research article design of a load torque based control strategy...

Research ArticleDesign of a Load Torque Based Control Strategy for ImprovingElectric Tractor Motor Energy Conversion Efficiency

Mengnan Liu1 Liyou Xu2 and Zhili Zhou2

1School of Mechanical and Precision Instrument Engineering Xirsquoan University of Technology No 5Jinhua South Road Beilin District Xirsquoan 710048 China2Vehicle amp Transportation Engineering Institute Henan University of Science and Technology No 48Xiyuan Road Jianxi District Luoyang 471003 China

Correspondence should be addressed to Mengnan Liu liumengnan27163com

Received 12 January 2016 Revised 23 March 2016 Accepted 31 March 2016

Academic Editor Luis J Yebra

Copyright copy 2016 Mengnan Liu 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

In order to improve the electrical conversion efficiency of an electric tractor motor a load torque based control strategy (LTCS) isdesigned in this paper by using a particle swarm optimization algorithm (PSO) By mathematically modeling electric-mechanicalperformance and theoretical energy waste of the electric motor as well as the transmission characteristics of the drivetrain theobjective function control relationship and analytical platform are established Torque and rotation speed of the motorrsquos outputshaft are defined asmanipulated variables LTCS searches the working points corresponding to the best energy conversion efficiencyvia PSO to control the running status of the electricmotor and uses logic and fuzzy rules to fit the search initialization for load torquefluctuation After using different plowing forces to imitate all the common tillage forces the simulation of traction experiment isconducted which proves that LTCS can make the tractor use electrical power efficiently and maintain agricultural applicability onfarmland conditions It provides a novel method of fabricating a more efficient electric motor used in the traction of an off-roadvehicle

1 Introduction

A potential development trend of farming power is that sus-tainable energies such as electricity and biodiesel will grad-ually and eventually replace the nonrenewable fossil fuels Anelectric tractor is one of the transformation directions Carliniet al presented a series hybrid electric powertrain for a smallcrawler tractor used for logging in forests It reached a 30increase in fuel economy and better ecological features incomparison with the traditional tractor [1] Florentsev et aldeveloped an electromechanical drive train for a 300 hp classtractor The plowing production was 2 higher compared tothe traditional tractor with power-shift drive train while fuelconsumption was lower by 18 [2] Based on our researchin the static analysis of a 180 hp class electric tractor thetractive efficiency average increased by 298 [3] Theseachievements show that the electric tractor has the structuraladvantage in energy conservation However in its drivetrainan electric motor acts as the engine whose energy efficiency

tightly links to the running status In fact owing to thediversity of farming works complexity of soil characteristicsand variation of driving resistance the load torque of thedrive wheel changes frequently and suddenly when tractorswork on the farm [4] Consequently themotor cannot alwaysmaintain high-level energy conversion efficiency Focusedon this problem control strategies designed for promotingthe energy efficiency of electric motors meet the developingrequirement of resource-saving and environment friendlyagricultural machinery technology

Related studies have been performed for improving theenergy conversion economy of electric vehicles By analyzingfive types of control strategies used in high-power vehiclesGarcia et al proved that the equivalent fuel consumptionminimization strategy had better applicability [5] Via com-parison with a batch Genetic Algorithm-based optimizationSorrentino et al designed a rule-based control strategyfor on-board energy management of series hybrid vehicleswhich could improve the fuel economy of hybrid solar

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 2548967 14 pageshttpdxdoiorg10115520162548967

2 Mathematical Problems in Engineering

vehicles [6] However researches like these only refer to themanagement optimization of energy systems that includedthe battery the electric generator powered by an inter-nal combustion engine (ICE) and other assistance energysources They also do not take electric energy-using deviceinto consideration which means such control strategies arenot suitable for the energy conversion economy improvementof the electric vehicle with a simple energy system such asa purely electric vehicle To account for this Shabbir andEvangelou investigated a real-time control strategy whichuses a control map computed off-line to maximize thedrivetrain efficiency of hybrid electric vehicles [7] Anothercontrol strategy was proposed by Osornio-Correa et al basedon the heuristic map created to analyze the restrictionsand benefits of using either of the on-board power plantsunder different driving conditions for maximum energyeconomy of a parallel hybrid electric vehicle [8] Howeverthose researches lack discussion of how to improve the EMenergy conversion efficiency In addition the establishmentof a control map requires extensive experimental data as apractical foundation (which means it would be difficult touse in product development phases of the vehicle) Wu et aloptimized principal parameters of both the powertrain andthe control strategy using a PSO and achieved an acceptableresult However the optimization of electric motor controlstrategy was also ignored [9] Elwer et al optimized thescaling factors of a fuzzy controller used for enhancingthe rapidity accuracy and robustness of the electric vehiclemotor [10] However the controller is not helpful in theimprovement ofmotor energy conversion efficiency By usingan adaptive network in a fuzzy inference system optimizationalgorithm the strategy put forth by Qian et al made theICE of series hybrid electric vehicle work with high energyconversion efficiency [11] Unfortunately in a series hybridelectric vehicle ICE is mechanically decoupled to the drivewheel and its mechanical power output is not constrainedby load characteristic Therefore the control strategy cannotbe imitatively used in traction motor In an ordinary electricdrivetrain or pure electric vehicle an electric motor works asthe sole energy conversion device so the energy conversionefficiency of the drivetrain (or the vehicle) is only promotedby means of controlling the working state of the electricmotor Nevertheless the energy conversion efficiency of theelectricmotor tightly couples with its rotate speed and torquewhich are also dependent upon the actual driving demandof the vehicle For the road vehicle complex and frequentlychanging road condition means it is impractical that con-trol of the mechanical characteristics of the electric motoris dependent upon its energy conversion efficiency whileneglecting the speed requirements of safety practicabilityand traffic laws However in the agricultural conditions ofthe tractor the frequent change of speed is not required andthe load force is normally stable Therefore we can try tocontrol the electricmotorrsquos running state for improved energyconversion efficiency In summary research on an efficientcontrol strategy for an electric tractor motor is both neededand innovative

This paper begins with establishing the mathematicalmodel that describes the electric-mechanical performance

EM GT MD

MC

ES

Driver

AP

PTOAI

Control flowMechanical energy flow

Electrical energy flowLoad force

Clutch

Figure 1 Scheme of an electric tractorrsquos drivetrain

and theoretical energy consumption of the electric motoras well as the transmission characteristics of the electrictractorThen it introduces the design of LTCS and how it cancontrol the electricmotor tomaintain high energy conversionefficiency Finally simulation of the traction experiment isconducted to verify the effect and agricultural applicabilityof LTCS

2 Mathematical Model

21 Introduction of the Electric Tractor Drivetrain Althoughthe electric tractor shares many common structural featureswith the common electric vehicle there are some significantdifferences between the two drivetrains Particularly theelectric vehicle layout is organized as shown in Figure 1 Theelectric tractor drivetrain is powered by the energy system(ES)The ES can contain the storage battery in a pure electrictractor or the ICE generator battery super-capacitor and soforth in a hybrid electric tractor The electric motor (EM)provides themechanical power for the drive wheel and powertake-off shaft (PTO) PTO joints with the EM via the clutchWhen the tractor only drives the agricultural implement (AI)the clutch decouples the mechanical connection betweenthe PTO and the drive wheel which makes the mechanicalpower flows of them be independent of each other Thegearbox transmission (GT) can transform the dynamic powerperformance field of the drive wheel via the gear shiftingoperation of driver And the GT directly transmits themechanical power to PTO which can make the rotate speedof PTO match with either the rotate speed of the EM orthe forward velocity of the electric tractor The main drive(MD) acts as the differential mechanism and final reducerof the transmission system By stepping on the acceleratorpedal (AP) the driver can control the EM through electricaladjustment of themotor controller (MC) Generally there aretwo types of load force exerted upon the electric tractor oneis driving force and the other is tilling force

22 Electric-Mechanical Performance of the Electric Motor(EM) According to the previous research the EM is

Mathematical Problems in Engineering 3

a brushless direct current motor (BLDC) [3] The voltage perphase can be expressed by

119880a = 119877s119868a + [(119871a minus 119871m) 119889119868a

119889119905] + 119890a

119880b = 119877s119868b + [(119871b minus 119871m) 119889119868b

119889119905] + 119890b

119880c = 119877s119868c + [(119871c minus 119871m) 119889119868c

119889119905] + 119890c

(1)

After equivalent transformation the electromechanicalcharacteristics of BLDC can be described by the followingequations [12]

119880t = 119877s119868s + [(119871n minus 119871m) 119889119868s

119889119905] + 119890s

119871 s = 119871n minus 119871m

119890s = 119896119864120596r

(2)

The electromagnetic torque of BLDC 119879e can be obtainedas follows

119879e =955 (119890a119868a + 119890b119868b + 119890c119868c)

120596r=955119890s119868s120596r

(3)

119879e = 119896119879119868s (4)

Depending on (3) and (4) the torque constant 119896119879 is

equal to back EMF constant 119896119864 after the dimension change

When BLDC is working on traction the electromagnetictorque of the motor can also be described by

119879e = 119879L + 119869119889120596r119889119905+ 119881120596r (5)

Based on the Laplace transform of (1)ndash(5) the electric-mechanical performance of BLDC can be expressed by thefollowing transfer function

120596r (119904) =119896119879

(119877s + 119904119871 s) (119904119869 + 119881) + 119896119864119896119879119880t (119904)

minus119877s + 119904119871 s

(119877s + 119904119871 s) (119904119869 + 119881) + 119896119864119896119879119879L (119904)

(6)

Consequently the steady state characteristic can be estab-lished

120596r =119896119879

119877s119881 + 119896119864119896119879119880t minus

119877s119877s119881 + 119896119864119896119879

119879L (7)

According to (4) (6) and (7) the mechanical perfor-mance of the EM can be linked to the controllable electricparameter

23 Energy Consumption Model of the EM When the EM isrunning electric power loss contains copper loss icon lossmechanical loss and constant power used for driving theMC

Copper loss 119875c is the prime waste of the BLDC This isdue to the fact that the stator winding impedance converts theelectric power to the thermal dissipated to the surroundingsIt can be obtained as follows [13]

119875c = 1198682

s 119877s (8)

According to (4) the value of the current is directlyproportional to the value of electromagnetic torqueThus wecan use a coefficient 119896c to describe the relationship betweenthe copper loss and the electromagnetic torque The copperloss can be rewritten as follows

119875c = 119896c1198792

e (9)

The copper loss coefficient 119896c can be calculated by

119896c =119877s1198962

119879

(10)

Icon loss power 119875i mainly contains magnetic hysteresisloss and current loss and its mechanisms are complex andchanging It mainly depends on the speed of rotor and isdescribed by

119875i = 119896i120596r (11)

In the BLDC 119896i can be approximately seen as a constantand can be measured by an experimental method

The mechanical loss 119875M output from the rotor is largelywasted on air resistance It can be obtained by

