research article optimal control strategy design...

Research ArticleOptimal Control Strategy Design Based on DynamicProgramming for a Dual-Motor Coupling-Propulsion System

Shuo Zhang Chengning Zhang Guangwei Han and Qinghui Wang

National Engineering Laboratory for Electric Vehicles School of Mechanical Engineering Beijing Institute of TechnologyBeijing 100081 China

Correspondence should be addressed to Shuo Zhang 2120110462biteducn

Received 7 June 2014 Accepted 10 July 2014 Published 23 July 2014

Academic Editor Rui Xiong

Copyright copy 2014 Shuo Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A dual-motor coupling-propulsion electric bus (DMCPEB) is modeled and its optimal control strategy is studied in this paperThe necessary dynamic features of energy loss for subsystems is modeled Dynamic programming (DP) technique is applied to findthe optimal control strategy including upshift threshold downshift threshold and power split ratio between the main motor andauxiliary motor Improved control rules are extracted from the DP-based control solution forming near-optimal control strategiesSimulation results demonstrate that a significant improvement in reducing energy loss due to the dual-motor coupling-propulsionsystem (DMCPS) running is realized without increasing the frequency of the mode switch

1 Introduction

The application of battery electric vehicle in public transportfield is a good way to improve the increasing air pollutionand shortage of oil resources problems Developing theelectric bus has significant meanings for energy savingemission reduction and the electric vehicle (EV) industrydevelopment The control of high-power drive system is oneof the key technologies for electric bus Dual-motor drivecoupled by planetary gear is an effective way to realize thehigh-power drive system Owing to the dual-power sourcenature the control strategy of DMCPEB is typically morecomplicated than that of traditional engine based vehicleTherefore system-level vehicle simulation methodology isoften applied to implement accurate sizing and matchingstudies and to develop effective energy control methodbefore the final design and physical prototyping

The power control strategy for electric vehicle can beroughly classified into three categories (see [1 2]) The firsttype employs heuristic control techniques such as controlrulesfuzzy logicneural networks for estimation and controlalgorithm development (see [3 4]) The second approachis based on static optimization methods (see [5 6]) Thethird type of EV control algorithms considers the dynamic

nature of the system when performing the optimization(see [7ndash9]) In addition the optimization is with respect toa time horizon rather than for an instant in time In generalpower split algorithms resulting from dynamic optimizationapproaches are more accurate under transient conditions butare computationally more intensive

In this paper dynamic programming (DP) techniqueis applied to solve the optimal control strategy problemof a DMCPEB The optimal control strategy solution overa driving cycle is obtained by minimizing a defined costfunction Two cases are solved an energy-loss-only case andan energy-lossshifting-frequency case The comparison ofthese two cases provides insight into the change needed whenthe additional objective of riding comfort is included How-ever the DP control actions are not implementable due totheir preview nature and heavy computational requirementThey are on the other hand a good design tool to analyzeassess and adjust other control strategies After studying thebehavior of the dynamic programming solution carefully weextract implementable rules These rules are used to improvea simple intuition-based algorithm It was found that theperformance of the rule-based algorithm can be improvedsignificantly

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 958239 9 pageshttpdxdoiorg1011552014958239

2 The Scientific World Journal

Main motor

Auxiliary motor

B

Gear reducerDifferential

mechanism andfinal drive ratio

Wheels

Figure 1The dual-motors coupling-propulsion electric bus model-ing configuration

Table 1 Basic parameters of the vehicle and DMCPS

Name Value UnitVehicle mass (119872vehicle) 18000 kgTire radius (119903) 04785 mRolling resistance coefficient (119891) 0015 NullWindward area (119860) 75438 m2

Air resistance coefficient (119862119863) 08 Null

Final drive ratio 1198940

634 NullMaximum torque of the motor(119879max)

410 Nm

Maximum rotate speed of themotor (119873max)

6000 rpm

Characteristic parameter of PGT(119870) 35 Null

The paper is organized as follows In Section 2 the dual-motor coupling-propulsion electric bus model is describedfollowed by an explanation of the preliminary rule-basedcontrol strategy The dynamic optimization problem and theDPprocedure are introduced in Section 3Theoptimal resultsfor the energy-loss-only and energy-lossshifting-frequencyoptimization cases are given in Section 4 Section 5 describesthe design of improved rule-based control strategies Finallyconclusions are presented in Section 6

2 DMCPEB Configuration andPreliminary Rule-Based Control Strategy

21 DMCPEBConfiguration andModeling The target vehicleis a conventional bus whose engine and part transmissionwere replaced by a DMCPS developed by Beijing Instituteof Technology [10] The schematic of the vehicle is given inFigure 1The power source was the main motor and auxiliarymotor and the two powers coupled together through a plan-etary gear trainThemain motor is connected to the sun gearwhile the auxiliary motor is connected to the ring gear Thecoupled power output through planet carrier and the planetcarrier was linked to the wheels by transmission system Bstands for a wet clutch which can realize mode switch bylocking the ring gear smoothly Important parameters of thevehicle and DMCPS are given in Table 1

22 Preliminary Rule-Based Control Strategy ComparedwithHEV BEVrsquos power management strategy seems much sim-pler as most of BEVs only have one driving motor whichmeans that the output power of motor is directly deter-mined by the driverrsquos power requirement For two-motorcoupled driving system there are four possible operatingmodes one-motor driving two-motor driving one-motorregenerative braking and two-motor regenerative brakingIn order to reduce the energy loss the power managementcontroller has to decide which operating mode to use anddetermine the proper power split between the two powersources while meeting the driverrsquos demandWhen the systemis working in two-motor condition the situation can beclassified into torque coupling and speed coupling accordingto the structure of the driving system For torque couplingdriving system the power split of power sources can berealized by determining the torque split while for the speedcoupling driving system the power split of power sourcescan be realized by determining the speed split betweenthe two sources The simple rule-based power managementstrategy was developed on the basis of engineering intuitionand simple analysis of vehiclersquos driving characteristics andvehiclersquos dynamic requirements [11] which is a very populardesign approach in electric vehicle According to the vehiclestatus the operation of the controller is determined by oneof the two control modes mode switch control and powersplit control The basic logic of each control rule is describedbelowMode Switch Control Based on the working property of thedriving system and the efficiency map of the motor if thevehicle speed exceeds V

119901+or is below V

119901minus the mode switch

control will be applied to determine whether the auxiliarymotor works or not as shown in (2) The relationship of V

119901minus

and V119901+

can be expressed as follows

V119901minus= V119901+minus 119860 (1)

one-motor to two-motor Vvehicle gt V119901+ 119875require ge 0

two-motor to one-motor Vvehicle lt V119901minus 119875require lt 0

(2)

The speed discrepancy 119860 is to avoid continual modeswitch which will influence the vehicle ride comfort

Power Split Control As this vehiclersquos driving system is speedcoupling mode the power split ratio is proportional to thespeed ratio There are two situations in terms of the powersplit control In one-motor working situation the drivingsystem does not need power split control The main motorwill provide all the needed power according to the vehiclespeed and the pedal motion In two-motor working situationconsidering the motorrsquos efficiency property the main motorwill be working on the fixed relative high speed point 119873mainand the auxiliary motor speed will change according to thevehicle speed requirements The output torque of motorswill change simultaneously according to the pedal motion

