A Vehicle Transmission Simulaor Applied o he Auomaed Driving C.LAROUCI, A.CHAIBET, M.BOUKHNIFER Laboraoire Commande e Sysèmes Ecole Supérieure des Techniques Aéronauiques e de Consrucion Auomobile (ESTACA) 3-3, rue Vicor Hugo, 93 Levallois Perre, France Absrac: This paper presens a vehicle ransmission simulaor coupled o a longiudinal vehicle dynamic model. The ransmission simulaor uses elecric acuaors o reproduce he mechanical characerisics of a real vehicle engine and is ransmission chain. The developed approach allows o validae ransmission and vehicle dynamic sudies (conrol of auomaic or roboized gearboes, es of hea engine, dynamic behavior and passenger comfor ) wihou need o he real ransmission sysem and he real environmen of he vehicle. The proposed sysem is used o carry ou a vehicle auomaed driving in he case of a car- following operaion. I. INTRODUCTION In he auomoive domain, manufacurers and equipmen suppliers seek, permanenly, o improve vehicle performances, o inroduce more and more inelligence and o ensure high safey [], [], [3]. So simulaors, effecive mehods and accurae models are very useful o reach his objecive and o minimize he cos and he ime devoed o he developmen phases of vehicles [], [], [], [7]. In his cone, his paper presens a ransmission chain simulaor coupled o a vehicle dynamic model and proposes an accurae equivalen sysem easy o be eploied o validae simulaion sudies in he auomoive domain wihou need o he real vehicle and is real environmen. The coupled model is applied o he vehicle auomaed conrol and safey domain for which he vehicle mus be able o achieve a whole of auonomous funcions. Among heses funcions: he heading variaion, change maneuver and a vehicle follower conrol sysem for a single vehicle by mainaining a safey disance [], []. The presen paper is organized as follows. In secion, he vehicle ransmission simulaor will be addressed and validaed hanks o simulaion and measuremen resuls. In secion 3, a vehicle dynamic model will be presened. Secion deals wih a proposed approach o couple he elecric simulaor o he vehicle dynamic model. In secion, he coupled model will be applied o he auomaed driving and simulaion resuls of a car following enario will be presened. II. THE VEHICLE TRANSMISSION SYSTEM SIMULATOR The elecric simulaor of he vehicle ransmission chain simulaes he mechanical characerisic of he ransmission sysem. This simulaor uses wo elecric acuaors conrolled wih dedicaed conrol laws. The firs one reproduces he dynamic driving orque developed by he hea engine and available a he oupu of he bridge, while he second one simulaes he resising orque imposed by he vehicle load (he whole resising effors o he vehicle advance plus inerias). ) Modeling of he real vehicle ransmission sysem: The figure illusraes he various forces applied o a vehicle during is moion on a road wih a slope of angle α. These forces include he driving force and he mean resising forces. z y Faero Frc α M.g Frr Fig.. Forces applied o a vehicle in a slope Fm, Faero, Frr and Frc are, respecively, he driving force, he aerodynamics force, he rolling fricion force and he resising force in a slope [9], []. To model he real vehicle ransmission sysem, we suppose ha he ransmission losses are negleced (he efficiency of cluch and gear bo reaches ) and only longiudinal forces are considered [], [], [3], []. Using hese assumpions, he following equaions can be wrien: A. According o he hea engine dωh ( J h + Jeb ) = Cm _ h Cr _ eb () J h and J eb are, respecively, he inerias of he hea engine and he inpu shaf of he gearbo. Ω h is he angular speed of he hea engine. C m _ h and Cr _ eb are, respecively, he hea engine orque and he resising orque (he resising orque a he inpu of he gearbo seen by he hea engine). B. According o he bridge dωsp + Jroues) = Cm _ sp Cr _ roues () J sp and J roues are, respecively, he ineria a he oupu of he bridge and he ineria of he wheels. Ω sp is he angular speed a he oupu of he bridge. Cm _ sp and Cr _ roues are, respecively, he orque a he oupu of he bridge and he resising orque a he wheels. C. According o he cenre of graviy of he vehicle dv M = Fm Faero Frr Frc (3) Fm 97---7-/9/$. 9 IEEE