119875M = 119896w1205963

r (12)

Themechanical power output and total power input of theelectric motor can be described by the following equations

119875out =119879L120596r9550

119875in = 119875out + 119875c + 119875i + 119875M + 119862

(13)

According to (7)ndash(13) the electric conversion energyefficiency 120578m may be established by

120578m =119875out119875in

=119879L120596r

119879L120596r + 9550 [119896c1198792

e + (119896i + 119896w1205962

r ) 120596r + 119862]

(14)

According to (14) which is the objective function of PSOsearching the theoretical relation of EM energy conversionefficiency to the mechanical performance can be established

24 Transmission Characteristics of the Drivetrain Whenthe electric tractor works in the farm the torque outputof the EM distributes to the driving wheel and PTO andovercomes the driving and working resistance respectivelyThe torque coupling relationship between the electric motor


shaft driving wheel and PTO can be obtained by applyingthe following equations

119879L120596r =119879TN120596TN120578g1205780

+119879w120596w1205781015840g120578a

119879L =119879TN119894g1198940120578g1205780

+119879w

1198941015840g119894a1205781015840

g120578a

120596r = 120596TN119894g1198940 = 120596w1198941015840

g119894a

(15)

When the tractor plows the force balance of the drive-train can be described by the following equations

119865TN = 119865g + 119865f + 119865p + 119865Af + 119865i

119865TN =119879TN

1000119903TN

119865g = 1198851198871ℎk119896

(16)

Driving speed and tractive force can be described asfollows

V = 0377119903120596r120578120575119894g1198940

119865T = 119865TN120578T

120578T = 120578c120578f120578120575

(17)

According to (15)ndash(17) the relationship between load andmechanical output of the EM can be expressed

3 Design of Load Torque Based ControlStrategy (LTCS)

31 Particle Swarm Optimization Algorithm (PSO) Introduc-tion In comparison with classical optimization methodsPSO is an efficient range-searching algorithm By select-ing the search threshold the population behavior can berestricted to only running under working conditions andpractical requirements It is a helpful advantage to ensurethat the control parameters produced by PSO conform to thespeed and torque requirement of farmingMoreover PSO candeal with nonsmooth noncontinuous and nondifferentiablefunctions simply with objective function information Com-pared with other intelligence algorithms such as the GeneticAlgorithm there is one simple operator velocity calculationin the PSO Using the simpler algorithm means shortercomputing time less memory and improved robustness [14]Therefore PSO is chosen here as the primary algorithm ofLTCS

By means of simulating bird flock preying behaviorparticle swarm optimization used widely in the engineeringfield has the advantage of high robustness and low complexity[15] In a searching space the particles population whichcontains 119899 particles can be built as 119883 = (119883

1 1198832 119883

119899)

The 119894th particle is a vector with 119898 dimensionalities and canbe built as 119883

119894= (1198831198941 1198831198942 119883

119894119898)119879 to express the position

of this particle namely a potential solution of the objectivefunction The fitness values of each 119883

119894may be calculated

by the objective function The speed of 119883119894can be built

as 119881119894= (1198811198941 1198811198942 119881

119894119899)119879 the individual best solution is

119884119894= (1198841198941 1198841198942 119884

119894119899)119879 and the swarm optimal solution is

119884119892= (1198841198921 1198841198922 119884

119892119899)119879 During the iterative process every

particle of the swarm uses its 119884119894and 119884

119892to update the 119881

119894and

119883119894 which can be described as follows

119881120574+1

119894119889= 120576119881120574

119894119889+ 11988811198771(119884120574

119894119889minus 119883120574

119894119889) + 11988821198772(119884120574

119892119889minus 119883120574

119894119889)

119883120574+1

119894119889= 119883120574

119894119889+ 119881120574+1

119894119889

(18)

where 119889 = 1 2 119899 119894 = 1 2 119898 and 1198771and 119877

2are

random numbers in [0 1]

32 Working Characteristic The 1804 series hybrid electrictractor was selected as the study object of this paper in aproject designed by taking the YTO-1804 as a prototype [3]Its drivetrain conforms to the description in Figure 1 and thespeed-traction force performance curve is built in Figure 2

When an 1804 hybrid works under heavy load gear ormoderate load gear the relationship between the drivingspeed and the traction force could be described by

119889119865T119889V

gt119889V119889119865T

(19)

When the tractor works under the light load gear ortransport gear the relationship can be described by thefollowing equation

119889V119889119865T

asymp119889119865T119889V

119889119865T119889V

lt119889V119889119865T

(20)

Since the 1804 hybrid always tills with a stable speedand main farm works are done by using heavy moderateand light load gear meeting the requirement of the tractionforce is more important than meeting the requirement of thespeed Additionally the control result can match the changeof traction force well and 119879L and 120596r are respectively definedas the independent variable and dependent variable of thePSO

33 Control Strategy Control function of the LTCS in thevehicle is shown in Figure 3 Compared with the electrictractor in Figure 1 the LTCS is added between the driverand the MC Two input signals which are respectivelyacquired from the position sensor on the accelerator pedal(AP) and the shift lever are deduced and calculated by LTCSAfterward based on internal rules LTCS provides controlsignals to the MC and energy system (ES) to control therunning status of the EM

When the position sensor measures the depth of AP loadtorque can be calculated by

119879L =119861 minus 119860 sdot 119873

119860 sdot (1 minus 119873)sdot 119879max (21)


0 10 20 30 40 50 600

10

20

30

40

G

H

I

J

K

L

D

E

F

C

A

B

A-B-CD-E-F

G-H-IJ-K-L

Tractive force (kN)

145Spee

d (k

mmiddothminus1)

dv

dFT=dFTdv

= 1

Transport gearLight load gear

Moderate load gearHeavy load gear

Figure 2 Speed-traction force performance curve of the 1804 serieshybrid electric tractor

EM GT MD

MC

AI

ES

Driver

AP

LTCS

CVT Clutch



Figure 3 Schematic representation of the control function for theelectric drivetrain

During every sampling time the internal task actions ofLTCS are built in Figure 4 which includes two parts One isthe search process of the best energy-using working pointand the other is the timely control of the search processinitialization

The best working point (1205961015840r 1198791015840

L) that corresponds to thebest electric energy efficiency of the drive motor is selected asthe searching target of the PSO searching process Because1198791015840Lshould be greater than 119879L the enclosure space [119879L 119879L + 119876] isdefined as the constraint 119876 is the adjustment torque

After every initialization signal the search process runsonly once Via (4) and (6) the searched best working pointwas used as the control parameter of the torque based currentfeedback control of the MC and the DC-AC converter ofthe energy system (ES) to respectively control the expectedphase current and input voltage until the next initializationoccurs which follows these rules

Table 1 Fuzzy rules to infer initialization

Deeping rate Footplate depthS M B

minusB INIT INIT INITminusM HOLD INIT INITS HOLD HOLD HOLD+M HOLD INIT INIT+B INIT INIT INIT

(1) In every sampling step the initialization signals sentby the time trigger and load torque controller aresynchronous and mutually independent When theinitialization is triggered the search process andfollowing control process occurred immediately

(2) Using the sampling step as the period the time triggerperiodically sends the initialization signal It is usedto deal with the accumulation of smaller AP positionchanges which cannot trigger the initialization signalof the load torque controller during every period

(3) In every period the initialization can also be con-trolled by the torque controller which judges theload torque changing status If the load change thatoccurred during this period is large enough the PSOsearching is initialized immediately

34 The Design of Load Torque Controller The load changedegree is judged by the gearshift and footplate positionswhich can be measured by the gear sensor and the APposition sensor

Shifting gears is an operation greatly affected by thesubjective intention of the driver In other words when thetractor meets visible topographic changes or the workingtype changes where the load torque will likely experience asignificant change the driver usually shifts the gear Logicalalgorithms are used to process the signal of the gearshiftposition If the driver shifts the gear (which means the loadtorque condition change is large enough) the controller sendsthe initialization signal

Under any gear the driver can estimate the load forcesituation by viewing the tachometer reading When the APposition is stable changing the tachometer reading meansthat the force balance on the EM shaft has been broken Thedriver should adjust the AP depth based on the change trendin the tachometer reading until the tractor speed is similar towhat it was previously A fuzzy controller is designed to dealwith the AP signal inferring the change degree of workingcondition and providing the initialization signal

Wang et al discussed the fuzzy rules that reflect therelationship between diver intention and AP operation [16]Based on that two of the fuzzy rules used for deducing theinitialization of LTCS are shown here in Table 1

The membership functions that belong to the footplatedepth the footplate deepening rate and the collection modeare described by Figures 5ndash7

In the case of the footplate depth it has three chosenmembership functions S small depth M moderate depthand B big depth They cover the full range of footplate


If the gear was shifted

If the load peaking occurred

Hold

Initialization

Signal of gearshift position

Signal of AP position

No

Yes

Yes

Equation (6) Equation (4)

ES

PSO search in (14)

Equation (21)

Search processInitialization

controlTime trigger

Loadtorquecontroller

No


EM MC

[TL TL + Q]

(120596998400r T998400L)

I998400s U998400t

U998400t

Figure 4 Schematic description of internal task actions within the LTCS

S BM

0020406081

Mem

bers

hip

10 03 04 05 06 07 08 0901 02

Footplate depth

Figure 5 Membership functions of the footplate depth

Footplate deepening rate

minusB minusM S +B+M

10 04 06 0802minus02minus04minus06minus08minus1

002040608

1

Mem

bers

hip

Figure 6 Membership functions of the footplate deepening rate

depth When the AP controls BLDC its control function isequivalent to the voltage control process of the potentiometerFor the torque control of BLDC the torque controlled byAP is normally proportional to the expected electric currentso the footplate depth membership functions are equallydistributed To transform the real domain into fuzzy domainscope [0 1] the quantization factor of footplate depth 120576d iscalculated by

120576d = 119860 (1 minus 119873) (22)

Collection mode

INIT HOLD

0020406081

Mem

bers

hip

10 03 04 05 06 07 08 0901 02

Figure 7 Membership functions of the collection mode

In the case of the footplate deepening rate five mem-bership functions are considered S small change rate +Mmoderate deepening rate minusM moderate returning rate +Bbig deepening rate and minusB big returning rate When thetractor speed increases with an unchanged AP positionwhich means the load torque reduces the driver may returnthe pedal until the speed changes back and vice versa Thusthe formulation of footplate deepening rate membershipfunctions should contain this caseThe quantization factor offootplate deepening rate 120576dr is calculated by

120576dr =119860 (1 minus 119873)

119905r (23)

Depending on the test of McGehee et al [17] 119905r can be setas 128 s

Regarding the output variables the collection modecontains two membership functions INIT the initializationof LTCS and HOLD nothing else changing in the loadtorque control process Because the opposition between


002

0406

081

1

050

minus05minus1 Footplate depth


02

03

04

05

06

07

08

Col

lect

ion

mod

e

Figure 8 Fuzzy surface

initialization and hold operations is definite and completetheir fuzzy domains are complementary