The Scientific World Journal 3

The detailed information of the speed split can be expressedas follows

119873119904=

119878vehicle times 60 times (1 + 119870)

36 times 119877tire times 2120587 times 1198940 times 1198942

119873119903 = 0

one-motor mode

119873119904= 119873main

119873119903 =119878vehicle times 60 times (1 + 119870)

36 times 119877tire times 2120587 times 1198940 times 1198942 times 119870minus119873119904

119870

two-motor mode

(3)

where 119873119904is the speed of main motor which is connected to

the sun gear directly and119873119903is the speed of auxiliary motor

which is connected to the ring gear directly 119870 can be got by119870 = 119885

119903119885119904 119885119903and 119885

119904is the number of tooth for ring gear

and sun gear

3 Dynamic Optimization Problem

Compared with rule-based algorithms the dynamic opti-mization approach can find the best control strategy relyingon a dynamic model (see [12 13]) Given a driving cycle theDP-based algorithm can obtain the optimal operating strat-egy minimizing the systemrsquos energy loss subject to the diverseconstraints A numerical-based DP approach is adopted inthis paper to solve this finite horizon dynamic optimizationproblem

31 Problem Formulation In the discrete-time format amodel of the battery electric vehicle can be expressed as

119909 (119896 + 1) = 119891 (119909 (119896) 119906 (119896)) (4)

where 119906(119896) is the vector of control variables such as shiftingcommand of the driving system and desired speed ratioincrements of the auxiliary motor 119909(119896) is the state vector ofthe system such as the working mode of the system (one-motor mode or two-motor mode) and the speed ratio of themotorsThe sampling time for the control problem is selectedto be one secondThe optimization goal is to find the controlinput 119906(119896) to minimize a cost function which consists of theweighted sum of energy loss and the frequency of the modechange The cost function to be minimized has the followingform

119869 =

119873minus1

sum

119896=0

119871 (119909 (119896) 119906 (119896))

=

119873minus1

sum

119896=0

119871119898 (119896) + 119871119886 (119896) + 119871119888 (119896) + 120572 times |Shift (119896)|

(5)

where 119873 is the duration of the driving cycle and 119871 is theinstantaneous cost including main-motor energy loss 119871

119898(119896)

auxiliary-motor loss 119871119886(119896) power-coupling gear-box loss

119871119888(119896) and mode change cost 120572 times |Shift(119896)| For an energy-

only problem the weighting factor120572 is set to be zeroThe case120572 gt 0 represents a comprehensive problem which considered

the energy loss and the number of mode changes Duringthe optimization it is necessary to impose the followinginequality constraints to ensure safereasonable operation ofthe main motor and auxiliary motor

119879119904 min (119873119904 (119896)) le 119879119904 (119873119904 (119896)) le 119879119904 max (119873119904 (119896))

119873119904 min le 119873119904 (119896) le 119873119904 max

119879119903 min (119873119903 (119896)) le 119879119903 (119873119903 (119896)) le 119879119903 max (119873119903 (119896))

119873119903 min le 119873119903 (119896) le 119873119903 max

(6)

where 119879119904is the output torque of the main motor and 119879

119903is the

output torque of the auxiliary motor In addition to satisfythe systems properties besides this basic constraints otherconstraints are needed

119873119904 (119896) times 119873119903 (119896) ge 0 (7)

this constrain is to avoid the power cyclingwhich can increasepower loss greatly and is undesirable in reality Anotherconstrain is that when 119873

119904= 0 the speed of 119873

119903should also

be zero This is because our current system only has one wetclutch and it is fixed with the ring gearThis means that whenthe vehicle is running the sun gear must be running too

32 Model Simplification The detailed DMCPS andDMCPEB models are not suitable for dynamic optimizationdue to their high number of states Thus a simplifiedbut sufficiently complex vehicle model is developed ThisDMCPS is a speed coupling system and can be calssifiedinto two working modes (one-motor working mode andtwo-motor working mode) As the two aspects are themain influence factors when the DMCPSrsquos parameters aredetermined it was decided that only these two state variablesneeded to be kept the two motorsrsquo speed ratio and DMCPSrsquosworkingmodeThe simplifications of the subsystemsmotorsvehicle transmission battery and the planetary gear trainare described below

Motors The electric motor characteristics are based on theefficiency data obtained from [10] as shown in Figure 2 FromTable 1 we can get that though the DMCPS needs twomotorsthey have the same specifications and they are of the sametype So here we only display one efficiency map of theelectricmotor Considering the regenerative braking here weassume that when the output torque of motor is negativethe efficiency is the same as when the motor output positivetorque whose value is the same as the absolute value of thenegative torque The motor efficiency 120578

119898can be expressed as

120578119898= 119891 (

1003816100381610038161003816119879119898 (119873119898)1003816100381610038161003816 119873119898) (8)

where |119879119898| is the absolute value of the motorrsquos output torque

and 119873119898is the rotate speed of the motor When the vehicle

is braking in emergency condition the DMCPS cannotprovide enough braking force Here the braking strategyis determined to be series strategy when the DMCPS canprovide enough brake force all the brake force will beprovided by the DMCPS and when the needed brake force


0 1000 2000 3000 4000 5000 60000

100

200

300

400

50060

60

6060 60

60

60

60

60

7070

70 70 70

70

70

70

70

8080

80

8080

80

80

80

80

8585

85 85

85

85

85

85

8585

85

85

90

90

90

90

9090

90

9090

90

90

90

Speed (rpm)

Torq

ue (N

m)

Figure 2 Efficiency map of the electric motor

exceeds the DMCPSrsquos ability the DMCPS will provide themaximum torque while the extra force will be provided bythe friction braking system The output torque 119879

119898(119873119898) can

be expressed as follows

1003816100381610038161003816119879119898 (119873119898)1003816100381610038161003816 =

10038161003816100381610038161003816119879119898req

10038161003816100381610038161003816if 1003816100381610038161003816119879119898max (119873119898)

1003816100381610038161003816 ge10038161003816100381610038161003816119879119898req

10038161003816100381610038161003816

1003816100381610038161003816119879119898max (119873119898)1003816100381610038161003816 if 1003816100381610038161003816119879119898max (119873119898)

1003816100381610038161003816 lt10038161003816100381610038161003816119879119898req

10038161003816100381610038161003816

(9)

where 119879119898req is the required torque

Vehicle The vehicle is modeled as a point mass

119881vehicle (119896 + 1) = 119881vehicle (119896)

+

( ( (119879119904 (119896) times (1 + 119870) times 1198940 times 1198942 minus 119879119887 (119896))

119903119905

minus119865119891minus 119865119886(119881vehicle (119896))) (119872119903)

minus1)

(10)

where 119879119887(119896) is the friction brake force 119894

0is the reduction

ratio of the gear reducer 119870 is the property parameter of theplanetary gear train 119865

