Research Article Sliding Mode Variable Structure Control...

Research ArticleSliding Mode Variable Structure Control andReal-Time Optimization of Dry Dual Clutch Transmissionduring the Vehiclersquos Launch

Zhiguo Zhao Haijun Chen and Qi Wang

School of Automotive Studies Tongji University Shanghai 201804 China

Correspondence should be addressed to Zhiguo Zhao zhiguozhaotongjieducn

Received 19 September 2013 Revised 5 November 2013 Accepted 5 November 2013 Published 2 February 2014

Academic Editor Hui Zhang

Copyright copy 2014 Zhiguo Zhao 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 reflect driving intention adequately and improve the launch performance of vehicle equipped with five-speed drydual clutch transmission (DCT) the issue of coordinating control between engine and clutch is researched which is based onthe DCT and prototype car developed independently Four-degree-of-freedom (DOF) launch dynamics equations are establishedTaking advantage of predictive control and genetic algorithm target tracing curves of engine speed and vehicle velocity areoptimally specified Slidingmode variable structure (SMVS) control strategy is designed to track these curvesThe rapid prototypingexperiment and test are respectively conducted on the DCT test bench and in the chassis dynamometer Results show that thedesigned SMVS control strategy not only effectively embodies the driverrsquos intention but also has strong robustness to the vehicleparameterrsquos variations

1 Introduction

Based on the automated mechanical transmission (AMT)if remodelling its transmission mechanism (including inputshaft positions of gear pairs and intermediate shaft) andadding a set of dry friction clutch and corresponding actuatordry dual clutch transmission (DCT) can be constructed Theproblem of traction interruption while gear shifting canalso be resolved effectively through the coordinating controlbetween two clutches and engine So the quality of shiftingand the power performance of vehicle can also be improved

As to the launch process of vehicle equipped with dryDCT single or double clutches can be adopted to launchLaunching with double clutches aims at balancing the slidingfriction work of twin clutches and lengthening their servicelife [1 2] but dual clutches participation mode can easilylead to power cycling inside the DCT so its feasibilityrequires further investigation By contrast when single clutchis involved the launch dynamics model and control logic ofDCT are the same as the AMTrsquos because the launch mod-elling and controlling of vehicle equipped with AMT have

been studied widely and profoundly Two degree-of-freedom(DOF) dynamics model has been set up and the optimalclutch engaging control law via minimum principle has beenfounded [3 4] Quadratic optimal launch controller has beendesigned and equivalent damping of AMT transmission hasalso been taken into account [5 6] Six-DOF launch dynamicsequations and clutchrsquos hydraulic actuator model have beenestablishedThe correspondingmodelrsquos parameters have beenalso obtained through experiments [7] Five-DOF launchmodel has been established and simplified and engine speeddecoupling control strategy has also been put forward [8]In addition fuzzy logic control method for the launchingprocess of AMT based on experience has been studied largelyand fuzzy input variables could be the accelerator pedalopening and its changing rate [9] or the deviation and itschanging rate between engine speed and target speed relatedto accelerator pedal [10] or the rotary speed differencebetween clutch driving plate and driven plate [11] Generallyoutput variables could be clutch engaging speed geneticalgorithm has been further used to optimize the fuzzy ruleset [12] Moreover in the aspect of launch control for vehicle

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 494731 18 pageshttpdxdoiorg1011552014494731

2 Mathematical Problems in Engineering

I

1st gears

2nd gears4th gears

3rd gears

5th gears

Clutch 1

Clutch 2

Reverse gears

(solid shaft)

Synchronizer 1

Synchronizer 2

Synchronizer 3

Synchronizer 4

Engine

Intermediate shaft

(hollow shaft)

Output shaft

Vehiclei4

i5

120596c1

Tc1

Ic1

bc1

120596c2

Tc2

Ic2bc2

120596e

Te

Ie

be

120596m

TsmIm

bs

120596s

Tf

iabm

Ig1

Ig2

Ig3

Ig4

Ig5

Igr

i1

i2

i3

Tmc1

Tmc2

Tcm1 or Tcm2

Tms

Input shaft NO1

Input shaft NO2

Figure 1 Five-speed dry DCT dynamic model

equipped with DCT clutch optimal engaging control lawhas been introduced by utilizing minimum principle andsynthetically taking shock intensity sliding friction workand engine output torque into consideration [13] Linearquadratic optimal control has been applied to simulate clutchengaging pressure in the launching process [14 15] Launchfuzzy intelligent control algorithm has been designed andoptimized by using accelerator pedal opening and its chang-ing rate clutch relative slip rate and engine speed differenceto describe the driving intention clutch engaging states andengine working condition respectively [16] Comparativelydouble-layer fuzzy intelligent control architecture has beenpresented by setting up clutch engaging fuzzy control rulesand real car chassis dynamometer test has been conducted[17]

But the above stated studies only focus on the control ofclutch engaging control rules rarely taking consideration ofthe issue of coordinating control between engine and clutchduring the vehiclersquos launch process and let alone the qualifi-cation of driverrsquos intention

Taking the factors such as driverrsquos intention enginecondition clutch state and shock intensity into account theissue of coordinating control between engine and clutch isinvestigated in the paper which is based on the DCT andprototype car developed independently Four degrees of free-dom (DOF) launch dynamics equations are established Thecomputational formulas of engine speed and clutch transfertorque in the launching process have also been quantifiedand given Taking advantage of predictive control and geneticalgorithm target tracing curves of engine speed and vehiclevelocity are optimally specified Sliding mode variable struc-ture (SMVS) control strategy has been designed to track thesecurves Based on the MatlabSimulink software platform andthe hardware-in-the-loop test bench the launch performanceof prototype car equipped with dry DCT has been simulatedunder different driving conditions and the rapid prototyping

experiment and test are respectively conducted on the DCTtest bench and in the chassis dynamometer

2 Mathematical Models

21 Five-Speed Dry DCT Dynamic Model The five-speeddry DCT described in the paper is made up of dry dualclutch module and its actuator four synchronizers and theiractuators and single intermediate shaft gear transmissionmechanism In order to study the dynamic characteristic ofsingle clutch in the launching process and develop relevantcoordinating control strategy the following assumptionsshould be made before modeling (1) Both wheelsrsquo momentof inertia and vehiclersquos translation quality are converted intothe transmission output shaftThe engine output shaft and theinput shaft intermediate shaft and output shaft of transmis-sion are regarded as rigid body with distributed parametersand concentrated inertia and the friction damping loss isconsidered respectively (2)Thedynamic process of the clutchactuator and the synchronizers as well as the heat fade of theclutch are not the focus of this paper (3)Neglect the elasticitybetween bearing and its block as well as the elasticity and gapin gear engagement Finally the established dynamicmodel offive-speed dry DCT after simplification is shown in Figure 1

In Figure 1 parameters and variables are defined asfollows

119868119890 equivalent moment of inertia of engine crankshaft

(including flywheel) and clutch driving plate1198681198881 Equivalent moment of inertia of clutch 1 driven

plate transmission NO1 input shaft (solid part) andrelevant odd number gears1198681198882 equivalent moment of inertia of clutch 2 driven

plate transmissionNO2 input shaft (hollowpart) andits relevant even number speed gears

Mathematical Problems in Engineering 3

119868119898 equivalent moment of inertia of transmission

intermediate shaft its relevant gears and final drivedriving part

119868119904 equivalent moment of inertia of final drive driven

part differential gears axle shafts wheels and com-plete vehicle which are equally converted into trans-mission output shaft

1198681198921 1198681198923 119868119892119903 moment of inertia of 1st 3rd and reverse

driven gears

1198681198922 1198681198924 1198681198925 moment of inertia of 2nd 4th and 5th

driving gears

1198941sim 1198945 119894119886 forward gear ratios and final drive ratio

119887119890 rotating viscous damping coefficient of engine

output shaft

1198871198881 rotating viscous damping coefficient of transmis-

sion NO1 input shaft




sion intermediate shaft

119887119904 equivalent rotating viscous damping coefficient of

axle shafts and wheels which are equally convertedinto transmission output shaft

120596119890 angular speed of engine crankshaft

1205961198881 angular speed of clutch 1 driven plate (or trans-

mission NO1 input shaft)



120596119898 angular speed of transmission intermediate shaft

120596119904 angular speed of transmission output shaft

119879119890 engine output torque

1198791198881 1198791198882 transfer torque of clutch 1 and clutch 2

1198791198881198981

1198791198881198982

torque of NO1 and NO2 input shaftsacting on intermediate shaft

1198791198981198881

1198791198981198882

torque of intermediate shaft reacting onNO1 and NO2 input shafts

119879119891 driving resistance torque which is equally con-

verted into transmission output shaft

22 Dynamics Equations for Five-Speed Dry DCT DCT canuse 1st speed gear or 2nd speed gear to start Take 1st speedgear launch for example Assuming that the engine is alreadyoperating in idle state the synchronizer 1 firstly engages tothe left gear (1st gear) Because the synchronizer engagingprocess does not belong to the research focus in this paperthe detailed analysis of synchronizer is neglected After theengagement of synchronizer the clutch 1 begins to engageto transmit the torque from the engine side until the end of

launching process During the launch process clutch 1 getsthrough four phases

Free Stroke Eliminating It is to eliminate the vacant distancebetween the clutch driving and driven plates

Slipping Friction before Half-Engaging The clutch begins toengage but the transmitted torque cannot overcome thevehicle resistance to move the vehicle

Sliding Friction after Half-Engaging The clutch is furtherengaged and the torque transmitted by clutch is able to forcethe vehicle to move

Full-Engaging after Synchronizing The engaging process andthe launching process finish

The first two phases have a small effect on the launchingquality and therefore the main research attention is focusedin the last two phases especially the third phase

The four-DOF dynamics equations on the phase of slip-ping friction after half-engaging can be expressed as follows

119868119890119890= 119879119890minus 1198791198881minus 119887119890120596119890

11986811988811198881= 1198791198881minus 1198791198981198881

minus 11988711988811205961198881

(119868119898+ 1198681198921

+ 11986811989221198942

2120578 + 11986811989241198942

4120578 + 11986811989251198942

5120578) 119898

= 1198791198881119898

minus 119879119904119898

minus 119887119898120596119898

119868119904119904= 119879119898119904

minus 119879119891minus 119887119904120596119904

(1)

where 119879119890= 119891(120572 120596

119890) 1198791198881198981

= 1198791198981198881

1198941120578 119879119898119904

= 119879119904119898119894119886120578 V = 120596

119904119877119882

1198791198881=

2

3(1198773

0minus 11987731

11987720minus 11987721

)1205831119865 (1199091) 1205961198881le 120596119890

1198791198711198881

1205961198881= 120596119890

(2)

119879119891= (

119862119889119860

2115V2 + 119898119892 sin 120579 + 119898119892 cos 120579119891 + 120575119898

119889V119889119905

)119877119882 (3)

120575 = 1 +1

119898

1198681198881119894211198942119886+ 1198681198981198942119886+ 119868119904+ 119868V

119877119882

(4)

Among above formulas 120572 is engine throttle opening119891(120572 120596

119890) denotes nonlinear function of engine output torque

120578 is transmitting efficiency of transmission shafts as well asfinal drive 120583

1is kinetic friction coefficient among friction

plates of clutch 1 1198770 1198771are internal and external radius of

friction plates of clutch 1 1199091is opening of clutch 1 119865(119909

1)

denotes positive pressure function of pressure plate of clutch1 1198791198711198881

is transfer torque after full-engaging of clutch 119898 isvehicle mass 119892 is gravity acceleration 119891 is rolling resistancecoefficient V is vehicle velocity 119862

119889is wind drag coefficient119860

is windward area 120579 is road slope 120575 is conversion coefficientof rotating mass 119877

119882is radius of wheel

For the sake of easily designing the controller furtherassumptions about motional relationship among the inputintermediate and output shafts of transmission should meetthe equations 120596

1199041198941198861198941= 1205961198981198941= 1205961198881 Then the DCT dynamic

model in Figure 1 can be simplified as that in Figure 2


Clutch 1

Clutch 2

Tc1

120596c2

Tc2120596e

Te

Iebe

120596s

Tf

120596c1

Tmsbo

Io

VehicleEngine

Figure 2 DCT dynamics model after simplification

Simplify formula (1) and then some two-DOF dynamicsequations are obtained

119868119890119890+ 119887119890120596119890= 119879119890minus 1198791198881

119868119900119904+ 119887119900120596119904= 1198791198881119894119890minus 119879119891

(5)

where parameters are defined as follows

119894119890= 11989411988611989411205782

119868119900= 119868119904+ (119868119898+ 1198681198921) 1198942

119886120578 + 11986811988811198942

11198942

1198861205782

+ 11986811989221198942

21198942

1198861205782

+ 11986811989241198942

41198942

1198861205782

+ 11986811989251198942

51198942

1198861205782

119887119900= 119887119904+ 1198871198981198942

119886120578 + 11988711988811198942

11198942

1198861205782

(6)

When the clutch is fully engaged 1198791198881

= 1198791198711198881 He clutch

transmitted torque 1198791198881is only determined by engine output

torque and driving resistance which satisfies

1198791198881=119868119900(119879119890minus 119887119890120596119890) + (119879

119891+ 119887119900120596119904) 1198681198901198941119894119886

119868119900+ 1198681198901198941198901198941119894119886

(7)

When the clutch is fully engages the vehicle is launchedin certain gear In this sense formula (5) can still be furthersimplified as a single-DOF dynamics equation

119868119889119904+ 119887119889120596119904= 119879119890119894119890minus 119879119891 (8)

where

119868119889= 119868119904+ (119868119898+ 1198681198921) 1198942

119886120578 + (119868

1198881+ 119868119890) 1198942

11198942

1198861205782

+ 11986811989221198942

21198942

1198861205782

+ 11986811989241198942

41198942

1198861205782

+ 11986811989251198942

51198942

1198861205782

119887119889= 119887119904+ 1198871198981198942

119886120578 + (119887

1198881+ 119887119890) 1198942

11198942

1198861205782

(9)

Synthesizing formulas (5) and (8) the DCT launchdynamic model after eliminating the null distance of clutchcan be seen as a hybrid model namely including a two-DOF sliding frictionmodel and a single-DOF stably operatedmodel The switching condition between the two models is120596119890= 1205961198881 The controller will be designed on the basis of this

hybrid model in the following

3 Coordinating Control and Real-TimeOptimization for Dry DCT

31 Launch Control Objectives The control objectives of dryDCT in the launching process are as follows

(1) reflect the driverrsquos intention adequately to let thedriver have different driving feel according to accel-erator pedal opening and its changing rate

(2) under the condition of meeting the requirements ofshock intensity and sliding friction work to decreasethe slipping friction work as much as possible andguarantee the launch comfort (shock intensity is10ms3 in German standard [18])

(3) take the effect of launching on enginersquos working stateinto account to avoid the flameout of the engine in thelaunching process

32 Launch Controller Design Architecture A layered archi-tecture of launching control is used as shown in Figure 3Theupper layer controller is applied to determine the optimalclutch transfer torque and engine target speed (or torque)while the lower one is used to implement a servocontrol ofclutch torque and a closed-loop control of engine torque (orspeed) The upper controller can further be divided into twoparts according to the activation order the sliding controlbefore the speed synchronization and engaging control afterthe speed synchronization The sliding control is aiming atthe sliding friction after half-engaging phase and also thecore of the launching control Based on the two-DOF modelduring the sliding phase the driving intention the closed-loop control of engine speed and clutch torque and canbe realized Relatively based on the single-DOF model theengaging control is for the full-engaging after synchronizingphase and to make the clutch engage completely as quickly aspossible and prevent engaged clutch plates from falling intosliding state again due to the change of engine output torqueMeanwhile engine output torque is adjusted to match thedemand torque Even though the driving anddriven plates arealready synchronized the launch controller does not send outan accomplishment signal Only if the engine output torqueis equal to the demand torque it sends out the signal

33 Launch Sliding Friction Process Control The inputs oflaunch slipping friction process control include acceleratorpedal opening engine speed wheel speed and so forth Theoutputs contain Clutch 1 target engaging pressure and enginedemand torque They would be realized through the slidingmode variable structure tracing control algorithm

(1)Determine target control variables The target controlvariables include engine target speed and vehicle target shockintensity The engine target speed should be proportional tothe accelerator pedal opening and its changing rate in orderto partially reflect the driverrsquos intention Taking engine targetspeed and vehicle target shock intensity asmeasuring index ofdriverrsquos intention the DCT launch controller can be designedwithout considering the concrete physical characteristics ofclutch actuators thus improving the generality of launchcontroller

(2) Target tracing controller design Based on simplifiedmodels of engine and transmission sliding mode variable


Control of clutch engaging process after synchronizing

Calculation of driverdemand torque

Driver demandtorque Tde

t lt 998779tYes

Yes

No

No

Switch control ofdemand torque

Engine targetEngine model and itstorque control model

Lower control

Engine realtorque Te

Single-DOF in 1st gear stably operatingdynamics model of dry dual clutchtransmission after synchronizing

pedal opening

d120573

dt

120573

Calculation ofequivalent acceleratorpedal opening

120573 Has the clutch been synchronized or notCalculations of speed differenceand slip rate between clutchdriving and driven plates

Clutch driven plate speed 120596c1

Engine real speed 120596e

Determination ofengine target speed

Engine target Sliding mode variablestructure tracingcontrol of engine speed


Clutch model and itstorque control model


Clutch real Tc1transfer torque

Lower controlDeterminationof target shockintensity

Target shock Determination oftarget wheel speed

Target wheelSliding mode variablestructure tracingcontrol of wheel speed

Real wheel speed 120596s

Clutch target

Control of starting sliding friction process

120573

Accelerator

output torque Trefe

transfer torque Trefc1

output torque Trefe

speed 120596refs

speed 120596refe

intensities jp andjs

Two-DOF starting dynamicsmodel of dry dual clutchtransmission after synchronizing

Figure 3 Design architecture of launch controller

structure controller is designed to track engine target speedand vehicle target shock intensity

331 Determining Method of Engine Target Speed The prin-ciples of determining engine target speed are as follows

(1) In order to avoid the stalling of engine and attrition ofclutch due to overhigh speed the target speed is notless than the engine idle speed (set as 800 rmin) andis limited to a maximum value (set as 2000 rmin) aswell

(2) Within optional limits of target speed on one handthe target speed changes along with the variation ofaccelerator pedal opening and its changing rate andit can ensure that engine has enough output power tomeet the launch demands under different conditionsOn the other hand the selected target speed canmakethe engine work in an economic area

(3) When the difference between engine real speed andclutch driven plate speed is more than the settingthreshold value Δ120596 and the clutch sliding frictiontime is less than the time variable 119905

119901 the engine target

speedwill coordinatewith the accelerator pedal open-ing and its changing rate If the condition is reversethe target speed will be fixed as synchronous speed120596119890(119905119904) namely the speed when engine and clutch

driven plate are at the moment of synchronizingThe calculation of engine target speed 120596ref

119890is shown

120596refe

tp

120596e(0)

120596e(ts)

ts

120596c1

Spee

d120596

(rad

s)

Time t (s)

Figure 4 Determination of engine target speed

in Figure 4 and Formula (10) The engine outputcharacteristic can be seen in Figure 15 Consider

120596ref119890

=

120596119890(119905119904) minus 120596119890(0)

119905119901

119905 + 120596119890(0) (120596

119890minus 1205961198881) ge Δ120596 119905 lt 119905

119901

120596119890(119905119904) other

(10)

where 120596119890(119905119904) and 120596

119890(0) respectively denote engine target

speed postsynchronizing and idle speed 119905119901is linearly increas-

ing time of engine speed 119905119904is time elapsed until clutch driving


Table 1 Engine synchronous target speed

Equivalent accelerator pedalopening 120573V

Engine synchronous targetspeed 120596

119890(119905119904)(rmin)

0sim10 100010sim20 100020sim30 110030sim40 120040sim50 130050sim60 140060sim70 150070sim80 160080sim90 170090sim100 2000

and driven plates are synchronized Δ120596 is set threshold valueof the difference between clutch driving and driven plates