Surface of the fuzzy rules can be viewed in Figure 8

4 Simulation of the Traction Experiment

41 Parameters and Conditions of the Simulation The simu-lation of the traction experiment is designed as a backwardtype Working conditions which act as the input of the simu-lationmodel are required to contain all the commonworkingresistances of the 1804 hybrid tractor According to thecommon soil conditions of the Northeast China region therolling resistance coefficient119891 is 01 the adhesion coefficientis 07 and the clayed ground whose soil specific resistancesrandomly changed from 0007 to 001 is tilled Parameters ofthe plowing resistances which imitate resistances of commonworking conditions are expressed in Table 2

Theworking condition in the simulation can be describedby Figure 9 (see data in Supplementary Material A inSupplementary Material available online at httpdxdoiorg10115520162548967)The equivalent resistance ranged from5 kN to 625 kN which agrees with the tractive force scope inFigure 2

According to our previous research [3] Table 3 shows thesimulative parameters of the 1804 hybrid drivetrain whichacts as the controlled object

Based on mass experimental data Zhou et al presentedthe theoretical models used to predict theoretical tractiveperformance of a wheeled tractor [18] According to thismodel the slip rate 120575 can be calculated by the followingequation

120575 = 120575lowastLn

120601max120601max minus 119871119865TN (119886119866 + ℎT119865TN)

(24)

In (24) 120575lowast and 120601max are fitting coefficients whose valuesare recommended as 00757 and 0624 under the common soilconditions of the Northeast China region The relationshipbetween 120578

120575and 120575 is 120578

120575= 1 minus 120575 The slip efficiency used in the

simulation is established in Figure 10In the simulation of plowing the clutch between GT

and PTO is separated Therefore the mechanical loss of

Table 2 Plowing parameters

Number 119885 119887l ℎk0 7 35 301 6 35 302 5 32 253 4 35 254 4 40 315 3 30 206 3 35 227 1 50 20

Table 3 Simulative parameters of the electric drivetrain

Part Parameter name Value and unit

Vehicle

Overall length 52mOverall width 269mOverall height 297m

119871 285mℎT 16m119866 11264 kN119903TN 09m119886 197m

GT

Heavy load gear ratio 538Moderate load gear ratio 388Light load gear ratio 263Transport gear ratio 165

120578g 9604

EM

Voltage rating 380VPeak voltage 540VTorque rating 4138Nsdotm

Rotate speed rating 300 rminReduction ratio 23

119875r 130 kW119877s 004Ω119869 00001 kgsdotm2119881 00368Nsdotmsdotminr119896c 015 kWN2sdotm2119896i 01 kWsdotminr119896w 12119890 minus 7 kWsdotmin3r3119896119864

00543Vsdotminr119896119879

05186NsdotmA119862 021 kW

MD 1198940

321205780

98

AP 119860 54∘119873 015

the agricultural implement (AI) is irrelevant The rest of theparameters of efficiency are calculated as

120578c = 1205780120578g

120578f =119866119891

119865TN

(25)

Accordingly the transmission efficiency 120578c is equal to9412 and the rolling efficiency 120578f is dynamically equal to112119865TN

Based on (22) and (23) 120576d and 120576dr of the load torquecontroller are respectively assigned as 448 and 3586


0 100 200 300 400 600 800

Heavy load scope

Moderate load scope

Light load scope

Transport scope

Gear shifting point

Maximum tractive force

Time (s)

0500 700

1 2 3 4 5 6 70

10

20

30

40

50

60

70

Equi

vale

nt re

sista

nce (

kN)

Figure 9 Tractive force of the simulation Note numbering 0ndash7 corresponds to the numbers of plowing parameters in Table 2

0 10 20 30 40 50 60 70 8060

70

80

90

100

Slip

effici

ency120578120575

()

Driving force FTN (kW)

Figure 10 Slip efficiency in the simulation

In the simulation the tractor working system is simplifiedas a longitudinal model which tills in a straight line and allthe side forces can be disregarded A driver response time tothe peak force is set as 01 s It is assumed that the driver canaccurately adjust the AP depth in accordance with the loadforce change The sampling step length is 5 s The load forcefluctuation owed to the AI and gear switching is ignored

42 PSO Setting in the Simulation In the simulation the PSOsearching process runs on the platform developed by Birge[19] Shi and Eberhart researched the set of inertia weights bythe simulation on the benchmark problems and found thatinertia weight starting with a value from 09 to 04 throughthe course of the run greatly improved the performance ofPSO [20]Thus the start weight value selected here is 09 andthe end weight value is 04

The determination of maximum velocity 119881119894max 1198881 and 1198882

is mainly based on the formula presented by Zhang et al asfollows [21]

119881119894max = 120582119883119894max

1198881= 1198882=120593

2

(26)

In this case the searching space of PSO is 2-dimensionaland the objective function (14) is unimodal Therefore it isrecommended that 120582 is equal to 005 and 120593 is set as 41

As stated earlier the PSO is searching for the best workingpoint in constraint [119879L 119879L+119876]The adjustment torque119876 is setas 05 kN for the purpose of promoting of the search accuracyIn addition in order to prevent the mechanical power of thesearched working point from exceeding the rating power ofthe EM the rotate speed of the EM should be bounded by therange119883

2max Thus119883119894max is described by

1198831max = 119877119879 = (119879L 119879L + 05)

1198832max = 119877MAV = (0

9550119875r119879L

)

(27)

In every control step the value of 119879L is dependent upon(21)

Shi and Eberhart advised that probably themost commonpopulation sizes of PSO are from 20 to 50 [20] Experimentalverification has found that there is no visible difference insearching results when the population size is respectively setas 20 30 40 and 50 To simplify we set the population sizeat 20

43 Analysis of the Simulation Result Figure 11 depicts thesearching result when the tractive force is 55 kN (whichbelongs to the heavy load scope) After 38 evolutions thepopulation fitness degree becomes stable The best workingpoint is searched as 256339 rmin 367697Nsdotm and theelectric energy conversion efficiency is 9238

Figure 12 depicts the searching result when the loadtorque is 14 kN (which belongs to the light load scope)After 20 evolutions the population fitness degree becomesstable The best working point was searched as 2188 rmin2864Nsdotm and the electric energy conversion efficiency was9283 The searching results on two situations show thatthe LTCS makes the result of PSO searching self-adaptive forthe tractive force In addition the convergent evolution timestestify that the set of PSO parameters make the searchingprocess sufficiently rapid


0 2000 4000 60000 20 40 60 80 100Evolution times

38

Best working pointPSO convergence curves

0

200

400

10minus003445

10minus003444

10minus003443

10minus003442

10minus003441

Valu

e of fi

tnes

s deg

ree 0923838 = fbest(367697 256339)

120596998400 r

T998400L

Figure 11 PSO searching on the heavy load situation

0 2000 40000

100

200

300

400

Valu

e of fi

tnes

s deg

ree

20 40 60 80 1000Evolution times


10minus00324

10minus00323

0928384 = fbest(286437 2188)

120596998400 r

T998400L

Figure 12 PSO searching on the light load situation

0 100 200 300 400 500 600 700 800Time (s)

0

1

Figure 13 Output of load torque controller in the simulation

The control single of the load torque controller in thesimulation is expressed by Figure 13 In comparison withFigure 9 when the hybrid works with heavy moderateand light load gear initialization signals can frequently beactivated by strong fluctuations in the load force After 680 s

when the load force begins to meet the transport conditionwith a relatively stable load force there is no signal outputIn conclusion the rules of the load torque controller canjudge the load force with acceptable accuracy and adaptivityThe initialization signalsrsquo superposition process during thesimulation is described in Supplementary Material B

Figure 14 depicts the simulative results of the voltage-current performance controlled by LTCS According to thediscussion of Figure 4 the current 119868s is defined as 119879

1015840

L whichfollows the relationship of (4) And the rotate speed of EM120596r is adjusted by changing the voltage

The load torque followed control method (LTFC) is usedpopularly in the BLDC control of the electric tractor Accord-ing to the excepted torque LTFC controls themechanical out-put of the EM by adjusting the phase current [12] Comparedwith another electric vehicle electric motor control strategythe speed followed controlmethod (which controls the BLDCwith expected speed) according to the discussion in Figure 2


050

100150200250300350400450

Volta

ge (V

)

200220240260280300320340360380400

Curr

ent (

A)

100 200 300 400 500 600 700 8000Time (s)

Figure 14The electrical characteristic controlled in the simulation

60708085

90

92925

91

D

E

A

B

Electric energy conversion efficiency of EM Ploughing speed scope Working point controlled by LTCSWorking point controlled by LTFC

0

1

2

3

4

5

6

7

8

9

40 45 50 55 60 6535Tractive force (kN)

Spee

d (k

mmiddothminus1)

Figure 15 Working points distribution of the high load gear

LTFC is more suitable for the farming working conditionswhich have high-level load force Thus we selected the LTFCas the comparison for analyzing the control performance ofLTCS

Figure 15 depicts the drivetrain working points of LTCSwhen the tractor works with heavy loads The figure showsthat some of working points are distributed on the edge of thespeed-traction force performance curve and others are in thecentral area near 925 Both of the two distributions are nearthe best efficiency area under an equivalent traction forceThespeed range of working points is 41 kmhsim58 kmh whichcan meet the speed scope of plowing

By comparing the heavy load control performance ofLTCS and LTFC in Figure 15 all of the working points of bothcontrol strategies canmeet the speed requirement of plowingbut the working points of LTCS present more efficient energyconversion

Figure 16 depicts the drivetrain working points when thetractor works with moderate load The energy conversionefficiency of the working points controlled by LTCS exceeds

607080

90

85

9192

925

93

D

E

H

G

F


0

2

4

6

8

10

12

14

16

Electric energy conversion efficiency of EM Cultivating and hoeing speed scopeWorking point controlled by LTCSWorking point controlled by LTFC

Spee

d (k

mmiddothminus1)

Figure 16 Working points distribution of moderate load gear

8 10 12 14 16 18 20 22 24 2660

7080

85

85

9091

92 925

93

GJ

H

K

Tractive force (kN)

0

5

10

15

20

25

Electric energy conversion efficiency of EM Speed range of sowing harrowing and stubble chopping Working point controlled by LTCSWorking point controlled by LTFC

Spee

d (k

mmiddothminus1)

Figure 17 Working points distribution of light load gear

921 When the traction force is less than 333 kN the effi-ciency can be greater than 925 In addition the speed rangeis 51 kmhsim74 kmh which meets the speed requirement ofcultivating and hoeing Compared with the case of LTFCLTCS presents more efficient speed and control performance

Figure 17 depicts the working pointsrsquo distribution whenthe tractor works with a light load As shown the energyconversion efficiency of EM controlled by LTCS is almost


607080

85

9190

92925

J

L

K

0

5

10

15

20

25

30

35

40


Electric energy conversion efficiency of EM

Working point controlled by LTCSWorking point controlled by LTFC

Spee

d (k

mmiddothminus1)