119891and 119865119886are the rolling resistance force

and the aerodynamic drag force respectively 119903119905is the tire

radius 119872119903is the effective mass of the vehicle and 119869

119903is the

equivalent moment of inertia of the rotating components inthe vehicle 119865

119891 119865119886 and 119872

119903can be got from the following

equations

119865119891= 119872vehicle times 119892 times 119891

119865119886=119862119863119860119906119886

215

119872119903= 119872vehicle +

119869119903

1199032

119905

(11)

where 119872vehicle is the mass of the vehicle 119892 is the gravityacceleration 119891 is the rolling resistance coefficient 119862

119863is

aerodynamic drag coefficient119860 is the effective projected areaof vehicle and 119906

119886is the speed of the vehicle

TransmissionTheworkingmodes (one-motorworkingmodeand two-motor working mode) are modeled as a discrete-time dynamic system with 1 s time increment

119898119909 (119896 + 1) =

1 119898119909 (119896) + Shift (119896) gt 1

0 119898119909 (119896) + Shift (119896) lt 0

119898119909 (119896) + Shift (119896) otherwise

(12)

where state 119898119909is the main working mode and the control

shift to the transmission is constrained to take on the valuesof minus1 0 and 1 representing downshift sustain and upshiftrespectively

The Battery The Lithium-Ion Battery is used A lot of workhas been done about estimating the state of charge (SOC)of the battery [14ndash16] which is very important for HEV andBEV As this papermainly focused on theDMCPS and for theBEV the batteries just provide the needed power and cannotbe optimized as the needed power is fixed according to thecertain drive cycle herewe assume that the battery can alwaysmeet the drive cyclersquos power requirement and no energy lossis coming from the battery

The Planetary Gear Train Based on the planetary geartrainrsquos working property we can get that different controlstrategy can also lead to the different energy loss due to thedifferent efficiency and so the planetary gear trainrsquos efficiencymodel should also be built to calculate the energy loss Asthe planetary gear train is a TWO-DOF mechanism theefficiency p

119864can be got from the following formula [17]

p119864119886=

119873119888

119873119904 (1 minus 119870) p119903(119904minus119888) minus 119873119903119870 (1 minus 119870) p119904(119903minus119888)

p119864119889=

119870119901p119904(119888minus119903)

119873119903+ p119903(119888minus119904)

119873119904

(1 + 119870119901)119873119888

(13)

where p119864119886

stands for the efficiency when the vehicle isaccelerating p

119864119889stands for the efficiency when the vehicle

is decelerating p119903(119904minus119888)

denotes the efficiency that when thering gear is fixed the power is input into the sun gear andoutput from planet carrier and p

119904(119903minus119888)denotes the efficiency

that when the sun gear is fixed the power is input into thering gear and output from planet carrier p

119904(119888minus119903)denotes the

efficiency that when the sun gear is fixed the power is inputinto the planet carrier and output from ring gear and p

119903(119888minus119904)

denotes the efficiency that when the ring gear is fixed thepower is input into the planet carrier and output from sungear

33 Dynamic Programming Method The DP technique isbased on Bellmanrsquos Principle of Optimality which states thatthe optimal policy can be obtained if we first solve a one stagesubproblem involving only the last stage and then graduallyextend to subproblems involving the last two stages last three


stages and so forth until the entire problem is solvedIn this manner the overall dynamic optimization problemcan be decomposed into a sequence of simpler minimizationproblems as follows (see [18 19])

Step119873 minus 1 consider

119869lowast

119873minus1(119909 (119873 minus 1))

= min119906(119873minus1)

[119871 (119909 (119873 minus 1) 119906 (119873 minus 1)) + 119866 (119909 (119873))] (14)

Step 119896 for 0 le 119896 lt 119873 minus 1

119869lowast

119896(119909 (119896))

= min119906(119896)

[119871 (119909 (119896) 119906 (119896)) + 119869lowast

119896+1(119909 (119896 + 1))]

(15)

where 119869lowast119896(119909(119896)) is the optimal cost-to-go function or optimal

value function at state 119909(119896) starting from time stage 119896 Itrepresents the optimal cost that if at stage119896 the system starts atstate 119909(119896) and follows the optimal control law thereafter untilthe final stage The above recursive equation is solved back-ward to find the optimal control policy The minimizationsare performed subject to the inequality constraints shown in(6) and the equality constraints imposed by the driving cycle

34 Numerical Computation As the DMCPS is a nonlinearsystem this DP has to be solved numerically by someapproximations A standard way to solve (15) numericallyis to use quantization and interpolation (see [2 18]) Forcontinuous state space and control space the state and controlvalues are first discretized into finite grids At each step of theoptimization search the function 119869

119896(119909(119896)) is evaluated only at

the grid points of the state variables If the next state 119909(119896 + 1)does not fall exactly on a quantized value then the values of119869lowast

119896(119909(119896)) in (15) as well as 119866(119909(119873)) in (14) are determined

through linear interpolation

4 Dynamic Programing Results

The DP procedure described above produces an optimaltime-varying state-feedback control law In the followingtwo cases are presented energy-loss-only problem andenergy-loss mode-change problem

41 Energy-Loss Optimization Results When optimizing foronly fuel economy the weighting 120572 is set to zeroThe Chinesetypical city drive cycle is used The simulation results of thevehicle under the DP policy are shown in Figures 3 4 and 5FromFigures 3 and 4we can get that when the vehicle speed islow themainmotor is going to provide the needed speed andpower and when the vehicle speed is high the motor speedtends to decrease to a very low point and the most vehiclespeed and power will be provided by the auxiliary motorThis is because the motor efficiency will be much lower inthe working condition of high speed and low output torqueFrom Figure 2 we can get that the motor efficiency will alsobe low in the working condition of low speed and low outputtorque but in this condition the output power is also low so

0 200 400 600 800 1000 1200 14000

20

40

60Chinese typical city drive cycle

Vehi

cle sp

eed

(km

h)

0 200 400 600 800 1000 1200 14000

2000

4000

6000Main motor

0 200 400 600 800 1000 1200 14000

2000

4000

6000Auxiliary motor

Time (s)

Rota

tion

spee

d(r

min

)Ro

tatio

n sp

eed

(rm

in)

Figure 3 The rotating speed of the two motors

0 200 400 600 800 1000 1200 14000

20

40


Vehi

cle sp

eed

(km

h)

0 200 400 600 800 1000 1200 1400minus200minus100

0100200 Main motor

Torq

ue (N

m)

0 200 400 600 800 1000 1200 1400minus500

0

500Auxiliary motor

Time (s)

Torq

ue (N

m)

Figure 4 The output torque of the two motors

the energy loss is lower than that in high speed Comparedwith themainmotor the auxiliarymotor tends towork on thehigh speed and high torque condition which is within highefficiency location

From Figure 5 we can get that the DMCPSrsquos energy losscan be classified into three categories main motor lossauxiliary motor loss and coupling box loss Among themthe auxiliary loss accounts for the main part while the mainmotor loss and coupling box loss are almost equal This isbucause the auxiliary motor is always working in the highpower condition although its working efficiency is relativelyhigher than the main motor


0 200 400 600 800 1000 1200 14000


Vehi

cle sp

eed

(km

h)

0 200 400 600 800 1000 1200 140005

1015

Main motor loss

(kJ)

0 200 400 600 800 1000 1200 140005

1015

Auxiliary motor loss

(kJ)

