Hindawi Publishing Corporation Mathmatical Problms in Enginring Volum 214, Articl ID 494731, 18 pags http://dx.doi.org/1.1155/214/494731 Rsarch Articl Sliding Mod Variabl Structur Control and Ral-Tim Optimization of Dry Dual Clutch Transmission during th Vhicl s Launch Zhiguo Zhao, Haijun Chn, and Qi Wang School of Automotiv Studis, Tongji Univrsity, Shanghai 2184, China Corrspondnc should b addrssd to Zhiguo Zhao; zhiguozhao@tongji.du.cn Rcivd 19 Sptmbr 213; Rvisd 5 Novmbr 213; Accptd 5 Novmbr 213; Publishd 2 Fbruary 214 Acadmic Editor: Hui Zhang Copyright 214 Zhiguo Zhao t al. This is an opn accss articl distributd undr th Crativ Commons Attribution Licns, which prmits unrstrictd us, distribution, and rproduction in any mdium, providd th original work is proprly citd. In ordr to rflct driving intntion adquatly and improv th launch prformanc of vhicl quippd with fiv-spd dry dual clutch transmission (DCT), th issu of coordinating control btwn ngin and clutch is rsarchd, which is basd on th DCT and prototyp car dvlopd indpndntly. Four-dgr-of-frdom (DOF) launch dynamics quations ar stablishd. Taking advantag of prdictiv control and gntic algorithm, targt tracing curvs of ngin spd and vhicl vlocity ar optimally spcifid. Sliding mod variabl structur (SMVS) control stratgy is dsignd to track ths curvs. Th rapid prototyping xprimnt and tst ar, rspctivly, conductd on th DCT tst bnch and in th chassis dynamomtr. Rsults show that th dsignd SMVS control stratgy not only ffctivly mbodis th drivr s intntion but also has strong robustnss to th vhicl paramtr s variations. 1. Introduction Basd on th automatd mchanical transmission (AMT), if rmodlling its transmission mchanism (including input shaft, positions of gar pairs, and intrmdiat shaft) and adding a st of dry friction clutch and corrsponding actuator, drydualclutchtransmission(dct)canbconstructd.th problm of traction intrruption, whil gar shifting, can also b rsolvd ffctivly through th coordinating control btwn two clutchs and ngin. So, th quality of shifting and th powr prformanc of vhicl can also b improvd. Astothlaunchprocssofvhiclquippdwithdry DCT, singl or doubl clutchs can b adoptd to launch. Launching with doubl clutchs aims at balancing th sliding friction work of twin clutchs and lngthning thir srvic lif [1, 2], but dual clutchs participation mod can asily lad to powr cycling insid th DCT, so its fasibility rquirs furthr invstigation. By contrast, whn singl clutch is involvd, th launch dynamics modl and control logic of DCTarthsamasthAMT s,bcausthlaunchmodlling and controlling of vhicl quippd with AMT hav bn studid widly and profoundly. Two dgr-of-frdom (DOF)dynamicsmodlhasbnstupandthoptimal clutch ngaging control law via minimum principl has bn foundd [3, 4]. Quadratic optimal launch controllr has bn dsignd and quivalnt damping of AMT transmission has also bn takn into account[5, 6]. Six-DOF launch dynamics quations and clutch s hydraulic actuator modl hav bn stablishd. Th corrsponding modl s paramtrs hav bn also obtaind through xprimnts [7]. Fiv-DOF launch modl has bn stablishd and simplifid, and ngin spd dcoupling control stratgy has also bn put forward [8]. In addition, fuzzy logic control mthod for th launching procss of AMT basd on xprinc has bn studid largly and fuzzy input variabls could b th acclrator pdal opning and its changing rat [9], or th dviation and its changing rat btwn ngin spd and targt spd rlatd to acclrator pdal [1], or th rotary spd diffrnc btwn clutch driving plat and drivn plat [11]. Gnrally, output variabls could b clutch ngaging spd; gntic algorithm has bn furthr usd to optimiz th fuzzy rul st [12]. Morovr, in th aspct of launch control for vhicl
2 Mathmatical Problms in Enginring 5th gars 3rd gars 1st gars I g5 Clutch 1 ω c1 b c1 T mc1 Input shaft NO.1 I c1 (solid shaft) T c1 i Synchronizr 2 2nd gars 1 i 3 4th gars I g1 I i 5 Rvrs gars Engin g3 Synchronizr 1 ω m I Intrmdiat shaft I m T b T sm cm1 or T cm2 I gr Synchronizr 4 b m i ω a i 4 T i 2 T c2 Synchronizr 3 Output shaft T mc2 Ic2 ω Input shaft NO.2 c2 b Clutch 2 c2 I (hollow shaft) g2 I g4 Vhicl ω s I b T s ms T f Figur 1: Fiv-spd dry DCT dynamic modl. quippd with DCT, clutch optimal ngaging control law has bn introducd by utilizing minimum principl and synthtically taking shock intnsity, sliding friction work, andnginoutputtorquintoconsidration[13]. Linar quadratic optimal control has bn applid to simulat clutch ngaging prssur in th launching procss [14, 15]. Launch fuzzy intllignt control algorithm has bn dsignd and optimizd by using acclrator pdal opning and its changing rat, clutch rlativ slip rat and ngin spd diffrnc to dscrib th driving intntion, clutch ngaging stats and ngin working condition, rspctivly [16]. Comparativly, doubl-layr fuzzy intllignt control architctur has bn prsntd by stting up clutch ngaging fuzzy control ruls and ral car chassis dynamomtr tst has bn conductd [17]. Butthabovstatdstudisonlyfocusonthcontrolof clutch ngaging control ruls, rarly taking considration of th issu of coordinating control btwn ngin and clutch during th vhicl s launch procss and lt alon th qualification of drivr s intntion. Taking th factors such as drivr s intntion, ngin condition, clutch stat, and shock intnsity into account, th issu of coordinating control btwn ngin and clutch is invstigatd in th papr, which is basd on th DCT and prototyp car dvlopd indpndntly. Four dgrs of frdom (DOF) launch dynamics quations ar stablishd. Th computational formulas of ngin spd and clutch transfr torquinthlaunchingprocsshavalsobnquantifid andgivn.takingadvantagofprdictivcontrolandgntic algorithm, targt tracing curvs of ngin spd and vhicl vlocity ar optimally spcifid. Sliding mod variabl structur (SMVS) control stratgy has bn dsignd to track ths curvs.basdonthmatlab/simulinksoftwarplatformand th hardwar-in-th-loop tst bnch, th launch prformanc of prototyp car quippd with dry DCT has bn simulatd undr diffrnt driving conditions, and th rapid prototyping xprimnt and tst ar, rspctivly, conductd on th DCT tst bnch and in th chassis dynamomtr. 