Figure 18 Working points distribution of transport gear

always superior The speed range is 85 kmhsim107 kmhwhich can meet the speed scope of sowing harrowingand stubble chopping In addition the maximum speedchange rate is 02 kmkNsdoth which can enhance the seedinguniformity

By contrast the speeds of all of the working pointscontrolled by LTFC are higher than the speed range ofsowing harrowing and stubble chopping This is becausewhen the tractor is working with AI the rotate speed of PTOis commonly changeless In the 1804 series hybrid electrictractor the rotate speed is 1000 rmin or 540 rmin Whenthe tractor speed exceeds the speed scope of its farming typethe farming quality may be decreased (eg for the sowinga faster tractor speed means longer seed spacing which willreduce the seeding rate and consequently decrease the cropproduction) Therefore LTFC is not suitable for the lightworking conditions of electric tractor

Figure 18 shows the distribution of working points whenLTCS is used for the transport condition Although theefficiencies of all of the working points can be approximatedto the maximum under an equivalent traction force thespeed is relatively slow for transporting which may reducethe conveying efficiency Furthermore when the 1804 hybridtransports out of the farm the control result cannot attainadequate traffic security and drive flexibility which meansLTCS is not appropriate for the road transport condition

In the design of LTCS load torque is used as theindependent variable of target function and the enclosurespace based on load torque is the only constraint of the PSOsearch Consequently the speed changes dependent on thestatus of the load force and that is why the speed cannot beadjusted independently and intentionally

Simulation results of energy conversion efficiency aredepicted in Figure 19 In each simulation the electric tractor

A B

LTCSLTFC

100 200 300 400 500 6000 700 800Time (s)

09

0905

091

0915

092

0925

093

0935

Ener

gy co

nver

sion

effici

ency

Figure 19 The comparison of energy conversion efficiency underthe control of LTCS and LTFC

131

108

LTCSLTFC

60708090

100110120130140150

Elec

tric

pow

er (k

W)

100 200 300 400 500 600 700 8000Time (s)

Figure 20 The comparison of ES power consumption under thecontrol of LTCS and LTFC

controlled by LTCS is more efficient than when controlled byLTFC in electric use In addition its mean energy conversionefficiency is 9246 and there are small improvementsin regions A and B The reason for this is that furtherimprovement of energy conversion efficiency is limited by therating power of electric motor which proves that the set ofPSO searching ranges are appropriate

Figure 20 depicts the electric power consumption of theES Due to the improvement of the EM energy conversionefficiency and the speed-limited function of LTCS the meanelectric power consumption can reduce by 23 kW and theenergy-saving effect of farming work can increase by 213in comparison with the LTFC

In summary when LTCS is used for working the farmthe electric tractor possesses superior agricultural adaptationand an obvious energy-saving effect In off-road conditionsthe electric tractor can also be engaged in some transportoperations where speed performance is not required In thefuture when the LTCS is used in a realistic environment thefollowing is recommended

(1) The objective function should be further amended byconsidering the change of temperature or be built byexperimental method


(2) The mechanical dynamic characteristics of the motoroutput shaft should be controlled by the PSOmethodpresented by Elwer et al [10]

(3) The control parameters of PSO should be optimizedby considering the hardware performance of the elec-tric control unit selected the principle is based on thepremise of appropriate precision so the convergencerate should be increased to the maximum speed

5 Conclusion

In this paper the load torque based control strategy used formaintaining high energy conversion efficiency of the tractionmotor in an electric tractor is presented and studied Thecontrol process contains a PSO search that seeks the bestworking point with maximum energy conversion efficiencyand initiation control andwhose target is to adjust the search-ing results dynamically based on peak torque First by themathematical modeling the relation between themechanicalcharacteristic and energy conversion is established and thenthe target function is performed Second by analyzing thespeed-traction force performance of the 1804 hybrid the loadtorque is selected as the constraint of the PSO search Bydescribing the schematic representation and the internal taskaction the control method and flow are obtained By makinglogic and fuzzy rules the torque controller based on driverintention was designed Finally after the working conditioncollection which covers most of the tillage force simulationof traction experiment is conducted The distribution ofinitialization signal output from the load torque controllerfits the load force fluctuation which means the initializationcontrol can be self-adaptive to the working condition and thesearch results can be time-sensitive Compared with LTFCLTCS maintains the energy conversion efficiency of the EMnear the maximum during the simulation time Meanwhilethe working speed is sufficiently stable for the requirementof agriculture uniformity and suitable for the speed scope oftillage

Nomenclature

119860 Maximum opening angle of AP (∘)119886 Distance from barycenter to front axle (m)119861 Depth of AP (∘)119887l Width of single ploughshare (cm)119862 Constant loss of EM (kW)1198881 1198882 Acceleration factors (-)

119890a 119890b 119890c Per phase back EMF (V)119890s Back electromotive force (V)119865Af Air resistance (kN)119865f Rolling resistance (kN)119865g Plowing resistance (kN)119865i Acceleration resistance (kN)119865p Slope resistance (kN)119865T Tractive force (kN)119865TN Driving force (kN)119891 Rolling resistance coefficient (-)119866 Tractor gravity (kN)

ℎk Plowing depth (cm)ℎT Hitch point height (m)119868a 119868b 119868c Per phase current (A)119868s Winding current (A)119894a Gear ratio of AI (-)119894g Gear ratio of GT (-)1198941015840

g Gear ratio between EM and PTO (-)1198940 Gear ratio of MD (-)119869 Rotational inertia of drivetrain (kgsdotm2)119896 Soil specific resistance (kNcm2)119896119864 Back EMF constant (Vsdotminr)

119896119879 Torque constant (NsdotmA)

119896c Copper loss coefficient (kWN2sdotm2)119896i Iron loss coefficient (kWsdotminr)119896w Air resistance coefficient (kWsdotmin3r3)119871 Wheelbase (m)119871a 119871b 119871c Per phase self-inductance (H)119871m Mutual inductance (H)119871n Self-inductance (H)119871 s Leakage inductance (H)119873 Free travel ratio of AP (-)119875c Copper loss (kW)119875i Icon loss (kW)119875in Electric power input of EM (kW)119875M Mechanical loss (kW)119875out Mechanical power output of EM (kW)119875r Rating power of EM (kW)119877MAV Searching range of rotate speed (rmin)119877s Stator winding resistance (Ω)119877119879 Searching range of torque (Nsdotm)

119903TN Rolling radius of drive wheel (m)119879e Electromagnetic torque (Nsdotm)119879L Load torque of EM (Nsdotm)119879max Maximum torque of EM (Nsdotm)119879TN Torque output of driving wheel (Nsdotm)119879w Torque output of AI (Nsdotm)119905r AP release time (s)119880a 119880b 119880c Per phase voltage (V)119880t Input voltage (V)119881 Viscous resistance coefficient (Nsdotmsdotminr)V Tractor speed (kmh)119885 Number of ploughshares (-)120596r Rotate speed of EM (rmin)120596TN Rotate speed of driving wheel (rmin)120596w Rotate speed of AI (rmin)120578a Mechanical efficiency of AI ()120578c Transmission efficiency ()120578f Rolling efficiency ()120578g Mechanical efficiency of GT ()1205781015840

g Mechanical efficiency between EM andPTO ()

120578m Electric conversion energy efficiency ofEM ()

120578T Tractive efficiency ()120578120575 Slip efficiency ()

1205780 Mechanical efficiency of MD ()

120576 Inertia weight (-)120576d Quantization factor of footplate depth (-)


120576dr Footplate deepening rate quantizationfactor (-)

120574 Number of iterations (-)120575 Slip rate (-)

Abbreviations

AI Agricultural implementAP Accelerator pedalBLDC Brushless direct current motorEM Electric motorEMF Electromotive forceES Energy systemGT Gearbox transmissionICE Internal combustion engineLTCS Load torque control strategyLTFC Load torque followed control methodMC Motor controllerMD Main drivePSO Particle swarm optimization algorithmPTO Power take-off shaft

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank the YTOGroup Corporationfor the study permission and technical supportThe project issupported by National Natural Science Foundation of China(no 51375145) Science and Technique Foundation of HenanProvince (Grant no 142102210424) and Research Program ofApplication Foundation and Advanced Technology of HenanProvince (no 152300410080) The authors thank Accdon forits linguistic assistance during the preparation of this paper

References

[1] M Carlini R I Abenavoli H Kormanski and K RudzinskaldquoHybrid electric propulsion system for a forest vehiclerdquo inProceedings of the 32nd Intersociety Energy Conversion Engineer-ing Conference vol 3 pp 2019ndash2023 Honolulu Hawaii USAAugust 1997

[2] S Florentsev D Izosimov L Makarov S Baida and ABelousov ldquoComplete traction electric equipment sets of electro-mechanical drive trains for tractorsrdquo in Proceedings of the IEEERegion 8 International Conference on Computational Technolo-gies in Electrical and Electronics Engineering (SIBIRCON rsquo10) pp611ndash616 IEEE Irkutsk Russia July 2010

[3] L Xu M Liu and Z Zhou ldquoDesign of drive system for serieshybrid electric tractorrdquo Transactions of the Chinese Society ofAgricultural Engineering vol 30 no 9 pp 11ndash18 2014

[4] J Wong Terramechanics and Off-Road Vehicle EngineeringTerrain Behaviour Off-Road Vehicle Performance and DesignElsevier 2nd edition 2010

[5] P Garcia J P Torreglosa L M Fernandez and F JuradoldquoControl strategies for high-power electric vehicles powered by

hydrogen fuel cell battery and supercapacitorrdquo Expert Systemswith Applications vol 40 no 12 pp 4791ndash4804 2013

[6] M Sorrentino G Rizzo and I Arsie ldquoAnalysis of a rule-basedcontrol strategy for on-board energy management of serieshybrid vehiclesrdquo Control Engineering Practice vol 19 no 12 pp1433ndash1441 2011

[7] W Shabbir and S A Evangelou ldquoReal-time control strategy tomaximize hybrid electric vehicle powertrain efficiencyrdquoAppliedEnergy vol 135 pp 512ndash522 2014

[8] C Osornio-Correa R Villarreal-Calva J Estavillo-GalsworthyA Molina-Cristobal and S Santillan-Gutierrez ldquoOptimizationof power train and control strategy of a hybrid electric vehiclefor maximum energy economyrdquo Ingenierıa Investigacion yTecnologıa vol 14 no 1 pp 65ndash80 2013

[9] J Wu C-H Zhang and N-X Cui ldquoPSO algorithm-basedparameter optimization for HEV powertrain and its controlstrategyrdquo International Journal of Automotive Technology vol 9no 1 pp 53ndash59 2008

