Range Extension Contol System fo Electic Vehicles Based on and Diving Foce Distibution Consideing Load Tansfe Sho Egami and Hioshi Fujimoto The Univesity of Tokyo 5--5, Kashiwanoha, Kashiwa, Chiba, 227-856 Japan Phone: +8-4-736-43 Fax: +8-4-736-432 Email: egami@fujilab.k.u-tokyo.ac.jp, fujimoto@k.u-tokyo.ac.jp Abstact Electic vehicles (EVs) ae moe highly efficient than intenal combustion engine vehicles. Howeve, EVs have a disadvantage in that the mileage pe chage is shot. In this pape, a ange extension contol system (RECS) based on a load tansfe is poposed. The minimum acceleation esistance can be ealized though diving foce distibution atio between font and ea wheels. Theefoe, the poposed RECS fulfills maximum efficiency. Simulations and expeiments ae caied out to confim the effectiveness of the poposed system. I. INTRODUCTION Recently, electic vehicles (EVs) ae actively eseached in ode to solve envionmental poblems and fossil fuel shotage. Hybid vehicles (HEVs) and EVs have aleady been maketed and they ae moe ecological than the intenal combustion engine vehicles (ICEVs). In addition to this ecological meit, EVs have the following advantages fom the view point of vehicle motion contol. In-wheel motos can be attached to each wheel and enables independent contol of each wheel. Regeneation bake is available. Geneated toque can be measued pecisely fom moto cuent. Toque esponse is fast. By making use of these advantages, the advanced vehicle motion contol can be achieved [], [2]. Fom this point of view, ou eseach goup has poposed many motion contol methods fo EVs [3], [4]. The electic moto, which is the powe souce of EVs, is much moe efficient than intenal combustion engine. Howeve, the enegy density of battey that is the enegy souce of EVs is only one tenth of the oil fuel. Theefoe, the mileage pe chage is shot in EVs. This is a citical issue fo widely use of EVs. Hence, in this pape, the ange extension contol system (RECS) based on a load tansfe of vehicle is poposed. This method can be used when the electic vehicle keeps an acceleation. The conventional vehicle system distibutes a toque in specific atio of the font and ea wheels as FWD, RWD, o 4WD. The poposed method minimizes the moto output by distibuting the optimum diving foce of font and ea wheels based on load tansfe consideation. When the vehicle keeps an acceleation, a component of nomal foce of vehicle is biased fom font wheel to ea wheel by the inetia foce acting on the chassis. The diving foce is a poduct of the oad fiction and the nomal foce on tie. The oad fiction depends on the slip atio. Theefoe, the slip atio equied fo a cetain diving foce vaies when the nomal foce is biased. In this method, the optimum diving foce distibution contol consideing nomal foce in font and ea wheels is poposed. The optimum distibution atio is deived. It is effective fo the extension of the miles pe chage so that the enegy equied fo the acceleation can be deceased. Simulations and expeiments ae caied out to confim the effectiveness of the poposed method. In this pape, the optimization method fom the moto output to the vehicle diving foce is examined. In addition to this method, ou eseach goup also studies the optimization method fom the moto output to tanslational speed and yawate [5], o fom the electic souce to the moto output consideing the electic loss [6]. II. EXPERIMENT VEHICLE The electic vehicle FPEV2-Kanon developed by authos s laboatoy was used fo expeiments. The oute-oto type in-wheel motos poduced by TOYO DENKI SEIZO K.K. ae installed as diving powetain in each wheel. Since these in-wheel motos ae diect dive system, the backlash of eduction gea does not influence the contol pefomance. These motos can be independently diven by invetes. Fig. shows FPEV2-Kanon and in-wheel motos. Table. I shows the specification of FPEV2-Kanon. In the poposed method, it is assumed that left and ight wheels geneate the same diving foces. Theefoe, it is applicable in not only a vehicle which each wheel independently can be diven but also a vehicle installed multiple powe souce fo font and ea wheel.