2. Mathmatical Modls 2.1. Fiv-Spd Dry DCT Dynamic Modl. Th fiv-spd dry DCT dscribd in th papr is mad up of dry dual clutch modul and its actuator, four synchronizrs and thir actuators,andsinglintrmdiatshaftgartransmission mchanism. In ordr to study th dynamic charactristic of singl clutch in th launching procss and dvlop rlvant coordinating control stratgy, th following assumptions should b mad bfor modling (1) Both whls momnt of inrtia and vhicl s translation quality ar convrtd into th transmission output shaft. Th ngin output shaft and th input shaft, intrmdiat shaft, and output shaft of transmission ar rgardd as rigid body with distributd paramtrs and concntratd inrtia, and th friction damping loss is considrd, rspctivly (2) Th dynamic procss of th clutch actuator and th synchronizrs, as wll as th hat fad of th clutch ar not th focus of this papr. (3) Nglct th lasticity btwn baring and its block, as wll as th lasticity and gap in gar ngagmnt. Finally th stablishd dynamic modl of fiv-spd dry DCT aftr simplification is shown in Figur 1. In Figur 1, paramtrs and variabls ar dfind as follows: I : quivalnt momnt of inrtia of ngin crankshaft (including flywhl) and clutch driving plat; I c1 : Equivalnt momnt of inrtia of clutch 1 drivn plat, transmission NO.1 input shaft (solid part), and rlvant odd numbr gars; I c2 : quivalnt momnt of inrtia of clutch 2 drivn plat, transmission NO.2 input shaft (hollow part) and its rlvant vn numbr spd gars;
Mathmatical Problms in Enginring 3 I m : quivalnt momnt of inrtia of transmission intrmdiat shaft, its rlvant gars, and final driv driving part; I s : quivalnt momnt of inrtia of final driv drivn part, diffrntial gars, axl shafts, whls, and complt vhicl, which ar qually convrtd into transmission output shaft; I g1,i g3,i gr : momnt of inrtia of 1st, 3rd, and rvrs drivn gars; I g2,i g4,i g5 : momnt of inrtia of 2nd, 4th, and 5th driving gars; i 1 i 5,i a : forward gar ratios and final driv ratio; b : rotating viscous damping cofficint of ngin output shaft; b c1 : rotating viscous damping cofficint of transmission NO.1 input shaft; b c2 : rotating viscous damping cofficint of transmission NO.2 input shaft; b m : rotating viscous damping cofficint of transmission intrmdiat shaft; b s : quivalnt rotating viscous damping cofficint of axl shafts and whls, which ar qually convrtd into transmission output shaft; ω : angular spd of ngin crankshaft; ω c1 : angular spd of clutch 1 drivn plat (or transmission NO.1 input shaft); ω c2 : angular spd of clutch 2 drivn plat (or transmission NO.2 input shaft); ω m : angular spd of transmission intrmdiat shaft; ω s : angular spd of transmission output shaft; T :nginoutputtorqu; T c1,t c2 : transfr torqu of clutch 1 and clutch 2; T cm1,t cm2 :torquofno.1andno.2inputshafts acting on intrmdiat shaft; T mc1,t mc2 : torqu of intrmdiat shaft racting on NO.1 and NO.2 input shafts; T f : driving rsistanc torqu which is qually convrtd into transmission output shaft. 2.2. Dynamics Equations for Fiv-Spd Dry DCT. DCT can us 1st spd gar or 2nd spd gar to start. Tak 1st spd gar launch for xampl. Assuming that th ngin is alrady oprating in idl stat, th synchronizr 1 firstly ngags to th lft gar (1st gar). Bcaus th synchronizr ngaging procss dos not blong to th rsarch focus in this papr, th dtaild analysis of synchronizr is nglctd. Aftr th ngagmnt of synchronizr, th clutch 1 bgins to ngag to transmit th torqu from th ngin sid until th nd of launching procss. During th launch procss, clutch 1 gts through four phass. Fr Strok Eliminating. It is to liminat th vacant distanc btwn th clutch driving and drivn plats. Slipping Friction bfor Half-Engaging. Th clutch bgins to ngag but th transmittd torqu cannot ovrcom th vhiclrsistanctomovthvhicl. Sliding Friction aftr Half-Engaging. Th clutch is furthr ngagd and th torqu transmittd by clutch is abl to forc th vhicl to mov. Full-Engaging aftr Synchronizing. Th ngaging procss and th launching procss finish. Th first two phass hav a small ffct on th launching quality and thrfor th main rsarch attntion is focusd in th last two phass, spcially th third phas. Th four-dof dynamics quations on th phas of slipping friction aftr half-ngaging can b xprssd as follows: I c1 I ω =T T c1 b ω, ω c1 =T c1 T mc1 b c1 ω c1, (I m +I g1 +I g2 i 2 2 η+i g4i 2 4 η+i g5i 2 5 η) ω m =T c1m T sm b m ω m, I s ω s =T ms T f b s ω s, whr T =f(α,ω ), T cm1 =T mc1 i 1 η, T ms =T sm i a η, V =ω s R W 2 T c1 = 3 (R3 R3 1 R 2 )μ 1 F(x 1 ) 1 ω c1 ω, T L c1 ω c1 =ω, T f =( C da 21.15 V2 +mgsin θ+mgcos θf+δm dv dt )R W, (3) δ=1+ 1 I c1 i 2 1 i2 a +I mi 2 a +I s +I V. (4) m R W Among abov formulas, α is ngin throttl opning. f(α, ω ) dnots nonlinar function of ngin output torqu. η is transmitting fficincy of transmission shafts as wll as final driv. μ 1 is kintic friction cofficint among friction plats of clutch 1. R, R 1 ar intrnal and xtrnal radius of friction plats of clutch 1. x 1 is opning of clutch 1. F(x 1 ) dnots positiv prssur function of prssur plat of clutch 1. T L c1 is transfr torqu aftr full-ngaging of clutch. m is vhicl mass. g is gravity acclration. f is rolling rsistanc cofficint. V is vhicl vlocity. C d is wind drag cofficint. A is windward ara. θ is road slop. δ is convrsion cofficint of rotating mass. R W is radius of whl. For th sak of asily dsigning th controllr, furthr assumptions about motional rlationship among th input, intrmdiat, and output shafts of transmission should mt th quations ω s i a i 1 =ω m i 1 =ω c1.thnthdctdynamic modl in Figur 1 can b simplifid as that in Figur 2. (1) (2)
