New Realtime Algorithm For Control Allocation of InWheel motor vehicle轮毂电机电动汽车转矩分配算法.docx
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New Realtime Algorithm For Control Allocation of InWheel motor vehicle轮毂电机电动汽车转矩分配算法.docx
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NewRealtimeAlgorithmForControlAllocationofInWheelmotorvehicle轮毂电机电动汽车转矩分配算法
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
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
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, H: (max(Ffl_B_max+0.5Df,Ffr_B_max-0.5Df),min(Frl_T_max+0.5Dr,Frr_T_max-0.5Dr)), I: (min(Ffl_T_max+0.5Df,Ffr_T_max-0.5Df),min(Frl_T_max+0.5Dr,Frr_T_max-0.5Dr)), J: (min(Ffl_T_max+0.5Df,Ffr_T_max-0.5Df),max(Frl_B_max+0.5Dr,Frr_B_max-0.5Dr)), K: (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, P: (Ffr_B_max-Ffl_T_max,Frr_T_max-Frl_B_max), Q: (Ffr_T_max-Ffl_B_max,Frr_T_max-Frl_B_max), R: (Ffr_T_max-Ffl_B_max,Frr_B_max-Frl_T_max), S: (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, FS 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 F: Front R: Rear F: 2in-wheelmotors R: 2in-wheelmotors F: 1singlemotor R: 2in-wheelmotors F: 2in-wheelmotors R: 1singlemotor F: 1singlemotor R: 1singlemotor F: nomotors R: 2in-wheelmotors Ff (Ffl+Ffr)/2 Ff (Ffl+Ffr)/2 Ff 0 Fr (Frr+Frl)/2 (Frr+Frl)/2 Fr Fr (Frr+Frl)/2 Df Ffr-Ffl 0 Ffr-Ffl 0 0 Dr Frr-Frl Frr-Frl 0 0 Frr-Frl 4.TestResults Theproposedcontrolallocationalgorithmhasbeenimplementedwiththefixed-pointCcode,andtheoff-lineandon-linesoftwaretestswerecarriedout. Table4.vehicleparameterswhichhave
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