Fdf Fef ω lf (a) FPEV2-Kanon Fd T N l l M Fd Fig. 2. Wheel Model Fig. 3. Bicycle Model (b) Moto Fig.. (c) Moto Expeimental vehicle TABLE I VEHICLE PARAMETER Vehicle Mass M 854 kg Wheelbase l 75 mm Distance fom cente of gavity : 3 mm to font/ea axle tead l f,l : 72 mm Gavity height h g.5 m Wheel Inetia J wf.24 Nms 2 Wheel Inetia J w.26 Nms 2 Wheel Radius.32 m A. Longitudial vehicle model III. VEHICLE MODELING In this subsection, the vehicle model fo diving foce contol is explained. Using one wheel model and bicycle model as shown in Fig. 2, Fig. 3, the equations both of the wheel and the vehicle in longitudinal vehicle motion can be epesented by J wi ω i = T i F di, () M V = F ef, (2) V wi = ω i, (3) whee ω i [ad/s] is the wheel angula velocity, V [m/s] is the vehicle velocity, V wi [m/s] is the wheel velocity, T i [Nm] is the moto toque, F di [N] is the diving foce, M[kg] is the mass of bicycle model, [m] is the wheel adius, and J wi [Nms 2 ] is the wheel inetia. The subscipt i is inseted the chaacte f o that means font o ea wheel. The mass of bicycle model is defined as M = M 2, (4) whee M is the vehicle mass. In the ight and left wheels, the same contolle is implemented in ode to make zeo yaw moment. The vehicle diving foce, shown in Fig. 3, is total diving foce of font and ea wheels. The slip atio is defined as F ef = F df + F d (5) λ i = V wi V max(v wi, V, ɛ), (6) Fiction coefficient µ.8.6.4.2.2.4.6.8 Slip atio λ Fig. 4. Fiction Cuve µ T + Fig. 5. N Fd µ ω Jws Vw - V Vw µ λ function Slip Ratio Ms λ V Vw Vehicle Model Diagam whee ɛ is the small constant value to avoid zeo denominato. The sign of diffeence between V wi and V is changed in poweing opeation and egeneation. In this pape, max(v wi, V, ɛ) = V wi is given all time because we conside acceleation only. The slip atio λ i is epesented by λ i = V wi V. (7) V wi The fiction coefficient µ i is a function of the slip atio λ i. In the simulation, Magic Fomula is adopted as the model of fiction cofficient cuve [7]. The diving foce F di is epesented as F di = µ i N i, (8) whee N i is the nomal foce. The dving foce is also defined as F di = D si λ i, (9) = D sn i λ i, () whee D si is the diving stiffness. In Fig. 4, when the slip atio λ i is small, the fiction coefficient µ i is linealy popotional to the slip atio λ i. In this pape, it is assumed that the slip atio is small because of the high fiction oad. Theefoe, the coefficient D s is constant. Coefficient D s depend on a condition of oad, and epesented by B. Nomal foce model D s = µ λ λ=. () In this subsection, the influence of load tansfe caused by longitudinal acceleation is explained. When the vehicle acceleates, the load tansfe of nomal foce influences the diving foce fo a unit slip atio. The nomal foce in font and ea wheels consideing a longitudinal acceleation is given as N f = l l Mg a xm h g l, (2) N = l f l Mg + a xm h g l, (3)
Slip atio.4.2..8.6.4.2 λ (a =.) f x λ (a =2.) f x λ (a =3.) f x λ (a =.) x λ (a =2.) x λ (a =3.) x Moto toque [Nm] 7 6 5 4 3 2 T (a =.) f x T f (a x =2.) T (a =3.) f x T (a x =.) T (a =2.) x T (a =3.) x Wheel velocity [km/h] 34 33 32 3 V (a =.) wf x V (a =2.) wf x V (a =3.) wf x V (a =.) w x V (a =2.) w x V (a =3.) w x.2.4.6.8.2.4.6.8 3.2.4.6.8 (a) Slip atio (b) Moto toque (c) Wheel velocity 84 835 83 825.74 x 4.72.7.68 2.75 x 4 2.7 2.65 2.6 2.55 Toque atio.625.62.65.6.65.6 a x =. a x =2. a x =3. 