[10] A S Elwer S A Wahsh M O Khalil and A M Nur-EldeenldquoIntelligent fuzzy controller using particle swarm optimizationfor control of permanent magnet synchronous motor forelectric vehiclerdquo in Proceedings of the 29th Annual Conferenceof the IEEE Industrial Electronics Society vol 2 pp 1762ndash1766Roanoke Va USA November 2003

[11] L Qian Z Gong and H Zhao ldquoSimulation of hybrid electricvehicle control strategy based on fuzzy neural networkrdquo Journalof System Simulation vol 18 no 5 pp 1384ndash1387 2006

[12] M Ehsani Y Gao and A Emadi Modern Electric HybridElectric and Fuel Cell Vehicle Fundamentals Theory andDesign CRC Press New York NY USA 2nd edition 2010

[13] J Larminie and J Lowry Electric Vehicle Technology ExplainedJohn Wiley amp Sons New York NY USA 2003

[14] Y Rahmat-Samii ldquoGenetic algorithm (GA) and particle swarmoptimization (PSO) in engineering electromagneticsrdquo in Pro-ceedings of the 17th International Conference on Applied Elec-tromagnetics and Communications pp 1ndash5 Dubrovnik CroatiaOctober 2003

[15] G Tomassetti and L Cagnina ldquoParticle swarm algorithms tosolve engineering problems a comparison of performancerdquoJournal of Engineering vol 2013 Article ID 435104 13 pages2013

[16] Q-N Wang X-Z Tang P-Y Wang and L Sun ldquoControlstrategy of hybrid electric vehicle based on driving intentionidentificationrdquo Journal of Jilin University (Engineering andTechnology Edition) vol 42 no 4 pp 789ndash795 2012

[17] D V McGehee E N Mazzae and G H S Baldwin ldquoDriverreaction time in crash a voidance research validation of adriving simulator study on a test trackrdquo in Proceedings of the 14thTriennial Congress of the International Ergonomics Associationand 44th Annual Meeting of the Human Factors and ErgonomicsSociety vol 44 no 20 pp 320ndash323 Santa Monica Calif USAJuly 2000

[18] Z Zhou Z Fang and W Zhang ldquoComputer aided analysison the theoretical tractive characteristics of tractorrdquo Journal ofLuoyang Institute of Technology vol 14 no 1 pp 1ndash6 1993

[19] B Birge ldquoPSOtmdasha particle swarm optimization toolbox foruse with matlabrdquo in Proceedings of the IEEE Swarm IntelligenceSymposium (SIS rsquo03) pp 182ndash186 Indianapolis Ind USA April2003

[20] Y Shi and R C Eberhart ldquoParameter selection in particleswarm optimizationrdquo in Evolutionary Programming VII 7th


International Conference EP98 San Diego California USAMarch 25ndash27 1998 Proceedings vol 1447 of Lecture Notes inComputer Science pp 591ndash600 Springer Berlin Germany 1998

[21] L-P Zhang H-J Yu and S-X Hu ldquoOptimal choice of param-eters for particle swarm optimizationrdquo Journal of ZhejiangUniversity Science vol 6 no 6 pp 528ndash534 2005

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


vehicles [6] However researches like these only refer to themanagement optimization of energy systems that includedthe battery the electric generator powered by an inter-nal combustion engine (ICE) and other assistance energysources They also do not take electric energy-using deviceinto consideration which means such control strategies arenot suitable for the energy conversion economy improvementof the electric vehicle with a simple energy system such asa purely electric vehicle To account for this Shabbir andEvangelou investigated a real-time control strategy whichuses a control map computed off-line to maximize thedrivetrain efficiency of hybrid electric vehicles [7] Anothercontrol strategy was proposed by Osornio-Correa et al basedon the heuristic map created to analyze the restrictionsand benefits of using either of the on-board power plantsunder different driving conditions for maximum energyeconomy of a parallel hybrid electric vehicle [8] Howeverthose researches lack discussion of how to improve the EMenergy conversion efficiency In addition the establishmentof a control map requires extensive experimental data as apractical foundation (which means it would be difficult touse in product development phases of the vehicle) Wu et aloptimized principal parameters of both the powertrain andthe control strategy using a PSO and achieved an acceptableresult However the optimization of electric motor controlstrategy was also ignored [9] Elwer et al optimized thescaling factors of a fuzzy controller used for enhancingthe rapidity accuracy and robustness of the electric vehiclemotor [10] However the controller is not helpful in theimprovement ofmotor energy conversion efficiency By usingan adaptive network in a fuzzy inference system optimizationalgorithm the strategy put forth by Qian et al made theICE of series hybrid electric vehicle work with high energyconversion efficiency [11] Unfortunately in a series hybridelectric vehicle ICE is mechanically decoupled to the drivewheel and its mechanical power output is not constrainedby load characteristic Therefore the control strategy cannotbe imitatively used in traction motor In an ordinary electricdrivetrain or pure electric vehicle an electric motor works asthe sole energy conversion device so the energy conversionefficiency of the drivetrain (or the vehicle) is only promotedby means of controlling the working state of the electricmotor Nevertheless the energy conversion efficiency of theelectricmotor tightly couples with its rotate speed and torquewhich are also dependent upon the actual driving demandof the vehicle For the road vehicle complex and frequentlychanging road condition means it is impractical that con-trol of the mechanical characteristics of the electric motoris dependent upon its energy conversion efficiency whileneglecting the speed requirements of safety practicabilityand traffic laws However in the agricultural conditions ofthe tractor the frequent change of speed is not required andthe load force is normally stable Therefore we can try tocontrol the electricmotorrsquos running state for improved energyconversion efficiency In summary research on an efficientcontrol strategy for an electric tractor motor is both neededand innovative

This paper begins with establishing the mathematicalmodel that describes the electric-mechanical performance

EM GT MD

MC

ES

Driver

AP

PTOAI



Clutch

Figure 1 Scheme of an electric tractorrsquos drivetrain

and theoretical energy consumption of the electric motoras well as the transmission characteristics of the electrictractorThen it introduces the design of LTCS and how it cancontrol the electricmotor tomaintain high energy conversionefficiency Finally simulation of the traction experiment isconducted to verify the effect and agricultural applicabilityof LTCS

2 Mathematical Model

21 Introduction of the Electric Tractor Drivetrain Althoughthe electric tractor shares many common structural featureswith the common electric vehicle there are some significantdifferences between the two drivetrains Particularly theelectric vehicle layout is organized as shown in Figure 1 Theelectric tractor drivetrain is powered by the energy system(ES)The ES can contain the storage battery in a pure electrictractor or the ICE generator battery super-capacitor and soforth in a hybrid electric tractor The electric motor (EM)provides themechanical power for the drive wheel and powertake-off shaft (PTO) PTO joints with the EM via the clutchWhen the tractor only drives the agricultural implement (AI)the clutch decouples the mechanical connection betweenthe PTO and the drive wheel which makes the mechanicalpower flows of them be independent of each other Thegearbox transmission (GT) can transform the dynamic powerperformance field of the drive wheel via the gear shiftingoperation of driver And the GT directly transmits themechanical power to PTO which can make the rotate speedof PTO match with either the rotate speed of the EM orthe forward velocity of the electric tractor The main drive(MD) acts as the differential mechanism and final reducerof the transmission system By stepping on the acceleratorpedal (AP) the driver can control the EM through electricaladjustment of themotor controller (MC) Generally there aretwo types of load force exerted upon the electric tractor oneis driving force and the other is tilling force

22 Electric-Mechanical Performance of the Electric Motor(EM) According to the previous research the EM is



119880a = 119877s119868a + [(119871a minus 119871m) 119889119868a

119889119905] + 119890a

119880b = 119877s119868b + [(119871b minus 119871m) 119889119868b

119889119905] + 119890b

119880c = 119877s119868c + [(119871c minus 119871m) 119889119868c

119889119905] + 119890c

(1)


119880t = 119877s119868s + [(119871n minus 119871m) 119889119868s

119889119905] + 119890s

119871 s = 119871n minus 119871m

119890s = 119896119864120596r

(2)


119879e =955 (119890a119868a + 119890b119868b + 119890c119868c)

120596r=955119890s119868s120596r

(3)

119879e = 119896119879119868s (4)




119879e = 119879L + 119869119889120596r119889119905+ 119881120596r (5)


120596r (119904) =119896119879

(119877s + 119904119871 s) (119904119869 + 119881) + 119896119864119896119879119880t (119904)

minus119877s + 119904119871 s

(119877s + 119904119871 s) (119904119869 + 119881) + 119896119864119896119879119879L (119904)

(6)


120596r =119896119879

119877s119881 + 119896119864119896119879119880t minus

119877s119877s119881 + 119896119864119896119879

119879L (7)




119875c = 1198682

s 119877s (8)


119875c = 119896c1198792

e (9)


119896c =119877s1198962

119879

(10)


119875i = 119896i120596r (11)



119875M = 119896w1205963

r (12)


119875out =119879L120596r9550

119875in = 119875out + 119875c + 119875i + 119875M + 119862

(13)


120578m =119875out119875in

=119879L120596r

119879L120596r + 9550 [119896c1198792

e + (119896i + 119896w1205962

r ) 120596r + 119862]

(14)





119879L120596r =119879TN120596TN120578g1205780

+119879w120596w1205781015840g120578a

119879L =119879TN119894g1198940120578g1205780

+119879w

1198941015840g119894a1205781015840

g120578a

120596r = 120596TN119894g1198940 = 120596w1198941015840

g119894a

(15)


119865TN = 119865g + 119865f + 119865p + 119865Af + 119865i

119865TN =119879TN

1000119903TN

119865g = 1198851198871ℎk119896

(16)


V = 0377119903120596r120578120575119894g1198940

119865T = 119865TN120578T

120578T = 120578c120578f120578120575

(17)





1 1198832 119883

119899)


119894= (1198831198941 1198831198942 119883





as 119881119894= (1198811198941 1198811198942 119881


119884119894= (1198841198941 1198841198942 119884


119884119892= (1198841198921 1198841198922 119884




119894and


119881120574+1

119894119889= 120576119881120574

119894119889+ 11988811198771(119884120574

119894119889minus 119883120574

119894119889) + 11988821198772(119884120574

119892119889minus 119883120574

119894119889)

119883120574+1

119894119889= 119883120574

119894119889+ 119881120574+1

119894119889

(18)

where 119889 = 1 2 119899 119894 = 1 2 119898 and 1198771and 119877

2are




119889119865T119889V

gt119889V119889119865T

(19)


119889V119889119865T

asymp119889119865T119889V

119889119865T119889V

lt119889V119889119865T

(20)




119879L =119861 minus 119860 sdot 119873



0 10 20 30 40 50 600

10

20

30

40

G

H

I

J

K

L

D

E

F

C

A

B

A-B-CD-E-F

G-H-IJ-K-L

Tractive force (kN)

145Spee

d (k

mmiddothminus1)

dv

dFT=dFTdv

= 1




EM GT MD

MC

AI

ES

Driver

AP

LTCS

CVT Clutch























Hold

Initialization



No

Yes

Yes


ES

PSO search in (14)