Wih F aero = ρ C Sf V, Frr = frr M g cos( α) Frc = M g sin( α), Ωh = Ωsp R, V = Ωsp R M: he oal vehicle mass. V: he vehicle longiudinal speed. ρ : he air densiy. C : he longiudinal aerodynamic drag coefficien. S f : he fronal (ransverse) secion of he vehicle. f rr : he coefficien of rolling fricion. g: he acceleraion of graviy. α : he slope angle. R : he loaded radius (ray of he driving wheel). R = R b R : he oal reducion raio. p R b and R p : he gearbo and he bridge raios. The ransmission is supposed wihou losses. So: C r _ roues = Fm R, Cm _ sp = C r _ eb R From he equaion 3, we deduce he flowing epression: dωsp + Jroues + M R ) = Cm _ sp Csr _ sp () Where C sr-sp is he oal resising orque in he seady sae a he oupu of he bridge (): 3 C = ρ C S R Ω + M g R [ sin( α) + frr cos( α) ] () sr _ sp f sp ) Modeling of he equivalen sysem: In order o reproduce he behavior of he real vehicle ransmission chain, an equivalen model using wo elecric acuaors is considered (figure ). In his model, he elecric acuaor M simulaes he hea engine, while he second acuaor (M) simulaes he resising forces. converer inerface M Elecric machine o simulae he hea engine Cluch Real-ime conrols A par of he ransmission chain Gearbo + bridge Fig.. A firs equivalen model M converer Elecric machine o simulae he resising forces inerface In order o work in a reduced orque ale and o validae he coupling of a ransmission model o a vehicle dynamic one, he previous configuraion (figure ) is reduced o a simplified configuraion where he acuaor M simulaes he whole resising orque due o aerodynamic fricions, rolling fricions, resising orque in a slope and ineria wih a orque reducion facor (). However, he elecric acuaor M simulaes boh he hea engine and he gearbo wih a orque reducion facor (). Considering = = yields: Ω h C m sp Ω = Ω = Ωsp = and C m _ = R Ω and Ω are he angular velociies of he elecric acuaors M and M. Therefore, he equaion can be wrien as follows: dω ( J sp + J roues ) = C m _ C r _ roues () The mechanical equaion on he common ree of he wo elecric acuaors is: dω ( J + J ) = Cm _ C (7) r _ J and J are he momen of ineria of he acuaors M and C and C r _ are heir orques. M. m _ 3) Torque conrol laws of he elecric acuaors: The orque conrol laws of he acuaors M and M ( Cm ref and C r ref ) are deduced by idenificaion beween he real ransmission model and he equivalen one []. R dω ( ) C m ref = Cm _ h R Jh + Jeb + fv Ω + C () s Cr ref 3 = ρ C S R Ω + M g R ( sin( α) + cos( α) ) (9) f dω + Jroues + M R ) ( J + J ) fv Ω Cs + f v and f v are he vious fricion coefficiens of he acuaors M and M. C s and C s are he orques induced by he dry fricions of he wo elecric acuaors. ) Simulaion resuls: A speed regulaor is included in he simulaion model. I deermines he posiion of he acceleraor pedal which allows o rack a desired speed. Moreover, he power converers conneced o he elecric acuaors have been opimized under hermal, elecromagneic compaibiliy (EMC) and efficiency consrains [], [], [7]. A vehicle saring es is carried ou o validae he modeling of he equivalen ransmission chain. I consiss o evaluae he ime necessary o reach a vehicle desired speed of 9 km/h (figure 3). Vehicle speed (km/h) 9 7 3 Fig. 3. A vehicle saring es The regulaor parameers are adjused o obain a vehicle saring ime (s in figure 3) close o he saring ime given by he manufacurer (.s) [9]. The figure presens he desired orque and he real one developed by he elecric acuaor M in a case of a road