0 200 400 600 800 1000 1200 140005

1015

Coupling box loss

Time (s)

(kJ)

Figure 5 Energy-loss distribution

42 Energy Loss and Shifting Frequency OptimizationResults To study the tradeoff between energy lossand shifting frequency the weight factors are varied120572 = [0 001 01 05 1 2 35 5 10] The possible values of 120572are chosen based on the reasonable meanings in formula (5)This tradeoff study is important in the early design processbecause it provides useful information about the sensitivitybetween the energy loss and shifting frequency The trend ofthe energy loss and the number of shifts with the change of120572 are shown in Figure 6 From Figure 6 we can get that when120572 lt 1 the number of shifts decreased rapidly (from 58 to 24)with the increase of 120572 while the energy loss increased onlya little which can be neglected When 120572 increases between1 and 2 the energy loss and number of shifts only changea little When 120572 increases from 2 to 5 the number of shiftsdecreases fast again and the energy loss increases fast When120572 exceeds 5 both the number of shifts and the energy lossstay constant So the reasonable value will be between 1 and2 Here we set 120572 = 2 for further discussion

From Figure 7 we can get that to reduce the number ofshifts the main motor tends to work more in the low speedCompared with Figure 5 the number of shifts reduces from58 to 22 which is only 38 of the original DP results whilethe energy loss increased from 5943 to 6431 KJ which onlyincreased 82

5 Development of ImprovedRule-Based Controls

The DP control policy is not implementable in real drivingconditions because it requires knowledge of future speedand load profile Nonetheless analyzing its behavior providesuseful insight into possible improvement of the rule-basedcontroller Based on the above discussion simulation resultshere we abstract the shift control strategy including upshiftand downshift strategy and power split strategy

0 1 2 3 4 5 6 7 8 9 100

20

40

60Number of shifts

0 1 2 3 4 5 6 7 8 9 106440

6460

6480

6500

6520Energy loss

(kJ)

120572

Figure 6The trend of the energy loss and number of shifts with thechange of 120572

0 200 400 600 800 1000 1200 140005

1015

Main motor loss

(kJ)

(kJ)

(kJ)

0 200 400 600 800 1000 1200 140005

1015


0 200 400 600 800 1000 1200 140005

1015

Coupling box loss

Time (s)

Figure 7 Energy-loss distribution for 120572 = 2

51 Working Mode Shift Control The working mode shift iscrucial to the reduction of energy loss and riding comfort Inthe original DP results the DMCPS needs frequent shiftingto reduce the energy loss which may influence the ridingcomfort and when 120572 = 2 the energy loss did not increasea lot but the shifting number is only 38 of the original DPresult Figures 8 and 9 show the abstracting procedure ofthe downshifting and upshifting threshold based on the DPresults data when 120572 = 2 In Figure 8 the first graph shows theworking condition when the vehicle is accelerating while thesecond graph shows the working condition when the vehicleis braking By drawing a line manually to depart the workingmode the shifting strategy can be got The merit of this workcompared with other methods is that this method not onlydetermined the reasonable shifting point but also helpedus decide when to upshift and downshift which can avoid


0 10 20 30 40 50 600

02

04

06

08

1

Acce

lera

tor p

edal

Vehicle acceleration

0 10 20 30 40 50 600

02

04

06

08

1

Speed (kmh)

Speed (kmh)

Brak

ing

peda

l

Vehicle braking

One-motor workingTwo-motor workingUpshifting threshold

One-motor workingTwo-motor workingDownshifting threshold

Figure 8 Abstracting of shifting strategy

13 14 15 16 17 18 190

01

02

03

04

05

06

07

08

09

1

Speed (kmh)

Peda

l pos

ition

New shifting strategy

Upshifting thresholdDownshifting threshold

Figure 9 New shifting strategy

frequent shifting in application And the result is expressedin Figure 9

52 Power Split Control In this section we study how powersplit control of the preliminary rule-based algorithm can be

0 10 20 30 40 50 60 70 800

010203040506070809

1

Speed (kmh)

PR

Optimal operating points (DP)Approximated optimal PR curve

Figure 10 New power split strategy

improved by analyzing the DP results when 120572 = 2The powersplit ratio PR can be expressed as follows

PR =119875119903

119875119903+ 119875119904

(16)

Two working modes are defined single motor workingmode (PR = 0) and power coupling working mode (0 lt

PR lt 1) It should be noted that the range of PR is[01) In one-motor working mode (PR = 0) as abovediscussed the control rule is unique Here we only talk aboutthe coupling condition Figure 10 gives the new power splitstrategy abstracted from the data based on DP results It canbe seen from the curve that the split ratio tends to fluctuatearound 077 when the speed exceeds 20 kmh this is becausethe planet mechanismrsquos property parameter119870 is set to 35 andin this ratio the efficiency of coupling box is relatively higherthan other ratios This demonstrates that though the energyloss from coupling box is not the most compared one withthe auxiliary motor it plays an important role in reducing theenergy loss

53 Performance Evaluation After incorporating the work-ing mode shift control and power split control outlined inthe previous sections the improved rule-based controlleris evaluated using Chinese typical city drive cycle Table 2shows the comparison of different control rules We can getfrom the table that the new rule-based strategy can reducethe DMCPSrsquos energy loss effectively Specificly the main lossis coming from the main motor in the preliminary rule-based strategy while in the new rule-based strategy and DPoperation the main loss is coming from the auxiliary motorThough the new rule-based strategy reduces the energy lossby about 22 the DMCPS still has a significant reducingpotential as the DP operation reduces the energy loss by369 From Table 3 we can get that the new rule-basedstrategy does not need to increase the shifting numberbut cannot improve the shifting performance too On thecontrary DP (120572 = 2) can realize reducing the shifting numberby about 1534


Table 2 Comparison of different control strategy in energy loss

Loss type Main motor (KJ) Auxiliary motor (KJ) Coupling box (KJ) Total (KJ) Improvement intotal ()

Preliminary rule-based 5302 2781 2158 10240 0New rule-based 2938 3017 2030 7987 22DP (120572 = 2) 1848 2691 1922 6461 369

Table 3 Comparison of different control strategy in shiftingnumber

Shiftingnumber

Improvementin total ()

Preliminary rule-based 26 0New rule-based 26 0DP (120572 = 2) 22 1534

6 Conclusion

Based on the simplified model DP is applied to solvethe globally optimal control strategy Designing the controlstrategy for DMCPEB by extracting rules from the dynamicprogramming results has the clear advantage of being nearoptimal accommodatingmultiple objectives and systematicDepending on the overall objective one can easily developcontrol laws that emphasize low energy loss and ridingcomfort By analyzing theDP results the approximate optimalupshift threshold downshift threshold and power split ratiowere determined The improved rule-based control strategycan reduce the energy loss by about 22while theDP (120572 = 2)can reduce the energy loss by 369

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors gratefully acknowledge the support from theNational Natural Science Foundation of China (Grant no51175040) and the Research Fund for the Doctoral Programof Higher Education of China (Grant no 20111101110037)

References

[1] Y Zou H Shi-Jie L Dong-Ge G Wei and X Hu ldquoOptimalenergy control strategy design for a hybrid electric vehiclerdquoDiscrete Dynamics in Nature and Society vol 2013 Article ID132064 8 pages 2013