Equation (21)


controlTime trigger


No


EM MC

[TL TL + Q]

(120596998400r T998400L)

I998400s U998400t

U998400t


S BM

0020406081

Mem

bers

hip

10 03 04 05 06 07 08 0901 02

Footplate depth





002040608

1

Mem

bers

hip



120576d = 119860 (1 minus 119873) (22)

Collection mode

INIT HOLD

0020406081

Mem

bers

hip

10 03 04 05 06 07 08 0901 02



120576dr =119860 (1 minus 119873)

119905r (23)




002

0406

081

1

050



02

03

04

05

06

07

08

Col

lect

ion

mod

e









120575 = 120575lowastLn


(24)


120575and 120575 is 120578





Number 119885 119887l ℎk0 7 35 301 6 35 302 5 32 253 4 35 254 4 40 315 3 30 206 3 35 227 1 50 20



Vehicle


119871 285mℎT 16m119866 11264 kN119903TN 09m119886 197m

GT


120578g 9604

EM




00543Vsdotminr119896119879

05186NsdotmA119862 021 kW

MD 1198940

321205780

98

AP 119860 54∘119873 015


120578c = 1205780120578g

120578f =119866119891

119865TN

(25)




0 100 200 300 400 600 800

Heavy load scope

Moderate load scope

Light load scope

Transport scope

Gear shifting point


Time (s)

0500 700

1 2 3 4 5 6 70

10

20

30

40

50

60

70

Equi

vale

nt re

sista

nce (

kN)


0 10 20 30 40 50 60 70 8060

70

80

90

100

Slip

effici

ency120578120575

()







119881119894max = 120582119883119894max

1198881= 1198882=120593

2

(26)




1198831max = 119877119879 = (119879L 119879L + 05)

1198832max = 119877MAV = (0

9550119875r119879L

)

(27)






0 2000 4000 60000 20 40 60 80 100Evolution times

38


0

200

400

10minus003445

10minus003444

10minus003443

10minus003442

10minus003441

Valu

e of fi

tnes

s deg

ree 0923838 = fbest(367697 256339)

120596998400 r

T998400L


0 2000 40000

100

200

300

400

Valu

e of fi

tnes

s deg

ree



10minus00324

10minus00323

0928384 = fbest(286437 2188)

120596998400 r

T998400L


0 100 200 300 400 500 600 700 800Time (s)

0

1





1015840




050

100150200250300350400450

Volta

ge (V

)

200220240260280300320340360380400

Curr

ent (

A)

100 200 300 400 500 600 700 8000Time (s)


60708085

90

92925

91

D

E

A

B


0

1

2

3

4

5

6

7

8

9


Spee

d (k

mmiddothminus1)






607080

90

85

9192

925

93

D

E

H

G

F


0

2

4

6

8

10

12

14

16


Spee

d (k

mmiddothminus1)


8 10 12 14 16 18 20 22 24 2660

7080

85

85

9091

92 925

93

GJ

H

K

Tractive force (kN)

0

5

10

15

20

25


Spee

d (k

mmiddothminus1)





607080

85

9190

92925

J

L

K

0

5

10

15

20

25

30

35

40




Spee

d (k

mmiddothminus1)







A B

LTCSLTFC

100 200 300 400 500 6000 700 800Time (s)

09

0905

091

0915

092

0925

093

0935

Ener

gy co

nver

sion

effici

ency


131

108

LTCSLTFC

60708090

100110120130140150

Elec

tric

pow

er (k

W)

100 200 300 400 500 600 700 8000Time (s)









5 Conclusion


Nomenclature
















Abbreviations


Competing Interests


Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119880a = 119877s119868a + [(119871a minus 119871m) 119889119868a

119889119905] + 119890a

119880b = 119877s119868b + [(119871b minus 119871m) 119889119868b

119889119905] + 119890b

119880c = 119877s119868c + [(119871c minus 119871m) 119889119868c

119889119905] + 119890c

(1)


119880t = 119877s119868s + [(119871n minus 119871m) 119889119868s

119889119905] + 119890s

119871 s = 119871n minus 119871m

119890s = 119896119864120596r

(2)


119879e =955 (119890a119868a + 119890b119868b + 119890c119868c)

120596r=955119890s119868s120596r

(3)

119879e = 119896119879119868s (4)




119879e = 119879L + 119869119889120596r119889119905+ 119881120596r (5)


120596r (119904) =119896119879

(119877s + 119904119871 s) (119904119869 + 119881) + 119896119864119896119879119880t (119904)

minus119877s + 119904119871 s

(119877s + 119904119871 s) (119904119869 + 119881) + 119896119864119896119879119879L (119904)

(6)


120596r =119896119879

119877s119881 + 119896119864119896119879119880t minus

119877s119877s119881 + 119896119864119896119879

119879L (7)




119875c = 1198682

s 119877s (8)


119875c = 119896c1198792

e (9)


119896c =119877s1198962

119879

(10)


119875i = 119896i120596r (11)



119875M = 119896w1205963

r (12)


119875out =119879L120596r9550

119875in = 119875out + 119875c + 119875i + 119875M + 119862

(13)


120578m =119875out119875in

=119879L120596r

119879L120596r + 9550 [119896c1198792

e + (119896i + 119896w1205962

r ) 120596r + 119862]

(14)





119879L120596r =119879TN120596TN120578g1205780

+119879w120596w1205781015840g120578a

119879L =119879TN119894g1198940120578g1205780

+119879w

1198941015840g119894a1205781015840

g120578a

120596r = 120596TN119894g1198940 = 120596w1198941015840

g119894a

(15)


119865TN = 119865g + 119865f + 119865p + 119865Af + 119865i

119865TN =119879TN

1000119903TN

119865g = 1198851198871ℎk119896

(16)


V = 0377119903120596r120578120575119894g1198940

119865T = 119865TN120578T

120578T = 120578c120578f120578120575

(17)





1 1198832 119883

119899)


119894= (1198831198941 1198831198942 119883





as 119881119894= (1198811198941 1198811198942 119881


119884119894= (1198841198941 1198841198942 119884


119884119892= (1198841198921 1198841198922 119884




119894and


119881120574+1

119894119889= 120576119881120574

119894119889+ 11988811198771(119884120574

119894119889minus 119883120574

119894119889) + 11988821198772(119884120574

119892119889minus 119883120574

119894119889)

119883120574+1

119894119889= 119883120574

119894119889+ 119881120574+1

119894119889

(18)

where 119889 = 1 2 119899 119894 = 1 2 119898 and 1198771and 119877

2are




119889119865T119889V

gt119889V119889119865T

(19)


119889V119889119865T

asymp119889119865T119889V

119889119865T119889V

lt119889V119889119865T

(20)




119879L =119861 minus 119860 sdot 119873



0 10 20 30 40 50 600

10

20

30

40

G

H

I

J

K

L

D

E

F

C

A

B

A-B-CD-E-F

G-H-IJ-K-L

Tractive force (kN)

145Spee

d (k

mmiddothminus1)

dv

dFT=dFTdv

= 1




EM GT MD

MC

AI

ES

Driver

AP

LTCS

CVT Clutch























Hold

Initialization



No

Yes

Yes


ES

PSO search in (14)

Equation (21)


controlTime trigger


No


EM MC

[TL TL + Q]

(120596998400r T998400L)

I998400s U998400t

U998400t


S BM

0020406081

Mem

bers

hip

10 03 04 05 06 07 08 0901 02

Footplate depth





002040608

1

Mem

bers

hip



120576d = 119860 (1 minus 119873) (22)

Collection mode

INIT HOLD

0020406081

Mem

bers

hip

10 03 04 05 06 07 08 0901 02



120576dr =119860 (1 minus 119873)

119905r (23)




002

0406

081

1

050



02

03

04

05

06

07

08

Col

lect

ion

mod

e









120575 = 120575lowastLn


(24)


120575and 120575 is 120578





Number 119885 119887l ℎk0 7 35 301 6 35 302 5 32 253 4 35 254 4 40 315 3 30 206 3 35 227 1 50 20



Vehicle


119871 285mℎT 16m119866 11264 kN119903TN 09m119886 197m

GT


120578g 9604

EM




00543Vsdotminr119896119879

05186NsdotmA119862 021 kW

MD 1198940

321205780

98

AP 119860 54∘119873 015


120578c = 1205780120578g

120578f =119866119891

119865TN

(25)




0 100 200 300 400 600 800

Heavy load scope

Moderate load scope

Light load scope

Transport scope

Gear shifting point


Time (s)

0500 700

1 2 3 4 5 6 70

10

20

30

40

50

60

70

Equi

vale

nt re

sista

nce (

kN)


0 10 20 30 40 50 60 70 8060

70

80

90

100

Slip

effici

ency120578120575

()







119881119894max = 120582119883119894max

1198881= 1198882=120593

2

(26)




1198831max = 119877119879 = (119879L 119879L + 05)

1198832max = 119877MAV = (0

9550119875r119879L

)

(27)






0 2000 4000 60000 20 40 60 80 100Evolution times

38


0

200

400

10minus003445

10minus003444

10minus003443

10minus003442

10minus003441

Valu

e of fi

tnes

s deg

ree 0923838 = fbest(367697 256339)

120596998400 r

T998400L


0 2000 40000

100

200

300

400

Valu

e of fi

tnes

s deg

ree



10minus00324

10minus00323

0928384 = fbest(286437 2188)

120596998400 r

T998400L


0 100 200 300 400 500 600 700 800Time (s)

0

1





1015840




050

100150200250300350400450

Volta

ge (V

)

200220240260280300320340360380400

Curr

ent (

A)

100 200 300 400 500 600 700 8000Time (s)


60708085

90

92925

91

D

E

A

B


0

1

2

3

4

5

6

7

8

9


Spee

d (k

mmiddothminus1)






607080

90

85

9192

925

93

D

E

H

G

F


0

2

4

6

8

10

12

14

16


Spee

d (k

mmiddothminus1)


8 10 12 14 16 18 20 22 24 2660

7080

85

85

9091

92 925

93

GJ

H

K

Tractive force (kN)

0

5

10

15

20

25


Spee

d (k

mmiddothminus1)





607080

85

9190

92925

J

L

K

0

5

10

15

20

25

30

35

40




Spee

d (k

mmiddothminus1)







A B

LTCSLTFC

100 200 300 400 500 6000 700 800Time (s)

09

0905

091

0915

092

0925

093

0935

Ener

gy co

nver

sion

effici

ency


131

108

LTCSLTFC

60708090

100110120130140150

Elec

tric

pow

er (k

W)

100 200 300 400 500 600 700 8000Time (s)









5 Conclusion


Nomenclature
















Abbreviations


Competing Interests


Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119879L120596r =119879TN120596TN120578g1205780

+119879w120596w1205781015840g120578a

119879L =119879TN119894g1198940120578g1205780

+119879w

1198941015840g119894a1205781015840

g120578a

120596r = 120596TN119894g1198940 = 120596w1198941015840

g119894a

(15)