profile characerized by differen slopes (figure ). This orque is he image of he orque available a he oupu of he bridge (wih a reducion coefficien = ). As a resul, he real orque is very close o he desired one. This orque is more imporan when he vehicle sars he move and when i s in fron of slopes in order o overcome he vehicle ineria and he addiional resising orque due o hese slopes. - The posiion of he acceleraor pedal. In his case, he roadway is supposed wihou slope. The vehicle desired speed is 3 km/h..*speed in km/h Commued speed Reference orque Real orque Torque in N.m Posiion of he acceleraor pedal Torque(N.m) - 3 7 9 Fig.. Real and reference (desired) orques of he machine M Slope(%) 3 3 7 9 Fig.. Slopes characerized he considered road profile ) Eperimenal validaion of he ransmission simulaor: In order o validae he ransmission simulaor, a measuremen es bench is carried ou (figure ): 3 7 9 Fig. 7. Measuremen (dashed lines) and simulaion (solid lines) resuls (vehicle desired speed 3km/h, slope=%) I is noed ha he simulaion resuls are very close o hose obained by measuremen. The vehicle reaches is desired speed afer s. The seady sae is characerized by a commued speed: he h one, a reduced orque:.nm (real orque: Nm) and a posiion of he acceleraor pedal: Pp=.. To validae he proposed ransmission simulaor in he case of a slope, a road profile wih a slope of value % is considered. The figure superimposes he measuremen and he simulaion resuls (he normalized vehicle speed, he orque developed by he acuaor M, he commied speeds and he posiion of he acceleraor pedal) in he case of a desired speed of km/h (he orque reducion coefficien is = ). 7.*speed in km/h Conrol uni power converers 3 Torque in N.m Commued speed Posiion of he acceleraor pedal 3 3 M Fig.. Measuremen (dashed lines) and simulaion (solid lines) resuls (vehicle desired speed km/h, slope=% and % afer km) M Fig.. Measuremen es bench The figure 7 superimposes he resuls of simulaion (solid lines) and measuremen (dashed lines) of he following parameers: - The normalized vehicle speed (vehicle speed divided by ), - The commied speeds, - The orque developed by he acuaor M which simulaes he hea engine and he gearbo. This orque is he image of he real orque available a he oupu of he bridge (wih a reducion coefficien = ), The vehicle speed drop phenomenon shown in his figure is obained when he vehicle is in fron of he slope (a ime = s). In fac, o overcome he addiional resising orque due o he slope, he driver eplois he maimal poenial of he acceleraor pedal (pp=) bu his acion is no sufficien o overcome he addiional orque. So a rerogressing of he commuaed speed from he 3 rd o he nd one mus be done. However, he auomaic change of he commued speeds prevens volunarily his rerogressing in order o es he effec of gearbo conrol sraegy. When he rerogressing of he commuaed speed o he nd one is allowed, he vehicle reaches again is desired speed (km/h). As he slope is supposed consan, he vehicle auomaic conrol keeps he
same posiion of he acceleraor pedal and he same commued speed. III. THE VEHICLE DYNAMIC MODEL A one degree-of-freedom of vehicle moion is used o validae he coupling approach and o design a longiudinal conrol in he case of single car following. In his sudy, he pich, he roll, he yaw, he ransversal and he verical dynamics are negleced. Moreover, he longiudinal slip beween he ire and he road is no considered. Under heses assumpions, he dynamic behaviour of a vehicle during longiudinal moion can be deribed by he following equaion []: ( M + R C V + M R sin( α ) = I a Te R Tb + R rr () Where: ( Je + R ( J wr + J wf + M R ) I = : he effecive vehicle R R ineria. T b : he brake orque, M rr : he rolling resisance orque, a: he longiudinal acceleraion, J wr and J wf : he rear and fron wheel inerias, J e : he engine / ransmission ineria, T e : he engine