4 Mathmatical Problms in Enginring Clutch 1 Engin T ω c1 s I b ω T Clutch 2 T c2 ω c1 ω c2 Vhicl T ms b o I o Figur 2: DCT dynamics modl aftr simplification. Simplify formula (1), and thn som two-dof dynamics quations ar obtaind: I o I ω +b ω =T T c1, ω s +b o ω s =T c1 i T f, whr paramtrs ar dfind as follows: i =i a i 1 η 2 I o =I s +(I m +I g1 )i 2 a η+i c1i 2 1 i2 a η2 +I g2 i 2 2 i2 a η2 +I g4 i 2 4 i2 a η2 +I g5 i 2 5 i2 a η2, b o =b s +b m i 2 a η+b c1i 2 1 i2 a η2. Whn th clutch is fully ngagd, T c1 = T L c1.hclutch transmittd torqu T c1 is only dtrmind by ngin output torqu and driving rsistanc, which satisfis: T c1 = I o (T b ω )+(T f +b o ω s )I i 1 i a. (7) I o +I i i 1 i a Whn th clutch is fully ngags, th vhicl is launchd in crtain gar. In this sns, formula (5) canstillbfurthr simplifid as a singl-dof dynamics quation: whr I d T f (5) (6) ω s +b d ω s =T i T f, (8) I d =I s +(I m +I g1 )i 2 a η+(i c1 +I )i 2 1 i2 a η2 +I g2 i 2 2 i2 a η2 +I g4 i 2 4 i2 a η2 +I g5 i 2 5 i2 a η2, b d =b s +b m i 2 a η+(b c1 +b )i 2 1 i2 a η2. Synthsizing formulas (5) and (8), th DCT launch dynamic modl aftr liminating th null distanc of clutch canbsnasahybridmodl,namlyincludingatwo- DOF sliding friction modl and a singl-dof stably opratd modl. Th switching condition btwn th two modls is ω =ω c1.thcontrollrwillbdsigndonthbasisofthis hybrid modl in th following. 3. Coordinating Control and Ral-Tim Optimization for Dry DCT 3.1. Launch Control Objctivs. Th control objctivs of dry DCT in th launching procss ar as follows: (9) (1) rflct th drivr s intntion adquatly to lt th drivr hav diffrnt driving fl according to acclrator pdal opning and its changing rat; (2) undr th condition of mting th rquirmnts of shock intnsity and sliding friction work, to dcras th slipping friction work as much as possibl and guarant th launch comfort (shock intnsity is 1 m/s 3 in Grman standard [18]); (3) tak th ffct of launching on ngin s working stat into account to avoid th flamout of th ngin in th launching procss. 3.2. Launch Controllr Dsign Architctur. Alayrdarchitctur of launching control is usd as shown in Figur 3.Th uppr layr controllr is applid to dtrmin th optimal clutch transfr torqu and ngin targt spd (or torqu), whil th lowr on is usd to implmnt a srvocontrol of clutch torqu and a closd-loop control of ngin torqu (or spd). Th uppr controllr can furthr b dividd into two parts according to th activation ordr: th sliding control bfor th spd synchronization and ngaging control aftr th spd synchronization. Th sliding control is aiming at th sliding friction aftr half-ngaging phas and also th cor of th launching control. Basd on th two-dof modl during th sliding phas, th driving intntion, th closdloop control of ngin spd and clutch torqu, and can b ralizd. Rlativly, basd on th singl-dof modl, th ngaging control is for th full-ngaging aftr synchronizing phas and to mak th clutch ngag compltly as quickly as possibl and prvnt ngagd clutch plats from falling into sliding stat again du to th chang of ngin output torqu. Manwhil, ngin output torqu is adjustd to match th dmandtorqu.evnthoughthdrivinganddrivnplatsar alrady synchronizd, th launch controllr dos not snd out an accomplishmnt signal. Only if th ngin output torqu isqualtothdmandtorqu,itsndsoutthsignal. 3.3. Launch Sliding Friction Procss Control. Th inputs of launch slipping friction procss control includ acclrator pdal opning, ngin spd, whl spd, and so forth. Th outputs contain Clutch 1 targt ngaging prssur and ngin dmand torqu. Thy would b ralizd through th sliding mod variabl structur tracing control algorithm. (1) Dtrmin targt control variabls. Th targt control variabls includ ngin targt spd and vhicl targt shock intnsity. Th ngin targt spd should b proportional to th acclrator pdal opning and its changing rat in ordr to partially rflct th drivr s intntion. Taking ngin targt spd and vhicl targt shock intnsity as masuring indx of drivr s intntion, th DCT launch controllr can b dsignd without considring th concrt physical charactristics of clutch actuators, thus improving th gnrality of launch controllr. (2) Targt tracing controllr dsign. Basd on simplifid modls of ngin and transmission, sliding mod variabl
Mathmatical Problms in Enginring 5 Control of clutch ngaging procss aftr synchronizing Acclrator pdal opning β dβ dt β Calculation of quivalnt β acclrator pdal opning Calculation of drivr dmand torqu Drivr dmand torqu T d t< t? Ys No No Has th clutch bn synchronizd or not? Control of starting sliding friction procss Ys Switch control of dmand torqu Engin targt output torqu T rf Singl-DOF in 1st gar stably oprating dynamics modl of dry dual clutch transmission aftr synchronizing Calculations of spd diffrnc and slip rat btwn clutch driving and drivn plats Engin modl and its torqu control modl Lowr control Engin ral torqu T Clutch drivn plat spd ω c1 Engin ral spd ω Two-DOF starting dynamics modl of dry dual clutch transmission aftr synchronizing Dtrmination of ngin targt spd Dtrmination of targt shock intnsity Engin targt Sliding mod variabl spd ω rf structur tracing control of ngin spd Targt shock intnsitis j p and j s Dtrmination of targt whl spd Engin targt output torqu T rf Targt whl spd ω rf s Figur 3: Dsign architctur of launch controllr. Engin ral torqu T Engin modl and its torqu control modl Sliding mod variabl structur tracing control of whl spd Clutch ral T c1 transfr torqu Lowr control Clutch targt transfr torqu Tc1 rf Clutch modl and its torqu control modl Ral whl spd ω s structur controllr is dsignd to track ngin targt spd and vhicl targt shock intnsity. 3.3.1. Dtrmining Mthod of Engin Targt Spd. Th principls of dtrmining ngin targt spd ar as follows. (1) In ordr to avoid th stalling of ngin and attrition of clutch du to ovrhigh spd, th targt spd is not lss than th ngin idl spd (st as 8 r/min) and is limitd to a maximum valu (st as 2 r/min) as wll. (2) Within optional limits of targt spd, on on hand, th targt spd changs along with th variation of acclrator pdal opning and its changing rat, and itcannsurthatnginhasnoughoutputpowrto mt th launch dmands undr diffrnt conditions. On th othr hand, th slctd targt spd can mak thnginworkinanconomicara. (3) Whn th diffrnc btwn ngin ral spd and clutch drivn plat spd is mor than th stting thrshold valu Δω and th clutch sliding friction tim is lss than th tim variabl t p, th ngin targt spd will coordinat with th acclrator pdal opning and its changing rat. If th condition is rvrs, th targt spd will b fixd as synchronous spd ω (t s ), namly, th spd whn ngin and clutch drivn plat ar at th momnt of synchronizing. Th calculation of ngin targt spd ω rf is shown Spd ω (rad/s) ω (t s ) ω () ω rf = ω c1 ω rf t p Figur 4: Dtrmination of ngin targt spd. in Figur4 and Formula (1). Th ngin output charactristiccanbsninfigur 15. Considr ω (t s ) ω () t p t+ω () (ω ω c1 ) Δω, t < t p, ω (t s ) othr, t s (1) whr ω (t s ) and ω (), rspctivly, dnot ngin targt spd postsynchronizing and idl spd. t p is linarly incrasing tim of ngin spd. t s is tim lapsd until clutch driving