In order to reflect the driverrsquos intention easily anddetermine 120596

119890(119905119904) equivalent accelerator pedal opening 120573V is

introduced to synthesize the information of accelerator pedalopening and its changing rate The relationship between 120573Vand 120596

119890(119905119904) is shown in Table 1

Consider

120573V (119905) = 120573 (119905) + 119896 120573 (119905) (11)

where 120573(119905) is real value of accelerator pedal opening 120573(119905)

is changing rate of accelerator pedal opening 119896 is weightindex and must be determined according to the practice toguarantee the 120573

119905(119905) falling into the scope of [0ndash100]

332 Determining Method of Target Shock Intensity in theLaunching Process The launch target shock intensity not onlyreflects the driverrsquos intention but also guarantees that theintensity is in a reasonable extent The friction process isdivided into three parts in [19] which qualitatively elaboratedcontrol key points when a vehicle was launched and itsclutch driving and driven plates were synchronizing In [20]the shock intensity while the clutch driving and drivenplates were synchronizing is derived which showed that itis proportional to the difference between engine accelerationand acceleration of clutch driven plate at the instant ofpresynchronization That is

119888(+) minus

119888(minus) =

119868119890

119868119890+ 119868119888119886

[119890(minus) minus

119888(minus)] (12)

where 119888(minus)

119888(+) denote accelerations of clutch driven plate

at the instant of presynchronization and post- synchroniza-tion

119890(minus) is engine acceleration at the instant of presynchro-

nization 119868ca is moment of inertia of complete vehicle and itstransmission system which are equally converted to clutchdriven plate

Suppose that the transmission system is rigid namelyV =

119904119877119882

= 1198881198941119894119886119877119882 The shock intensity of vehicle can

Table 2 Driverrsquos intention

Launch mode Slow Moderate AbruptEquivalent acceleratorpedal opening 120573V

0sim20 20sim50 50sim100

Target shock intensity119895119901(ms3) 05 15 25

be equally converted into the shock intensity of clutch drivenplate Consider Formula (12) If the difference between engineacceleration and acceleration of clutch driven plate is zero theshock intensity will be zero at the moment of synchronizingThe condition is called no-impact synchronizing conditionAs the engine target speed is determined in precedingpassage namely the rotary speed difference is less than thethreshold value Δ120596 or the elapsed time of sliding frictionprocess is more than the time variable 119905

119901 the engine speed

remains constant as the same as synchronous target speedSo the engine acceleration is zero For the sake of no-impactat the moment of synchronizing the speed of clutch drivenplate should be equal to the target speed and its accelerationshould be zero

The authors divide the launch sliding friction process intothree phases determine the target shock intensity in differentphases and obtain related target vehicle acceleration andtarget vehicle velocity via integral It is shown in Figure 5

Phase One During the time slot 0 sim 119905119901 the target shock

intensity 119895119901is positive It changes along with the equivalent

acceleration which reflects the driverrsquos intention As theparticularity of creeping launchthat is the clutch drivingand driven plates should maintain slipping state during thewhole launching process without considering their speedsynchronization In view of this creeping launch is out ofconsideration in this paper Therefore on the basis of equiv-alent accelerator pedal opening and engine output torquecapacity driverrsquos intention is divided into three categories[3 6] which is shown in Table 2

Phase Two During the time slot 119905119901

sim 119905119904 the target shock

intensity 119895119901is negative The main goal is to lower the vehicle

acceleration so that the speed and acceleration of clutchdriven plate stay the same as the enginersquos at the moment ofsynchronizing in order to realize no-impact synchronizingThe values are synchronous target speed and zero respec-tively Theoretically different values are selected accordingto different target shock intensity in Phase One Howeverconsidering that clutch driving plate and its driven plate areapproaching to synchronize the target shock intensity 119895

119904is set

as a constant value in order to accelerate the engaging speedand decrease the total sliding friction work in the launchingprocess Equations can be established as follows

119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0

051198951199011199052

119901+ 119895119901119905119901(119905119904minus 119905119901) + 05119895

119904(119905119904minus 119905119901)2

= 120596 (119905119904) 119877119882

(13)


js

ts

Time t (s)

Shoc

k in

tens

ityj

(ms3)

tp

jp

(a) Target shock intensity

ts

Time t (s)

Acce

lera

tiona

(ms2)

tp

(b) Target vehicle acceleration

ts

Time t (s)

Velo

city

(ms

)

tp

(c) Target vehicle velocity

Figure 5 Target curves in the launching process

where 119895119901is target shock intensity in phase one of sliding

friction process 119895119904is target shock intensity in Phase Two of

sliding friction process 120596(119905119904) is speed of clutch driven plate

at time 119905119904 namely the synchronous target speed

By solving formula (13) the following can be obtained

119905119901= radic

120596 (119905119904) 119877119882

(05119895119901minus 051198952

119901119895119904)

119905119904= 119905119901(1 minus

119895119901

119895119904

)

(14)

According to equivalent accelerator pedal opening at theinitial moment of sliding friction process the synchronoustarget speed and target shock intensity in Phase One can beobtained by looking up Tables 1 and 2 respectively Basedon above values 119905

119901and 119905119904 the target speed of clutch 1 in the

sliding friction process will be listed in the following throughthe integral of 119895

119901and 119895119904twice

120596ref119904

= int119905119904

0

int119905119904

0

119895

119877119882

119889119905

120596ref1198881

= 120596ref1199041198941119894119886

(15)

Note that both 119905119901and 119905119904are measured in a coordinate

system whose origin is the initial moment of sliding frictionprocess

PhaseThree During the time slot over 119905119904 clutch driving plate

and its driven part are already synchronized andDCTmodelis switched from sliding frictionmodel to 1st speed gear stablyoperated model So the control of sliding friction makes nosense any more In order to meet the requirement of no-impact synchronizing the target acceleration is set as zeroand the target speed is constant

333 Rolling Determination of Target Value and GeneticOptimization of Shock Intensity The determining method ofengine target speed and launch target shock intensity statedabove can ensure no stalling of engine and ride comfortof vehicle in the launching process and partially reflect thedriverrsquos intention but some shortages also exist as follows

(1) Engine synchronizing target speed and target shockintensity in Phase One are only based on equiva-lent accelerator pedal opening at the initial momentof sliding friction process without considering thewhole sliding friction process The transformation ofequivalent accelerator pedal opening obviously doesnot accord with the fact

(2) Neglect the sliding friction work in the launchingprocess when determining the target speed


0

1

2

3

t0

middotmiddotmiddot

middot middot middot

Time t (s)

Velocity(m

s)

t0 + Δt t0 + 2Δt t0 + 3Δt

Figure 6 Schematic diagram of the rolling calculation of launchtarget vehicle velocity

In order to overcome the above shortages predictive con-trol thoughts are used to optimize the target curves online Itmeans that during a time slot (namely at an optimizing step)these variables such as 120596

119890(119905119904) 119905119901 119905119904 and 119895

119901can be obtained

by minimizing the sliding friction work on the basis of theequivalent accelerator pedal opening and vehicle velocityAnd then the target curves can also be obtained

Determination of Rolling Algorithm of Target Vehicle VelocityThe target vehicle velocity curve is recalculated in a timeinterval Δ119905 Both vehicle velocity and acceleration are notequal to 0 at every calculation moment Figure 6 shows thatV0 V1 V2 and V

3represent the target vehicle velocities at these

moments of 1199050 1199050+ Δ119905 119905

0+ 2Δ119905 and 119905

0+ 3Δ119905 respectively

Figure 7 shows the calculation method of target vehiclevelocity in a certain time According to the condition of no-impact synchronizing formula (13) can be rewritten as

119886 (1199050) + 119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0

V (1199050) + 119886 (119905

0) 119905119901+1

21198951199011199052

119901+ (120572 (119905

0) + 119895119901119905119901) (119905119904minus 119905119901)

+1

2119895119904(119905119904minus 119905119901)2

= 120596 (119905119904) 119877119882

(16)

where 1199050is optimizingmoment 120572(119905

0) denotes vehicle acceler-

ation at the optimizingmoment V(1199050)denotes vehicle velocity

at the optimizing moment and 120596119890(119905119904) denotes synchronous

target revolving speed which updates its value at everyoptimizing step according to virtual accelerator pedal signalby looking up Table 1

In a word firstly at every optimizing step synchronoustarget rotary speed 120596

119890(119905119904) and target shock intensity are

obtained by looking upTables 1 and 2 according to the currentequivalent accelerator pedal opening Secondly solve (16) andget the latest values of 119905

119901 119905119904 Finally according to formula (15)

we get the target vehicle velocity in the launching process

The rolling determining method of engine target speedresembles the above description According to (10) followingformula can be obtained

120596ref119890

=

120596119890(119905119904) minus 120596119890(0)

119905119901

119905 + 120596119890(0) (120596

119890minus 1205961198881) ge Δ120596

1199050lt 119905 lt (119905

0+ 119905119901)

120596119890(119905119904) other

(17)

Determination of Optimal Algorithm of Target Shock IntensityThe target shock intensity stated above is obtained by lookingup Tables But it does not ensure that the target curve isoptimal It is discussed below how to determine 119895

119901and 119895

119904

through genetic algorithm and real-time optimization In thetime slot 119905

0sim 1199050+ 119905119904 the predictive sliding friction work is

119882 = int1199050+119905119904

1199050

1198881(120596

ref119890

minus 1205961198881) 119889119905

1198881=119868119900ref119904

+ 119887119900120596ref119904

+ 119898119892119877119882120583

11989411988611989411205782

(18)

where 1198881is estimated clutch transfer torque If |119879

1198881minus1198881| lt 120576

estimated value 1198881replaces real value 119879

1198881 and target shock

intensities 119895119901and 119895119904can be obtained byminimizing the sliding

friction work The selected fitness function based on geneticalgorithm is the reciprocal of predictive sliding friction work

119865 =1

119882 (19)

The optimizing process of parameters 119895119901and 119895

119904can be

seen in Figure 8

334 Design of Sliding Mode Variable Structure TracingController Based on the design of previous details the targetvehicle velocity and target engine speed are already obtainedin the launch sliding friction process However whether itcan track accurately or not depends on the performanceof launch controller completely Considering immeasurabledriving resistance a kind of sliding mode variable structurecontrol algorithm with interference rejection has been putforward in the paper which aims at tracking engine speed andwheel speed accurately

Regardless of the influence of temperature and slip speeddifference on clutch friction coefficient 120583

1 the relationship

between pressure 1198651of the clutch pressure plate and its

transfer torque is determined uniquely when the internal andexternal radius of friction plates are given For the sake ofeasy description clutch transfer torque is used to describe theclutch engaging law in the following

Tracing Control of Wheel Speed On the basis of launchdynamics equations of DCT transmission system (referringto Formula (5)) supposing 119909

1= 120579119904 1199092= 120596119904 there is

1= 1199092

2=

119894119890

119868119900

1198791198881minus1198870

1198680

1199092minus119879119891

1198680

(20)


t0 t0 + ts

a(t0)

Time t (s)

Acce

lera

tiona

(ms2)

t0 + tp

(a) Target acceleration

(t0)

t0 t0 + ts

Time t (s)

Velo

city

(ms

)

t0 + tp

(b) Target vehicle velocity

Figure 7 Calculation schematic diagram of target vehicle velocity at time 1199050

Equivalentacceleratorpedal opening

Rollingdetermination

of engine speedand vehicle

velocity

Engine target speed

Clutchtransfertorque

estimation

Clutch driven plate target speed

Targ

et im

pact

stren

gth

optim

izat

ion

Geneticalgorithm

Calculationsof estimated

slidingfriction

energy andfitness

function

jp and js after optimizing

Figure 8 Optimizing process of target shock intensity

Supposing that 1198901= 119909119903minus1199091 1198902= 119903minus1199092 1199061= 1198791198881 where

119909119903is the expectation of 119909

1 there is

[1198901

1198902

] = [

[

0 1

0 minus1198870

1198680

]

]

[1198901

1198902

] + [

[

0

minus119894119890

1198680

]

]

1199061+ [

0

1198912

] + [0

1198913

] (21)

where 1198912= 119903+ (11986801198870)119903 which is measurable interference

and 1198913= 1198791198911198680 which is immeasurable interference related

to the driving resistanceIn order to reduce the gain of sliding mode variable

structure it should contract the upper and lower boundariesof interference as much as possible According to the compu-tational formula of driving resistance the rolling resistanceis regarded as a part of measurable interference namelymeasurable interference 119891

2can be rewritten as

1198911015840

2= 119903+1198680

1198870

119903+119898119892119891

1198870

(22)

And the immeasurable interference1198913can be rewritten as

1198911015840

3=119879119891

1198680

minus119898119892119891

1198870

(23)

The switching function is designed as119904 = 11988811198901+ 11988821198902 (24)

where 1198881gt 0 1198882gt 0 Take the approaching rate

119904 = minus119896 sdot 119904 minus 119889 sdot 119892 (119904) + 11988821198911015840

3 (25)

where 119889 gt |11988821198911015840

3|

119892 (119904) =

sgn (119904) |119904| ge120587

2119901

sin (119901 sdot 119904) |119904| lt120587

2119901

119901 gt 0 (26)

While it is 119901 rarr infin 119892(119904) rarr sgn(119904) The control input 1199061

is calculated via the formula below

1199061=

1198680

1198882119894119890

[119896 sdot 119904 + 119889 sdot 119892 (119904) + 1198902(1198881minus 1198882

1198870

1198680

) + 11988821198911015840

2] (27)

Tracing Control of Engine Speed Because engine model isa double-input (119879

119890and 119879

1198881)-single-output (120596

119890) model and

clutch transfer torque 1198791198881is available in use of wheel speed

tracing controller stated previously 1198791198881

is a measurableinterference of enginemodel Based on the rotation dynamicsof crankshaft (refer to Formula (5)) we can suppose that


100

90

80

70

60

50

40

30

20

10

0050 15 2 25 3 35 41

Time t (s)

Acce

lera

tion

peda

l ope

ning120573

()

NO1 conditionNO2 condition

(a) Acceleration pedal opening value

0500

15 2 25 3 35 41

250

200

150

100

50

Time t (s)

Targ

et sp

eed120596

(rad

s)

Clutch on the NO1 conditionEngine on the NO1 conditionClutch on the NO2 conditionEngine on the NO2 condition

(b) Target rotational speed

050 15 2 25 3 35 410

250

200

150

100

50

Time t (s)

Real

spee

d120596

(rad

s)


(c) Actual rotational speed

050 15 2 25 3 35 41

6

4

2

0

minus2

minus4

minus6

Time t (s)

Targ

et sh

ock

inte

nsityj

(ms3)


(d) Target impact strength

050 15 2 25 3 35 41

6

4

2

0

minus2

minus4

minus6

Time t (s)

Real

shoc

k in

tens

ityj

(ms3)


(e) Actual impact strength

140

120

100

80

60

40

20

0050 15 2 25 3 35 41

Time t (s)

Engi

ne o

utpu

t tor

queT

e(N

m)


(f) Engine output torque

Figure 9 Continued


050 15 2 25 3 35 41

140

120

100

80

60

40

20

0

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)


(g) Clutch transfer torque

050 15 2 25 3 35 41

20

18

16

14

12

10

8

6

4

2

0

Time t (s)

Vehi

cle v

eloc

ity

(km

h)


(h) Vehicle velocity

Figure 9 Simulation results of launch performance

1199091119890

= 120579119890 1119890

= 120579119890= 120596119890 1198901119890

= 119909119903119890minus 1199091119890 1198902119890

= 119903119890minus 1199092119890

where 119909119903119890is the expectation of 120579

119890 namely

[1198901119890

1198902119890

] = [

[

0 1

0 minus119887119890

119868119890

]

]

[1198901119890

1198902119890

] + [

[

0

minus1

119868119890

]

]

1199062+ [

0

1198912119890

] (28)

where 1199062= 119879119890 1198912119890

= (1198791198881119868119890) + 119903119890+ (119887119890119868119890)119903119890 which are

measurable interferencesThe switching function is designed as

119904119890= 11988811198901198901119890+ 11988821198901198902119890 (29)


119904119890= minus119896119890sdot 119904119890minus 119889119890sdot 119892 (119904119890) (30)

where 119889119890gt |11988821198901198912119890|

119892 (119904) =

sgn (119904) |119904| ge120587

2119901119890

sin (119901119890sdot 119904) |119904| lt

120587

2119901119890

119901 gt 0 (31)

The control output 1199062is calculated via the following

formula

1199062=119868119890

1198882

[119896119890sdot 119904119890+ 119889119890sdot 119892 (119904119890) + 1198902119890(1198881119890minus 1198882119890

119887119890

119868119890

) + 11988821198901198912119890]

(32)

34 Switching Control of Engine Demand Torque in theEngaging Process after Synchronizing When engine speedand clutch driven plate speed approach to synchronizing and

reach set threshold values according to switching conditionsDCT launch models switch over namely the two-DOF slid-ing friction model transforms into the single-DOF 1st speedgear stable operated model At the moment the controllerof sliding friction process does not work any longer Andswitching controller of demand torque begins to work whichis in charge of converting engine torque into driver demandtorque It satisfies

119879119889

119890= 119879119871

119890+ 119870119890119905 (33)

119870119890= (

119879119889119890minus 119879119871119890

Δ119905) (34)

wherein 119879119871119890is real engine torque at the switching moment

of DCT launch models 119879119889119890is driver demand torque 119870

119890is

changing slope of engine torque and Δ119905 is switching timeelapsed of demand torque

In order to meet the requirement of vehicle shockintensity in the switching process Δ119905 has a minimum valueAccording to the 1st speed gear stably operated model(formula (8)) shock intensity is proportional to the changingrate of engine torque regardless of driving resistance andfriction damping That is

119895 =119894119890119877119882

119868119889

119890 (35)

According to the requirement of shock intensity in thelaunching process namely 119895 le 10ms3 the upper limitedvalue of changing rate of engine torque can be calculatedTheminimum time elapsed in the switching process of torque alsocan be obtained on the basis of formula (33)


050 15 2 25 3 35 41

25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

etp

(s)

Time t (s)


(a) Optimizing process of 119905119901

050 15 2 25 3 35 41

3

25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

ets

(s)

Time t (s)


(b) Optimizing process of 119905119904

050 15 2 25 3 35 41

100

90

80

70

60

50

40

30

20

10

0

Real valueEstimated value

Clut

ch tr

ansfe

r tor

queT

c1(N

m)

Time t (s)

(c) Clutch transfer torque under NO1 condition

050 15 2 25 3 35 41

100

90

80

70

60

50

40

30

20

10

0


Clut

ch tr

ansfe

r tor

queT

c1(N

m)

Time t (s)

(d) Clutch transfer torque under NO2 condition

Figure 10 Comparisons of results of rolling optimization under NO1 and NO2 condition

Similarly according to the two-DOF launch model (For-mula (5)) in the launch sliding friction process we knowthat vehicle shock intensity in the sliding friction process isproportional to the changing rate of clutch transfer torqueregardless of driving resistance and friction damping Sothere is

119895 =119894119890119877119882

1198680

1198881 (36)

4 Simulation Results and Analysis

Based on the previously established dynamic model of dryDCT and its launch controller the launch simulation model

of vehicle equipped with dry DCT is built on the Mat-labsimulink software platform Immediately the perfor-mance of vehicle is simulated under typical launch conditionThe detailed parameters of adopted DCT can be seen in theappendix

Figure 9 and Table 3 demonstrate simulation results oflaunch condition which are defined as that the changing rateof accelerator pedal angle is constant and that the final valuesare different It means that changing rate of accelerator is04 sminus1 and that the final values are 20 and 40 respectivelyRelatively they are called NO1 and NO2 conditions respec-tively which are shown in Figure 9(a) Compared with NO4condition (it reaches the final value at 1 s) NO3 conditionrequires a slower launch process