[2] C C Lin H Peng J W Grizzle and J M Kang ldquoPowermanagement strategy for a parallel hybrid electric truckrdquo IEEETransactions on Control Systems Technology vol 11 no 6 pp839ndash849 2003

[3] B M Baumann G Washington B C Glenn and G RizzonildquoMechatronic design and control of hybrid electric vehiclesrdquoIEEEASME Transactions on Mechatronics vol 5 no 1 pp 58ndash72 2000

[4] N J Schouten M A Salman and N A Kheir ldquoFuzzy logiccontrol for parallel hybrid vehiclesrdquo IEEE Transactions onControl Systems Technology vol 10 no 3 pp 460ndash468 2002

[5] C Kim E NamGoong and S Lee ldquoFuel economy optimizationfor parallel hybrid vehicles with CVTrdquo SAE Paper 1999-01-11481999

[6] G Paganelli G Ercole A Brahma Y Guezennec and GRizzoni ldquoA general formulation for the instantaneous controlof the power split in charge-sustaining hybrid electric vehiclesrdquoin Proceedings of the 5th International Symposium on AdvancedVehicle Control Ann Arbor Mich USA 2000

[7] A Brahma Y Guezennec and G Rizzoni ldquoDynamic optimiza-tion of mechanical electrical power flow in parallel hybrid elec-tric vehiclesrdquo in Proceedings of the 5th International Symposiumon Advanced Vehicle Control Ann Arbor Mich USA 2000

[8] U Zoelch and D Schroeder ldquoDynamic optimization methodfor design and rating of the components of a hybrid vehiclerdquoInternational Journal of Vehicle Design vol 19 no 1 pp 1ndash131998

[9] C-C Lin J Kang J W Grizzle and H Peng ldquoEnergymanagement strategy for a parallel hybrid electric truckrdquo inProceedings of the American Control Conference pp 2878ndash2883Arlington Va USA June 2001

[10] X H WuMatching and control strategy of dual motors coupleddriving system on electric buses [PhD thesis] Institute ofTechnology Beijing China 2011

[11] P D Bowles Modeling and energy management for a parallelhybrid electric vehicle (PHEV) with continuously variable trans-mission (CVT) [MS thesis] University ofMichiganAnnArborMich USA 1999

[12] H He H Tang and X Wang ldquoGlobal optimal energy man-agement strategy research for a plug-in series-parallel hybridelectric bus by using dynamic programmingrdquo MathematicalProblems in Engineering vol 2013 Article ID 708261 11 pages2013

[13] R Wang and S M Lukic ldquoDynamic programming techniquein hybrid electric vehicle optimizationrdquo in Proceedings of theIEEE International Electric Vehicle Conference (IEVC 12) pp 1ndash8 Greenville SC USA March 2012

[14] R Xiong X Gong C C Mi and F Sun ldquoA robust state-of-charge estimator for multiple types of lithium-ion batter-ies using adaptive extended Kalman filterrdquo Journal of PowerSources vol 243 pp 805ndash816 2013

[15] R Xiong F Sun X Gong and C Gao ldquoA data-driven basedadaptive state of charge estimator of lithium-ion polymerbattery used in electric vehiclesrdquo Applied Energy vol 113 pp1421ndash1433 2014

[16] R Xiong F Sun Z Chen andHHe ldquoA data-drivenmulti-scaleextendedKalman filtering based parameter and state estimationapproach of lithium-ion polymer battery in electric vehiclesrdquoApplied Energy vol 113 pp 463ndash476 2014


[17] E Pennestri L Mariti P P Valentini and V H MucinoldquoEfficiency evaluation of gearboxes for parallel hybrid vehiclestheory and applicationsrdquo Mechanism and Machine Theory vol49 pp 157ndash176 2012

[18] D P Bertsekas Dynamic Programming and Optimal ControlAthena Scientific Belmont Mass USA 1995

[19] Y Zou S Hou E Han L Liu and R Chen ldquoDynamicprogramming-based energymanagement strategy optimizationfor hybrid electric commercial vehiclerdquo Automotive Engineer-ing vol 34 no 8 pp 663ndash668 2012

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of


Journal ofPetroleum Engineering


Industrial EngineeringJournal of


Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of


Journal of


Renewable Energy

Submit your manuscripts athttpwwwhindawicom


StructuresJournal of


RotatingMachinery


EnergyJournal of


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Nuclear InstallationsScience and Technology of


Solar EnergyJournal of


Wind EnergyJournal of


Nuclear EnergyInternational Journal of


High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Main motor

Auxiliary motor

B

Gear reducerDifferential

mechanism andfinal drive ratio

Wheels

Figure 1The dual-motors coupling-propulsion electric bus model-ing configuration

Table 1 Basic parameters of the vehicle and DMCPS

Name Value UnitVehicle mass (119872vehicle) 18000 kgTire radius (119903) 04785 mRolling resistance coefficient (119891) 0015 NullWindward area (119860) 75438 m2

Air resistance coefficient (119862119863) 08 Null

Final drive ratio 1198940

634 NullMaximum torque of the motor(119879max)

410 Nm

Maximum rotate speed of themotor (119873max)

6000 rpm

Characteristic parameter of PGT(119870) 35 Null

The paper is organized as follows In Section 2 the dual-motor coupling-propulsion electric bus model is describedfollowed by an explanation of the preliminary rule-basedcontrol strategy The dynamic optimization problem and theDPprocedure are introduced in Section 3Theoptimal resultsfor the energy-loss-only and energy-lossshifting-frequencyoptimization cases are given in Section 4 Section 5 describesthe design of improved rule-based control strategies Finallyconclusions are presented in Section 6

2 DMCPEB Configuration andPreliminary Rule-Based Control Strategy

21 DMCPEBConfiguration andModeling The target vehicleis a conventional bus whose engine and part transmissionwere replaced by a DMCPS developed by Beijing Instituteof Technology [10] The schematic of the vehicle is given inFigure 1The power source was the main motor and auxiliarymotor and the two powers coupled together through a plan-etary gear trainThemain motor is connected to the sun gearwhile the auxiliary motor is connected to the ring gear Thecoupled power output through planet carrier and the planetcarrier was linked to the wheels by transmission system Bstands for a wet clutch which can realize mode switch bylocking the ring gear smoothly Important parameters of thevehicle and DMCPS are given in Table 1

22 Preliminary Rule-Based Control Strategy ComparedwithHEV BEVrsquos power management strategy seems much sim-pler as most of BEVs only have one driving motor whichmeans that the output power of motor is directly deter-mined by the driverrsquos power requirement For two-motorcoupled driving system there are four possible operatingmodes one-motor driving two-motor driving one-motorregenerative braking and two-motor regenerative brakingIn order to reduce the energy loss the power managementcontroller has to decide which operating mode to use anddetermine the proper power split between the two powersources while meeting the driverrsquos demandWhen the systemis working in two-motor condition the situation can beclassified into torque coupling and speed coupling accordingto the structure of the driving system For torque couplingdriving system the power split of power sources can berealized by determining the torque split while for the speedcoupling driving system the power split of power sourcescan be realized by determining the speed split betweenthe two sources The simple rule-based power managementstrategy was developed on the basis of engineering intuitionand simple analysis of vehiclersquos driving characteristics andvehiclersquos dynamic requirements [11] which is a very populardesign approach in electric vehicle According to the vehiclestatus the operation of the controller is determined by oneof the two control modes mode switch control and powersplit control The basic logic of each control rule is describedbelowMode Switch Control Based on the working property of thedriving system and the efficiency map of the motor if thevehicle speed exceeds V