6 Mathmatical Problms in Enginring Tabl 1: Engin synchronous targt spd. Equivalnt acclrator pdal opning β V /% Engin synchronous targt spd ω (t s )/(r/min) 1 1 1 2 1 2 3 11 3 4 12 4 5 13 5 6 14 6 7 15 7 8 16 8 9 17 9 1 2 and drivn plats ar synchronizd. Δω is st thrshold valu ofthdiffrncbtwnclutchdrivinganddrivnplats. In ordr to rflct th drivr s intntion asily and dtrmin ω (t s ), quivalnt acclrator pdal opning β V is introducd to synthsiz th information of acclrator pdal opning and its changing rat. Th rlationship btwn β V and ω (t s ) is shown in Tabl 1. Considr β V (t) =β(t) +k β (t), (11) whr β(t) is ral valu of acclrator pdal opning. β(t) is changing rat of acclrator pdal opning. k is wight indx and must b dtrmind according to th practic to guarant th β t (t) falling into th scop of [ 1]. 3.3.2. Dtrmining Mthod of Targt Shock Intnsity in th Launching Procss. Th launch targt shock intnsity not only rflcts th drivr s intntion, but also guarants that th intnsity is in a rasonabl xtnt. Th friction procss is dividd into thr parts in [19], which qualitativly laboratd control ky points whn a vhicl was launchd and its clutch driving and drivn plats wr synchronizing. In [2], th shock intnsity whil th clutch driving and drivn plats wr synchronizing is drivd, which showd that it is proportional to th diffrnc btwn ngin acclration and acclration of clutch drivn plat at th instant of prsynchronization. That is I ω c (+) ω c ( ) = [ ω I +I ( ) ca ω c ( )], (12) whr ω c ( ), ω c (+) dnot acclrations of clutch drivn plat at th instant of prsynchronization and post- synchronization. ω ( ) is ngin acclration at th instant of prsynchronization. I ca is momnt of inrtia of complt vhicl and its transmission systm, which ar qually convrtd to clutch drivn plat. Suppos that th transmission systm is rigid; namly, V = ω s R W = ω c i 1 i a R W. Th shock intnsity of vhicl can Tabl 2: Drivr s intntion. Launch mod Slow Modrat Abrupt Equivalnt acclrator pdal opning β V /% 2 2 5 5 1 Targt shock intnsity j p /(m/s 3 ).5 1.5 2.5 b qually convrtd into th shock intnsity of clutch drivn plat. Considr Formula (12). If th diffrnc btwn ngin acclration and acclration of clutch drivn plat is zro, th shock intnsity will b zro at th momnt of synchronizing. Th condition is calld no-impact synchronizing condition. As th ngin targt spd is dtrmind in prcding passag, namly, th rotary spd diffrnc is lss than th thrshold valu Δω or th lapsd tim of sliding friction procssismorthanthtimvariablt p, th ngin spd rmains constant as th sam as synchronous targt spd. Sothnginacclrationiszro.Forthsakofno-impact at th momnt of synchronizing, th spd of clutch drivn platshouldbqualtothtargtspdanditsacclration should b zro. Th authors divid th launch sliding friction procss into thr phass, dtrmin th targt shock intnsity in diffrnt phass, and obtain rlatd targt vhicl acclration and targt vhicl vlocity via intgral. It is shown in Figur 5. Phas On. Duringthtimslot t p,thtargtshock intnsity j p is positiv. It changs along with th quivalnt acclration, which rflcts th drivr s intntion. As th particularity of crping launch,that is, th clutch driving and drivn plats should maintain slipping stat during th whol launching procss without considring thir spd synchronization. In viw of this, crping launch is out of considration in this papr. Thrfor, on th basis of quivalnt acclrator pdal opning and ngin output torqu capacity, drivr s intntion is dividd into thr catgoris [3, 6], which is shown in Tabl 2. Phas Two. Duringthtimslott p t s,thtargtshock intnsity j p is ngativ. Th main goal is to lowr th vhicl acclration, so that th spd and acclration of clutch drivn plat stay th sam as th ngin s at th momnt of synchronizing in ordr to raliz no-impact synchronizing. Th valus ar synchronous targt spd and zro, rspctivly. Thortically, diffrnt valus ar slctd according to diffrnt targt shock intnsity in Phas On. Howvr, considring that clutch driving plat and its drivn plat ar approaching to synchroniz, th targt shock intnsity j s is st as a constant valu in ordr to acclrat th ngaging spd and dcras th total sliding friction work in th launching procss. Equations can b stablishd as follows: j p t p +j s (t s t p )=,.5j p t 2 p +j pt p (t s t p ) +.5j s (t s t p ) 2 =ω(t s )R W, (13)
Mathmatical Problms in Enginring 7 Shock intnsity j (m/s 3 ) j p t p t s Acclration a (m/s 2 ) j s (a) Targt shock intnsity t p t s (b) Targt vhicl acclration Vlocity (m/s) t p t s (c) Targt vhicl vlocity Figur 5: Targt curvs in th launching procss. whr j p is targt shock intnsity in phas on of sliding friction procss, j s is targt shock intnsity in Phas Two of sliding friction procss. ω(t s ) is spd of clutch drivn plat at tim t s, namly, th synchronous targt spd. By solving formula (13), th following can b obtaind: ω(t t p = s )R W (.5j p.5jp 2/j s), t s =t p (1 j p j s ). (14) According to quivalnt acclrator pdal opning at th initial momnt of sliding friction procss, th synchronous targt spd and targt shock intnsity in Phas On can b obtaind by looking up Tabls 1 and 2, rspctivly.basd on abov valus t p and t s, th targt spd of clutch 1 in th sliding friction procss will b listd in th following through th intgral of j p and j s twic: ω rf s t s = t s j R W dt, ω rf c1 =ωrf s i 1 i a. (15) Not that both t p and t s armasurdinacoordinat systm whos origin is th initial momnt of sliding friction procss. Phas Thr.Duringthtimslotovrt s,clutchdrivingplat and its drivn part ar alrady synchronizd, and DCT modl is switchd from sliding friction modl to 1st spd gar stably opratd modl. So th control of sliding friction maks no sns any mor. In ordr to mt th rquirmnt of noimpact synchronizing, th targt acclration is st as zro and th targt spd is constant. 3.3.3. Rolling Dtrmination of Targt Valu and Gntic Optimization of Shock Intnsity. Th dtrmining mthod of ngin targt spd and launch targt shock intnsity statd abov can nsur no stalling of ngin and rid comfort of vhicl in th launching procss and partially rflct th drivr s intntion, but som shortags also xist as follows. (1) Engin synchronizing targt spd and targt shock intnsityinphasonaronlybasdonquivalnt acclrator pdal opning at th initial momnt of sliding friction procss, without considring th whol sliding friction procss. Th transformation of quivalnt acclrator pdal opning obviously dos not accord with th fact. (2) Nglct th sliding friction work in th launching procss whn dtrmining th targt spd.