(a) Photo of dry DCT test bench

Key signal

Accelerator pedal signal

Brake pedal signal

Shifting knob signal

Clutch 1 position signal


1st 3rd gears position signal

2nd 4th gears position signal

5th gear position signal

Reverse gear position signal

control system

Monitor PC andcontroldesk interface

Clutch 1 actuator

Clutch 2 actuator

Shifting motor of 1stand 3rd gears

Shifting motor of 2ndand 4th gears

Shifting motor of 5thand reverse gears

MicroAutoBox

(b) Interfaces of DCT prototyping controller

Figure 11 DCT test bench and prototyping controller

Table 3 Comparisons of simulated results of NO1 and NO2 con-ditions

Working condition NO1 NO2Time elapsed when clutch driving anddriven plates are synchronized 119905

119904s 2355 2535

Vehicle velocity when clutch driving anddriven plates are synchronized V(kmh) 81052 96367

Time elapsed when the demand torqueswitch over (119905

119904+ Δ119905)s 314 333

Vehicle velocity when the demand torqueswitch over 119907(kmh) 83558 10371

Total slipping friction work119882J 37399 47673Time elapsed for launch 119905s 314 333

In Figures 9(b) 9(c) and 9(g) and Table 3 both thesynchronizing moment of clutch driving and driven platesand the switching finishing moment under NO1 conditionare earlier than that of NO2 working condition At anymoment vehicle velocity is quite little under NO1 conditionSo it can be concluded that the designed launch controllercan reflect the driving intention In Figures 9(d) and 9(e)launch impact strengths are less than 10ms3 whichmeet thedemands In Figures 9(f) and 9(g) engine output and clutchtransfer torque can also be divided into five parts

Figures 10(a) and 10(b) demonstrate optimal time vari-ables 119905

119901and 119905

119904calculated at every rolling optimization

The total optimizing frequency is 22 under NO1 conditionwhile the time elapsed is 153 s at the last optimizationRelatively the total optimizing frequency is 24 times underNO2 condition while the time elapsed is 164 s at the lastoptimization Figures 10(c) and 10(d) show that estimatedvalue of119879

1198881is quite approaching to its real value in the launch

sliding friction process It ensures that sliding friction is leastin the launching process to some degree

5 Rapid Prototyping Experiments for DryDCT in the Launching Process

51 Five-Speed Dry DCT Transmission Actuator In order toshorten the development cycle of dry DCT control systemand test the real-time property and effectiveness of slid-ing mode variable structure control algorithm as well theresearch group has established a dry DCT test bench (shownin Figure 11(a)) and used MicroAutoBox1401 of dSPACECorporation as prototype controller Somemodels are set upsuch as five-speed dry DCT vehicle models (including enginemean value model DCT model and vehicle longitudinaldynamics model) and DCT control strategymodelThe rapidprototyping experiments are conducted at the same time

The interfaces of dryDCT prototype controller are shownin Figure 11(b) Before testing calibrate the signals of sensorsfirstly and test the working performance of actuator motordriving units and actuator mechanisms in an open loop inorder to ensure the reliability of hardware system Secondlytest and verify the coordinating control strategy of clutchtorque in a closed-loop Thirdly conduct the rapid proto-typing experiments of sliding mode variable structure uppercoordinating control strategy after proving its effectivenessand calibrating relative control parameters

52 Results and Analysis of Rapid Prototyping Tests Bymeansof making use of RTI1401 toolbox offered by dSPACE Cor-poration defining input signal pins such as accelerator pedalsignal brake pedal signal and contacting with the previouslydesigned DCT launch upper control module the uppercontroller can be established

The launch trigger signal is defined as follows when thecurrent speed gear is 1st speed gear the brake pedal signal iszero (in loose state) The accelerator pedal opening is morethan or equal to 3 A trigger signal for preselecting 2ndspeed gear is delayed 05 s after the launch is finished

The trigger signal of shifting 1st speed gear to the 2nd onecan be defined as follows when the vehicle velocity is bigger


Time t (s)

100

80

60

40

20

08 10 12 14 16

Acce

lera

tor p

edal

ope

ning120573

()

(a) Acceleration pedal opening

250

200

150

100

50

0

EngineClutch oneClutch two

8 10 12 14 16

Time t (s)

Targ

et ro

tatio

nal s

peed120596

(rad

s)



8 10 12 14 16

250

200

150

100

50

0

Time t (s)

Real

spee

d120596

(rad

s)

(c) Real rotational speed

10

5

0

minus5

minus108 10 12 14 16

Shoc

k in

tens

ityj

(ms3)

Time t (s)

(d) Shock intensity

7

6

5

4

3

2

1

08 9 10 11 12 13 14 15 16 17

Time t (s)

Slid

ing

fric

tion

wor

kW

(kJ)

(e) Sliding friction work

Time t (s)8 10 12 14 16

120

100

80

60

40

20

0

Torq

ueT

(Nm

)


(f) Torque

Figure 12 Continued


25

20

15

10

5

0

Time t (s)8 10 12 14 16

Vehi

cle v

eloc

ity

(km

h)

(g) Vehicle velocity

120

100

80

60

40

20

08 9 10 11 12 13

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)

Estimated valueReal value

(h) Clutch transfer torque

25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

et(s

)

8 9 10 11 12 13

Time t (s)

tPts

(i) Optimization process of launch variables

15

10

5

0

Clut

ch se

para

ting

strok

ex(m

m)

Time t (s)8 10 12 14 16

Clutch one target valueClutch one actual value

Clutch two target valueClutch two actual value

(j) Tracing response of clutch separating stroke

Figure 12 Rapid prototyping experiment results of launch and shifting from the 1st gear to the 2nd one

Figure 13 Photo of real car chassis dynamometer test

than the 1st to 2nd gear shifting speed 12 kmh and the targetgear is 2nd gear

The rapid prototyping experiment results of upper con-troller are demonstrated in Figure 12 and Table 4 It can

Table 4 Rapid prototyping experiment results of dry DCT in thelaunching process

Launch moment 1199050s 9425

Synchronizing moment of launch clutch 1 driving anddriven plates (119905

0+ 119905119904)s 1196

Vehicle velocity at the synchronizing moment of clutch1 V(kmh) 9029

Switching finishing moment of launch demand toque(1199050+ 119905119904+ Δ119905)s 1274

Vehicle velocity at the switching finishing moment ofdemand toque V(kmh) 9498

Total sliding friction work119882J 4416Rolling optimization frequency of time variable 24Time elapsed for launch 119905s 3315

be seen that the performance indexes of shock intensityand sliding friction work meet the standard demands in


100

80

60

40

20

08194 8198 8202 8206 821 8214

Time t (s)

Acce

lera

tor o

peni

ng120573

()

(a) Accelerator pedal opening

8194 8198 8202 8206 821 8214

350

300

250

200

150

100

50

0

EngineTransmission input shaft

Time t (s)

Rota

tiona

l spe

ed120596

(rad

s)

(b) Rotational speed

8194 8198 8202 8206 821 8214

10

5

0

minus5

Time t (s)

Shoc

k in

tens

ityj

(ms3)

(c) Shock intensity

Figure 14 Results of dry DCT prototype car chassis dynamometer test

the launching process and that results of rapid prototypingexperiments coincide with simulated results It is also provedthat the stated slidingmode variable structure dryDCTuppercontroller can meet the requirement of real-time controlbased on real-time optimization

6 Chassis Dynamometer Test of Real CarEquipped with Dry DCT

After rapid prototyping experiments the independentlydevelopmental five-speed dry DCT control unit is used toreplace theMicroAutoBox1401 rapid prototype controller Onthe basis of simulation and bench test results the corre-sponding MAP of prototype car equipped with dry DCT isrecalibrated After DCT software is developed the real carchassis dynamometer test is conducted The test photo isshown in Figure 13

The results of launch test can be seen in Figure 14 Theexperiment results demonstrate that on the basis of sliding

mode variable structure upper coordinating control strategythe developed dry DCT control software not only reflectsthe launch riding comfort of vehicle but also reflects thevariation of driverrsquos intention

As can been seen from Figure 14 under the proposedlaunching strategies the vehicle is launched within 2 s andthe shock intensity is below 10ms3 Besides when theaccelerator pedal opening is increasing the correspondingshock intensity is relatively larger which is consistent with thecontrol strategies Comparedwith the rapid prototyping teststhe results obtained in the chassis dynamometer test are alsoconsistent thus validating the effectiveness of the proposedcontrol strategies

7 Conclusion

Thefour-DOF launch dynamicsmodel of five-speed dryDCTis established After simplifying the model two-DOF slidingfriction model and single-DOF in-gear operation model areobtained which provide a basis for the design and control

Mathematical Problems in Engineering 17Th

e eng

ine o

utpu

t tor

que (

Nm

)

The throttle openingThe engine rotating speed (rmin)

The engine output torque characteristic

250

200

150

100

50

0100

8060

4020

0 10002000

30004000

50006000

Figure 15

Table 5 The parameters of adopted DCT

Parameters Value119868119890 0273 kgsdotm2

1198681198881 0014 kgsdotm2

1198681198882 0014 kgsdotm2

119868119898 001 kgsdotm2

119868119904 1470392 kgsdotm2

I1198921

simI1198925 0005 kgsdotm2

119868119892119903 0005 kgsdotm2

i1 simi53615 2042 1257

0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2

119860 2095m119862119889 0293

119877119908 0308m

120578 0921198770 0228m

1198771 015m

of launch controller Driverrsquos intention is reflected by usingengine speed and vehicle shock intensity Taking advantageof the idea of predictive control and genetic algorithm thetracing curves of engine speed and vehicle target velocity aredetermined by rolling optimization online The sliding modevariable structure controller (SMVS) is designed Launchsimulatingmodel is built on theMATLABSimulink softwareplatform for the dry DCT the launch rapid prototyping

experiment is conducted Simulation and experiment resultsshow that the designed SMVS coordinating controller caneffectively reflect the driverrsquos intention and improve the vehi-clersquos launch performance Furthermore chassis dynamometertest result of DCT prototype car also shows that the proposedSMVS launch coordinating control strategy is effective andfeasible

Appendices

A The Engine Output Characteristics (Map)

See Figure 15

B The Parameters of Adopted DCT in ThisPaper

See Table 5

Conflict of Interests

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

References

[1] D Qin Y Liu J Hu and R Chen ldquoControl and simulation oflaunch with two clutches for dual clutch transmissionsrdquoChineseJournal of Mechanical Engineering vol 46 no 18 pp 121ndash1272010

[2] D Qin and Q Chen ldquoUniversal clutch starting control ofAMTDCT automatic transmission based on optimal controlrdquoChinese Journal of Mechanical Engineering vol 47 no 12 pp85ndash91 2011

[3] C Sun and J Zhang ldquoOptimal control applied in automaticclutch engagements of vehiclesrdquo Chinese Journal of MechanicalEngineering vol 17 no 2 pp 280ndash283 2004

[4] Q-H Chen D-T Qin and X Ye ldquoOptimal control about AMTheavy-duty truck starting clutchrdquoChina Journal of Highway andTransport vol 23 no 1 pp 116ndash121 2010

[5] F Garofalo L Glielmo L Iannelli et al ldquoOptimal tracking forautomotive dry clutch engagementrdquo in Proceedings of the Inter-national Federation of Automatic Control (IFAC rsquo02) pp 367ndash372 2002

[6] I A Amir D T Qin and J J Liu ldquoA control strategy on launchup a vehicle with AMTrdquo Information Technology Journal vol 4no 2 pp 140ndash145 2005

[7] G Lucente M Montanari and C Rossi ldquoModelling of anautomated manual transmission systemrdquo Mechatronics vol 17no 2-3 pp 73ndash91 2007

[8] A Serrarens M Dassen and M Steinbuch ldquoSimulation andcontrol of an automotive dry clutchrdquo in Proceedings of the 2004American Control Conference (AAC rsquo04) pp 4078ndash4083 July2004

[9] C H Yu H Y Chen and H R Ding ldquoA study on fuzzy controlof AMT clutch in launch phaserdquo Automotive Engineering vol27 no 4 pp 423ndash426 2004

[10] Z Qi Q Chen and A Ge ldquoFuzzy control of the AMT vehiclersquosstarting process based on genetic algorithmrdquo Chinese Journal ofMechanical Engineering vol 37 no 4 pp 8ndash24 2001


[11] M Yong D Y Sun D T Qin et al ldquoResearch on partial fuzzycontrol of car clutch in launch phaserdquo Automotive Technologyvol 12 pp 12ndash15 2008

[12] H Kong F Ren and Y M Ren ldquoApplication of the geneticalgorithm to optimizing fuzzy control strategy in the vehiclersquoslaunch processrdquo Journal of Hefei University of Technology vol32 no 1 pp 21ndash23 2009

[13] M X Wu J W Zhang T L Lu et al ldquoResearch on optimalcontrol for dry dual-clutch engagement during launchrdquo Journalof Automobile Engineering vol 224 no 6 pp 749ndash763 2010

[14] G Q Wu and D M Zhan ldquoA research on the way of clutchactuation during DCT upshift based on optimality theoryrdquoAutomotive Engineering vol 31 no 3 2009

[15] Y Li Z Zhao and T Zhang ldquoResearch on optimal control oftwin clutch engagement pressure for dual clutch transmissionrdquoChina Mechanical Engineering vol 21 no 12 pp 1496ndash15012010

[16] W Yang Q Chen GWu and D Qin ldquoStarting control strategyfor dual clutch transmission based on intelligent control andthe performance simulationrdquo Chinese Journal of MechanicalEngineering vol 44 no 11 pp 178ndash185 2008

[17] Y Liu D Qin H Jiang and Y Zhang ldquoA systematic model fordynamics and control of dual clutch transmissionsrdquo Journal ofMechanical Design Transactions of the ASME vol 131 no 6 pp0610121ndash0610127 2009

[18] Y S Zhao Integrated control of dual clutch transmission system[MS thesis] Chongqing University

[19] H-O Liu H-Y Chen H-R Ding and Z-B He ldquoAdaptiveclutch engaging process control for automatic mechanicaltransmissionrdquo Journal of Beijing Institute of Technology vol 14no 2 pp 170ndash174 2005

[20] F Garofalo L Glielmo L Iannelli et al ldquoSmooth engagementfor automotive dry clutchrdquo in Proceedings of the IEEE ControlSystems Society Conference vol 1 pp 529ndash534 2001

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


I

1st gears

2nd gears4th gears

3rd gears

5th gears

Clutch 1

Clutch 2

Reverse gears

(solid shaft)

Synchronizer 1

Synchronizer 2

Synchronizer 3

Synchronizer 4

Engine

Intermediate shaft

(hollow shaft)

Output shaft

Vehiclei4

i5

120596c1

Tc1

Ic1

bc1

120596c2

Tc2

Ic2bc2

120596e

Te

Ie

be

120596m

TsmIm

bs

120596s

Tf

iabm

Ig1

Ig2

Ig3

Ig4

Ig5

Igr

i1

i2

i3

Tmc1

Tmc2

Tcm1 or Tcm2

Tms

Input shaft NO1

Input shaft NO2

Figure 1 Five-speed dry DCT dynamic model

equipped with DCT clutch optimal engaging control lawhas been introduced by utilizing minimum principle andsynthetically taking shock intensity sliding friction workand engine output torque into consideration [13] Linearquadratic optimal control has been applied to simulate clutchengaging pressure in the launching process [14 15] Launchfuzzy intelligent control algorithm has been designed andoptimized by using accelerator pedal opening and its chang-ing rate clutch relative slip rate and engine speed differenceto describe the driving intention clutch engaging states andengine working condition respectively [16] Comparativelydouble-layer fuzzy intelligent control architecture has beenpresented by setting up clutch engaging fuzzy control rulesand real car chassis dynamometer test has been conducted[17]

But the above stated studies only focus on the control ofclutch engaging control rules rarely taking consideration ofthe issue of coordinating control between engine and clutchduring the vehiclersquos launch process and let alone the qualifi-cation of driverrsquos intention

Taking the factors such as driverrsquos intention enginecondition clutch state and shock intensity into account theissue of coordinating control between engine and clutch isinvestigated in the paper which is based on the DCT andprototype car developed independently Four degrees of free-dom (DOF) launch dynamics equations are established Thecomputational formulas of engine speed and clutch transfertorque in the launching process have also been quantifiedand given Taking advantage of predictive control and geneticalgorithm target tracing curves of engine speed and vehiclevelocity are optimally specified Sliding mode variable struc-ture (SMVS) control strategy has been designed to track thesecurves Based on the MatlabSimulink software platform andthe hardware-in-the-loop test bench the launch performanceof prototype car equipped with dry DCT has been simulatedunder different driving conditions and the rapid prototyping

experiment and test are respectively conducted on the DCTtest bench and in the chassis dynamometer

2 Mathematical Models

21 Five-Speed Dry DCT Dynamic Model The five-speeddry DCT described in the paper is made up of dry dualclutch module and its actuator four synchronizers and theiractuators and single intermediate shaft gear transmissionmechanism In order to study the dynamic characteristic ofsingle clutch in the launching process and develop relevantcoordinating control strategy the following assumptionsshould be made before modeling (1) Both wheelsrsquo momentof inertia and vehiclersquos translation quality are converted intothe transmission output shaftThe engine output shaft and theinput shaft intermediate shaft and output shaft of transmis-sion are regarded as rigid body with distributed parametersand concentrated inertia and the friction damping loss isconsidered respectively (2)Thedynamic process of the clutchactuator and the synchronizers as well as the heat fade of theclutch are not the focus of this paper (3)Neglect the elasticitybetween bearing and its block as well as the elasticity and gapin gear engagement Finally the established dynamicmodel offive-speed dry DCT after simplification is shown in Figure 1

In Figure 1 parameters and variables are defined asfollows

119868119890 equivalent moment of inertia of engine crankshaft

(including flywheel) and clutch driving plate1198681198881 Equivalent moment of inertia of clutch 1 driven

plate transmission NO1 input shaft (solid part) andrelevant odd number gears1198681198882 equivalent moment of inertia of clutch 2 driven

plate transmissionNO2 input shaft (hollowpart) andits relevant even number speed gears







driven gears


driving gears



output shaft


















1198791198881198981

1198791198881198982


1198791198981198881

1198791198981198882












119868119890119890= 119879119890minus 1198791198881minus 119887119890120596119890

11986811988811198881= 1198791198881minus 1198791198981198881

minus 11988711988811205961198881

(119868119898+ 1198681198921

+ 11986811989221198942

2120578 + 11986811989241198942

4120578 + 11986811989251198942

5120578) 119898

= 1198791198881119898

minus 119879119904119898

minus 119887119898120596119898

119868119904119904= 119879119898119904

minus 119879119891minus 119887119904120596119904

(1)

where 119879119890= 119891(120572 120596

119890) 1198791198881198981

= 1198791198981198881

1198941120578 119879119898119904

= 119879119904119898119894119886120578 V = 120596

119904119877119882

1198791198881=

2

3(1198773

0minus 11987731

11987720minus 11987721

)1205831119865 (1199091) 1205961198881le 120596119890

1198791198711198881

1205961198881= 120596119890

(2)

119879119891= (

119862119889119860

2115V2 + 119898119892 sin 120579 + 119898119892 cos 120579119891 + 120575119898

119889V119889119905

)119877119882 (3)

120575 = 1 +1

119898

1198681198881119894211198942119886+ 1198681198981198942119886+ 119868119904+ 119868V

119877119882

(4)







1)










Clutch 1

Clutch 2

Tc1

120596c2

Tc2120596e

Te

Iebe

120596s

Tf

120596c1

Tmsbo

Io

VehicleEngine



119868119890119890+ 119887119890120596119890= 119879119890minus 1198791198881

119868119900119904+ 119887119900120596119904= 1198791198881119894119890minus 119879119891

(5)


119894119890= 11989411988611989411205782

119868119900= 119868119904+ (119868119898+ 1198681198921) 1198942

119886120578 + 11986811988811198942

11198942

1198861205782

+ 11986811989221198942

21198942

1198861205782

+ 11986811989241198942

41198942

1198861205782

+ 11986811989251198942

51198942

1198861205782

119887119900= 119887119904+ 1198871198981198942

119886120578 + 11988711988811198942

11198942

1198861205782

(6)