119865TN = 119865g + 119865f + 119865p + 119865Af + 119865i

119865TN =119879TN

1000119903TN

119865g = 1198851198871ℎk119896

(16)


V = 0377119903120596r120578120575119894g1198940

119865T = 119865TN120578T

120578T = 120578c120578f120578120575

(17)





1 1198832 119883

119899)


119894= (1198831198941 1198831198942 119883





as 119881119894= (1198811198941 1198811198942 119881


119884119894= (1198841198941 1198841198942 119884


119884119892= (1198841198921 1198841198922 119884




119894and


119881120574+1

119894119889= 120576119881120574

119894119889+ 11988811198771(119884120574

119894119889minus 119883120574

119894119889) + 11988821198772(119884120574

119892119889minus 119883120574

119894119889)

119883120574+1

119894119889= 119883120574

119894119889+ 119881120574+1

119894119889

(18)

where 119889 = 1 2 119899 119894 = 1 2 119898 and 1198771and 119877

2are




119889119865T119889V

gt119889V119889119865T

(19)


119889V119889119865T

asymp119889119865T119889V

119889119865T119889V

lt119889V119889119865T

(20)




119879L =119861 minus 119860 sdot 119873



0 10 20 30 40 50 600

10

20

30

40

G

H

I

J

K

L

D

E

F

C

A

B

A-B-CD-E-F

G-H-IJ-K-L

Tractive force (kN)

145Spee

d (k

mmiddothminus1)

dv

dFT=dFTdv

= 1




EM GT MD

MC

AI

ES

Driver

AP

LTCS

CVT Clutch























Hold

Initialization



No

Yes

Yes


ES

PSO search in (14)

Equation (21)


controlTime trigger


No


EM MC

[TL TL + Q]

(120596998400r T998400L)

I998400s U998400t

U998400t


S BM

0020406081

Mem

bers

hip

10 03 04 05 06 07 08 0901 02

Footplate depth





002040608

1

Mem

bers

hip



120576d = 119860 (1 minus 119873) (22)

Collection mode

INIT HOLD

0020406081

Mem

bers

hip

10 03 04 05 06 07 08 0901 02



120576dr =119860 (1 minus 119873)

119905r (23)




002

0406

081

1

050



02

03

04

05

06

07

08

Col

lect

ion

mod

e









120575 = 120575lowastLn


(24)


120575and 120575 is 120578





Number 119885 119887l ℎk0 7 35 301 6 35 302 5 32 253 4 35 254 4 40 315 3 30 206 3 35 227 1 50 20



Vehicle


119871 285mℎT 16m119866 11264 kN119903TN 09m119886 197m

GT


120578g 9604

EM




00543Vsdotminr119896119879

05186NsdotmA119862 021 kW

MD 1198940

321205780

98

AP 119860 54∘119873 015


120578c = 1205780120578g

120578f =119866119891

119865TN

(25)




0 100 200 300 400 600 800

Heavy load scope

Moderate load scope

Light load scope

Transport scope

Gear shifting point


Time (s)

0500 700

1 2 3 4 5 6 70

10

20

30

40

50

60

70

Equi

vale

nt re

sista

nce (

kN)


0 10 20 30 40 50 60 70 8060

70

80

90

100

Slip

effici

ency120578120575

()







119881119894max = 120582119883119894max

1198881= 1198882=120593

2

(26)




1198831max = 119877119879 = (119879L 119879L + 05)

1198832max = 119877MAV = (0

9550119875r119879L

)

(27)






0 2000 4000 60000 20 40 60 80 100Evolution times

38


0

200

400

10minus003445

10minus003444

10minus003443

10minus003442

10minus003441

Valu

e of fi

tnes

s deg

ree 0923838 = fbest(367697 256339)

120596998400 r

T998400L


0 2000 40000

100

200

300

400

Valu

e of fi

tnes

s deg

ree



10minus00324

10minus00323

0928384 = fbest(286437 2188)

120596998400 r

T998400L


0 100 200 300 400 500 600 700 800Time (s)

0

1





1015840




050

100150200250300350400450

Volta

ge (V

)

200220240260280300320340360380400

Curr

ent (

A)

100 200 300 400 500 600 700 8000Time (s)


60708085

90

92925

91

D

E

A

B


0

1

2

3

4

5

6

7

8

9


Spee

d (k

mmiddothminus1)






607080

90

85

9192

925

93

D

E

H

G

F


0

2

4

6

8

10

12

14

16


Spee

d (k

mmiddothminus1)


8 10 12 14 16 18 20 22 24 2660

7080

85

85

9091

92 925

93

GJ

H

K

Tractive force (kN)

0

5

10

15

20

25


Spee

d (k

mmiddothminus1)





607080

85

9190

92925

J

L

K

0

5

10

15

20

25

30

35

40




Spee

d (k

mmiddothminus1)







A B

LTCSLTFC

100 200 300 400 500 6000 700 800Time (s)

09

0905

091

0915

092

0925

093

0935

Ener

gy co

nver

sion

effici

ency


131

108

LTCSLTFC

60708090

100110120130140150

Elec

tric

pow

er (k

W)

100 200 300 400 500 600 700 8000Time (s)









5 Conclusion


Nomenclature
















Abbreviations


Competing Interests


Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 10 20 30 40 50 600

10

20

30

40

G

H

I

J

K

L

D

E

F

C

A

B

A-B-CD-E-F

G-H-IJ-K-L

Tractive force (kN)

145Spee

d (k

mmiddothminus1)

dv

dFT=dFTdv

= 1




EM GT MD

MC

AI

ES

Driver

AP

LTCS

CVT Clutch























Hold

Initialization



No

Yes

Yes


ES

PSO search in (14)

Equation (21)


controlTime trigger


No


EM MC

[TL TL + Q]

(120596998400r T998400L)

I998400s U998400t

U998400t


S BM

0020406081

Mem

bers

hip

10 03 04 05 06 07 08 0901 02

Footplate depth





002040608

1

Mem

bers

hip



120576d = 119860 (1 minus 119873) (22)

Collection mode

INIT HOLD

0020406081

Mem

bers

hip

10 03 04 05 06 07 08 0901 02



120576dr =119860 (1 minus 119873)

119905r (23)




002

0406

081

1

050



02

03

04

05

06

07

08

Col

lect

ion

mod

e









120575 = 120575lowastLn


(24)


120575and 120575 is 120578





Number 119885 119887l ℎk0 7 35 301 6 35 302 5 32 253 4 35 254 4 40 315 3 30 206 3 35 227 1 50 20



Vehicle


119871 285mℎT 16m119866 11264 kN119903TN 09m119886 197m

GT


120578g 9604

EM




00543Vsdotminr119896119879

05186NsdotmA119862 021 kW

MD 1198940

321205780

98

AP 119860 54∘119873 015


120578c = 1205780120578g

120578f =119866119891

119865TN

(25)




0 100 200 300 400 600 800

Heavy load scope

Moderate load scope

Light load scope

Transport scope

Gear shifting point


Time (s)

0500 700

1 2 3 4 5 6 70

10

20

30

40

50

60

70

Equi

vale

nt re

sista

nce (

kN)


0 10 20 30 40 50 60 70 8060

70

80

90

100

Slip

effici

ency120578120575

()







119881119894max = 120582119883119894max

1198881= 1198882=120593

2

(26)




1198831max = 119877119879 = (119879L 119879L + 05)

1198832max = 119877MAV = (0

9550119875r119879L

)

(27)






0 2000 4000 60000 20 40 60 80 100Evolution times

38


0

200

400

10minus003445

10minus003444

10minus003443

10minus003442

10minus003441

Valu

e of fi

tnes

s deg

ree 0923838 = fbest(367697 256339)

120596998400 r

T998400L


0 2000 40000

100

200

300

400

Valu

e of fi

tnes

s deg

ree



10minus00324

10minus00323

0928384 = fbest(286437 2188)

120596998400 r

T998400L


0 100 200 300 400 500 600 700 800Time (s)

0

1





1015840




050

100150200250300350400450

Volta

ge (V

)

200220240260280300320340360380400

Curr

ent (

A)

100 200 300 400 500 600 700 8000Time (s)


60708085

90

92925

91

D

E

A

B


0

1

2

3

4

5

6

7

8

9


Spee

d (k

mmiddothminus1)






607080

90

85

9192

925

93

D

E

H

G

F


0

2

4

6

8

10

12

14

16


Spee

d (k

mmiddothminus1)


8 10 12 14 16 18 20 22 24 2660

7080

85

85

9091

92 925

93

GJ

H

K

Tractive force (kN)

0

5

10

15

20

25


Spee

d (k

mmiddothminus1)





607080

85

9190

92925

J

L

K

0

5

10

15

20

25

30

35

40




Spee

d (k

mmiddothminus1)







A B

LTCSLTFC

100 200 300 400 500 6000 700 800Time (s)

09

0905

091

0915

092

0925

093

0935

Ener

gy co

nver

sion

effici

ency


131

108

LTCSLTFC

60708090

100110120130140150

Elec

tric

pow

er (k

W)

100 200 300 400 500 600 700 8000Time (s)









5 Conclusion


Nomenclature
















Abbreviations


Competing Interests


Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Hold

Initialization



No

Yes

Yes


ES

PSO search in (14)

Equation (21)


controlTime trigger


No


EM MC

[TL TL + Q]

(120596998400r T998400L)

I998400s U998400t

U998400t


S BM

0020406081

Mem

bers

hip

10 03 04 05 06 07 08 0901 02

Footplate depth





002040608

1

Mem

bers

hip



120576d = 119860 (1 minus 119873) (22)

Collection mode

INIT HOLD

0020406081

Mem

bers

hip

10 03 04 05 06 07 08 0901 02



120576dr =119860 (1 minus 119873)

119905r (23)




002

0406

081

1

050



02

03

04

05

06

07

08

Col

lect

ion

mod

e









120575 = 120575lowastLn


(24)


120575and 120575 is 120578





Number 119885 119887l ℎk0 7 35 301 6 35 302 5 32 253 4 35 254 4 40 315 3 30 206 3 35 227 1 50 20



Vehicle


119871 285mℎT 16m119866 11264 kN119903TN 09m119886 197m

GT


120578g 9604

EM




00543Vsdotminr119896119879

05186NsdotmA119862 021 kW

MD 1198940

321205780

98

AP 119860 54∘119873 015


120578c = 1205780120578g

120578f =119866119891

119865TN

(25)




0 100 200 300 400 600 800

Heavy load scope

Moderate load scope

Light load scope

Transport scope

Gear shifting point


Time (s)

0500 700

1 2 3 4 5 6 70

10

20

30

40

50

60

70

Equi

vale

nt re

sista

nce (

kN)


0 10 20 30 40 50 60 70 8060

70

80

90

100

Slip

effici

ency120578120575

()







119881119894max = 120582119883119894max

1198881= 1198882=120593

2

(26)




