl+Ffr=2Ff,（3）

Frr+Frl=2Fr,

Ffr-Ffl=Df,

Frr-Frl=Dr.

ThentheaboveproblemAintheTable1canberewrittenasproblemB.Atthesametime,wecancalculatethefourmotorsforceusingthefollowingequations,

Ffl=Ff-0.5Df,（4）

Ffr=Ff+0.5Df,

Frl=Fr-0.5Dr,

Frr=Fr+0.5Dr,

AstoproblemB,thefollowingproblemshouldbesolved,

1）togetthesetoffeasiblesolutionsofFf,Fr

2）togetthesetoffeasiblesolutionsofDf,Dr

3）modifyF_PedalsothattheconstraintsaboutMisalwayssatisfied,becausedesiredyawmomentMgreatlyinfluencethestabilityofvehicle

4）Ifnecessary,modifyMsothatproblemBhasonesolutionatleast.

Figure1.ArchitectureoftheproposedcontrolallocationmethodastoproblemB

2.2ThePropertiesofTheFeasibleSetsof（Ff,Fr）,（Df,Dr）

Theorem1:

thefeasiblesolutionsof（Ff,Fr）shouldlieintherectangularareaHIJK,whichcanbeseeninfigure2,

（max（Ffl_B_max+0.5Df,Ffr_B_max-0.5Df）,min（Frl_T_max+0.5Dr,Frr_T_max-0.5Dr））,

（min（Ffl_T_max+0.5Df,Ffr_T_max-0.5Df）,min（Frl_T_max+0.5Dr,Frr_T_max-0.5Dr））,

（min（Ffl_T_max+0.5Df,Ffr_T_max-0.5Df）,max（Frl_B_max+0.5Dr,Frr_B_max-0.5Dr））,

（max（Ffl_B_max+0.5Df,Ffr_B_max-0.5Df）,max（Frl_B_max+0.5Dr,Frr_B_max-0.5Dr））.

Proof:

AccordingtotheinequalitiesinTable2,wehave,

Ffl_B_max

Ffr_B_max

Wecanget,

max（Ffl_B_max+0.5Df,Ffr_B_max-0.5Df）

From,

Frl_B_max

Frr_B_max

Wecanget,

max（Frl_B_max+0.5Dr,Frr_B_max-0.5Dr）

ItisnotedthattherectangularareaHIJKcanbedescribedbyinequalities（5）,（6）.QED.

Figure2.GraphtodeterminethefeasiblesolutionsetsofFr,Ff.

Theorem2:

whenF_Pedal>0.

TheintersectionlinesegmentbetweenHIJKandthelinedescribedbyequation（1.1）exists,ifthenecessaryconditionsthat（Df,Dr）liesintherectangularareaUVWXissatisfied,whichcanbeseeninfigure3.

Proof:

WhenF_Pedal>0,linedefinedbyequation（1.1）shouldliebetweenpointIandpointKinfigure2,whichcanbewrittenasthefollowinginequalities.

WeshouldnoticethatrectangularareaUVWXisdenotedbyinequality（10）.QED.

Figure3.GraphwhichcanbeusedtodeterminethefeasiblesolutionofDr,Df.

Remark1:

whenF_Pedal≤0,thepointKinfigure2shouldlieonleftbehindofthelineFf+Fr=0.

Thismeansthat

（11）

Theorem3:

thefeasiblesetsof（Df,Dr）shouldlieintherectangularareaPQRS,whichshowninfigure3,

（Ffr_B_max-Ffl_T_max,Frr_T_max-Frl_B_max）,

（Ffr_T_max-Ffl_B_max,Frr_T_max-Frl_B_max）,

（Ffr_T_max-Ffl_B_max,Frr_B_max-Frl_T_max）,

（Ffr_B_max-Ffl_T_max,Frr_B_max-Frl_T_max）.

Proof:

Frominequalities

（2）inTable1,wehave,

Ffr_B_max

-Ffl_T_max<-Ffl<-Ffl_B_max,-Frl_T_max<-Frl<-Frl_B_max;

Addtheabovetwoinequalities,weget,

Ffr_B_max-Ffl_T_max

Frr_B_max-Frl_T_max

whichcanberewrittenas,

Ffr_B_max-Ffl_T_max

Frr_B_max-Frl_T_max

ItisnotedthattherectangularareaPQRScanbedenotedbyinequality（12）.QED.

Theorem4:

TherectangularareaHIJKinFigure2alwaysexist,if（Df,Dr）lieintheareaPQRSinFigure3.

Proof:

ThenecessaryandsufficientconditionsthatrectangularareaHIJKinFigure2alwaysexist,canbewrittenas,

If（Df,Dr）lieintherectangularareaPQRSinFigure3,thenwecangetthefollowinginequalities,

and

QED.

2.3CalculateFeasibleSolutionsofDf,Dr

（Df,Dr）shouldlieinthelinesegmentCDinFigure3.

2.4Calculate（Min_Ff,Max_Fr）,（Max_Ff,Min_Fr）

（Min_Ff,Max_Fr）,（Max_Ff,Min_Fr）arethetwoendpointsofthelinesegmentMNinFigure2.

2.5ArbitrationofFf,Fr

Infigure1,thearbitrationalgorithmis,

3.Furtherdiscussion

3.1CalculationoftheMotorOutputPeakTorque

Thepeaktorqueofeachmotor,Ffl_B_max,Ffl_T_max,Ffr_B_max,Ffr_T_max,Frl_B_max,Frl_T_max,Frr_B_max,Frr_T_max,isextremelyimportanttotheproposedalgorithm.Table2showhowmotorspecification/systemprotectionfunction/failureaffectsthemotorpeaktorque.

Table2.calculationofthemotoroutputpeaktorque

MotorSpecification,

Tmax

Systemsafetyprotection（suchasmotoroverheatprotection,inverteroverheatprotection）,k_temp

Failureshutoff,

Tmotor_max

=f（MotorSpecification,

Temperature,

FailureStatus）

=Tmax×k_temp×FS

FS=0,thecaseneedshutoffthemotor,ifthefollowingfailureoccurs:

sensorfault,shortfault,isolationfault,inverterfailure,CAN

communicationfault,etc;

FS=1,otherwise

3.2ApplicationFieldoftheProposedMethod

Accordingtotheabovediscussing,wecanseethattheproposedcontrolallocationmethodcanalsobeenappliedinmanyotherconfigurationsoffour-wheel-drivevehicle,whichcanbeseeninTable3.Iftheabovemethodinthispaperisappliedtoothervehiclepowertrainconfigurations,thedefinitionofFf,Fr,Df,DrshouldbeenchangedaccordinglywhichcanbeenseeninTable3.

Table3.four-wheel-drivepowertrainconfigurationwhichcanusetheproposedmethod

Front

Rear

2in-wheelmotors

1singlemotor

2in-wheelmotors

1singlemotor

nomotors

2in-wheelmotors

（Ffl+Ffr）/2

（Frr+Frl）/2

Ffr-Ffl

Frr-Frl

4.TestResults

Theproposedcontrolallocationalgorithmhasbeenimplementedwiththefixed-pointCcode,andtheoff-lineandon-linesoftwaretestswerecarriedout.

Table4.vehicleparameterswhichhavebeenus

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