= 1198791198711198881 He clutch



1198791198881=119868119900(119879119890minus 119887119890120596119890) + (119879

119891+ 119887119900120596119904) 1198681198901198941119894119886

119868119900+ 1198681198901198941198901198941119894119886

(7)


119868119889119904+ 119887119889120596119904= 119879119890119894119890minus 119879119891 (8)

where

119868119889= 119868119904+ (119868119898+ 1198681198921) 1198942

119886120578 + (119868

1198881+ 119868119890) 1198942

11198942

1198861205782

+ 11986811989221198942

21198942

1198861205782

+ 11986811989241198942

41198942

1198861205782

+ 11986811989251198942

51198942

1198861205782

119887119889= 119887119904+ 1198871198981198942

119886120578 + (119887

1198881+ 119887119890) 1198942

11198942

1198861205782

(9)
















t lt 998779tYes

Yes

No

No



Lower control



pedal opening

d120573

dt

120573















Clutch target


120573

Accelerator

output torque Trefe


output torque Trefe

speed 120596refs

speed 120596refe












119890is shown

120596refe

tp

120596e(0)

120596e(ts)

ts

120596c1

Spee

d120596

(rad

s)

Time t (s)



120596ref119890

=

120596119890(119905119904) minus 120596119890(0)

119905119901

119905 + 120596119890(0) (120596

119890minus 1205961198881) ge Δ120596 119905 lt 119905

119901

120596119890(119905119904) other

(10)

where 120596119890(119905119904) and 120596








119890(119905119904)(rmin)






119890(119905119904) is shown in Table 1

Consider

120573V (119905) = 120573 (119905) + 119896 120573 (119905) (11)





119888(+) minus

119888(minus) =

119868119890

119868119890+ 119868119888119886


119888(minus)] (12)

where 119888(minus)






119904119877119882




0sim20 20sim50 50sim100













119904is set


119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0

051198951199011199052

119901+ 119895119901119905119901(119905119904minus 119905119901) + 05119895

119904(119905119904minus 119905119901)2

= 120596 (119905119904) 119877119882

(13)


js

ts

Time t (s)

Shoc

k in

tens

ityj

(ms3)

tp

jp


ts

Time t (s)

Acce

lera

tiona

(ms2)

tp


ts

Time t (s)

Velo

city

(ms

)

tp








119905119901= radic

120596 (119905119904) 119877119882

(05119895119901minus 051198952

119901119895119904)

119905119904= 119905119901(1 minus

119895119901

119895119904

)

(14)




119901and 119895119904twice

120596ref119904

= int119905119904

0

int119905119904

0

119895

119877119882

119889119905

120596ref1198881

= 120596ref1199041198941119894119886

(15)









0

1

2

3

t0

middotmiddotmiddot


Time t (s)

Velocity(m

s)

t0 + Δt t0 + 2Δt t0 + 3Δt



119890(119905119904) 119905119901 119905119904 and 119895





moments of 1199050 1199050+ Δ119905 119905

0+ 2Δ119905 and 119905



119886 (1199050) + 119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0

V (1199050) + 119886 (119905

0) 119905119901+1

21198951199011199052

119901+ (120572 (119905

0) + 119895119901119905119901) (119905119904minus 119905119901)

+1

2119895119904(119905119904minus 119905119901)2

= 120596 (119905119904) 119877119882

(16)












120596ref119890

=

120596119890(119905119904) minus 120596119890(0)

119905119901

119905 + 120596119890(0) (120596

119890minus 1205961198881) ge Δ120596

1199050lt 119905 lt (119905

0+ 119905119901)

120596119890(119905119904) other

(17)


119901and 119895

119904



119882 = int1199050+119905119904

1199050

1198881(120596

ref119890

minus 1205961198881) 119889119905

1198881=119868119900ref119904

+ 119887119900120596ref119904

+ 119898119892119877119882120583

11989411988611989411205782

(18)


1198881minus1198881| lt 120576





119865 =1

119882 (19)


119904can be

seen in Figure 8



1 the relationship




1= 120579119904 1199092= 120596119904 there is

1= 1199092

2=

119894119890

119868119900

1198791198881minus1198870

1198680

1199092minus119879119891

1198680

(20)


t0 t0 + ts

a(t0)

Time t (s)

Acce

lera

tiona

(ms2)

t0 + tp


(t0)

t0 t0 + ts

Time t (s)

Velo

city

(ms

)

t0 + tp






velocity

Engine target speed


estimation


Targ

et im

pact

stren

gth

optim

izat

ion

Geneticalgorithm


slidingfriction

energy andfitness

function





1 there is

[1198901

1198902

] = [

[

0 1

0 minus1198870

1198680

]

]

[1198901

1198902

] + [

[

0

minus119894119890

1198680

]

]

1199061+ [

0

1198912

] + [0

1198913

] (21)






1198911015840

2= 119903+1198680

1198870

119903+119898119892119891

1198870

(22)


1198911015840

3=119879119891

1198680

minus119898119892119891

1198870

(23)




3 (25)

where 119889 gt |11988821198911015840

3|

119892 (119904) =

sgn (119904) |119904| ge120587

2119901

sin (119901 sdot 119904) |119904| lt120587

2119901

119901 gt 0 (26)



1199061=

1198680

1198882119894119890

[119896 sdot 119904 + 119889 sdot 119892 (119904) + 1198902(1198881minus 1198882

1198870

1198680

) + 11988821198911015840

2] (27)


119890and 119879


119890) model and





100

90

80

70

60

50

40

30

20

10

0050 15 2 25 3 35 41

Time t (s)

Acce

lera

tion

peda

l ope

ning120573

()



0500

15 2 25 3 35 41

250

200

150

100

50

Time t (s)

Targ

et sp

eed120596

(rad

s)



050 15 2 25 3 35 410

250

200

150

100

50

Time t (s)

Real

spee

d120596

(rad

s)



050 15 2 25 3 35 41

6

4

2

0

minus2

minus4

minus6

Time t (s)

Targ

et sh

ock

inte

nsityj

(ms3)



050 15 2 25 3 35 41

6

4

2

0

minus2

minus4

minus6

Time t (s)

Real

shoc

k in

tens

ityj

(ms3)



140

120

100

80

60

40

20

0050 15 2 25 3 35 41

Time t (s)

Engi

ne o

utpu

t tor

queT

e(N

m)



Figure 9 Continued


050 15 2 25 3 35 41

140

120

100

80

60

40

20

0

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)



050 15 2 25 3 35 41

20

18

16

14

12

10

8

6

4

2

0

Time t (s)

Vehi

cle v

eloc

ity

(km

h)




1199091119890

= 120579119890 1119890

= 120579119890= 120596119890 1198901119890

= 119909119903119890minus 1199091119890 1198902119890

= 119903119890minus 1199092119890


119890 namely

[1198901119890

1198902119890

] = [

[

0 1

0 minus119887119890

119868119890

]

]

[1198901119890

1198902119890

] + [

[

0

minus1

119868119890

]

]

1199062+ [

0

1198912119890

] (28)

where 1199062= 119879119890 1198912119890

= (1198791198881119868119890) + 119903119890+ (119887119890119868119890)119903119890 which are


119904119890= 11988811198901198901119890+ 11988821198901198902119890 (29)



where 119889119890gt |11988821198901198912119890|

119892 (119904) =

sgn (119904) |119904| ge120587

2119901119890

sin (119901119890sdot 119904) |119904| lt

120587

2119901119890

119901 gt 0 (31)


formula

1199062=119868119890

1198882

[119896119890sdot 119904119890+ 119889119890sdot 119892 (119904119890) + 1198902119890(1198881119890minus 1198882119890

119887119890

119868119890

) + 11988821198901198912119890]

(32)



119879119889

119890= 119879119871

119890+ 119870119890119905 (33)

119870119890= (

119879119889119890minus 119879119871119890

Δ119905) (34)



119890is



119895 =119894119890119877119882

119868119889

119890 (35)



050 15 2 25 3 35 41

25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

etp

(s)

Time t (s)



050 15 2 25 3 35 41

3

25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

ets

(s)

Time t (s)



050 15 2 25 3 35 41

100

90

80

70

60

50

40

30

20

10

0


Clut

ch tr

ansfe

r tor

queT

c1(N

m)

Time t (s)


050 15 2 25 3 35 41

100

90

80

70

60

50

40

30

20

10

0


Clut

ch tr

ansfe

r tor

queT

c1(N

m)

Time t (s)




119895 =119894119890119877119882

1198680

1198881 (36)







Key signal


Brake pedal signal








control system


Clutch 1 actuator

Clutch 2 actuator




MicroAutoBox





119904s 2355 2535



119904+ Δ119905)s 314 333





119901and 119905












Time t (s)

100

80

60

40

20

08 10 12 14 16

Acce

lera

tor p

edal

ope

ning120573

()


250

200

150

100

50

0


8 10 12 14 16

Time t (s)

Targ

et ro

tatio

nal s

peed120596

(rad

s)



8 10 12 14 16

250

200

150

100

50

0

Time t (s)

Real

spee

d120596

(rad

s)


10

5

0

minus5

minus108 10 12 14 16

Shoc

k in

tens

ityj

(ms3)

Time t (s)

(d) Shock intensity

7

6

5

4

3

2

1

08 9 10 11 12 13 14 15 16 17

Time t (s)

Slid

ing

fric

tion

wor

kW

(kJ)


Time t (s)8 10 12 14 16

120

100

80

60

40

20

0

Torq

ueT

(Nm

)


(f) Torque

Figure 12 Continued


25

20

15

10

5

0

Time t (s)8 10 12 14 16

Vehi

cle v

eloc

ity

(km

h)


120

100

80

60

40

20

08 9 10 11 12 13

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)



25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

et(s

)

8 9 10 11 12 13

Time t (s)

tPts


15

10

5

0

Clut

ch se

para

ting

strok

ex(m

m)

Time t (s)8 10 12 14 16











0+ 119905119904)s 1196







100

80

60

40

20

08194 8198 8202 8206 821 8214

Time t (s)

Acce

lera

tor o

peni

ng120573

()


8194 8198 8202 8206 821 8214

350

300

250

200

150

100

50

0


Time t (s)

Rota

tiona

l spe

ed120596

(rad

s)


8194 8198 8202 8206 821 8214

10

5

0

minus5

Time t (s)

Shoc

k in

tens

ityj

(ms3)

(c) Shock intensity








7 Conclusion



e eng

ine o

utpu

t tor

que (

Nm

)



250

200

150

100

50

0100

8060

4020

0 10002000

30004000

50006000

Figure 15



1198681198881 0014 kgsdotm2

1198681198882 0014 kgsdotm2

119868119898 001 kgsdotm2

119868119904 1470392 kgsdotm2

I1198921


119868119892119903 0005 kgsdotm2

i1 simi53615 2042 1257

0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2

119860 2095m119862119889 0293

119877119908 0308m

120578 0921198770 0228m

1198771 015m



Appendices


See Figure 15


See Table 5



References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra















driven gears


driving gears



output shaft


















1198791198881198981

1198791198881198982


1198791198981198881

1198791198981198882












119868119890119890= 119879119890minus 1198791198881minus 119887119890120596119890

11986811988811198881= 1198791198881minus 1198791198981198881

minus 11988711988811205961198881

(119868119898+ 1198681198921

+ 11986811989221198942

2120578 + 11986811989241198942

4120578 + 11986811989251198942

5120578) 119898

= 1198791198881119898

minus 119879119904119898

minus 119887119898120596119898

119868119904119904= 119879119898119904

minus 119879119891minus 119887119904120596119904

(1)

where 119879119890= 119891(120572 120596

119890) 1198791198881198981

= 1198791198981198881

1198941120578 119879119898119904

= 119879119904119898119894119886120578 V = 120596

119904119877119882

1198791198881=

2

3(1198773

0minus 11987731

11987720minus 11987721

)1205831119865 (1199091) 1205961198881le 120596119890

1198791198711198881

1205961198881= 120596119890

(2)

119879119891= (

119862119889119860

2115V2 + 119898119892 sin 120579 + 119898119892 cos 120579119891 + 120575119898

119889V119889119905

)119877119882 (3)

120575 = 1 +1

119898

1198681198881119894211198942119886+ 1198681198981198942119886+ 119868119904+ 119868V

119877119882

(4)







1)










Clutch 1

Clutch 2

Tc1

120596c2

Tc2120596e

Te

Iebe

120596s

Tf

120596c1

Tmsbo

Io

VehicleEngine



119868119890119890+ 119887119890120596119890= 119879119890minus 1198791198881

119868119900119904+ 119887119900120596119904= 1198791198881119894119890minus 119879119891

(5)


119894119890= 11989411988611989411205782

119868119900= 119868119904+ (119868119898+ 1198681198921) 1198942

119886120578 + 11986811988811198942

11198942

1198861205782

+ 11986811989221198942

21198942

1198861205782

+ 11986811989241198942

41198942

1198861205782

+ 11986811989251198942

51198942

1198861205782

119887119900= 119887119904+ 1198871198981198942

119886120578 + 11988711988811198942

11198942

1198861205782

(6)


= 1198791198711198881 He clutch



1198791198881=119868119900(119879119890minus 119887119890120596119890) + (119879

119891+ 119887119900120596119904) 1198681198901198941119894119886

119868119900+ 1198681198901198941198901198941119894119886

(7)


119868119889119904+ 119887119889120596119904= 119879119890119894119890minus 119879119891 (8)

where

119868119889= 119868119904+ (119868119898+ 1198681198921) 1198942

119886120578 + (119868

1198881+ 119868119890) 1198942

11198942

1198861205782

+ 11986811989221198942

21198942

1198861205782

+ 11986811989241198942

41198942

1198861205782

+ 11986811989251198942

51198942

1198861205782

119887119889= 119887119904+ 1198871198981198942

119886120578 + (119887

1198881+ 119887119890) 1198942

11198942

1198861205782

(9)
















t lt 998779tYes

Yes

No

No



Lower control



pedal opening

d120573

dt

120573















Clutch target


120573

Accelerator

output torque Trefe


output torque Trefe

speed 120596refs

speed 120596refe












119890is shown

120596refe

tp

120596e(0)

120596e(ts)

ts

120596c1

Spee

d120596

(rad

s)

Time t (s)



120596ref119890

=

120596119890(119905119904) minus 120596119890(0)

119905119901

119905 + 120596119890(0) (120596

119890minus 1205961198881) ge Δ120596 119905 lt 119905

119901

120596119890(119905119904) other

(10)

where 120596119890(119905119904) and 120596








119890(119905119904)(rmin)






119890(119905119904) is shown in Table 1

Consider

120573V (119905) = 120573 (119905) + 119896 120573 (119905) (11)





119888(+) minus

119888(minus) =

119868119890

119868119890+ 119868119888119886


119888(minus)] (12)

where 119888(minus)






119904119877119882




0sim20 20sim50 50sim100













119904is set


119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0

051198951199011199052

119901+ 119895119901119905119901(119905119904minus 119905119901) + 05119895

119904(119905119904minus 119905119901)2

= 120596 (119905119904) 119877119882

(13)


js

ts

Time t (s)

Shoc

k in

tens

ityj

(ms3)

tp

jp


ts

Time t (s)

Acce

lera

tiona

(ms2)

tp


ts

Time t (s)

Velo

city

(ms

)

tp








119905119901= radic

120596 (119905119904) 119877119882

(05119895119901minus 051198952

119901119895119904)

119905119904= 119905119901(1 minus

119895119901

119895119904

)

(14)




119901and 119895119904twice

120596ref119904

= int119905119904

0

int119905119904

0

119895

119877119882

119889119905

120596ref1198881

= 120596ref1199041198941119894119886

(15)









0

1

2

3

t0

middotmiddotmiddot


Time t (s)

Velocity(m

s)

t0 + Δt t0 + 2Δt t0 + 3Δt



119890(119905119904) 119905119901 119905119904 and 119895





moments of 1199050 1199050+ Δ119905 119905

0+ 2Δ119905 and 119905



119886 (1199050) + 119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0

V (1199050) + 119886 (119905

0) 119905119901+1

21198951199011199052

119901+ (120572 (119905

0) + 119895119901119905119901) (119905119904minus 119905119901)

+1

2119895119904(119905119904minus 119905119901)2

= 120596 (119905119904) 119877119882

(16)












120596ref119890

=

120596119890(119905119904) minus 120596119890(0)

119905119901

119905 + 120596119890(0) (120596

119890minus 1205961198881) ge Δ120596

1199050lt 119905 lt (119905

0+ 119905119901)

120596119890(119905119904) other

(17)


119901and 119895

119904



119882 = int1199050+119905119904

1199050

1198881(120596

ref119890

minus 1205961198881) 119889119905

1198881=119868119900ref119904

+ 119887119900120596ref119904

+ 119898119892119877119882120583

11989411988611989411205782

(18)


1198881minus1198881| lt 120576





119865 =1

119882 (19)


119904can be

seen in Figure 8



1 the relationship




1= 120579119904 1199092= 120596119904 there is

1= 1199092

2=

119894119890

119868119900

1198791198881minus1198870

1198680

1199092minus119879119891

1198680

(20)


t0 t0 + ts

a(t0)

Time t (s)

Acce

lera

tiona

(ms2)

t0 + tp


(t0)

t0 t0 + ts

Time t (s)

Velo

city

(ms

)

t0 + tp






velocity

Engine target speed


estimation


Targ

et im

pact

stren

gth

optim

izat

ion

Geneticalgorithm


slidingfriction

energy andfitness

function





1 there is

[1198901

1198902

] = [

[

0 1

0 minus1198870

1198680

]

]

[1198901

1198902

] + [

[

0

minus119894119890

1198680

]

]

1199061+ [

0

1198912

] + [0

1198913

] (21)






1198911015840

2= 119903+1198680

1198870

119903+119898119892119891

1198870

(22)


1198911015840

3=119879119891

1198680

minus119898119892119891

1198870

(23)




3 (25)

where 119889 gt |11988821198911015840

3|

119892 (119904) =

sgn (119904) |119904| ge120587

2119901

sin (119901 sdot 119904) |119904| lt120587

2119901

119901 gt 0 (26)



1199061=

1198680

1198882119894119890

[119896 sdot 119904 + 119889 sdot 119892 (119904) + 1198902(1198881minus 1198882

1198870

1198680

) + 11988821198911015840

2] (27)


119890and 119879


119890) model and





100

90

80

70

60

50

40

30

20

10

0050 15 2 25 3 35 41

Time t (s)

Acce

lera

tion

peda

l ope

ning120573

()



0500

15 2 25 3 35 41

250

200

150

100

50

Time t (s)

Targ

et sp

eed120596

(rad

s)



050 15 2 25 3 35 410

250

200

150

100

50

Time t (s)

Real

spee

d120596

(rad

s)



050 15 2 25 3 35 41

6

4

2

0

minus2

minus4

minus6

Time t (s)

Targ

et sh

ock

inte

nsityj

(ms3)



050 15 2 25 3 35 41

6

4

2

0

minus2

minus4

minus6

Time t (s)

Real

shoc

k in

tens

ityj

(ms3)



140

120

100

80

60

40

20

0050 15 2 25 3 35 41

Time t (s)

Engi

ne o

utpu

t tor

queT

e(N

m)



Figure 9 Continued


050 15 2 25 3 35 41

140

120

100

80

60

40

20

0

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)



050 15 2 25 3 35 41

20

18

16

14

12

10

8

6

4

2

0

Time t (s)

Vehi

cle v

eloc

ity

(km

h)




1199091119890

= 120579119890 1119890

= 120579119890= 120596119890 1198901119890

= 119909119903119890minus 1199091119890 1198902119890

= 119903119890minus 1199092119890


119890 namely

[1198901119890

1198902119890

] = [

[

0 1

0 minus119887119890

119868119890

]

]

[1198901119890

1198902119890

] + [

[

0

minus1

119868119890

]

]

1199062+ [

0

1198912119890

] (28)

where 1199062= 119879119890 1198912119890

= (1198791198881119868119890) + 119903119890+ (119887119890119868119890)119903119890 which are