119901+or is below V

119901minus the mode switch

control will be applied to determine whether the auxiliarymotor works or not as shown in (2) The relationship of V

119901minus

and V119901+

can be expressed as follows

V119901minus= V119901+minus 119860 (1)

one-motor to two-motor Vvehicle gt V119901+ 119875require ge 0

two-motor to one-motor Vvehicle lt V119901minus 119875require lt 0

(2)

The speed discrepancy 119860 is to avoid continual modeswitch which will influence the vehicle ride comfort

Power Split Control As this vehiclersquos driving system is speedcoupling mode the power split ratio is proportional to thespeed ratio There are two situations in terms of the powersplit control In one-motor working situation the drivingsystem does not need power split control The main motorwill provide all the needed power according to the vehiclespeed and the pedal motion In two-motor working situationconsidering the motorrsquos efficiency property the main motorwill be working on the fixed relative high speed point 119873mainand the auxiliary motor speed will change according to thevehicle speed requirements The output torque of motorswill change simultaneously according to the pedal motion



119873119904=



119873119903 = 0

one-motor mode

119873119904= 119873main



119870

two-motor mode

(3)




119903119885119904 119885119903and 119885


and sun gear




119909 (119896 + 1) = 119891 (119909 (119896) 119906 (119896)) (4)


119869 =

119873minus1

sum

119896=0

119871 (119909 (119896) 119906 (119896))

=

119873minus1

sum

119896=0

119871119898 (119896) + 119871119886 (119896) + 119871119888 (119896) + 120572 times |Shift (119896)|

(5)


119898(119896)





119879119904 min (119873119904 (119896)) le 119879119904 (119873119904 (119896)) le 119879119904 max (119873119904 (119896))

119873119904 min le 119873119904 (119896) le 119873119904 max

119879119903 min (119873119903 (119896)) le 119879119903 (119873119903 (119896)) le 119879119903 max (119873119903 (119896))

119873119903 min le 119873119903 (119896) le 119873119903 max

(6)


119903is the


119873119904 (119896) times 119873119903 (119896) ge 0 (7)


119904= 0 the speed of 119873

119903should also





120578119898= 119891 (

1003816100381610038161003816119879119898 (119873119898)1003816100381610038161003816 119873119898) (8)





0 1000 2000 3000 4000 5000 60000

100

200

300

400

50060

60

6060 60

60

60

60

60

7070

70 70 70

70

70

70

70

8080

80

8080

80

80

80

80

8585

85 85

85

85

85

85

8585

85

85

90

90

90

90

9090

90

9090

90

90

90

Speed (rpm)

Torq

ue (N

m)



119898(119873119898) can


1003816100381610038161003816119879119898 (119873119898)1003816100381610038161003816 =

10038161003816100381610038161003816119879119898req

10038161003816100381610038161003816if 1003816100381610038161003816119879119898max (119873119898)

1003816100381610038161003816 ge10038161003816100381610038161003816119879119898req

10038161003816100381610038161003816

1003816100381610038161003816119879119898max (119873119898)1003816100381610038161003816 if 1003816100381610038161003816119879119898max (119873119898)

1003816100381610038161003816 lt10038161003816100381610038161003816119879119898req

10038161003816100381610038161003816

(9)



119881vehicle (119896 + 1) = 119881vehicle (119896)

+


119903119905


minus1)

(10)


0is the reduction





119903is the


119891 119865119886 and 119872


equations


119865119886=119862119863119860119906119886

215

119872119903= 119872vehicle +

119869119903

1199032

119905

(11)


119863is




119898119909 (119896 + 1) =

1 119898119909 (119896) + Shift (119896) gt 1

0 119898119909 (119896) + Shift (119896) lt 0

119898119909 (119896) + Shift (119896) otherwise

(12)






p119864119886=

119873119888


p119864119889=

119870119901p119904(119888minus119903)

119873119903+ p119903(119888minus119904)

119873119904

(1 + 119870119901)119873119888

(13)

where p119864119886









119903(119888minus119904)






119869lowast

119873minus1(119909 (119873 minus 1))

= min119906(119873minus1)

[119871 (119909 (119873 minus 1) 119906 (119873 minus 1)) + 119866 (119909 (119873))] (14)


119869lowast

119896(119909 (119896))

= min119906(119896)

[119871 (119909 (119896) 119906 (119896)) + 119869lowast

119896+1(119909 (119896 + 1))]

(15)











0 200 400 600 800 1000 1200 14000

20

40


Vehi

cle sp

eed

(km

h)

0 200 400 600 800 1000 1200 14000

2000

4000

6000Main motor

0 200 400 600 800 1000 1200 14000

2000

4000

6000Auxiliary motor

Time (s)

Rota

tion

spee

d(r

min

)Ro

tatio

n sp

eed

(rm

in)


0 200 400 600 800 1000 1200 14000

20

40


Vehi

cle sp

eed

(km

h)

0 200 400 600 800 1000 1200 1400minus200minus100

0100200 Main motor

Torq

ue (N

m)

0 200 400 600 800 1000 1200 1400minus500

0

500Auxiliary motor

Time (s)

Torq

ue (N

m)





0 200 400 600 800 1000 1200 14000


Vehi

cle sp

eed

(km

h)

0 200 400 600 800 1000 1200 140005

1015

Main motor loss

(kJ)

0 200 400 600 800 1000 1200 140005

1015


(kJ)

0 200 400 600 800 1000 1200 140005

1015

Coupling box loss

Time (s)

(kJ)






0 1 2 3 4 5 6 7 8 9 100

20

40

60Number of shifts

0 1 2 3 4 5 6 7 8 9 106440

6460

6480

6500

6520Energy loss

(kJ)

120572


0 200 400 600 800 1000 1200 140005

1015

Main motor loss

(kJ)

(kJ)

(kJ)

0 200 400 600 800 1000 1200 140005

1015


0 200 400 600 800 1000 1200 140005

1015

Coupling box loss

Time (s)




0 10 20 30 40 50 600

02

04

06

08

1

Acce

lera

tor p

edal


0 10 20 30 40 50 600

02

04

06

08

1

Speed (kmh)

Speed (kmh)

Brak

ing

peda

l

Vehicle braking




13 14 15 16 17 18 190

01

02

03

04

05

06

07

08

09

1

Speed (kmh)

Peda

l pos

ition






0 10 20 30 40 50 60 70 800

010203040506070809

1

Speed (kmh)

PR




PR =119875119903

119875119903+ 119875119904

(16)









Shiftingnumber



6 Conclusion




Acknowledgments


References

























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



















119873119904=



119873119903 = 0

one-motor mode

119873119904= 119873main



119870

two-motor mode

(3)




119903119885119904 119885119903and 119885


and sun gear




119909 (119896 + 1) = 119891 (119909 (119896) 119906 (119896)) (4)