orque, C : he longiudinal aerodynamic drag coefficien. IV. COUPLING OF THE TRANSMISSION SIMULATOR TO THE VEHICLE DYNAMIC MODEL The coupled model (figure9) associaes he ransmission simulaor and he vehicle dynamic model. The engine orque (Te) of he dynamic model is generaed by he ransmission simulaor presened in secion II. This coupled model allows o carry ou car following concep, various ransmission and dynamic behavior sudies and o opimize specific vehicle es benches wihou need o he real ransmission sysem and he real environmen of he vehicle. Moreover, i allows o carry ou HIL works and real ime conrol by combining sofware par (vehicle dynamic model) and hardware par (ransmission sysem) (figure 9). Desired speed Acual (real) speed Posiion of he acceleraor pedal + - Speed conroller converer Vehicle ransmission simulaor M Real ime conrol M Acuaor Acuaor converer Fig. 9. Block diagram of he coupled model Driving orque Vehicle dynamic model V. APPLICATION TO THE VEHICLE AUTOMATED DRIVING On he auomaed vehicles concep, he vehicle mus be able o achieve a whole of auonomous funcions. Among hese funcions, speed and spacing conrols are sudied in his par. The objecive is o mainain he safey disance beween ow vehicles during a car-following siuaion (figure ). Leader vehicle V l Iner-vehicular disance Fig.. Car following concep Follower vehicle ) Deripion of he car-following enario: The principle of he car-following enario is ha he follower vehicle should follow he moion of he leader vehicle by respecing a desired iner-vehicular disance (d rdes ). This safey disance is a funcion of he follower vehicle speed (V f ) and a consan headway ime policy (h) (equaion ) [9]. drdes = do + h Vf () d is he sopping disance. A PID conroller is synhesised o minimise he error beween he real disance (dr) and he desired one (d rdes ). Noe ha: d r is he real relaive disance beween he rear of he leader vehicle and he fron of he follower vehicle. The headway ime and he sopping disance are respecively fied o seconds and meers [9]. ) Simulaion resuls: The figure shows he leader and he follower vehicle speeds. Longiudinal speed (km/h) follower vehicle speed leader vehicle speed Time (s) Fig.. Leader (dashed line) and follower (solid line) speeds Iniially: The follower vehicle and he leader one are locaed on he same lane and he iner disance is 3m. The vehicle leader moves wih an iniial speed of km/h, he following vehicle evolves wih an iniial speed of km/h. The desired disance is 7.m. The leader vehicle acceleraes o reach he speed 9 km/h a ime = s, hen i coninues is rajecory wih his same speed unil = s, afer i deceleraes (from 9 km/h o km/h) and evolves a he speed km/h for a duraion of s. V f
A ime = 7s, he leader vehicle acceleraes o reach once again he speed 9 km/h and hen i coninues is rajecory wih he same speed. In order o show he effeciveness of he proposed conrol, a wind gus is inroduced, a ime = s, as a disurbance on he leader vehicle. As resuls, in order o respec he safey disance beween he wo vehicles, he follower vehicle follows he same speed profile as he leader one (acceleraion unil = s o reach he speed 9km/h, deceleraion a = s o reach he speed km/h, acceleraion a = 7s o reach again he speed 9km/h and rejecion of he wind disurbance beween s and s). The figure shows he desired iner-vehicular disance (safey disance) and he real one. Disance (m) 7 3 desired disance real disance Time (s) Fig..Safey (solid line) and real (dashed line) disances I can be seen ha he spacing error ends oward zero afer he vehicle saring. The figure 3 shows he longiudinal acceleraion of he follower vehicle. Longiudinal acceleraion of he follower vehicle (m/s ) 3 - Fig.3. Longiudinal acceleraion of he follower vehicle Noe ha he vehicle-following enario is carried ou wih respec o he passengers comfor (acceleraion