119904119890= 11988811198901198901119890+ 11988821198901198902119890 (29)



where 119889119890gt |11988821198901198912119890|

119892 (119904) =

sgn (119904) |119904| ge120587

2119901119890

sin (119901119890sdot 119904) |119904| lt

120587

2119901119890

119901 gt 0 (31)


formula

1199062=119868119890

1198882

[119896119890sdot 119904119890+ 119889119890sdot 119892 (119904119890) + 1198902119890(1198881119890minus 1198882119890

119887119890

119868119890

) + 11988821198901198912119890]

(32)



119879119889

119890= 119879119871

119890+ 119870119890119905 (33)

119870119890= (

119879119889119890minus 119879119871119890

Δ119905) (34)



119890is



119895 =119894119890119877119882

119868119889

119890 (35)



050 15 2 25 3 35 41

25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

etp

(s)

Time t (s)



050 15 2 25 3 35 41

3

25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

ets

(s)

Time t (s)



050 15 2 25 3 35 41

100

90

80

70

60

50

40

30

20

10

0


Clut

ch tr

ansfe

r tor

queT

c1(N

m)

Time t (s)


050 15 2 25 3 35 41

100

90

80

70

60

50

40

30

20

10

0


Clut

ch tr

ansfe

r tor

queT

c1(N

m)

Time t (s)




119895 =119894119890119877119882

1198680

1198881 (36)







Key signal


Brake pedal signal








control system


Clutch 1 actuator

Clutch 2 actuator




MicroAutoBox





119904s 2355 2535



119904+ Δ119905)s 314 333





119901and 119905












Time t (s)

100

80

60

40

20

08 10 12 14 16

Acce

lera

tor p

edal

ope

ning120573

()


250

200

150

100

50

0


8 10 12 14 16

Time t (s)

Targ

et ro

tatio

nal s

peed120596

(rad

s)



8 10 12 14 16

250

200

150

100

50

0

Time t (s)

Real

spee

d120596

(rad

s)


10

5

0

minus5

minus108 10 12 14 16

Shoc

k in

tens

ityj

(ms3)

Time t (s)

(d) Shock intensity

7

6

5

4

3

2

1

08 9 10 11 12 13 14 15 16 17

Time t (s)

Slid

ing

fric

tion

wor

kW

(kJ)


Time t (s)8 10 12 14 16

120

100

80

60

40

20

0

Torq

ueT

(Nm

)


(f) Torque

Figure 12 Continued


25

20

15

10

5

0

Time t (s)8 10 12 14 16

Vehi

cle v

eloc

ity

(km

h)


120

100

80

60

40

20

08 9 10 11 12 13

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)



25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

et(s

)

8 9 10 11 12 13

Time t (s)

tPts


15

10

5

0

Clut

ch se

para

ting

strok

ex(m

m)

Time t (s)8 10 12 14 16











0+ 119905119904)s 1196







100

80

60

40

20

08194 8198 8202 8206 821 8214

Time t (s)

Acce

lera

tor o

peni

ng120573

()


8194 8198 8202 8206 821 8214

350

300

250

200

150

100

50

0


Time t (s)

Rota

tiona

l spe

ed120596

(rad

s)


8194 8198 8202 8206 821 8214

10

5

0

minus5

Time t (s)

Shoc

k in

tens

ityj

(ms3)

(c) Shock intensity








7 Conclusion



e eng

ine o

utpu

t tor

que (

Nm

)



250

200

150

100

50

0100

8060

4020

0 10002000

30004000

50006000

Figure 15



1198681198881 0014 kgsdotm2

1198681198882 0014 kgsdotm2

119868119898 001 kgsdotm2

119868119904 1470392 kgsdotm2

I1198921


119868119892119903 0005 kgsdotm2

i1 simi53615 2042 1257

0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2

119860 2095m119862119889 0293

119877119908 0308m

120578 0921198770 0228m

1198771 015m



Appendices


See Figure 15


See Table 5



References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Clutch 1

Clutch 2

Tc1

120596c2

Tc2120596e

Te

Iebe

120596s

Tf

120596c1

Tmsbo

Io

VehicleEngine



119868119890119890+ 119887119890120596119890= 119879119890minus 1198791198881

119868119900119904+ 119887119900120596119904= 1198791198881119894119890minus 119879119891

(5)


119894119890= 11989411988611989411205782

119868119900= 119868119904+ (119868119898+ 1198681198921) 1198942

119886120578 + 11986811988811198942

11198942

1198861205782

+ 11986811989221198942

21198942

1198861205782

+ 11986811989241198942

41198942

1198861205782

+ 11986811989251198942

51198942

1198861205782

119887119900= 119887119904+ 1198871198981198942

119886120578 + 11988711988811198942

11198942

1198861205782

(6)


= 1198791198711198881 He clutch



1198791198881=119868119900(119879119890minus 119887119890120596119890) + (119879

119891+ 119887119900120596119904) 1198681198901198941119894119886

119868119900+ 1198681198901198941198901198941119894119886

(7)


119868119889119904+ 119887119889120596119904= 119879119890119894119890minus 119879119891 (8)

where

119868119889= 119868119904+ (119868119898+ 1198681198921) 1198942

119886120578 + (119868

1198881+ 119868119890) 1198942

11198942

1198861205782

+ 11986811989221198942

21198942

1198861205782

+ 11986811989241198942

41198942

1198861205782

+ 11986811989251198942

51198942

1198861205782

119887119889= 119887119904+ 1198871198981198942

119886120578 + (119887

1198881+ 119887119890) 1198942

11198942

1198861205782

(9)
















t lt 998779tYes

Yes

No

No



Lower control



pedal opening

d120573

dt

120573















Clutch target


120573

Accelerator

output torque Trefe


output torque Trefe

speed 120596refs

speed 120596refe












119890is shown

120596refe

tp

120596e(0)

120596e(ts)

ts

120596c1

Spee

d120596

(rad

s)

Time t (s)



120596ref119890

=

120596119890(119905119904) minus 120596119890(0)

119905119901

119905 + 120596119890(0) (120596

119890minus 1205961198881) ge Δ120596 119905 lt 119905

119901

120596119890(119905119904) other

(10)

where 120596119890(119905119904) and 120596








119890(119905119904)(rmin)






119890(119905119904) is shown in Table 1

Consider

120573V (119905) = 120573 (119905) + 119896 120573 (119905) (11)





119888(+) minus

119888(minus) =

119868119890

119868119890+ 119868119888119886


119888(minus)] (12)

where 119888(minus)






119904119877119882




0sim20 20sim50 50sim100













119904is set


119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0

051198951199011199052

119901+ 119895119901119905119901(119905119904minus 119905119901) + 05119895

119904(119905119904minus 119905119901)2

= 120596 (119905119904) 119877119882

(13)


js

ts

Time t (s)

Shoc

k in

tens

ityj

(ms3)

tp

jp


ts

Time t (s)

Acce

lera

tiona

(ms2)

tp


ts

Time t (s)

Velo

city

(ms

)

tp








119905119901= radic

120596 (119905119904) 119877119882

(05119895119901minus 051198952

119901119895119904)

119905119904= 119905119901(1 minus

119895119901

119895119904

)

(14)




119901and 119895119904twice

120596ref119904

= int119905119904

0

int119905119904

0

119895

119877119882

119889119905

120596ref1198881

= 120596ref1199041198941119894119886

(15)









0

1

2

3

t0

middotmiddotmiddot


Time t (s)

Velocity(m

s)

t0 + Δt t0 + 2Δt t0 + 3Δt



119890(119905119904) 119905119901 119905119904 and 119895





moments of 1199050 1199050+ Δ119905 119905

0+ 2Δ119905 and 119905



119886 (1199050) + 119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0

V (1199050) + 119886 (119905

0) 119905119901+1

21198951199011199052

119901+ (120572 (119905

0) + 119895119901119905119901) (119905119904minus 119905119901)

+1

2119895119904(119905119904minus 119905119901)2

= 120596 (119905119904) 119877119882

(16)












120596ref119890

=

120596119890(119905119904) minus 120596119890(0)

119905119901

119905 + 120596119890(0) (120596

119890minus 1205961198881) ge Δ120596

1199050lt 119905 lt (119905

0+ 119905119901)

120596119890(119905119904) other

(17)


119901and 119895

119904



119882 = int1199050+119905119904

1199050

1198881(120596

ref119890

minus 1205961198881) 119889119905

1198881=119868119900ref119904

+ 119887119900120596ref119904

+ 119898119892119877119882120583

11989411988611989411205782

(18)


1198881minus1198881| lt 120576





119865 =1

119882 (19)


119904can be

seen in Figure 8



1 the relationship




1= 120579119904 1199092= 120596119904 there is

1= 1199092

2=

119894119890

119868119900

1198791198881minus1198870

1198680

1199092minus119879119891

1198680

(20)


t0 t0 + ts

a(t0)

Time t (s)

Acce

lera

tiona

(ms2)

t0 + tp


(t0)

t0 t0 + ts

Time t (s)

Velo

city

(ms

)

t0 + tp






velocity

Engine target speed


estimation


Targ

et im

pact

stren

gth

optim

izat

ion

Geneticalgorithm


slidingfriction

energy andfitness

function





1 there is

[1198901

1198902

] = [

[

0 1

0 minus1198870

1198680

]

]

[1198901

1198902

] + [

[

0

minus119894119890

1198680

]

]

1199061+ [

0

1198912

] + [0

1198913

] (21)






1198911015840

2= 119903+1198680

1198870

119903+119898119892119891

1198870

(22)


1198911015840

3=119879119891

1198680

minus119898119892119891

1198870

(23)




3 (25)

where 119889 gt |11988821198911015840

3|

119892 (119904) =

sgn (119904) |119904| ge120587

2119901

sin (119901 sdot 119904) |119904| lt120587

2119901

119901 gt 0 (26)



1199061=

1198680

1198882119894119890

[119896 sdot 119904 + 119889 sdot 119892 (119904) + 1198902(1198881minus 1198882

1198870

1198680

) + 11988821198911015840

2] (27)


119890and 119879


119890) model and





100

90

80

70

60

50

40

30

20

10

0050 15 2 25 3 35 41

Time t (s)

Acce

lera

tion

peda

l ope

ning120573

()



0500

15 2 25 3 35 41

250

200

150

100

50

Time t (s)

Targ

et sp

eed120596

(rad

s)



050 15 2 25 3 35 410

250

200

150

100

50

Time t (s)

Real

spee

d120596

(rad

s)



050 15 2 25 3 35 41

6

4

2

0

minus2

minus4

minus6

Time t (s)

Targ

et sh

ock

inte

nsityj

(ms3)



050 15 2 25 3 35 41

6

4

2

0

minus2

minus4

minus6

Time t (s)

Real

shoc

k in

tens

ityj

(ms3)



140

120

100

80

60

40

20

0050 15 2 25 3 35 41

Time t (s)

Engi

ne o

utpu

t tor

queT

e(N

m)



Figure 9 Continued


050 15 2 25 3 35 41

140

120

100

80

60

40

20

0

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)



050 15 2 25 3 35 41

20

18

16

14

12

10

8

6

4

2

0

Time t (s)

Vehi

cle v

eloc

ity

(km

h)




1199091119890

= 120579119890 1119890

= 120579119890= 120596119890 1198901119890

= 119909119903119890minus 1199091119890 1198902119890

= 119903119890minus 1199092119890


119890 namely

[1198901119890

1198902119890

] = [

[

0 1

0 minus119887119890

119868119890

]

]

[1198901119890

1198902119890

] + [

[

0

minus1

119868119890

]

]

1199062+ [

0

1198912119890

] (28)

where 1199062= 119879119890 1198912119890

= (1198791198881119868119890) + 119903119890+ (119887119890119868119890)119903119890 which are


119904119890= 11988811198901198901119890+ 11988821198901198902119890 (29)



where 119889119890gt |11988821198901198912119890|

119892 (119904) =

sgn (119904) |119904| ge120587

2119901119890

sin (119901119890sdot 119904) |119904| lt

120587

2119901119890

119901 gt 0 (31)


formula

1199062=119868119890

1198882

[119896119890sdot 119904119890+ 119889119890sdot 119892 (119904119890) + 1198902119890(1198881119890minus 1198882119890

119887119890

119868119890

) + 11988821198901198912119890]

(32)



119879119889

119890= 119879119871

119890+ 119870119890119905 (33)

119870119890= (

119879119889119890minus 119879119871119890

Δ119905) (34)



119890is



119895 =119894119890119877119882

119868119889

119890 (35)



050 15 2 25 3 35 41

25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

etp

(s)

Time t (s)



050 15 2 25 3 35 41

3

25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

ets

(s)

Time t (s)



050 15 2 25 3 35 41

100

90

80

70

60

50

40

30

20

10

0


Clut

ch tr

ansfe

r tor

queT

c1(N

m)

Time t (s)


050 15 2 25 3 35 41

100

90

80

70

60

50

40

30

20

10

0


Clut

ch tr

ansfe

r tor

queT

c1(N

m)

Time t (s)




119895 =119894119890119877119882

1198680

1198881 (36)







Key signal


Brake pedal signal








control system


Clutch 1 actuator

Clutch 2 actuator




MicroAutoBox





119904s 2355 2535



119904+ Δ119905)s 314 333





119901and 119905












Time t (s)

100

80

60

40

20

08 10 12 14 16

Acce

lera

tor p

edal

ope

ning120573

()


250

200

150

100

50

0


8 10 12 14 16

Time t (s)

Targ

et ro

tatio

nal s

peed120596

(rad

s)



8 10 12 14 16

250

200

150

100

50

0

Time t (s)

Real

spee

d120596

(rad

s)


10

5

0

minus5

minus108 10 12 14 16

Shoc

k in

tens

ityj

(ms3)

Time t (s)

(d) Shock intensity

7

6

5

4

3

2

1

08 9 10 11 12 13 14 15 16 17

Time t (s)

Slid

ing

fric

tion

wor

kW

(kJ)


Time t (s)8 10 12 14 16

120

100

80

60

40

20

0

Torq

ueT

(Nm

)


(f) Torque

Figure 12 Continued


25

20

15

10

5

0

Time t (s)8 10 12 14 16

Vehi

cle v

eloc

ity

(km

h)


120

100

80

60

40

20

08 9 10 11 12 13

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)



25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

et(s

)

8 9 10 11 12 13

Time t (s)

tPts


15

10

5

0

Clut

ch se

para

ting

strok

ex(m

m)

Time t (s)8 10 12 14 16











0+ 119905119904)s 1196







100

80

60

40

20

08194 8198 8202 8206 821 8214

Time t (s)

Acce

lera

tor o

peni

ng120573

()


8194 8198 8202 8206 821 8214

350

300

250

200

150

100

50

0


Time t (s)

Rota

tiona

l spe

ed120596

(rad

s)


8194 8198 8202 8206 821 8214

10

5

0

minus5

Time t (s)

Shoc

k in

tens

ityj

(ms3)

(c) Shock intensity








7 Conclusion



e eng

ine o

utpu

t tor

que (

Nm

)



250

200

150

100

50

0100

8060

4020

0 10002000

30004000

50006000

Figure 15



1198681198881 0014 kgsdotm2

1198681198882 0014 kgsdotm2

119868119898 001 kgsdotm2

119868119904 1470392 kgsdotm2

I1198921


119868119892119903 0005 kgsdotm2

i1 simi53615 2042 1257

0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2

119860 2095m119862119889 0293

119877119908 0308m

120578 0921198770 0228m

1198771 015m



Appendices


See Figure 15


See Table 5



References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra













t lt 998779tYes

Yes

No

No



Lower control



pedal opening

d120573

dt

120573















Clutch target


120573

Accelerator

output torque Trefe


output torque Trefe

speed 120596refs

speed 120596refe












119890is shown

120596refe

tp

120596e(0)

120596e(ts)

ts

120596c1

Spee

d120596

(rad

s)

Time t (s)



120596ref119890

=

120596119890(119905119904) minus 120596119890(0)

119905119901

119905 + 120596119890(0) (120596

119890minus 1205961198881) ge Δ120596 119905 lt 119905

119901

120596119890(119905119904) other

(10)

where 120596119890(119905119904) and 120596








119890(119905119904)(rmin)






119890(119905119904) is shown in Table 1

Consider

120573V (119905) = 120573 (119905) + 119896 120573 (119905) (11)





119888(+) minus

119888(minus) =

119868119890

119868119890+ 119868119888119886


119888(minus)] (12)

where 119888(minus)






119904119877119882




0sim20 20sim50 50sim100













119904is set


119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0

051198951199011199052

119901+ 119895119901119905119901(119905119904minus 119905119901) + 05119895

119904(119905119904minus 119905119901)2

= 120596 (119905119904) 119877119882

(13)


js

ts

Time t (s)

Shoc

k in

tens

ityj

(ms3)

tp

jp


ts

Time t (s)

Acce

lera

tiona

(ms2)

tp


ts

Time t (s)

Velo

city

(ms

)

tp








119905119901= radic

120596 (119905119904) 119877119882

(05119895119901minus 051198952

119901119895119904)

119905119904= 119905119901(1 minus

119895119901

119895119904

)

(14)




119901and 119895119904twice

120596ref119904

= int119905119904

0

int119905119904

0

119895

119877119882

119889119905

120596ref1198881

= 120596ref1199041198941119894119886

(15)









0

1

2

3

t0

middotmiddotmiddot


Time t (s)

Velocity(m

s)

t0 + Δt t0 + 2Δt t0 + 3Δt



119890(119905119904) 119905119901 119905119904 and 119895





moments of 1199050 1199050+ Δ119905 119905

0+ 2Δ119905 and 119905



119886 (1199050) + 119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0

V (1199050) + 119886 (119905

0) 119905119901+1

21198951199011199052

119901+ (120572 (119905

0) + 119895119901119905119901) (119905119904minus 119905119901)

+1

2119895119904(119905119904minus 119905119901)2

= 120596 (119905119904) 119877119882

(16)












120596ref119890

=

120596119890(119905119904) minus 120596119890(0)

119905119901

119905 + 120596119890(0) (120596

119890minus 1205961198881) ge Δ120596

1199050lt 119905 lt (119905

0+ 119905119901)

120596119890(119905119904) other

(17)


119901and 119895

119904



119882 = int1199050+119905119904

1199050

1198881(120596

ref119890

minus 1205961198881) 119889119905

1198881=119868119900ref119904

+ 119887119900120596ref119904

+ 119898119892119877119882120583

11989411988611989411205782

(18)


1198881minus1198881| lt 120576





119865 =1

119882 (19)


119904can be

seen in Figure 8



1 the relationship




1= 120579119904 1199092= 120596119904 there is

1= 1199092

2=

119894119890

119868119900

1198791198881minus1198870

1198680

1199092minus119879119891

1198680

(20)


t0 t0 + ts

a(t0)

Time t (s)

Acce

lera

tiona

(ms2)

t0 + tp


(t0)

t0 t0 + ts

Time t (s)

Velo

city

(ms

)

t0 + tp






velocity

Engine target speed


estimation


Targ

et im

pact

stren

gth

optim

izat

ion

Geneticalgorithm


slidingfriction

energy andfitness

function





1 there is

[1198901

1198902

] = [

[

0 1

0 minus1198870

1198680

]

]

[1198901

1198902

] + [

[

0

minus119894119890

1198680

]

]

1199061+ [

0

1198912

] + [0

1198913

] (21)






1198911015840

2= 119903+1198680

1198870

119903+119898119892119891

1198870

(22)


1198911015840

3=119879119891

1198680

minus119898119892119891

1198870

(23)




3 (25)

where 119889 gt |11988821198911015840

3|

119892 (119904) =

sgn (119904) |119904| ge120587

2119901

sin (119901 sdot 119904) |119904| lt120587

2119901

119901 gt 0 (26)



1199061=

1198680

1198882119894119890

[119896 sdot 119904 + 119889 sdot 119892 (119904) + 1198902(1198881minus 1198882

1198870

1198680

) + 11988821198911015840

2] (27)