8 Mathmatical Problms in Enginring Vlocity (m/s) 3 2 1 t t +Δt t +2Δt t +3Δt Figur 6: Schmatic diagram of th rolling calculation of launch targt vhicl vlocity. In ordr to ovrcom th abov shortags, prdictiv control thoughts ar usd to optimiz th targt curvs onlin. It mans that during a tim slot (namly, at an optimizing stp), ths variabls, such as ω (t s ), t p, t s,andj p canbobtaind by minimizing th sliding friction work on th basis of th quivalnt acclrator pdal opning and vhicl vlocity. And thn th targt curvs can also b obtaind. Dtrmination of Rolling Algorithm of Targt Vhicl Vlocity. Th targt vhicl vlocity curv is rcalculatd in a tim intrval Δt. Both vhicl vlocity and acclration ar not qual to at vry calculation momnt. Figur 6 shows that V, V 1, V 2,andV 3 rprsnt th targt vhicl vlocitis at ths momnts of t, t +Δt, t +2Δt,andt +3Δt,rspctivly. Figur 7 shows th calculation mthod of targt vhicl vlocity in a crtain tim. According to th condition of noimpact synchronizing, formula (13) can b rwrittn as: a(t )+j p t p +j s (t s t p )=, V (t )+a(t )t p + 1 2 j pt 2 p +(α(t )+j p t p )(t s t p ) + 1 2 j s(t s t p ) 2 =ω(t s )R W, (16) whr t is optimizing momnt, α(t ) dnots vhicl acclration at th optimizing momnt, V(t ) dnots vhicl vlocity at th optimizing momnt, and ω (t s ) dnots synchronous targt rvolving spd, which updats its valu at vry optimizing stp according to virtual acclrator pdal signal by looking up Tabl 1. In a word, firstly at vry optimizing stp, synchronous targt rotary spd ω (t s ) and targt shock intnsity ar obtaind by looking up Tabls 1 and 2 according to th currnt quivalnt acclrator pdal opning. Scondly solv (16) and gt th latst valus of t p, t s. Finally according to formula (15), wgtthtargtvhiclvlocityinthlaunchingprocss. Th rolling dtrmining mthod of ngin targt spd rsmbls th abov dscription. According to (1), following formula can b obtaind: ω rf = ω (t s ) ω () t+ω t (), (ω ω c1 ) Δω, p t <t<(t +t p ), ω (t s ), othr. (17) Dtrmination of Optimal Algorithm of Targt Shock Intnsity. Th targt shock intnsity statd abov is obtaind by looking up Tabls. But it dos not nsur that th targt curv is optimal. It is discussd blow how to dtrmin j p and j s through gntic algorithm and ral-tim optimization. In th tim slot t t +t s, th prdictiv sliding friction work is t +t s W= T c1 (ω rf ω c1 )dt, t T c1 = I o ωrf s +b o ω rf s +mgr W μ i a i 1 η 2, (18) whr T c1 is stimatd clutch transfr torqu. If T c1 T c1 <ε, stimatd valu T c1 rplacs ral valu T c1,andtargtshock intnsitis j p and j s can b obtaind by minimizing th sliding friction work. Th slctd fitnss function basd on gntic algorithm is th rciprocal of prdictiv sliding friction work: F= 1 W. (19) Th optimizing procss of paramtrs j p and j s can b sn in Figur 8. 3.3.4. Dsign of Sliding Mod Variabl Structur Tracing Controllr. Basd on th dsign of prvious dtails, th targt vhicl vlocity and targt ngin spd ar alrady obtaind in th launch sliding friction procss. Howvr, whthr it can track accuratly or not, dpnds on th prformanc of launch controllr compltly. Considring immasurabl driving rsistanc, a kind of sliding mod variabl structur control algorithm with intrfrnc rjction has bn put forward in th papr, which aims at tracking ngin spd and whl spd accuratly. Rgardlss of th influnc of tmpratur and slip spd diffrnc on clutch friction cofficint μ 1,thrlationship btwn prssur F 1 of th clutch prssur plat and its transfr torqu is dtrmind uniquly, whn th intrnal and xtrnal radius of friction plats ar givn. For th sak of asy dscription, clutch transfr torqu is usd to dscrib th clutch ngaging law in th following. Tracing Control of Whl Spd. On th basis of launch dynamics quations of DCT transmission systm (rfrring to Formula (5)), supposing x 1 =θ s, x 2 =ω s,thris: x 1 =x 2, x 2 = i T I c1 b x o I 2 T f. I (2)
Mathmatical Problms in Enginring 9 Acclration a (m/s 2 ) a(t ) Vlocity (m/s) (t ) t t +t p t +t s t t +t p t +t s (a) Targt acclration (b) Targt vhicl vlocity Figur 7: Calculation schmatic diagram of targt vhicl vlocity at tim t. Equivalnt acclrator pdal opning Rolling dtrmination of ngin spd and vhicl vlocity Engin targt spd Clutch transfr torqu stimation Clutch drivn plat targt spd Calculations of stimatd sliding friction nrgy and fitnss function j p and j s aftr optimizing Targt impact strngth optimization Gntic algorithm Figur 8: Optimizing procss of targt shock intnsity. Supposing that 1 =x r x 1, 2 = x r x 2, u 1 =T c1,whr x r is th xpctation of x 1,thris [ 1 1 ]=[ 2 b ] [ 1]+[ [ I 2 i ] u 1 +[ ]+[ ], (21) f ] [ I 2 f 3 ] whr f 2 = x r +(I /b ) x r, which is masurabl intrfrnc, and f 3 =T f /I, which is immasurabl intrfrnc rlatd to th driving rsistanc. In ordr to rduc th gain of sliding mod variabl structur, it should contract th uppr and lowr boundaris of intrfrnc as much as possibl. According to th computational formula of driving rsistanc, th rolling rsistanc is rgardd as a part of masurabl intrfrnc; namly, masurabl intrfrnc f 2 canbrwrittnas f 2 = x r + I x b r + mgf. (22) b And th immasurabl intrfrnc f 3 can b rwrittn as f 3 = T f mgf. (23) I b Th switching function is dsignd as s=c 1 1 +c 2 2, (24) whr c 1 >, c 2 >. Tak th approaching rat: whr d> c 2 f 3, s= k s d g(s) +c 2 f 3, (25) sgn (s) g (s) = sin (p s) s π 2p s < π 2p p>. (26) Whil it is p, g(s) sgn(s).thcontrolinputu 1 is calculatd via th formula blow: u 1 = I b [k s + d g (s) + c 2 i 2 (c 1 c 2 )+c I 2 f 2 ]. (27) Tracing Control of Engin Spd. Bcaus ngin modl is adoubl-input(t and T c1 )-singl-output (ω ) modl and clutch transfr torqu T c1 is availabl in us of whl spd tracing controllr statd prviously, T c1 is a masurabl intrfrnc of ngin modl. Basd on th rotation dynamics of crankshaft (rfr to Formula (5)), w can suppos that