beween -.g and.g) [9]. VI. CONCLUSION A vehicle ransmission simulaor coupled o a longiudinal vehicle dynamic model have been developed and applied o he auomaed driving in he case of a car-following siuaion. The equivalen ransmission sysem uses elecric acuaors wih dedicaed conrol laws o reproduce he real characerisics of he ransmission chain. The coupled model allows o validae ransmission and vehicle dynamic sudies wihou need o he real ransmission sysem and he real environmen of he vehicle. This coupled sysem is used o carry ou a car-following conrol o ensure a desired iner-vehicular spacing wih a respec o passengers comfor. VII. REFERENCES [] A. Chaibe, L. Nouvelière S. Mammar, M. Neo, Backsepping Conrol Synhesis For Boh Longiudinal And Laeral Auomaed Low Speed Vehicle, IEEE, Inelligen Vehicles, IV, Las vegas. [] Ronghuai Qi Guichi Hu Kai Jiang «A New Vehicle Inelligen Navigaion Alarm Sysem Based on SB7 Microprocessor», IEEE Inernaional Conference on Informaion Acquisiion, ICIA 7. [3] Szczepaniak, C.; Szosland, A.S. «Fuzzy logic conrol of moor vehicle, IEEE Inelligen Vehicle Symposium, 7- June Pages 3-39 vol. [] U.Kiencke, L.Nielsen «Auomoive Conrol Sysems For Engine, Driveline and Vehicle», Springer, SAE inernaional,. [] F.Bardin «SIVTHEC, a research program o evaluae high power baeries ageing in acual use», EVS7 Ocober, Monréal. [] P. Deuszkiewicz, S. Radkowski «On-line condiion monioring of a power ransmission uni of a rail vehicle», Mechanical Sysems and Signal Processing journal, Volume 7, Issue, November 3, Pages 3-33. [7] L.Nouvelière, S.Mammar, J. Saine-Marie, «longiudinal conrol of low speed auomaed vehicles using a second order sliding mode conrol, Inelligen Vehicle Symposium IV, Japan,. [] C.Larouci, E.Dehon, A.Haraka, G.Feld, «Modeling and Conrol of he Vehicle Transmission Sysem Using Elecric Acuaors; Inegraion of a Cluch», IEEE ISIE 7, June -7, 7, Vigo, Spain. [9] BOSCH, Memeno of auomoive echnology, Boh Ediion, Germany,. [] M.Minakawa, J.Nakahara, J.Ninomiya, Y. Orimoo «Mehod for measuring force ransmied from road surface o ires and is applicaions», JSAE Review, Volume, Issue, Ocober 999, Pages 79-. [] H.Liang, K.To Chong, T.Soo No, S.Y.Yi «Vehicle longiudinal brake conrol using variable parameer sliding conrol», Conrol Engineering Pracice, Volume, Issue, April 3, Pages 3-. [] K.Nakamura, H.Kosaka, K.Kadoa, K.Shimizu «Developmen of a moor-assised WD sysem for small fron-wheel-drive vehicles», JSAE Review, Volume, Issue, Ocober 3, Pages 7-. [3] K.Sawase, Y.Sano «Applicaion of acive yaw conrol o vehicle dynamics by uilizing driving/breaking force», JSAE Review, Volume, Issue, April 999, Pages 9-9. [] G. Krick «Behaviour of yres driven in sof ground wih side slip», Journal of Terramechanics, Volume 9, Issue, 973, Pages 9-3. [] C.Larouci, J.P.Ferrieu, L.Gerbaud, J.Roude, J.P.Keradec «Volume Opimizaion of a PFC Flyback Srucure Under Elecromagneic Compaibiliy, Loss and Temperaure Consrains», Elecronics Specialiss Conference IEEE PESC, June 3-7,, Ausralia, pp:. [] C.Larouci, J.P.Keradec, J.P.Ferrieu, L.Gerbaud, J.Roude «Copper losses of Flyback ransformer: Search for analyical epressions», IEEE Transacion on Magneics, vol. 39, issue 3, par, May 3, pp: 7 7. [7] C.Larouci «Opimizaion of a V/V dc-dc Converer For Vehicular Elecrical Nework», s IEEE Spring Vehicular Technology Conference IEEE VTC -Spring, May 3-June,, Sockholm, Sweden, pp: 93-93. [] Hung Pham, Masayoshi Tomizuka, J. Karl Hedrick, «Inegraed Maneuvering Conrol for Auomaed Highway Sysems Based on a Magneic Reference/Sensing Sysem», UCB-ITS-PRR-97-, California PATH Research Repor, Universiy of California, Berkeley, 997. [9] Marinez J. and Canudas-de-Wi C. «A Safe Longiudinal Conrol for Adapive Cruise Conrol and Sop-and-Go Scenarios», IEEE Transacion on Conrol Sysem Technology, Vol. No., March 7.