119890and 119879


119890) model and





100

90

80

70

60

50

40

30

20

10

0050 15 2 25 3 35 41

Time t (s)

Acce

lera

tion

peda

l ope

ning120573

()



0500

15 2 25 3 35 41

250

200

150

100

50

Time t (s)

Targ

et sp

eed120596

(rad

s)



050 15 2 25 3 35 410

250

200

150

100

50

Time t (s)

Real

spee

d120596

(rad

s)



050 15 2 25 3 35 41

6

4

2

0

minus2

minus4

minus6

Time t (s)

Targ

et sh

ock

inte

nsityj

(ms3)



050 15 2 25 3 35 41

6

4

2

0

minus2

minus4

minus6

Time t (s)

Real

shoc

k in

tens

ityj

(ms3)



140

120

100

80

60

40

20

0050 15 2 25 3 35 41

Time t (s)

Engi

ne o

utpu

t tor

queT

e(N

m)



Figure 9 Continued


050 15 2 25 3 35 41

140

120

100

80

60

40

20

0

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)



050 15 2 25 3 35 41

20

18

16

14

12

10

8

6

4

2

0

Time t (s)

Vehi

cle v

eloc

ity

(km

h)




1199091119890

= 120579119890 1119890

= 120579119890= 120596119890 1198901119890

= 119909119903119890minus 1199091119890 1198902119890

= 119903119890minus 1199092119890


119890 namely

[1198901119890

1198902119890

] = [

[

0 1

0 minus119887119890

119868119890

]

]

[1198901119890

1198902119890

] + [

[

0

minus1

119868119890

]

]

1199062+ [

0

1198912119890

] (28)

where 1199062= 119879119890 1198912119890

= (1198791198881119868119890) + 119903119890+ (119887119890119868119890)119903119890 which are


119904119890= 11988811198901198901119890+ 11988821198901198902119890 (29)



where 119889119890gt |11988821198901198912119890|

119892 (119904) =

sgn (119904) |119904| ge120587

2119901119890

sin (119901119890sdot 119904) |119904| lt

120587

2119901119890

119901 gt 0 (31)


formula

1199062=119868119890

1198882

[119896119890sdot 119904119890+ 119889119890sdot 119892 (119904119890) + 1198902119890(1198881119890minus 1198882119890

119887119890

119868119890

) + 11988821198901198912119890]

(32)



119879119889

119890= 119879119871

119890+ 119870119890119905 (33)

119870119890= (

119879119889119890minus 119879119871119890

Δ119905) (34)



119890is



119895 =119894119890119877119882

119868119889

119890 (35)



050 15 2 25 3 35 41

25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

etp

(s)

Time t (s)



050 15 2 25 3 35 41

3

25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

ets

(s)

Time t (s)



050 15 2 25 3 35 41

100

90

80

70

60

50

40

30

20

10

0


Clut

ch tr

ansfe

r tor

queT

c1(N

m)

Time t (s)


050 15 2 25 3 35 41

100

90

80

70

60

50

40

30

20

10

0


Clut

ch tr

ansfe

r tor

queT

c1(N

m)

Time t (s)




119895 =119894119890119877119882

1198680

1198881 (36)







Key signal


Brake pedal signal








control system


Clutch 1 actuator

Clutch 2 actuator




MicroAutoBox





119904s 2355 2535



119904+ Δ119905)s 314 333





119901and 119905












Time t (s)

100

80

60

40

20

08 10 12 14 16

Acce

lera

tor p

edal

ope

ning120573

()


250

200

150

100

50

0


8 10 12 14 16

Time t (s)

Targ

et ro

tatio

nal s

peed120596

(rad

s)



8 10 12 14 16

250

200

150

100

50

0

Time t (s)

Real

spee

d120596

(rad

s)


10

5

0

minus5

minus108 10 12 14 16

Shoc

k in

tens

ityj

(ms3)

Time t (s)

(d) Shock intensity

7

6

5

4

3

2

1

08 9 10 11 12 13 14 15 16 17

Time t (s)

Slid

ing

fric

tion

wor

kW

(kJ)


Time t (s)8 10 12 14 16

120

100

80

60

40

20

0

Torq

ueT

(Nm

)


(f) Torque

Figure 12 Continued


25

20

15

10

5

0

Time t (s)8 10 12 14 16

Vehi

cle v

eloc

ity

(km

h)


120

100

80

60

40

20

08 9 10 11 12 13

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)



25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

et(s

)

8 9 10 11 12 13

Time t (s)

tPts


15

10

5

0

Clut

ch se

para

ting

strok

ex(m

m)

Time t (s)8 10 12 14 16











0+ 119905119904)s 1196







100

80

60

40

20

08194 8198 8202 8206 821 8214

Time t (s)

Acce

lera

tor o

peni

ng120573

()


8194 8198 8202 8206 821 8214

350

300

250

200

150

100

50

0


Time t (s)

Rota

tiona

l spe

ed120596

(rad

s)


8194 8198 8202 8206 821 8214

10

5

0

minus5

Time t (s)

Shoc

k in

tens

ityj

(ms3)

(c) Shock intensity








7 Conclusion



e eng

ine o

utpu

t tor

que (

Nm

)



250

200

150

100

50

0100

8060

4020

0 10002000

30004000

50006000

Figure 15



1198681198881 0014 kgsdotm2

1198681198882 0014 kgsdotm2

119868119898 001 kgsdotm2

119868119904 1470392 kgsdotm2

I1198921


119868119892119903 0005 kgsdotm2

i1 simi53615 2042 1257

0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2

119860 2095m119862119889 0293

119877119908 0308m

120578 0921198770 0228m

1198771 015m



Appendices


See Figure 15


See Table 5



References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra













119890(119905119904)(rmin)






119890(119905119904) is shown in Table 1

Consider

120573V (119905) = 120573 (119905) + 119896 120573 (119905) (11)





119888(+) minus

119888(minus) =

119868119890

119868119890+ 119868119888119886


119888(minus)] (12)

where 119888(minus)






119904119877119882




0sim20 20sim50 50sim100













119904is set


119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0

051198951199011199052

119901+ 119895119901119905119901(119905119904minus 119905119901) + 05119895

119904(119905119904minus 119905119901)2

= 120596 (119905119904) 119877119882

(13)


js

ts

Time t (s)

Shoc

k in

tens

ityj

(ms3)

tp

jp


ts

Time t (s)

Acce

lera

tiona

(ms2)

tp


ts

Time t (s)

Velo

city

(ms

)

tp








119905119901= radic

120596 (119905119904) 119877119882

(05119895119901minus 051198952

119901119895119904)

119905119904= 119905119901(1 minus

119895119901

119895119904

)

(14)




119901and 119895119904twice

120596ref119904

= int119905119904

0

int119905119904

0

119895

119877119882

119889119905

120596ref1198881

= 120596ref1199041198941119894119886

(15)









0

1

2

3

t0

middotmiddotmiddot


Time t (s)

Velocity(m

s)

t0 + Δt t0 + 2Δt t0 + 3Δt



119890(119905119904) 119905119901 119905119904 and 119895





moments of 1199050 1199050+ Δ119905 119905

0+ 2Δ119905 and 119905



119886 (1199050) + 119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0

V (1199050) + 119886 (119905

0) 119905119901+1

21198951199011199052

119901+ (120572 (119905

0) + 119895119901119905119901) (119905119904minus 119905119901)

+1

2119895119904(119905119904minus 119905119901)2

= 120596 (119905119904) 119877119882

(16)












120596ref119890

=

120596119890(119905119904) minus 120596119890(0)

119905119901

119905 + 120596119890(0) (120596

119890minus 1205961198881) ge Δ120596

1199050lt 119905 lt (119905

0+ 119905119901)

120596119890(119905119904) other

(17)


119901and 119895

119904



119882 = int1199050+119905119904

1199050

1198881(120596

ref119890

minus 1205961198881) 119889119905

1198881=119868119900ref119904

+ 119887119900120596ref119904

+ 119898119892119877119882120583

11989411988611989411205782

(18)


1198881minus1198881| lt 120576





119865 =1

119882 (19)


119904can be

seen in Figure 8



1 the relationship




1= 120579119904 1199092= 120596119904 there is

1= 1199092

2=

119894119890

119868119900

1198791198881minus1198870

1198680

1199092minus119879119891

1198680

(20)


t0 t0 + ts

a(t0)

Time t (s)

Acce

lera

tiona

(ms2)

t0 + tp


(t0)

t0 t0 + ts

Time t (s)

Velo

city

(ms

)

t0 + tp






velocity

Engine target speed


estimation


Targ

et im

pact

stren

gth

optim

izat

ion

Geneticalgorithm


slidingfriction

energy andfitness

function





1 there is

[1198901

1198902

] = [

[

0 1

0 minus1198870

1198680

]

]

[1198901

1198902

] + [

[

0

minus119894119890

1198680

]

]

1199061+ [

0

1198912

] + [0

1198913

] (21)






1198911015840

2= 119903+1198680

1198870

119903+119898119892119891

1198870

(22)


1198911015840

3=119879119891

1198680

minus119898119892119891

1198870

(23)




3 (25)

where 119889 gt |11988821198911015840

3|

119892 (119904) =

sgn (119904) |119904| ge120587

2119901

sin (119901 sdot 119904) |119904| lt120587

2119901

119901 gt 0 (26)



1199061=

1198680

1198882119894119890

[119896 sdot 119904 + 119889 sdot 119892 (119904) + 1198902(1198881minus 1198882

1198870

1198680

) + 11988821198911015840

2] (27)


119890and 119879


119890) model and





100

90

80

70

60

50

40

30

20

10

0050 15 2 25 3 35 41

Time t (s)

Acce

lera

tion

peda

l ope

ning120573

()



0500

15 2 25 3 35 41

250

200

150

100

50

Time t (s)

Targ

et sp

eed120596

(rad

s)



050 15 2 25 3 35 410

250

200

150

100

50

Time t (s)

Real

spee

d120596

(rad

s)



050 15 2 25 3 35 41

6

4

2

0

minus2

minus4

minus6

Time t (s)

Targ

et sh

ock

inte

nsityj

(ms3)



050 15 2 25 3 35 41

6

4

2

0

minus2

minus4

minus6

Time t (s)

Real

shoc

k in

tens

ityj

(ms3)



140

120

100

80

60

40

20

0050 15 2 25 3 35 41

Time t (s)

Engi

ne o

utpu

t tor

queT

e(N

m)



Figure 9 Continued


050 15 2 25 3 35 41

140

120

100

80

60

40

20

0

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)



050 15 2 25 3 35 41

20

18

16

14

12

10

8

6

4

2

0

Time t (s)

Vehi

cle v

eloc

ity

(km

h)




1199091119890

= 120579119890 1119890

= 120579119890= 120596119890 1198901119890

= 119909119903119890minus 1199091119890 1198902119890

= 119903119890minus 1199092119890


119890 namely

[1198901119890

1198902119890

] = [

[

0 1

0 minus119887119890

119868119890

]

]

[1198901119890

1198902119890

] + [

[

0

minus1

119868119890

]

]

1199062+ [

0

1198912119890

] (28)

where 1199062= 119879119890 1198912119890

= (1198791198881119868119890) + 119903119890+ (119887119890119868119890)119903119890 which are


119904119890= 11988811198901198901119890+ 11988821198901198902119890 (29)



where 119889119890gt |11988821198901198912119890|

119892 (119904) =

sgn (119904) |119904| ge120587

2119901119890

sin (119901119890sdot 119904) |119904| lt

120587

2119901119890

119901 gt 0 (31)


formula

1199062=119868119890

1198882

[119896119890sdot 119904119890+ 119889119890sdot 119892 (119904119890) + 1198902119890(1198881119890minus 1198882119890

119887119890

119868119890

) + 11988821198901198912119890]

(32)



119879119889

119890= 119879119871

119890+ 119870119890119905 (33)

119870119890= (

119879119889119890minus 119879119871119890

Δ119905) (34)



119890is



119895 =119894119890119877119882

119868119889

119890 (35)



050 15 2 25 3 35 41

25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

etp

(s)

Time t (s)



050 15 2 25 3 35 41

3

25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

ets

(s)

Time t (s)



050 15 2 25 3 35 41

100

90

80

70

60

50

40

30

20

10

0


Clut

ch tr

ansfe

r tor

queT

c1(N

m)

Time t (s)


050 15 2 25 3 35 41

100

90

80

70

60

50

40

30

20

10

0


Clut

ch tr

ansfe

r tor

queT

c1(N

m)

Time t (s)




119895 =119894119890119877119882

1198680

1198881 (36)







Key signal


Brake pedal signal








control system


Clutch 1 actuator

Clutch 2 actuator




MicroAutoBox





119904s 2355 2535



119904+ Δ119905)s 314 333





119901and 119905












Time t (s)

100

80

60

40

20

08 10 12 14 16

Acce

lera

tor p

edal

ope

ning120573

()


250

200

150

100

50

0


8 10 12 14 16

Time t (s)

Targ

et ro

tatio

nal s

peed120596

(rad

s)



8 10 12 14 16

250

200

150

100

50

0

Time t (s)

Real

spee

d120596

(rad

s)


10

5

0

minus5

minus108 10 12 14 16

Shoc

k in

tens

ityj

(ms3)

Time t (s)

(d) Shock intensity

7

6

5

4

3

2

1

08 9 10 11 12 13 14 15 16 17

Time t (s)

Slid

ing

fric

tion

wor

kW

(kJ)


Time t (s)8 10 12 14 16

120

100

80

60

40

20

0

Torq

ueT

(Nm

)


(f) Torque

Figure 12 Continued


25

20

15

10

5

0

Time t (s)8 10 12 14 16

Vehi

cle v

eloc

ity

(km

h)


120

100

80

60

40

20

08 9 10 11 12 13

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)



25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

et(s

)

8 9 10 11 12 13

Time t (s)

tPts


15

10

5

0

Clut

ch se

para

ting

strok

ex(m

m)

Time t (s)8 10 12 14 16











0+ 119905119904)s 1196







100

80

60

40

20

08194 8198 8202 8206 821 8214

Time t (s)

Acce

lera

tor o

peni

ng120573

()


8194 8198 8202 8206 821 8214

350

300

250

200

150

100

50

0


Time t (s)

Rota

tiona

l spe

ed120596

(rad

s)


8194 8198 8202 8206 821 8214

10

5

0

minus5

Time t (s)

Shoc

k in

tens

ityj

(ms3)

(c) Shock intensity








7 Conclusion



e eng

ine o

utpu

t tor

que (

Nm

)



250

200

150

100

50

0100

8060

4020

0 10002000

30004000

50006000

Figure 15



1198681198881 0014 kgsdotm2

1198681198882 0014 kgsdotm2

119868119898 001 kgsdotm2

119868119904 1470392 kgsdotm2

I1198921


119868119892119903 0005 kgsdotm2

i1 simi53615 2042 1257

0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2

119860 2095m119862119889 0293

119877119908 0308m

120578 0921198770 0228m

1198771 015m



Appendices


See Figure 15


See Table 5



References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










js

ts

Time t (s)

Shoc

k in

tens

ityj

(ms3)

tp

jp


ts

Time t (s)

Acce

lera

tiona

(ms2)

tp


ts

Time t (s)

Velo

city

(ms

)

tp








119905119901= radic

120596 (119905119904) 119877119882

(05119895119901minus 051198952

119901119895119904)

119905119904= 119905119901(1 minus

119895119901

119895119904

)

(14)




119901and 119895119904twice

120596ref119904

= int119905119904

0

int119905119904

0

119895

119877119882

119889119905

120596ref1198881

= 120596ref1199041198941119894119886

(15)









0

1

2

3

t0

middotmiddotmiddot


Time t (s)

Velocity(m

s)

t0 + Δt t0 + 2Δt t0 + 3Δt



119890(119905119904) 119905119901 119905119904 and 119895





moments of 1199050 1199050+ Δ119905 119905

0+ 2Δ119905 and 119905



119886 (1199050) + 119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0

V (1199050) + 119886 (119905

0) 119905119901+1

21198951199011199052

119901+ (120572 (119905

0) + 119895119901119905119901) (119905119904minus 119905119901)

+1

2119895119904(119905119904minus 119905119901)2

= 120596 (119905119904) 119877119882

(16)












120596ref119890

=

120596119890(119905119904) minus 120596119890(0)

119905119901

119905 + 120596119890(0) (120596

119890minus 1205961198881) ge Δ120596

1199050lt 119905 lt (119905

0+ 119905119901)

120596119890(119905119904) other

(17)


119901and 119895

119904



119882 = int1199050+119905119904

1199050

1198881(120596

ref119890

minus 1205961198881) 119889119905

1198881=119868119900ref119904

+ 119887119900120596ref119904

+ 119898119892119877119882120583

11989411988611989411205782

(18)


1198881minus1198881| lt 120576





119865 =1

119882 (19)


119904can be

seen in Figure 8



1 the relationship




1= 120579119904 1199092= 120596119904 there is

1= 1199092

2=

119894119890

119868119900

1198791198881minus1198870

1198680

1199092minus119879119891

1198680

(20)


t0 t0 + ts

a(t0)

Time t (s)

Acce

lera

tiona

(ms2)

t0 + tp


(t0)

t0 t0 + ts

Time t (s)

Velo

city

(ms

)

t0 + tp






velocity

Engine target speed


estimation


Targ

et im

pact

stren

gth

optim

izat

ion

Geneticalgorithm


slidingfriction

energy andfitness

function





1 there is

[1198901

1198902

] = [

[

0 1

0 minus1198870

1198680

]

]

[1198901

1198902

] + [

[

0

minus119894119890

1198680

]

]

1199061+ [

0

1198912

] + [0

1198913

] (21)






1198911015840

2= 119903+1198680

1198870

119903+119898119892119891

1198870

(22)


1198911015840

3=119879119891

1198680

minus119898119892119891

1198870

(23)




3 (25)

where 119889 gt |11988821198911015840

3|

119892 (119904) =

sgn (119904) |119904| ge120587

2119901

sin (119901 sdot 119904) |119904| lt120587

2119901

119901 gt 0 (26)



1199061=

1198680

1198882119894119890

[119896 sdot 119904 + 119889 sdot 119892 (119904) + 1198902(1198881minus 1198882

1198870

1198680

) + 11988821198911015840

2] (27)


119890and 119879


119890) model and





100

90

80

70

60

50

40

30

20

10

0050 15 2 25 3 35 41

Time t (s)

Acce

lera

tion

peda

l ope

ning120573

()



0500

15 2 25 3 35 41

250

200

150

100

50

Time t (s)

Targ

et sp

eed120596

(rad

s)



050 15 2 25 3 35 410

250

200

150

100

50

Time t (s)

Real

spee

d120596

(rad

s)



050 15 2 25 3 35 41

6

4

2

0

minus2

minus4

minus6

Time t (s)

Targ

et sh

ock

inte

nsityj

(ms3)



050 15 2 25 3 35 41

6

4

2

0

minus2

minus4

minus6

Time t (s)

Real

shoc

k in

tens

ityj

(ms3)



140

120

100

80

60

40

20

0050 15 2 25 3 35 41

Time t (s)

Engi

ne o

utpu

t tor

queT

e(N

m)



Figure 9 Continued


050 15 2 25 3 35 41

140

120

100

80

60

40

20

0

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)



050 15 2 25 3 35 41

20

18

16

14

12

10

8

6

4

2

0

Time t (s)

Vehi

cle v

eloc

ity

(km

h)




1199091119890

= 120579119890 1119890

= 120579119890= 120596119890 1198901119890

= 119909119903119890minus 1199091119890 1198902119890

= 119903119890minus 1199092119890


119890 namely

[1198901119890

1198902119890

] = [

[

0 1

0 minus119887119890

119868119890

]

]

[1198901119890

1198902119890

] + [

[

0

minus1

119868119890

]

]

1199062+ [

0

1198912119890

] (28)

where 1199062= 119879119890 1198912119890

= (1198791198881119868119890) + 119903119890+ (119887119890119868119890)119903119890 which are