119869 =

119873minus1

sum

119896=0

119871 (119909 (119896) 119906 (119896))

=

119873minus1

sum

119896=0

119871119898 (119896) + 119871119886 (119896) + 119871119888 (119896) + 120572 times |Shift (119896)|

(5)


119898(119896)





119879119904 min (119873119904 (119896)) le 119879119904 (119873119904 (119896)) le 119879119904 max (119873119904 (119896))

119873119904 min le 119873119904 (119896) le 119873119904 max

119879119903 min (119873119903 (119896)) le 119879119903 (119873119903 (119896)) le 119879119903 max (119873119903 (119896))

119873119903 min le 119873119903 (119896) le 119873119903 max

(6)


119903is the


119873119904 (119896) times 119873119903 (119896) ge 0 (7)


119904= 0 the speed of 119873

119903should also





120578119898= 119891 (

1003816100381610038161003816119879119898 (119873119898)1003816100381610038161003816 119873119898) (8)





0 1000 2000 3000 4000 5000 60000

100

200

300

400

50060

60

6060 60

60

60

60

60

7070

70 70 70

70

70

70

70

8080

80

8080

80

80

80

80

8585

85 85

85

85

85

85

8585

85

85

90

90

90

90

9090

90

9090

90

90

90

Speed (rpm)

Torq

ue (N

m)



119898(119873119898) can


1003816100381610038161003816119879119898 (119873119898)1003816100381610038161003816 =

10038161003816100381610038161003816119879119898req

10038161003816100381610038161003816if 1003816100381610038161003816119879119898max (119873119898)

1003816100381610038161003816 ge10038161003816100381610038161003816119879119898req

10038161003816100381610038161003816

1003816100381610038161003816119879119898max (119873119898)1003816100381610038161003816 if 1003816100381610038161003816119879119898max (119873119898)

1003816100381610038161003816 lt10038161003816100381610038161003816119879119898req

10038161003816100381610038161003816

(9)



119881vehicle (119896 + 1) = 119881vehicle (119896)

+


119903119905


minus1)

(10)


0is the reduction





119903is the


119891 119865119886 and 119872


equations


119865119886=119862119863119860119906119886

215

119872119903= 119872vehicle +

119869119903

1199032

119905

(11)


119863is




119898119909 (119896 + 1) =

1 119898119909 (119896) + Shift (119896) gt 1

0 119898119909 (119896) + Shift (119896) lt 0

119898119909 (119896) + Shift (119896) otherwise

(12)






p119864119886=

119873119888


p119864119889=

119870119901p119904(119888minus119903)

119873119903+ p119903(119888minus119904)

119873119904

(1 + 119870119901)119873119888

(13)

where p119864119886









119903(119888minus119904)






119869lowast

119873minus1(119909 (119873 minus 1))

= min119906(119873minus1)

[119871 (119909 (119873 minus 1) 119906 (119873 minus 1)) + 119866 (119909 (119873))] (14)


119869lowast

119896(119909 (119896))

= min119906(119896)

[119871 (119909 (119896) 119906 (119896)) + 119869lowast

119896+1(119909 (119896 + 1))]

(15)











0 200 400 600 800 1000 1200 14000

20

40


Vehi

cle sp

eed

(km

h)

0 200 400 600 800 1000 1200 14000

2000

4000

6000Main motor

0 200 400 600 800 1000 1200 14000

2000

4000

6000Auxiliary motor

Time (s)

Rota

tion

spee

d(r

min

)Ro

tatio

n sp

eed

(rm

in)


0 200 400 600 800 1000 1200 14000

20

40


Vehi

cle sp

eed

(km

h)

0 200 400 600 800 1000 1200 1400minus200minus100

0100200 Main motor

Torq

ue (N

m)

0 200 400 600 800 1000 1200 1400minus500

0

500Auxiliary motor

Time (s)

Torq

ue (N

m)





0 200 400 600 800 1000 1200 14000


Vehi

cle sp

eed

(km

h)

0 200 400 600 800 1000 1200 140005

1015

Main motor loss

(kJ)

0 200 400 600 800 1000 1200 140005

1015


(kJ)

0 200 400 600 800 1000 1200 140005

1015

Coupling box loss

Time (s)

(kJ)






0 1 2 3 4 5 6 7 8 9 100

20

40

60Number of shifts

0 1 2 3 4 5 6 7 8 9 106440

6460

6480

6500

6520Energy loss

(kJ)

120572


0 200 400 600 800 1000 1200 140005

1015

Main motor loss

(kJ)

(kJ)

(kJ)

0 200 400 600 800 1000 1200 140005

1015


0 200 400 600 800 1000 1200 140005

1015

Coupling box loss

Time (s)




0 10 20 30 40 50 600

02

04

06

08

1

Acce

lera

tor p

edal


0 10 20 30 40 50 600

02

04

06

08

1

Speed (kmh)

Speed (kmh)

Brak

ing

peda

l

Vehicle braking




13 14 15 16 17 18 190

01

02

03

04

05

06

07

08

09

1

Speed (kmh)

Peda

l pos

ition






0 10 20 30 40 50 60 70 800

010203040506070809

1

Speed (kmh)

PR




PR =119875119903

119875119903+ 119875119904

(16)









Shiftingnumber



6 Conclusion




Acknowledgments


References

























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















0 1000 2000 3000 4000 5000 60000

100

200

300

400

50060

60

6060 60

60

60

60

60

7070

70 70 70

70

70

70

70

8080

80

8080

80

80

80

80

8585

85 85

85

85

85

85

8585

85

85

90

90

90

90

9090

90

9090

90

90

90

Speed (rpm)

Torq

ue (N

m)



119898(119873119898) can


1003816100381610038161003816119879119898 (119873119898)1003816100381610038161003816 =

10038161003816100381610038161003816119879119898req

10038161003816100381610038161003816if 1003816100381610038161003816119879119898max (119873119898)

1003816100381610038161003816 ge10038161003816100381610038161003816119879119898req

10038161003816100381610038161003816

1003816100381610038161003816119879119898max (119873119898)1003816100381610038161003816 if 1003816100381610038161003816119879119898max (119873119898)

1003816100381610038161003816 lt10038161003816100381610038161003816119879119898req

10038161003816100381610038161003816

(9)



119881vehicle (119896 + 1) = 119881vehicle (119896)

+


119903119905


minus1)

(10)


0is the reduction





119903is the


119891 119865119886 and 119872


equations


119865119886=119862119863119860119906119886

215

119872119903= 119872vehicle +

119869119903

1199032

119905

(11)


119863is




119898119909 (119896 + 1) =

1 119898119909 (119896) + Shift (119896) gt 1

0 119898119909 (119896) + Shift (119896) lt 0

119898119909 (119896) + Shift (119896) otherwise

(12)






p119864119886=

119873119888


p119864119889=

119870119901p119904(119888minus119903)

119873119903+ p119903(119888minus119904)

119873119904

(1 + 119870119901)119873119888

(13)

where p119864119886









119903(119888minus119904)






119869lowast

119873minus1(119909 (119873 minus 1))

= min119906(119873minus1)