1 Mathmatical Problms in Enginring 1 25 Acclration pdal opning β (%) 9 8 7 6 5 4 3 2 1 Targt spd ω (rad/s) 2 15 1 5.5 1 1.5 2 2.5 3 3.5 4.5 1 1.5 2 2.5 3 3.5 4 NO.1 condition NO.2 condition (a) Acclration pdal opning valu Clutch on th NO.1 condition Engin on th NO.1 condition Clutch on th NO.2 condition Engin on th NO.2 condition (b) Targt rotational spd 25 6 Ral spd ω (rad/s) 2 15 1 5 Targt shock intnsity j (m/s 3 ) 4 2 2 4.5 1 1.5 2 2.5 3 3.5 4 Clutch on th NO.1 condition Engin on th NO.1 condition Clutch on th NO.2 condition Engin on th NO.2 condition (c) Actual rotational spd 6.5 1 1.5 2 2.5 3 3.5 4 NO.1 condition NO.2 condition (d) Targt impact strngth Ral shock intnsity j (m/s 3 ) 6 4 2 2 4 6.5 1 1.5 2 2.5 3 3.5 4 NO.1 condition NO.2 condition () Actual impact strngth Engin output torqu T (Nm) 14 12 1 8 6 4 2.5 1 1.5 2 2.5 3 3.5 4 NO.1 condition NO.2 condition (f) Engin output torqu Figur 9: Continud.
Mathmatical Problms in Enginring 11 Clutch transfr torqu T c1 (Nm) 14 12 1 8 6 4 2.5 1 1.5 2 2.5 3 3.5 4 NO.1 condition NO.2 condition (g) Clutch transfr torqu Vhicl vlocity (km/h) 2 18 16 14 12 1 8 6 4 2.5 1 1.5 2 2.5 3 3.5 4 NO.1 condition NO.2 condition (h) Vhicl vlocity Figur 9: Simulation rsults of launch prformanc. x 1 =θ, x 1 = θ =ω, 1 =x r x 1, 2 = x r x 2, whr x r is th xpctation of θ ;namly, 1]=[ 2 [ 1 b ] [ 1]+[ [ I 2 1 ] ] [ I ] u 2 +[ f 2 ], (28) whr u 2 =T, f 2 =(T c1 /I )+ x r +(b /I ) x r,whichar masurabl intrfrncs. Th switching function is dsignd as s =c 1 1 +c 2 2, (29) whr c 1 >, c 2 >. Tak th approaching rat: whr d > c 2 f 2, s = k s d g(s ), (3) sgn (s), s π, 2p g (s) = sin (p s), s < π 2p p>. (31) Th control output u 2 is calculatd via th following formula: u 2 = I b [k c s +d g(s )+ 2 (c 1 c 2 )+c 2 I 2 f 2 ]. (32) 3.4. Switching Control of Engin Dmand Torqu in th Engaging Procss aftr Synchronizing. Whn ngin spd and clutch drivn plat spd approach to synchronizing and rach st thrshold valus according to switching conditions, DCT launch modls switch ovr; namly, th two-dof sliding friction modl transforms into th singl-dof 1st spd gar stabl opratd modl. At th momnt, th controllr of sliding friction procss dos not work any longr. And switching controllr of dmand torqu bgins to work, which is in charg of convrting ngin torqu into drivr dmand torqu. It satisfis T d =TL +K t, (33) K =( Td TL Δt ), (34) whrin T L is ral ngin torqu at th switching momnt of DCT launch modls, T d is drivr dmand torqu, K is changing slop of ngin torqu, and Δt is switching tim lapsd of dmand torqu. In ordr to mt th rquirmnt of vhicl shock intnsity in th switching procss, Δt has a minimum valu. According to th 1st spd gar stably opratd modl (formula (8)), shock intnsity is proportional to th changing rat of ngin torqu rgardlss of driving rsistanc and friction damping. That is j= i R W I d T. (35) According to th rquirmnt of shock intnsity in th launching procss, namly, j 1m/s 3,thupprlimitd valuofchangingratofngintorqucanbcalculatd.th minimumtimlapsdinthswitchingprocssoftorqualso can b obtaind on th basis of formula (33).
12 Mathmatical Problms in Enginring 2.5 3 Optimization variabl t p (s) 2 1.5 1.5 Optimization variabl t s (s) 2.5 2 1.5 1.5.5 1 1.5 2 2.5 3 3.5 4 1 9 NO.1 condition NO.2 condition (a) Optimizing procss of t p.5 1 1.5 2 2.5 3 3.5 4 1 9 NO.1 condition NO.2 condition (b) Optimizing procss of t s Clutch transfr torqu T c1 (Nm) 8 7 6 5 4 3 2 Clutch transfr torqu T c1 (Nm) 8 7 6 5 4 3 2 1 1.5 1 1.5 2 2.5 3 3.5 4.5 1 1.5 2 2.5 3 3.5 4 Ral valu Estimatd valu Ral valu Estimatd valu (c) Clutch transfr torqu undr NO.1 condition (d) Clutch transfr torqu undr NO.2 condition Figur 1: Comparisons of rsults of rolling optimization undr NO.1 and NO.2 condition. Similarly, according to th two-dof launch modl (Formula (5)) in th launch sliding friction procss, w know that vhicl shock intnsity in th sliding friction procss is proportional to th changing rat of clutch transfr torqu rgardlss of driving rsistanc and friction damping. So thr is j= i R W I 4. Simulation Rsults and Analysis T c1. (36) Basd on th prviously stablishd dynamic modl of dry DCT and its launch controllr, th launch simulation modl of vhicl quippd with dry DCT is built on th Matlab/simulink softwar platform. Immdiatly, th prformanc of vhicl is simulatd undr typical launch condition. Th dtaild paramtrs of adoptd DCT can b sn in th appndix. Figur9 and Tabl 3 dmonstrat simulation rsults of launch condition, which ar dfind as that th changing rat of acclrator pdal angl is constant and that th final valus ar diffrnt. It mans that changing rat of acclrator is.4 s 1 and that th final valus ar 2% and 4% rspctivly. Rlativly, thy ar calld NO.1 and NO.2 conditions rspctivly, which ar shown in Figur 9(a).CompardwithNO.4 condition (it rachs th final valu at 1 s), NO.3 condition rquirs a slowr launch procss.