119904119890= 11988811198901198901119890+ 11988821198901198902119890 (29)



where 119889119890gt |11988821198901198912119890|

119892 (119904) =

sgn (119904) |119904| ge120587

2119901119890

sin (119901119890sdot 119904) |119904| lt

120587

2119901119890

119901 gt 0 (31)


formula

1199062=119868119890

1198882

[119896119890sdot 119904119890+ 119889119890sdot 119892 (119904119890) + 1198902119890(1198881119890minus 1198882119890

119887119890

119868119890

) + 11988821198901198912119890]

(32)



119879119889

119890= 119879119871

119890+ 119870119890119905 (33)

119870119890= (

119879119889119890minus 119879119871119890

Δ119905) (34)



119890is



119895 =119894119890119877119882

119868119889

119890 (35)



050 15 2 25 3 35 41

25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

etp

(s)

Time t (s)



050 15 2 25 3 35 41

3

25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

ets

(s)

Time t (s)



050 15 2 25 3 35 41

100

90

80

70

60

50

40

30

20

10

0


Clut

ch tr

ansfe

r tor

queT

c1(N

m)

Time t (s)


050 15 2 25 3 35 41

100

90

80

70

60

50

40

30

20

10

0


Clut

ch tr

ansfe

r tor

queT

c1(N

m)

Time t (s)




119895 =119894119890119877119882

1198680

1198881 (36)







Key signal


Brake pedal signal








control system


Clutch 1 actuator

Clutch 2 actuator




MicroAutoBox





119904s 2355 2535



119904+ Δ119905)s 314 333





119901and 119905












Time t (s)

100

80

60

40

20

08 10 12 14 16

Acce

lera

tor p

edal

ope

ning120573

()


250

200

150

100

50

0


8 10 12 14 16

Time t (s)

Targ

et ro

tatio

nal s

peed120596

(rad

s)



8 10 12 14 16

250

200

150

100

50

0

Time t (s)

Real

spee

d120596

(rad

s)


10

5

0

minus5

minus108 10 12 14 16

Shoc

k in

tens

ityj

(ms3)

Time t (s)

(d) Shock intensity

7

6

5

4

3

2

1

08 9 10 11 12 13 14 15 16 17

Time t (s)

Slid

ing

fric

tion

wor

kW

(kJ)


Time t (s)8 10 12 14 16

120

100

80

60

40

20

0

Torq

ueT

(Nm

)


(f) Torque

Figure 12 Continued


25

20

15

10

5

0

Time t (s)8 10 12 14 16

Vehi

cle v

eloc

ity

(km

h)


120

100

80

60

40

20

08 9 10 11 12 13

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)



25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

et(s

)

8 9 10 11 12 13

Time t (s)

tPts


15

10

5

0

Clut

ch se

para

ting

strok

ex(m

m)

Time t (s)8 10 12 14 16











0+ 119905119904)s 1196







100

80

60

40

20

08194 8198 8202 8206 821 8214

Time t (s)

Acce

lera

tor o

peni

ng120573

()


8194 8198 8202 8206 821 8214

350

300

250

200

150

100

50

0


Time t (s)

Rota

tiona

l spe

ed120596

(rad

s)


8194 8198 8202 8206 821 8214

10

5

0

minus5

Time t (s)

Shoc

k in

tens

ityj

(ms3)

(c) Shock intensity








7 Conclusion



e eng

ine o

utpu

t tor

que (

Nm

)



250

200

150

100

50

0100

8060

4020

0 10002000

30004000

50006000

Figure 15



1198681198881 0014 kgsdotm2

1198681198882 0014 kgsdotm2

119868119898 001 kgsdotm2

119868119904 1470392 kgsdotm2

I1198921


119868119892119903 0005 kgsdotm2

i1 simi53615 2042 1257

0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2

119860 2095m119862119889 0293

119877119908 0308m

120578 0921198770 0228m

1198771 015m



Appendices


See Figure 15


See Table 5



References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0

1

2

3

t0

middotmiddotmiddot


Time t (s)

Velocity(m

s)

t0 + Δt t0 + 2Δt t0 + 3Δt



119890(119905119904) 119905119901 119905119904 and 119895





moments of 1199050 1199050+ Δ119905 119905

0+ 2Δ119905 and 119905



119886 (1199050) + 119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0

V (1199050) + 119886 (119905

0) 119905119901+1

21198951199011199052

119901+ (120572 (119905

0) + 119895119901119905119901) (119905119904minus 119905119901)

+1

2119895119904(119905119904minus 119905119901)2

= 120596 (119905119904) 119877119882

(16)












120596ref119890

=

120596119890(119905119904) minus 120596119890(0)

119905119901

119905 + 120596119890(0) (120596

119890minus 1205961198881) ge Δ120596

1199050lt 119905 lt (119905

0+ 119905119901)

120596119890(119905119904) other

(17)


119901and 119895

119904



119882 = int1199050+119905119904

1199050

1198881(120596

ref119890

minus 1205961198881) 119889119905

1198881=119868119900ref119904

+ 119887119900120596ref119904

+ 119898119892119877119882120583

11989411988611989411205782

(18)


1198881minus1198881| lt 120576





119865 =1

119882 (19)


119904can be

seen in Figure 8



1 the relationship




1= 120579119904 1199092= 120596119904 there is

1= 1199092

2=

119894119890

119868119900

1198791198881minus1198870

1198680

1199092minus119879119891

1198680

(20)


t0 t0 + ts

a(t0)

Time t (s)

Acce

lera

tiona

(ms2)

t0 + tp


(t0)

t0 t0 + ts

Time t (s)

Velo

city

(ms

)

t0 + tp






velocity

Engine target speed


estimation


Targ

et im

pact

stren

gth

optim

izat

ion

Geneticalgorithm


slidingfriction

energy andfitness

function





1 there is

[1198901

1198902

] = [

[

0 1

0 minus1198870

1198680

]

]

[1198901

1198902

] + [

[

0

minus119894119890

1198680

]

]

1199061+ [

0

1198912

] + [0

1198913

] (21)






1198911015840

2= 119903+1198680

1198870

119903+119898119892119891

1198870

(22)


1198911015840

3=119879119891

1198680

minus119898119892119891

1198870

(23)




3 (25)

where 119889 gt |11988821198911015840

3|

119892 (119904) =

sgn (119904) |119904| ge120587

2119901

sin (119901 sdot 119904) |119904| lt120587

2119901

119901 gt 0 (26)



1199061=

1198680

1198882119894119890

[119896 sdot 119904 + 119889 sdot 119892 (119904) + 1198902(1198881minus 1198882

1198870

1198680

) + 11988821198911015840

2] (27)


119890and 119879


119890) model and





100

90

80

70

60

50

40

30

20

10

0050 15 2 25 3 35 41

Time t (s)

Acce

lera

tion

peda

l ope

ning120573

()



0500

15 2 25 3 35 41

250

200

150

100

50

Time t (s)

Targ

et sp

eed120596

(rad

s)



050 15 2 25 3 35 410

250

200

150

100

50

Time t (s)

Real

spee

d120596

(rad

s)



050 15 2 25 3 35 41

6

4

2

0

minus2

minus4

minus6

Time t (s)

Targ

et sh

ock

inte

nsityj

(ms3)



050 15 2 25 3 35 41

6

4

2

0

minus2

minus4

minus6

Time t (s)

Real

shoc

k in

tens

ityj

(ms3)



140

120

100

80

60

40

20

0050 15 2 25 3 35 41

Time t (s)

Engi

ne o

utpu

t tor

queT

e(N

m)



Figure 9 Continued


050 15 2 25 3 35 41

140

120

100

80

60

40

20

0

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)



050 15 2 25 3 35 41

20

18

16

14

12

10

8

6

4

2

0

Time t (s)

Vehi

cle v

eloc

ity

(km

h)




1199091119890

= 120579119890 1119890

= 120579119890= 120596119890 1198901119890

= 119909119903119890minus 1199091119890 1198902119890

= 119903119890minus 1199092119890


119890 namely

[1198901119890

1198902119890

] = [

[

0 1

0 minus119887119890

119868119890

]

]

[1198901119890

1198902119890

] + [

[

0

minus1

119868119890

]

]

1199062+ [

0

1198912119890

] (28)

where 1199062= 119879119890 1198912119890

= (1198791198881119868119890) + 119903119890+ (119887119890119868119890)119903119890 which are


119904119890= 11988811198901198901119890+ 11988821198901198902119890 (29)



where 119889119890gt |11988821198901198912119890|

119892 (119904) =

sgn (119904) |119904| ge120587

2119901119890

sin (119901119890sdot 119904) |119904| lt

120587

2119901119890

119901 gt 0 (31)


formula

1199062=119868119890

1198882

[119896119890sdot 119904119890+ 119889119890sdot 119892 (119904119890) + 1198902119890(1198881119890minus 1198882119890

119887119890

119868119890

) + 11988821198901198912119890]

(32)



119879119889

119890= 119879119871

119890+ 119870119890119905 (33)

119870119890= (

119879119889119890minus 119879119871119890

Δ119905) (34)



119890is



119895 =119894119890119877119882

119868119889

119890 (35)



050 15 2 25 3 35 41

25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

etp

(s)

Time t (s)



050 15 2 25 3 35 41

3

25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

ets

(s)

Time t (s)



050 15 2 25 3 35 41

100

90

80

70

60

50

40

30

20

10

0


Clut

ch tr

ansfe

r tor

queT

c1(N

m)

Time t (s)


050 15 2 25 3 35 41

100

90

80

70

60

50

40

30

20

10

0


Clut

ch tr

ansfe

r tor

queT

c1(N

m)

Time t (s)




119895 =119894119890119877119882

1198680

1198881 (36)







Key signal


Brake pedal signal








control system


Clutch 1 actuator

Clutch 2 actuator




MicroAutoBox





119904s 2355 2535



119904+ Δ119905)s 314 333





119901and 119905












Time t (s)

100

80

60

40

20

08 10 12 14 16

Acce

lera

tor p

edal

ope

ning120573

()


250

200

150

100

50

0


8 10 12 14 16

Time t (s)

Targ

et ro

tatio

nal s

peed120596

(rad

s)



8 10 12 14 16

250

200

150

100

50

0

Time t (s)

Real

spee

d120596

(rad

s)


10

5

0

minus5

minus108 10 12 14 16

Shoc

k in

tens

ityj

(ms3)

Time t (s)

(d) Shock intensity

7

6

5

4

3

2

1

08 9 10 11 12 13 14 15 16 17

Time t (s)

Slid

ing

fric

tion

wor

kW

(kJ)


Time t (s)8 10 12 14 16

120

100

80

60

40

20

0

Torq

ueT

(Nm

)


(f) Torque

Figure 12 Continued


25

20

15

10

5

0

Time t (s)8 10 12 14 16

Vehi

cle v

eloc

ity

(km

h)


120

100

80

60

40

20

08 9 10 11 12 13

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)



25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

et(s

)

8 9 10 11 12 13

Time t (s)

tPts


15

10

5

0

Clut

ch se

para

ting

strok

ex(m

m)

Time t (s)8 10 12 14 16











0+ 119905119904)s 1196







100

80

60

40

20

08194 8198 8202 8206 821 8214

Time t (s)

Acce

lera

tor o

peni

ng120573

()


8194 8198 8202 8206 821 8214

350

300

250

200

150

100

50

0


Time t (s)

Rota

tiona

l spe

ed120596

(rad

s)


8194 8198 8202 8206 821 8214

10

5

0

minus5

Time t (s)

Shoc

k in

tens

ityj

(ms3)

(c) Shock intensity








7 Conclusion



e eng

ine o

utpu

t tor

que (

Nm

)



250

200

150

100

50

0100

8060

4020

0 10002000

30004000

50006000

Figure 15



1198681198881 0014 kgsdotm2

1198681198882 0014 kgsdotm2

119868119898 001 kgsdotm2

119868119904 1470392 kgsdotm2

I1198921


119868119892119903 0005 kgsdotm2

i1 simi53615 2042 1257

0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2

119860 2095m119862119889 0293

119877119908 0308m

120578 0921198770 0228m

1198771 015m



Appendices


See Figure 15


See Table 5



References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










t0 t0 + ts

a(t0)

Time t (s)

Acce

lera

tiona

(ms2)

t0 + tp


(t0)

t0 t0 + ts

Time t (s)

Velo

city

(ms

)

t0 + tp






velocity

Engine target speed


estimation


Targ

et im

pact

stren

gth

optim

izat

ion

Geneticalgorithm


slidingfriction

energy andfitness

function





1 there is

[1198901

1198902

] = [

[

0 1

0 minus1198870

1198680

]

]

[1198901

1198902

] + [

[

0

minus119894119890

1198680

]

]

1199061+ [

0

1198912

] + [0

1198913

] (21)






1198911015840

2= 119903+1198680

1198870

119903+119898119892119891

1198870

(22)


1198911015840

3=119879119891

1198680

minus119898119892119891

1198870

(23)




3 (25)

where 119889 gt |11988821198911015840

3|

119892 (119904) =

sgn (119904) |119904| ge120587

2119901

sin (119901 sdot 119904) |119904| lt120587

2119901

119901 gt 0 (26)



1199061=

1198680

1198882119894119890

[119896 sdot 119904 + 119889 sdot 119892 (119904) + 1198902(1198881minus 1198882

1198870

1198680

) + 11988821198911015840

2] (27)


119890and 119879


119890) model and





100

90

80

70

60

50

40

30

20

10

0050 15 2 25 3 35 41

Time t (s)

Acce

lera

tion

peda

l ope

ning120573

()



0500

15 2 25 3 35 41

250

200

150

100

50

Time t (s)

Targ

et sp

eed120596

(rad

s)



050 15 2 25 3 35 410

250

200

150

100

50

Time t (s)

Real

spee

d120596

(rad

s)



050 15 2 25 3 35 41

6

4

2

0

minus2

minus4

minus6

Time t (s)

Targ

et sh

ock

inte

nsityj

(ms3)



050 15 2 25 3 35 41

6

4

2

0

minus2

minus4

minus6

Time t (s)

Real

shoc

k in

tens

ityj

(ms3)



140

120

100

80

60

40

20

0050 15 2 25 3 35 41

Time t (s)

Engi

ne o

utpu

t tor

queT

e(N

m)



Figure 9 Continued


050 15 2 25 3 35 41

140

120

100

80

60

40

20

0

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)



050 15 2 25 3 35 41

20

18

16

14

12

10

8

6

4

2

0

Time t (s)

Vehi

cle v

eloc

ity

(km

h)




1199091119890

= 120579119890 1119890

= 120579119890= 120596119890 1198901119890

= 119909119903119890minus 1199091119890 1198902119890

= 119903119890minus 1199092119890


119890 namely

[1198901119890

1198902119890

] = [

[

0 1

0 minus119887119890

119868119890

]

]

[1198901119890

1198902119890

] + [

[

0

minus1

119868119890

]

]

1199062+ [

0

1198912119890

] (28)

where 1199062= 119879119890 1198912119890

= (1198791198881119868119890) + 119903119890+ (119887119890119868119890)119903119890 which are


119904119890= 11988811198901198901119890+ 11988821198901198902119890 (29)



where 119889119890gt |11988821198901198912119890|

119892 (119904) =

sgn (119904) |119904| ge120587

2119901119890

sin (119901119890sdot 119904) |119904| lt

120587

2119901119890

119901 gt 0 (31)


formula

1199062=119868119890

1198882

[119896119890sdot 119904119890+ 119889119890sdot 119892 (119904119890) + 1198902119890(1198881119890minus 1198882119890

119887119890

119868119890

) + 11988821198901198912119890]

(32)



119879119889

119890= 119879119871

119890+ 119870119890119905 (33)

119870119890= (

119879119889119890minus 119879119871119890

Δ119905) (34)



119890is



119895 =119894119890119877119882

119868119889

119890 (35)



050 15 2 25 3 35 41

25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

etp

(s)

Time t (s)



050 15 2 25 3 35 41

3

25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

ets

(s)

Time t (s)



050 15 2 25 3 35 41

100

90

80

70

60

50

40

30

20

10

0


Clut

ch tr

ansfe

r tor

queT

c1(N

m)

Time t (s)


050 15 2 25 3 35 41

100

90

80

70

60

50

40

30

20

10

0


Clut

ch tr

ansfe

r tor

queT

c1(N

m)

Time t (s)




119895 =119894119890119877119882

1198680

1198881 (36)







Key signal


Brake pedal signal








control system


Clutch 1 actuator

Clutch 2 actuator




MicroAutoBox





119904s 2355 2535



119904+ Δ119905)s 314 333





119901and 119905












Time t (s)

100

80

60

40

20

08 10 12 14 16

Acce

lera

tor p

edal

ope

ning120573

()


250

200

150

100

50

0


8 10 12 14 16

Time t (s)

Targ

et ro

tatio

nal s

peed120596

(rad

s)



8 10 12 14 16

250

200

150

100

50

0

Time t (s)

Real

spee

d120596

(rad

s)


10

5

0

minus5

minus108 10 12 14 16

Shoc

k in

tens

ityj

(ms3)

Time t (s)

(d) Shock intensity

7

6

5

4

3

2

1

08 9 10 11 12 13 14 15 16 17

Time t (s)

Slid

ing

fric

tion

wor

kW

(kJ)


Time t (s)8 10 12 14 16

120

100

80

60

40

20

0

Torq

ueT

(Nm

)


(f) Torque

Figure 12 Continued


25

20

15

10

5

0

Time t (s)8 10 12 14 16

Vehi

cle v

eloc

ity

(km

h)


120

100

80

60

40

20

08 9 10 11 12 13

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)



25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

et(s

)

8 9 10 11 12 13

Time t (s)

tPts


15

10

5

0

Clut

ch se

para

ting

strok

ex(m

m)

Time t (s)8 10 12 14 16











0+ 119905119904)s 1196







100

80

60

40

20

08194 8198 8202 8206 821 8214

Time t (s)

Acce

lera

tor o

peni

ng120573

()


8194 8198 8202 8206 821 8214

350

300

250

200

150

100

50

0


Time t (s)

Rota

tiona

l spe

ed120596

(rad

s)


8194 8198 8202 8206 821 8214

10

5

0

minus5

Time t (s)

Shoc

k in

tens

ityj

(ms3)

(c) Shock intensity








7 Conclusion



e eng

ine o

utpu

t tor

que (

Nm

)



250

200

150

100

50

0100

8060

4020

0 10002000

30004000

50006000

Figure 15



1198681198881 0014 kgsdotm2

1198681198882 0014 kgsdotm2

119868119898 001 kgsdotm2

119868119904 1470392 kgsdotm2

I1198921


119868119892119903 0005 kgsdotm2

i1 simi53615 2042 1257

0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2

119860 2095m119862119889 0293

119877119908 0308m

120578 0921198770 0228m

1198771 015m



Appendices


See Figure 15


See Table 5



References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










100

90

80

70

60

50

40

30

20

10

0050 15 2 25 3 35 41

Time t (s)

Acce

lera

tion

peda

l ope

ning120573

()



0500

15 2 25 3 35 41

250

200

150

100

50

Time t (s)

Targ

et sp

eed120596

(rad

s)



050 15 2 25 3 35 410

250

200

150

100

50

Time t (s)

Real

spee

d120596

(rad

s)



050 15 2 25 3 35 41

6

4

2

0

minus2

minus4

minus6

Time t (s)

Targ

et sh

ock

inte

nsityj

(ms3)



050 15 2 25 3 35 41

6

4

2

0

minus2

minus4

minus6

Time t (s)

Real

shoc

k in

tens

ityj

(ms3)



140

120

100

80

60

40

20

0050 15 2 25 3 35 41

Time t (s)

Engi

ne o

utpu

t tor

queT

e(N

m)



Figure 9 Continued


050 15 2 25 3 35 41

140

120

100

80

60

40

20

0

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)



050 15 2 25 3 35 41

20

18

16

14

12

10

8

6

4

2

0

Time t (s)

Vehi

cle v

eloc

ity

(km

h)