1198831max = 119877119879 = (119879L 119879L + 05)

1198832max = 119877MAV = (0

9550119875r119879L

)

(27)






0 2000 4000 60000 20 40 60 80 100Evolution times

38


0

200

400

10minus003445

10minus003444

10minus003443

10minus003442

10minus003441

Valu

e of fi

tnes

s deg

ree 0923838 = fbest(367697 256339)

120596998400 r

T998400L


0 2000 40000

100

200

300

400

Valu

e of fi

tnes

s deg

ree



10minus00324

10minus00323

0928384 = fbest(286437 2188)

120596998400 r

T998400L


0 100 200 300 400 500 600 700 800Time (s)

0

1





1015840




050

100150200250300350400450

Volta

ge (V

)

200220240260280300320340360380400

Curr

ent (

A)

100 200 300 400 500 600 700 8000Time (s)


60708085

90

92925

91

D

E

A

B


0

1

2

3

4

5

6

7

8

9


Spee

d (k

mmiddothminus1)






607080

90

85

9192

925

93

D

E

H

G

F


0

2

4

6

8

10

12

14

16


Spee

d (k

mmiddothminus1)


8 10 12 14 16 18 20 22 24 2660

7080

85

85

9091

92 925

93

GJ

H

K

Tractive force (kN)

0

5

10

15

20

25


Spee

d (k

mmiddothminus1)





607080

85

9190

92925

J

L

K

0

5

10

15

20

25

30

35

40




Spee

d (k

mmiddothminus1)







A B

LTCSLTFC

100 200 300 400 500 6000 700 800Time (s)

09

0905

091

0915

092

0925

093

0935

Ener

gy co

nver

sion

effici

ency


131

108

LTCSLTFC

60708090

100110120130140150

Elec

tric

pow

er (k

W)

100 200 300 400 500 600 700 8000Time (s)









5 Conclusion


Nomenclature
















Abbreviations


Competing Interests


Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










002

0406

081

1

050



02

03

04

05

06

07

08

Col

lect

ion

mod

e









120575 = 120575lowastLn


(24)


120575and 120575 is 120578





Number 119885 119887l ℎk0 7 35 301 6 35 302 5 32 253 4 35 254 4 40 315 3 30 206 3 35 227 1 50 20



Vehicle


119871 285mℎT 16m119866 11264 kN119903TN 09m119886 197m

GT


120578g 9604

EM




00543Vsdotminr119896119879

05186NsdotmA119862 021 kW

MD 1198940

321205780

98

AP 119860 54∘119873 015


120578c = 1205780120578g

120578f =119866119891

119865TN

(25)




0 100 200 300 400 600 800

Heavy load scope

Moderate load scope

Light load scope

Transport scope

Gear shifting point


Time (s)

0500 700

1 2 3 4 5 6 70

10

20

30

40

50

60

70

Equi

vale

nt re

sista

nce (

kN)


0 10 20 30 40 50 60 70 8060

70

80

90

100

Slip

effici

ency120578120575

()







119881119894max = 120582119883119894max

1198881= 1198882=120593

2

(26)




1198831max = 119877119879 = (119879L 119879L + 05)

1198832max = 119877MAV = (0

9550119875r119879L

)

(27)






0 2000 4000 60000 20 40 60 80 100Evolution times

38


0

200

400

10minus003445

10minus003444

10minus003443

10minus003442

10minus003441

Valu

e of fi

tnes

s deg

ree 0923838 = fbest(367697 256339)

120596998400 r

T998400L


0 2000 40000

100

200

300

400

Valu

e of fi

tnes

s deg

ree



10minus00324

10minus00323

0928384 = fbest(286437 2188)

120596998400 r

T998400L


0 100 200 300 400 500 600 700 800Time (s)

0

1





1015840




050

100150200250300350400450

Volta

ge (V

)

200220240260280300320340360380400

Curr

ent (

A)

100 200 300 400 500 600 700 8000Time (s)


60708085

90

92925

91

D

E

A

B


0

1

2

3

4

5

6

7

8

9


Spee

d (k

mmiddothminus1)






607080

90

85

9192

925

93

D

E

H

G

F


0

2

4

6

8

10

12

14

16


Spee

d (k

mmiddothminus1)


8 10 12 14 16 18 20 22 24 2660

7080

85

85

9091

92 925

93

GJ

H

K

Tractive force (kN)

0

5

10

15

20

25


Spee

d (k

mmiddothminus1)





607080

85

9190

92925

J

L

K

0

5

10

15

20

25

30

35

40




Spee

d (k

mmiddothminus1)







A B

LTCSLTFC

100 200 300 400 500 6000 700 800Time (s)

09

0905

091

0915

092

0925

093

0935

Ener

gy co

nver

sion

effici

ency


131

108

LTCSLTFC

60708090

100110120130140150

Elec

tric

pow

er (k

W)

100 200 300 400 500 600 700 8000Time (s)









5 Conclusion


Nomenclature
















Abbreviations


Competing Interests


Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 100 200 300 400 600 800

Heavy load scope

Moderate load scope

Light load scope

Transport scope

Gear shifting point


Time (s)

0500 700

1 2 3 4 5 6 70

10

20

30

40

50

60

70

Equi

vale

nt re

sista

nce (

kN)


0 10 20 30 40 50 60 70 8060

70

80

90

100

Slip

effici

ency120578120575

()







119881119894max = 120582119883119894max

1198881= 1198882=120593

2

(26)




1198831max = 119877119879 = (119879L 119879L + 05)

1198832max = 119877MAV = (0

9550119875r119879L

)

(27)






0 2000 4000 60000 20 40 60 80 100Evolution times

38


0

200

400

10minus003445

10minus003444

10minus003443

10minus003442

10minus003441

Valu

e of fi

tnes

s deg

ree 0923838 = fbest(367697 256339)

120596998400 r

T998400L


0 2000 40000

100

200

300

400

Valu

e of fi

tnes

s deg

ree



10minus00324

10minus00323

0928384 = fbest(286437 2188)

120596998400 r

T998400L


0 100 200 300 400 500 600 700 800Time (s)

0

1





1015840




050

100150200250300350400450

Volta

ge (V

)

200220240260280300320340360380400

Curr

ent (

A)

100 200 300 400 500 600 700 8000Time (s)


60708085

90

92925

91

D

E

A

B


0

1

2

3

4

5

6

7

8

9


Spee

d (k

mmiddothminus1)






607080

90

85

9192

925

93

D

E

H

G

F


0

2

4

6

8

10

12

14

16


Spee

d (k

mmiddothminus1)


8 10 12 14 16 18 20 22 24 2660

7080

85

85

9091

92 925

93

GJ

H

K

Tractive force (kN)

0

5

10

15

20

25


Spee

d (k

mmiddothminus1)





607080

85

9190

92925

J

L

K

0

5

10

15

20

25

30

35

40




Spee

d (k

mmiddothminus1)







A B

LTCSLTFC

100 200 300 400 500 6000 700 800Time (s)

09

0905

091

0915

092

0925

093

0935

Ener

gy co

nver

sion

effici

ency


131

108

LTCSLTFC

60708090

100110120130140150

Elec

tric

pow

er (k

W)

100 200 300 400 500 600 700 8000Time (s)









5 Conclusion


Nomenclature
















Abbreviations


Competing Interests


Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 2000 4000 60000 20 40 60 80 100Evolution times

38


0

200

400

10minus003445

10minus003444

10minus003443

10minus003442

10minus003441

Valu

e of fi

tnes

s deg

ree 0923838 = fbest(367697 256339)

120596998400 r

T998400L


0 2000 40000

100

200

300

400

Valu

e of fi

tnes

s deg

ree



10minus00324

10minus00323

0928384 = fbest(286437 2188)

120596998400 r

T998400L


0 100 200 300 400 500 600 700 800Time (s)

0

1





1015840




050

100150200250300350400450

Volta

ge (V

)

200220240260280300320340360380400

Curr

ent (

A)

100 200 300 400 500 600 700 8000Time (s)


60708085

90

92925

91

D

E

A

B


0

1

2

3

4

5

6

7

8

9


Spee

d (k

mmiddothminus1)






607080

90

85

9192

925

93

D

E

H

G

F


0

2

4

6

8

10

12

14

16


Spee

d (k

mmiddothminus1)


8 10 12 14 16 18 20 22 24 2660

7080

85

85

9091

92 925

93

GJ

H

K

Tractive force (kN)

0

5

10

15

20

25


Spee

d (k

mmiddothminus1)





607080

85

9190

92925

J

L

K

0

5

10

15

20

25

30

35

40




Spee

d (k

mmiddothminus1)







A B

LTCSLTFC

100 200 300 400 500 6000 700 800Time (s)

09

0905

091

0915

092

0925

093

0935

Ener

gy co

nver

sion

effici

ency


131

108

LTCSLTFC

60708090

100110120130140150

Elec

tric

pow

er (k

W)

100 200 300 400 500 600 700 8000Time (s)









5 Conclusion


Nomenclature
















Abbreviations


Competing Interests


Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










050

100150200250300350400450

Volta

ge (V

)

200220240260280300320340360380400

Curr

ent (

A)

100 200 300 400 500 600 700 8000Time (s)


60708085

90

92925

91

D

E

A

B


0

1

2

3

4

5

6

7

8

9


Spee

d (k

mmiddothminus1)






607080

90

85

9192

925

93

D

E

H

G

F


0

2

4

6

8

10

12

14

16


Spee

d (k

mmiddothminus1)


8 10 12 14 16 18 20 22 24 2660

7080

85

85

9091

92 925

93

GJ

H

K

Tractive force (kN)

0

5

10

15

20

25


Spee

d (k

mmiddothminus1)





607080

85

9190

92925

J

L

K

0

5

10

15

20

25

30

35

40




Spee

d (k

mmiddothminus1)







A B

LTCSLTFC

100 200 300 400 500 6000 700 800Time (s)

09

0905

091

0915

092

0925

093

0935

Ener

gy co

nver

sion

effici

ency


131

108

LTCSLTFC

60708090

100110120130140150

Elec

tric

pow

er (k

W)

100 200 300 400 500 600 700 8000Time (s)









5 Conclusion


Nomenclature
















Abbreviations


Competing Interests


Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










607080

85

9190

92925

J

L

K

0

5

10

15

20

25

30

35

40




Spee

d (k

mmiddothminus1)







A B

LTCSLTFC

100 200 300 400 500 6000 700 800Time (s)

09

0905

091

0915

092

0925

093

0935

Ener

gy co

nver

sion

effici

ency


131

108

LTCSLTFC

60708090

100110120130140150

Elec

tric

pow

er (k

W)

100 200 300 400 500 600 700 8000Time (s)









5 Conclusion


Nomenclature
















Abbreviations


Competing Interests


Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












5 Conclusion


Nomenclature
















Abbreviations


Competing Interests


Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Abbreviations


Competing Interests


Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra



















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article design of a load torque based control strategy...

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