[119871 (119909 (119873 minus 1) 119906 (119873 minus 1)) + 119866 (119909 (119873))] (14)


119869lowast

119896(119909 (119896))

= min119906(119896)

[119871 (119909 (119896) 119906 (119896)) + 119869lowast

119896+1(119909 (119896 + 1))]

(15)











0 200 400 600 800 1000 1200 14000

20

40


Vehi

cle sp

eed

(km

h)

0 200 400 600 800 1000 1200 14000

2000

4000

6000Main motor

0 200 400 600 800 1000 1200 14000

2000

4000

6000Auxiliary motor

Time (s)

Rota

tion

spee

d(r

min

)Ro

tatio

n sp

eed

(rm

in)


0 200 400 600 800 1000 1200 14000

20

40


Vehi

cle sp

eed

(km

h)

0 200 400 600 800 1000 1200 1400minus200minus100

0100200 Main motor

Torq

ue (N

m)

0 200 400 600 800 1000 1200 1400minus500

0

500Auxiliary motor

Time (s)

Torq

ue (N

m)





0 200 400 600 800 1000 1200 14000


Vehi

cle sp

eed

(km

h)

0 200 400 600 800 1000 1200 140005

1015

Main motor loss

(kJ)

0 200 400 600 800 1000 1200 140005

1015


(kJ)

0 200 400 600 800 1000 1200 140005

1015

Coupling box loss

Time (s)

(kJ)






0 1 2 3 4 5 6 7 8 9 100

20

40

60Number of shifts

0 1 2 3 4 5 6 7 8 9 106440

6460

6480

6500

6520Energy loss

(kJ)

120572


0 200 400 600 800 1000 1200 140005

1015

Main motor loss

(kJ)

(kJ)

(kJ)

0 200 400 600 800 1000 1200 140005

1015


0 200 400 600 800 1000 1200 140005

1015

Coupling box loss

Time (s)




0 10 20 30 40 50 600

02

04

06

08

1

Acce

lera

tor p

edal


0 10 20 30 40 50 600

02

04

06

08

1

Speed (kmh)

Speed (kmh)

Brak

ing

peda

l

Vehicle braking




13 14 15 16 17 18 190

01

02

03

04

05

06

07

08

09

1

Speed (kmh)

Peda

l pos

ition






0 10 20 30 40 50 60 70 800

010203040506070809

1

Speed (kmh)

PR




PR =119875119903

119875119903+ 119875119904

(16)









Shiftingnumber



6 Conclusion




Acknowledgments


References

























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of




















119869lowast

119873minus1(119909 (119873 minus 1))

= min119906(119873minus1)

[119871 (119909 (119873 minus 1) 119906 (119873 minus 1)) + 119866 (119909 (119873))] (14)


119869lowast

119896(119909 (119896))

= min119906(119896)

[119871 (119909 (119896) 119906 (119896)) + 119869lowast

119896+1(119909 (119896 + 1))]

(15)











0 200 400 600 800 1000 1200 14000

20

40


Vehi

cle sp

eed

(km

h)

0 200 400 600 800 1000 1200 14000

2000

4000

6000Main motor

0 200 400 600 800 1000 1200 14000

2000

4000

6000Auxiliary motor

Time (s)

Rota

tion

spee

d(r

min

)Ro

tatio

n sp

eed

(rm

in)


0 200 400 600 800 1000 1200 14000

20

40


Vehi

cle sp

eed

(km

h)

0 200 400 600 800 1000 1200 1400minus200minus100

0100200 Main motor

Torq

ue (N

m)

0 200 400 600 800 1000 1200 1400minus500

0

500Auxiliary motor

Time (s)

Torq

ue (N

m)





0 200 400 600 800 1000 1200 14000


Vehi

cle sp

eed

(km

h)

0 200 400 600 800 1000 1200 140005

1015

Main motor loss

(kJ)

0 200 400 600 800 1000 1200 140005

1015


(kJ)

0 200 400 600 800 1000 1200 140005

1015

Coupling box loss

Time (s)

(kJ)






0 1 2 3 4 5 6 7 8 9 100

20

40

60Number of shifts

0 1 2 3 4 5 6 7 8 9 106440

6460

6480

6500

6520Energy loss

(kJ)

120572


0 200 400 600 800 1000 1200 140005

1015

Main motor loss

(kJ)

(kJ)

(kJ)

0 200 400 600 800 1000 1200 140005

1015


0 200 400 600 800 1000 1200 140005

1015

Coupling box loss

Time (s)




0 10 20 30 40 50 600

02

04

06

08

1

Acce

lera

tor p

edal


0 10 20 30 40 50 600

02

04

06

08

1

Speed (kmh)

Speed (kmh)

Brak

ing

peda

l

Vehicle braking




13 14 15 16 17 18 190

01

02

03

04

05

06

07

08

09

1

Speed (kmh)

Peda

l pos

ition






0 10 20 30 40 50 60 70 800

010203040506070809

1

Speed (kmh)

PR




PR =119875119903

119875119903+ 119875119904

(16)









Shiftingnumber



6 Conclusion




Acknowledgments


References

























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















0 200 400 600 800 1000 1200 14000


Vehi

cle sp

eed

(km

h)

0 200 400 600 800 1000 1200 140005

1015

Main motor loss

(kJ)

0 200 400 600 800 1000 1200 140005

1015


(kJ)

0 200 400 600 800 1000 1200 140005

1015

Coupling box loss

Time (s)

(kJ)






0 1 2 3 4 5 6 7 8 9 100

20

40

60Number of shifts

0 1 2 3 4 5 6 7 8 9 106440

6460

6480

6500

6520Energy loss

(kJ)

120572


0 200 400 600 800 1000 1200 140005

1015

Main motor loss

(kJ)

(kJ)

(kJ)

0 200 400 600 800 1000 1200 140005

1015


0 200 400 600 800 1000 1200 140005

1015

Coupling box loss

Time (s)




0 10 20 30 40 50 600

02

04

06

08

1

Acce

lera

tor p

edal


0 10 20 30 40 50 600

02

04

06

08

1

Speed (kmh)

Speed (kmh)

Brak

ing

peda

l

Vehicle braking




13 14 15 16 17 18 190

01

02

03

04

05

06

07

08

09

1

Speed (kmh)

Peda

l pos

ition






0 10 20 30 40 50 60 70 800

010203040506070809

1

Speed (kmh)

PR




PR =119875119903

119875119903+ 119875119904

(16)









Shiftingnumber



6 Conclusion




Acknowledgments


References

























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















0 10 20 30 40 50 600

02

04

06

08

1

Acce

lera

tor p

edal


0 10 20 30 40 50 600

02

04

06

08

1

Speed (kmh)

Speed (kmh)

Brak

ing

peda

l

Vehicle braking




13 14 15 16 17 18 190

01

02

03

04

05

06

07

08

09

1

Speed (kmh)

Peda

l pos

ition






0 10 20 30 40 50 60 70 800

010203040506070809

1

Speed (kmh)

PR




PR =119875119903

119875119903+ 119875119904

(16)









Shiftingnumber



6 Conclusion




Acknowledgments


References

























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of






















Shiftingnumber



6 Conclusion




Acknowledgments


References

























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of

























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of

















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