1199091119890

= 120579119890 1119890

= 120579119890= 120596119890 1198901119890

= 119909119903119890minus 1199091119890 1198902119890

= 119903119890minus 1199092119890


119890 namely

[1198901119890

1198902119890

] = [

[

0 1

0 minus119887119890

119868119890

]

]

[1198901119890

1198902119890

] + [

[

0

minus1

119868119890

]

]

1199062+ [

0

1198912119890

] (28)

where 1199062= 119879119890 1198912119890

= (1198791198881119868119890) + 119903119890+ (119887119890119868119890)119903119890 which are


119904119890= 11988811198901198901119890+ 11988821198901198902119890 (29)



where 119889119890gt |11988821198901198912119890|

119892 (119904) =

sgn (119904) |119904| ge120587

2119901119890

sin (119901119890sdot 119904) |119904| lt

120587

2119901119890

119901 gt 0 (31)


formula

1199062=119868119890

1198882

[119896119890sdot 119904119890+ 119889119890sdot 119892 (119904119890) + 1198902119890(1198881119890minus 1198882119890

119887119890

119868119890

) + 11988821198901198912119890]

(32)



119879119889

119890= 119879119871

119890+ 119870119890119905 (33)

119870119890= (

119879119889119890minus 119879119871119890

Δ119905) (34)



119890is



119895 =119894119890119877119882

119868119889

119890 (35)



050 15 2 25 3 35 41

25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

etp

(s)

Time t (s)



050 15 2 25 3 35 41

3

25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

ets

(s)

Time t (s)



050 15 2 25 3 35 41

100

90

80

70

60

50

40

30

20

10

0


Clut

ch tr

ansfe

r tor

queT

c1(N

m)

Time t (s)


050 15 2 25 3 35 41

100

90

80

70

60

50

40

30

20

10

0


Clut

ch tr

ansfe

r tor

queT

c1(N

m)

Time t (s)




119895 =119894119890119877119882

1198680

1198881 (36)







Key signal


Brake pedal signal








control system


Clutch 1 actuator

Clutch 2 actuator




MicroAutoBox





119904s 2355 2535



119904+ Δ119905)s 314 333





119901and 119905












Time t (s)

100

80

60

40

20

08 10 12 14 16

Acce

lera

tor p

edal

ope

ning120573

()


250

200

150

100

50

0


8 10 12 14 16

Time t (s)

Targ

et ro

tatio

nal s

peed120596

(rad

s)



8 10 12 14 16

250

200

150

100

50

0

Time t (s)

Real

spee

d120596

(rad

s)


10

5

0

minus5

minus108 10 12 14 16

Shoc

k in

tens

ityj

(ms3)

Time t (s)

(d) Shock intensity

7

6

5

4

3

2

1

08 9 10 11 12 13 14 15 16 17

Time t (s)

Slid

ing

fric

tion

wor

kW

(kJ)


Time t (s)8 10 12 14 16

120

100

80

60

40

20

0

Torq

ueT

(Nm

)


(f) Torque

Figure 12 Continued


25

20

15

10

5

0

Time t (s)8 10 12 14 16

Vehi

cle v

eloc

ity

(km

h)


120

100

80

60

40

20

08 9 10 11 12 13

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)



25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

et(s

)

8 9 10 11 12 13

Time t (s)

tPts


15

10

5

0

Clut

ch se

para

ting

strok

ex(m

m)

Time t (s)8 10 12 14 16











0+ 119905119904)s 1196







100

80

60

40

20

08194 8198 8202 8206 821 8214

Time t (s)

Acce

lera

tor o

peni

ng120573

()


8194 8198 8202 8206 821 8214

350

300

250

200

150

100

50

0


Time t (s)

Rota

tiona

l spe

ed120596

(rad

s)


8194 8198 8202 8206 821 8214

10

5

0

minus5

Time t (s)

Shoc

k in

tens

ityj

(ms3)

(c) Shock intensity








7 Conclusion



e eng

ine o

utpu

t tor

que (

Nm

)



250

200

150

100

50

0100

8060

4020

0 10002000

30004000

50006000

Figure 15



1198681198881 0014 kgsdotm2

1198681198882 0014 kgsdotm2

119868119898 001 kgsdotm2

119868119904 1470392 kgsdotm2

I1198921


119868119892119903 0005 kgsdotm2

i1 simi53615 2042 1257

0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2

119860 2095m119862119889 0293

119877119908 0308m

120578 0921198770 0228m

1198771 015m



Appendices


See Figure 15


See Table 5



References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










050 15 2 25 3 35 41

140

120

100

80

60

40

20

0

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)



050 15 2 25 3 35 41

20

18

16

14

12

10

8

6

4

2

0

Time t (s)

Vehi

cle v

eloc

ity

(km

h)




1199091119890

= 120579119890 1119890

= 120579119890= 120596119890 1198901119890

= 119909119903119890minus 1199091119890 1198902119890

= 119903119890minus 1199092119890


119890 namely

[1198901119890

1198902119890

] = [

[

0 1

0 minus119887119890

119868119890

]

]

[1198901119890

1198902119890

] + [

[

0

minus1

119868119890

]

]

1199062+ [

0

1198912119890

] (28)

where 1199062= 119879119890 1198912119890

= (1198791198881119868119890) + 119903119890+ (119887119890119868119890)119903119890 which are


119904119890= 11988811198901198901119890+ 11988821198901198902119890 (29)



where 119889119890gt |11988821198901198912119890|

119892 (119904) =

sgn (119904) |119904| ge120587

2119901119890

sin (119901119890sdot 119904) |119904| lt

120587

2119901119890

119901 gt 0 (31)


formula

1199062=119868119890

1198882

[119896119890sdot 119904119890+ 119889119890sdot 119892 (119904119890) + 1198902119890(1198881119890minus 1198882119890

119887119890

119868119890

) + 11988821198901198912119890]

(32)



119879119889

119890= 119879119871

119890+ 119870119890119905 (33)

119870119890= (

119879119889119890minus 119879119871119890

Δ119905) (34)



119890is



119895 =119894119890119877119882

119868119889

119890 (35)



050 15 2 25 3 35 41

25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

etp

(s)

Time t (s)



050 15 2 25 3 35 41

3

25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

ets

(s)

Time t (s)



050 15 2 25 3 35 41

100

90

80

70

60

50

40

30

20

10

0


Clut

ch tr

ansfe

r tor

queT

c1(N

m)

Time t (s)


050 15 2 25 3 35 41

100

90

80

70

60

50

40

30

20

10

0


Clut

ch tr

ansfe

r tor

queT

c1(N

m)

Time t (s)




119895 =119894119890119877119882

1198680

1198881 (36)







Key signal


Brake pedal signal








control system


Clutch 1 actuator

Clutch 2 actuator




MicroAutoBox





119904s 2355 2535



119904+ Δ119905)s 314 333





119901and 119905












Time t (s)

100

80

60

40

20

08 10 12 14 16

Acce

lera

tor p

edal

ope

ning120573

()


250

200

150

100

50

0


8 10 12 14 16

Time t (s)

Targ

et ro

tatio

nal s

peed120596

(rad

s)



8 10 12 14 16

250

200

150

100

50

0

Time t (s)

Real

spee

d120596

(rad

s)


10

5

0

minus5

minus108 10 12 14 16

Shoc

k in

tens

ityj

(ms3)

Time t (s)

(d) Shock intensity

7

6

5

4

3

2

1

08 9 10 11 12 13 14 15 16 17

Time t (s)

Slid

ing

fric

tion

wor

kW

(kJ)


Time t (s)8 10 12 14 16

120

100

80

60

40

20

0

Torq

ueT

(Nm

)


(f) Torque

Figure 12 Continued


25

20

15

10

5

0

Time t (s)8 10 12 14 16

Vehi

cle v

eloc

ity

(km

h)


120

100

80

60

40

20

08 9 10 11 12 13

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)



25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

et(s

)

8 9 10 11 12 13

Time t (s)

tPts


15

10

5

0

Clut

ch se

para

ting

strok

ex(m

m)

Time t (s)8 10 12 14 16











0+ 119905119904)s 1196







100

80

60

40

20

08194 8198 8202 8206 821 8214

Time t (s)

Acce

lera

tor o

peni

ng120573

()


8194 8198 8202 8206 821 8214

350

300

250

200

150

100

50

0


Time t (s)

Rota

tiona

l spe

ed120596

(rad

s)


8194 8198 8202 8206 821 8214

10

5

0

minus5

Time t (s)

Shoc

k in

tens

ityj

(ms3)

(c) Shock intensity








7 Conclusion



e eng

ine o

utpu

t tor

que (

Nm

)



250

200

150

100

50

0100

8060

4020

0 10002000

30004000

50006000

Figure 15



1198681198881 0014 kgsdotm2

1198681198882 0014 kgsdotm2

119868119898 001 kgsdotm2

119868119904 1470392 kgsdotm2

I1198921


119868119892119903 0005 kgsdotm2

i1 simi53615 2042 1257

0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2

119860 2095m119862119889 0293

119877119908 0308m

120578 0921198770 0228m

1198771 015m



Appendices


See Figure 15


See Table 5



References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










050 15 2 25 3 35 41

25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

etp

(s)

Time t (s)



050 15 2 25 3 35 41

3

25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

ets

(s)

Time t (s)



050 15 2 25 3 35 41

100

90

80

70

60

50

40

30

20

10

0


Clut

ch tr

ansfe

r tor

queT

c1(N

m)

Time t (s)


050 15 2 25 3 35 41

100

90

80

70

60

50

40

30

20

10

0


Clut

ch tr

ansfe

r tor

queT

c1(N

m)

Time t (s)




119895 =119894119890119877119882

1198680

1198881 (36)







Key signal


Brake pedal signal








control system


Clutch 1 actuator

Clutch 2 actuator




MicroAutoBox





119904s 2355 2535



119904+ Δ119905)s 314 333





119901and 119905












Time t (s)

100

80

60

40

20

08 10 12 14 16

Acce

lera

tor p

edal

ope

ning120573

()


250

200

150

100

50

0


8 10 12 14 16

Time t (s)

Targ

et ro

tatio

nal s

peed120596

(rad

s)



8 10 12 14 16

250

200

150

100

50

0

Time t (s)

Real

spee

d120596

(rad

s)


10

5

0

minus5

minus108 10 12 14 16

Shoc

k in

tens

ityj

(ms3)

Time t (s)

(d) Shock intensity

7

6

5

4

3

2

1

08 9 10 11 12 13 14 15 16 17

Time t (s)

Slid

ing

fric

tion

wor

kW

(kJ)


Time t (s)8 10 12 14 16

120

100

80

60

40

20

0

Torq

ueT

(Nm

)


(f) Torque

Figure 12 Continued


25

20

15

10

5

0

Time t (s)8 10 12 14 16

Vehi

cle v

eloc

ity

(km

h)


120

100

80

60

40

20

08 9 10 11 12 13

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)



25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

et(s

)

8 9 10 11 12 13

Time t (s)

tPts


15

10

5

0

Clut

ch se

para

ting

strok

ex(m

m)

Time t (s)8 10 12 14 16











0+ 119905119904)s 1196







100

80

60

40

20

08194 8198 8202 8206 821 8214

Time t (s)

Acce

lera

tor o

peni

ng120573

()


8194 8198 8202 8206 821 8214

350

300

250

200

150

100

50

0


Time t (s)

Rota

tiona

l spe

ed120596

(rad

s)


8194 8198 8202 8206 821 8214

10

5

0

minus5

Time t (s)

Shoc

k in

tens

ityj

(ms3)

(c) Shock intensity








7 Conclusion



e eng

ine o

utpu

t tor

que (

Nm

)



250

200

150

100

50

0100

8060

4020

0 10002000

30004000

50006000

Figure 15



1198681198881 0014 kgsdotm2

1198681198882 0014 kgsdotm2

119868119898 001 kgsdotm2

119868119904 1470392 kgsdotm2

I1198921


119868119892119903 0005 kgsdotm2

i1 simi53615 2042 1257

0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2

119860 2095m119862119889 0293

119877119908 0308m

120578 0921198770 0228m

1198771 015m



Appendices


See Figure 15


See Table 5



References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Key signal


Brake pedal signal








control system


Clutch 1 actuator

Clutch 2 actuator




MicroAutoBox





119904s 2355 2535



119904+ Δ119905)s 314 333





119901and 119905












Time t (s)

100

80

60

40

20

08 10 12 14 16

Acce

lera

tor p

edal

ope

ning120573

()


250

200

150

100

50

0


8 10 12 14 16

Time t (s)

Targ

et ro

tatio

nal s

peed120596

(rad

s)



8 10 12 14 16

250

200

150

100

50

0

Time t (s)

Real

spee

d120596

(rad

s)


10

5

0

minus5

minus108 10 12 14 16

Shoc

k in

tens

ityj

(ms3)

Time t (s)

(d) Shock intensity

7

6

5

4

3

2

1

08 9 10 11 12 13 14 15 16 17

Time t (s)

Slid

ing

fric

tion

wor

kW

(kJ)


Time t (s)8 10 12 14 16

120

100

80

60

40

20

0

Torq

ueT

(Nm

)


(f) Torque

Figure 12 Continued


25

20

15

10

5

0

Time t (s)8 10 12 14 16

Vehi

cle v

eloc

ity

(km

h)


120

100

80

60

40

20

08 9 10 11 12 13

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)



25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

et(s

)

8 9 10 11 12 13

Time t (s)

tPts


15

10

5

0

Clut

ch se

para

ting

strok

ex(m

m)

Time t (s)8 10 12 14 16











0+ 119905119904)s 1196







100

80

60

40

20

08194 8198 8202 8206 821 8214

Time t (s)

Acce

lera

tor o

peni

ng120573

()


8194 8198 8202 8206 821 8214

350

300

250

200

150

100

50

0


Time t (s)

Rota

tiona

l spe

ed120596

(rad

s)


8194 8198 8202 8206 821 8214

10

5

0

minus5

Time t (s)

Shoc

k in

tens

ityj

(ms3)

(c) Shock intensity








7 Conclusion



e eng

ine o

utpu

t tor

que (

Nm

)



250

200

150

100

50

0100

8060

4020

0 10002000

30004000

50006000

Figure 15



1198681198881 0014 kgsdotm2

1198681198882 0014 kgsdotm2

119868119898 001 kgsdotm2

119868119904 1470392 kgsdotm2

I1198921


119868119892119903 0005 kgsdotm2

i1 simi53615 2042 1257

0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2

119860 2095m119862119889 0293

119877119908 0308m

120578 0921198770 0228m

1198771 015m



Appendices


See Figure 15


See Table 5



References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Time t (s)

100

80

60

40

20

08 10 12 14 16

Acce

lera

tor p

edal

ope

ning120573

()


250

200

150

100

50

0


8 10 12 14 16

Time t (s)

Targ

et ro

tatio

nal s

peed120596

(rad

s)



8 10 12 14 16

250

200

150

100

50

0

Time t (s)

Real

spee

d120596

(rad

s)


10

5

0

minus5

minus108 10 12 14 16

Shoc

k in

tens

ityj

(ms3)

Time t (s)

(d) Shock intensity

7

6

5

4

3

2

1

08 9 10 11 12 13 14 15 16 17

Time t (s)

Slid

ing

fric

tion

wor

kW

(kJ)


Time t (s)8 10 12 14 16

120

100

80

60

40

20

0

Torq

ueT

(Nm

)


(f) Torque

Figure 12 Continued


25

20

15

10

5

0

Time t (s)8 10 12 14 16

Vehi

cle v

eloc

ity

(km

h)


120

100

80

60

40

20

08 9 10 11 12 13

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)



25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

et(s

)

8 9 10 11 12 13

Time t (s)

tPts


15

10

5

0

Clut

ch se

para

ting

strok

ex(m

m)

Time t (s)8 10 12 14 16











0+ 119905119904)s 1196







100

80

60

40

20

08194 8198 8202 8206 821 8214

Time t (s)

Acce

lera

tor o

peni

ng120573

()


8194 8198 8202 8206 821 8214

350

300

250

200

150

100

50

0


Time t (s)

Rota

tiona

l spe

ed120596

(rad

s)


8194 8198 8202 8206 821 8214

10

5

0

minus5

Time t (s)

Shoc

k in

tens

ityj

(ms3)

(c) Shock intensity








7 Conclusion



e eng

ine o

utpu

t tor

que (

Nm

)



250

200

150

100

50

0100

8060

4020

0 10002000

30004000

50006000

Figure 15



1198681198881 0014 kgsdotm2

1198681198882 0014 kgsdotm2

119868119898 001 kgsdotm2

119868119904 1470392 kgsdotm2

I1198921


119868119892119903 0005 kgsdotm2

i1 simi53615 2042 1257

0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2

119860 2095m119862119889 0293

119877119908 0308m

120578 0921198770 0228m

1198771 015m



Appendices


See Figure 15


See Table 5



References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










25

20

15

10

5

0

Time t (s)8 10 12 14 16

Vehi

cle v

eloc

ity

(km

h)


120

100

80

60

40

20

08 9 10 11 12 13

Time t (s)

Clut

ch tr

ansfe

r tor

queT

c1(N

m)



25

2

15

1

05

0

Opt

imiz

atio

n va

riabl

et(s

)

8 9 10 11 12 13

Time t (s)

tPts


15

10

5

0

Clut

ch se

para

ting

strok

ex(m

m)

Time t (s)8 10 12 14 16











0+ 119905119904)s 1196







100

80

60

40

20

08194 8198 8202 8206 821 8214

Time t (s)

Acce

lera

tor o

peni

ng120573

()


8194 8198 8202 8206 821 8214

350

300

250

200

150

100

50

0


Time t (s)

Rota

tiona

l spe

ed120596

(rad

s)


8194 8198 8202 8206 821 8214

10

5

0

minus5

Time t (s)

Shoc

k in

tens

ityj

(ms3)

(c) Shock intensity








7 Conclusion



e eng

ine o

utpu

t tor

que (

Nm

)



250

200

150

100

50

0100

8060

4020

0 10002000

30004000

50006000

Figure 15



1198681198881 0014 kgsdotm2

1198681198882 0014 kgsdotm2

119868119898 001 kgsdotm2

119868119904 1470392 kgsdotm2

I1198921


119868119892119903 0005 kgsdotm2

i1 simi53615 2042 1257

0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2

119860 2095m119862119889 0293

119877119908 0308m

120578 0921198770 0228m

1198771 015m



Appendices


See Figure 15


See Table 5



References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










100

80

60

40

20

08194 8198 8202 8206 821 8214

Time t (s)

Acce

lera

tor o

peni

ng120573

()


8194 8198 8202 8206 821 8214

350

300

250

200

150

100

50

0


Time t (s)

Rota

tiona

l spe

ed120596

(rad

s)


8194 8198 8202 8206 821 8214

10

5

0

minus5

Time t (s)

Shoc

k in

tens

ityj

(ms3)

(c) Shock intensity








7 Conclusion



e eng

ine o

utpu

t tor

que (

Nm

)



250

200

150

100

50

0100

8060

4020

0 10002000

30004000

50006000

Figure 15



1198681198881 0014 kgsdotm2

1198681198882 0014 kgsdotm2

119868119898 001 kgsdotm2

119868119904 1470392 kgsdotm2

I1198921


119868119892119903 0005 kgsdotm2

i1 simi53615 2042 1257

0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2

119860 2095m119862119889 0293

119877119908 0308m

120578 0921198770 0228m

1198771 015m



Appendices


See Figure 15


See Table 5



References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










e eng

ine o

utpu

t tor

que (

Nm

)



250

200

150

100

50

0100

8060

4020

0 10002000

30004000

50006000

Figure 15



1198681198881 0014 kgsdotm2

1198681198882 0014 kgsdotm2

119868119898 001 kgsdotm2

119868119904 1470392 kgsdotm2

I1198921


119868119892119903 0005 kgsdotm2

i1 simi53615 2042 1257

0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2

119860 2095m119862119889 0293

119877119908 0308m

120578 0921198770 0228m

1198771 015m



Appendices


See Figure 15


See Table 5



References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Research Article Sliding Mode Variable Structure Control...

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