Mathmatical Problms in Enginring 13 Ky signal Acclrator pdal signal Brak pdal signal Shifting knob signal Clutch 1 position signal Clutch 2 position signal 1st, 3rd gars position signal 2nd, 4th gars position signal 5th gar position signal Rvrs gar position signal MicroAutoBox control systm Monitor PC and controldsk intrfac Clutch 1 actuator Clutch 2 actuator Shifting motor of 1st and 3rd gars Shifting motor of 2nd and 4th gars Shifting motor of 5th and rvrs gars (a) Photo of dry DCT tst bnch (b) Intrfacs of DCT prototyping controllr Figur 11: DCT tst bnch and prototyping controllr. Tabl 3: Comparisons of simulatd rsults of NO.1 and NO.2 conditions. Working condition NO.1 NO.2 Tim lapsd whn clutch driving and drivn plats ar synchronizd t s /s 2.355 2.535 Vhicl vlocity whn clutch driving and drivn plats ar synchronizd V/(km/h) 8.152 9.6367 Tim lapsd whn th dmand torqu switch ovr (t s +Δt)/s 3.14 3.33 Vhicl vlocity whn th dmand torqu switch ovr v/(km/h) 8.3558 1.371 Total slipping friction work W/J 3739.9 4767.3 Tim lapsd for launch t/s 3.14 3.33 In Figurs 9(b), 9(c), and 9(g) and Tabl 3, both th synchronizing momnt of clutch driving and drivn plats and th switching finishing momnt undr NO.1 condition ar arlir than that of NO.2 working condition. At any momnt, vhicl vlocity is quit littl undr NO.1 condition. So it can b concludd that th dsignd launch controllr can rflct th driving intntion. In Figurs 9(d) and 9(), launch impact strngths ar lss than 1 m/s 3,whichmtth dmands. In Figurs 9(f) and 9(g), ngin output and clutch transfrtorqucanalsobdividdintofivparts. Figurs 1(a) and 1(b) dmonstrat optimal tim variabls t p and t s calculatd at vry rolling optimization. Th total optimizing frquncy is 22 undr NO.1 condition, whil th tim lapsd is 1.53 s at th last optimization. Rlativly, th total optimizing frquncy is 24 tims undr NO.2 condition, whil th tim lapsd is 1.64 s at th last optimization. Figurs 1(c) and 1(d) show that stimatd valu of T c1 is quit approaching to its ral valu in th launch sliding friction procss. It nsurs that sliding friction is last in th launching procss to som dgr. 5. Rapid Prototyping Exprimnts for Dry DCT in th Launching Procss 5.1. Fiv-Spd Dry DCT Transmission Actuator. In ordr to shortn th dvlopmnt cycl of dry DCT control systm and tst th ral-tim proprty and ffctivnss of sliding mod variabl structur control algorithm as wll, th rsarch group has stablishd a dry DCT tst bnch (shown in Figur 11(a)) and usd MicroAutoBox141 of dspace Corporation as prototyp controllr. Som modls ar st up, such as fiv-spd dry DCT vhicl modls (including ngin man valu modl, DCT modl, and vhicl longitudinal dynamics modl) and DCT control stratgy modl. Th rapid prototyping xprimnts ar conductd at th sam tim. Th intrfacs of dry DCT prototyp controllr ar shown in Figur 11(b). Bfor tsting, calibrat th signals of snsors firstly and tst th working prformanc of actuator motor drivingunitsandactuatormchanismsinanopnloopin ordr to nsur th rliability of hardwar systm. Scondly, tst and vrify th coordinating control stratgy of clutch torqu in a closd-loop. Thirdly, conduct th rapid prototyping xprimnts of sliding mod variabl structur uppr coordinating control stratgy aftr proving its ffctivnss and calibrating rlativ control paramtrs. 5.2. Rsults and Analysis of Rapid Prototyping Tsts. By mans ofmakingusofrti141toolboxoffrdbydspacecorporation, dfining input signal pins such as acclrator pdal signal, brak pdal signal, and contacting with th prviously dsignd DCT launch uppr control modul, th uppr controllrcanbstablishd. Th launch triggr signal is dfind as follows: whn th currnt spd gar is 1st spd gar, th brak pdal signal is zro (in loos stat). Th acclrator pdal opning is mor thanorqualto3%.atriggrsignalforprslcting2nd spd gar is dlayd.5 s aftr th launch is finishd. Th triggr signal of shifting 1st spd gar to th 2nd on can b dfind as follows: whn th vhicl vlocity is biggr
14 Mathmatical Problms in Enginring 1 25 Acclrator pdal opning β (%) 8 6 4 2 Targt rotational spd ω (rad/s) 2 15 1 5 8 1 12 14 16 8 1 12 14 16 Engin Clutch on Clutch two (a) Acclration pdal opning (b) Targt rotational spd 25 1 Ral spd ω (rad/s) 2 15 1 5 Shock intnsity j (m/s 3 ) 5 5 8 1 12 14 16 Engin Clutch on Clutch two (c) Ral rotational spd 1 8 1 12 14 16 (d) Shock intnsity Sliding friction work W (kj) 7 6 5 4 3 2 1 8 9 1 11 12 13 14 15 16 17 Torqu T (Nm) 12 1 8 6 4 2 8 1 12 14 16 Engin Clutch on Clutch two () Sliding friction work (f) Torqu Figur 12: Continud.
Mathmatical Problms in Enginring 15 Vhicl vlocity (km/h) 25 2 15 1 5 8 1 12 14 16 Clutch transfr torqu T c1 (Nm) 12 1 8 6 4 2 8 9 1 11 12 13 Estimatd valu Ral valu 2.5 (g) Vhicl vlocity 15 (h) Clutch transfr torqu Optimization variabl t (s) 2 1.5 1.5 8 9 1 11 12 13 t P t s (i) Optimization procss of launch variabls Clutch sparating strok x (mm) 1 5 8 1 12 14 16 Clutch on targt valu Clutch on actual valu Clutch two targt valu Clutch two actual valu (j) Tracing rspons of clutch sparating strok Figur 12: Rapid prototyping xprimnt rsults of launch and shifting from th 1st gar to th 2nd on. Tabl 4: Rapid prototyping xprimnt rsults of dry DCT in th launching procss. Figur 13: Photo of ral car chassis dynamomtr tst. than th 1st to 2nd gar shifting spd 12 km/h and th targt gar is 2nd gar. Th rapid prototyping xprimnt rsults of uppr controllr ar dmonstratd in Figur12 and Tabl 4. It can Launch momnt t /s 9.425 Synchronizing momnt of launch clutch 1 driving and drivn plats (t +t s )/s 11.96 Vhicl vlocity at th synchronizing momnt of clutch 1 V/(km/h) 9.29 Switching finishing momnt of launch dmand toqu (t +t s +Δt)/s 12.74 Vhicl vlocity at th switching finishing momnt of dmand toqu V/(km/h) 9.498 Total sliding friction work W/J 4416 Rolling optimization frquncy of tim variabl 24 Tim lapsd for launch t/s 3.315 b sn that th prformanc indxs of shock intnsity and sliding friction work mt th standard dmands in
16 Mathmatical Problms in Enginring Acclrator opning β (%) 1 8 6 4 2 819.4 819.8 82.2 82.6 821 821.4 (a) Acclrator pdal opning 1 Rotational spd ω (rad/s) 35 3 25 2 15 1 5 819.4 819.8 82.2 82.6 821 821.4 Engin Transmission input shaft (b) Rotational spd Shock intnsity j (m/s 3 ) 5 5 819.4 819.8 82.2 82.6 821 821.4 (c) Shock intnsity Figur 14: Rsults of dry DCT prototyp car chassis dynamomtr tst. th launching procss and that rsults of rapid prototyping xprimnts coincid with simulatd rsults. It is also provd that th statd sliding mod variabl structur dry DCT uppr controllr can mt th rquirmnt of ral-tim control basd on ral-tim optimization. 6. Chassis Dynamomtr Tst of Ral Car Equippd with Dry DCT Aftr rapid prototyping xprimnts, th indpndntly dvlopmntal fiv-spd dry DCT control unit is usd to rplac th MicroAutoBox141 rapid prototyp controllr. On th basis of simulation and bnch tst rsults, th corrsponding MAP of prototyp car quippd with dry DCT is rcalibratd. Aftr DCT softwar is dvlopd, th ral car chassis dynamomtr tst is conductd. Th tst photo is shown in Figur 13. Th rsults of launch tst can b sn in Figur 14. Th xprimnt rsults dmonstrat that on th basis of sliding mod variabl structur uppr coordinating control stratgy, th dvlopd dry DCT control softwar not only rflcts th launch riding comfort of vhicl, but also rflcts th variation of drivr s intntion. As can bn sn from Figur 14, undr th proposd launching stratgis, th vhicl is launchd within 2 s and th shock intnsity is blow 1 m/s 3. Bsids, whn th acclrator pdal opning is incrasing, th corrsponding shock intnsity is rlativly largr, which is consistnt with th control stratgis. Compard with th rapid prototyping tsts, th rsults obtaind in th chassis dynamomtr tst ar also consistnt, thus validating th ffctivnss of th proposd control stratgis. 7. Conclusion Th four-dof launch dynamics modl of fiv-spd dry DCT is stablishd. Aftr simplifying th modl, two-dof sliding friction modl and singl-dof in-gar opration modl ar obtaind, which provid a basis for th dsign and control
Mathmatical Problms in Enginring 17 Th ngin output torqu (Nm) Th ngin output torqu charactristic 25 2 15 1 5 1 8 6 6 5 4 4 2 3 2 1 Paramtrs Th throttl opning Figur 15 Th ngin rotating spd (r/min) Tabl 5: Th paramtrs of adoptd DCT. Valu I.273 kg m 2 I c1.14 kg m 2 I c2.14 kg m 2 I m.1 kg m 2 I s 147.392 kg m 2 I g1 I g5.5 kg m 2 I gr.5 kg m 2 i 1 i 3.615, 2.42, 1.257 5.99,.714 i a 3.895 b.1 b c1.1 b c2.1 b m.1 b s.1 m 155 kg f.137 g 9.8 m/s 2 A 2.95 m C d.293 R w.38 m η.92 R.228 m.15 m R 1 of launch controllr. Drivr s intntion is rflctd by using ngin spd and vhicl shock intnsity. Taking advantag of th ida of prdictiv control and gntic algorithm, th tracing curvs of ngin spd and vhicl targt vlocity ar dtrmind by rolling optimization onlin. Th sliding mod variabl structur controllr (SMVS) is dsignd. Launch simulating modl is built on th MATLAB/Simulink softwar platform for th dry DCT. th launch rapid prototyping xprimnt is conductd. Simulation and xprimnt rsults show that th dsignd SMVS coordinating controllr can ffctivly rflct th drivr s intntion and improv th vhicl s launch prformanc. Furthrmor, chassis dynamomtr tst rsult of DCT prototyp car also shows that th proposd SMVS launch coordinating control stratgy is ffctiv and fasibl. Appndics A. Th Engin Output Charactristics (Map) S Figur 15. B. Th Paramtrs of Adoptd DCT in This Papr STabl 5. Conflict of Intrsts Th authors dclar that thr is no conflict of intrsts rgarding th publication of this papr. Rfrncs [1] D. Qin, Y. Liu, J. Hu, and R. Chn, Control and simulation of launch with two clutchs for dual clutch transmissions, Chins Journal of Mchanical Enginring, vol. 46, no. 18, pp. 121 127, 21. [2] D. Qin and Q. Chn, Univrsal clutch starting control of AMT/DCT automatic transmission basd on optimal control, Chins Journal of Mchanical Enginring, vol.47,no.12,pp. 85 91, 211. [3]C.SunandJ.Zhang, Optimalcontrolapplidinautomatic clutch ngagmnts of vhicls, Chins Journal of Mchanical Enginring,vol.17,no.2,pp.28 283,24. [4] Q.-H. Chn, D.-T. Qin, and X. Y, Optimal control about AMT havy-duty truck starting clutch, China Journal of Highway and Transport,vol.23,no.1,pp.116 121,21. [5] F. Garofalo, L. Glilmo, L. Iannlli t al., Optimal tracking for automotiv dry clutch ngagmnt, in Procdings of th Intrnational Fdration of Automatic Control (IFAC 2), pp.367 372, 22. [6] I.A.Amir,D.T.Qin,andJ.J.Liu, Acontrolstratgyonlaunch up a vhicl with AMT, Information Tchnology Journal,vol.4, no. 2, pp. 14 145, 25. [7]G.Lucnt,M.Montanari,andC.Rossi, Modllingofan automatd manual transmission systm, Mchatronics, vol. 17, no. 2-3, pp. 73 91, 27. [8] A. Srrarns, M. Dassn, and M. Stinbuch, Simulation and control of an automotiv dry clutch, in Procdings of th 24 Amrican Control Confrnc (AAC 4), pp.478 483,July 24. [9] C. H. Yu, H. Y. Chn, and H. R. Ding, A study on fuzzy control of AMT clutch in launch phas, Automotiv Enginring, vol. 27,no.4,pp.423 426,24. [1] Z. Qi, Q. Chn, and A. G, Fuzzy control of th AMT vhicl s starting procss basd on gntic algorithm, Chins Journal of Mchanical Enginring,vol.37,no.4,pp.8 24,21.
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