82.2.4.6.8.66.2.4.6.8 2.5.2.4.6.8.595.2.4.6.8 (d) Total moto output (a x =.) (e) Total moto output (a x =2.) (f) Total moto output (a x =3.) (g) Toque atio Fig. 6. Each Quantity fo Diving Foce Distibution Ratio whee a x [m/s 2 ] is the longitudinal acceleation. Theefoe, the diving foce of font and ea wheels is descibed as F df = D s( l l Mg a xm h g l )λ f, (4) F d = D s( l f l Mg + a xm h g l )λ. (5) In font and ea wheels, the diving foce fo a unit slip atio is diffeent. IV. DRIVING FORCE DISTRIBUTION LAWS In this section, total moto output is estimated fo font and ea diving foce distibution contol. The moto powe is a poduct of the moto toque and the wheel angula velocity. fo vehicle diving foce is intoduced. The diving foce in font and ea wheel is defined as F d = k f F ef, (6) F df = ( k f )F ef, (7) F ef = F df + F d. (8) Total moto output changes since a unit slip atio to diving foce fo any diving foce distibution atio changes. The equation both of the moto toque and the wheel angula velocity based on slip atio is epesented by T i = F di + J wi ω i, (9) ω i = V. (2) λ i The moto toque is attibuted to the diving foce and the otating inetial foce in the wheel. The otating inetial foce is a function of slip atio, and that equation is epesented by J wi ω i = J wi ( ax + V λ ) i λ i ( λ i ) 2. (2) In this pape, the steady state of diving foce is only assumed fo the loss evaluation. Theefoe the deivative tem of slip atio λ i in (2) is ignoed. The moto output and some quantity elated to the moto powe fo diving foce wee calculated. In this simulation, the vehicle specification, shown in Table. I is used. It is assumed that the vehicle is acceleated by the diving foce F ef = Ma x at 3 [km/h]. The simulation esult fo modifying the diving foce distibution atio is shown in Fig. 6. Fig. 6(a) shows that the slip atio to the diving foce vaies fo any distibution atio due to the influence of nomal foce on tie. Fig. 6(b) and Fig. 6(c) show that the moto toque is dominated by diving foce, and the wheel velocity is elatively infulenced by the slip atio. It is confimed that total moto output fo specific diving distibution atio is minimum fom Fig. 6(d), Fig. 6(e) and Fig. 6(f). This diving foce distibution atio is the optimum distibution atio. It is also shown that the optimum distibution atio changes because the influence of load tansfe becomes lage with inceasing the acceleation. The popotion of the toque based on the diving foce to the inetial toque is defined as T atio = J wf ω f + J w ω. (22) F df + F d Fom Fig. 6(g), the popotion of the inetial toque is much less than that of the toque based on the diving foce. A. Deivation of the optimum distibution atio In this subsection, the deivation of the optimum distibution atio fo the vehicle diving foce is explained. The moto toque model, ignoed the inetial toque, is given as T i = F di. (23) The inetial toque is much less than the toque based on the diving foce as shown in Fig. 6(g). Theefoe, it is adequate fo the deivation of optimum distibution atio. Total moto
Fef* -kopt kopt Fdf + Diving Foce Contolle yf* Wheel Speed Refeence cal ωf* + ω* Fd+ y* Diving Foce Wheel Speed + Contolle Refeence cal Fig. 7. Wheel Speed Contolle Wheel Speed Contolle Diving Foce Obseve Diving Foce Obseve Tf* T* Vehicle Plant V ωf ω Optimal Diving Foce Distibution Contol System T + Fig. 8. Fd - + - τs+ ^ Fd Jws Jns τs+ ω Diving Foce Obseve output is sum of the moto output in font and ea wheels. Fom moto toque in (23) and wheel angula velocity in (2), the total moto powe is epesented by P out = P f + P, = ω f T f + ω T, = V F ef ( kf λ f + k f λ ), (24) λ f = ( k f )F ef D sn f, (25) λ = k f F ef D sn. (26) The optimum diving foce atio is intoduced by solving patial diffeential equation with espect to the distibution atio k f. The optimum diving foce is epesented by k opt = N N + N f. (27) V. DRIVING FORCE DISTRIBUTION CONTROL SYSTEM A. The contol input of diving foce In this subsection, the contol input fo diving foce is explained. Fom (9), (), the slip atio can be used fo the contol input of diving foce. The slip atio is inconvenient fo contol input of the diving foce. Thus the contol input y i meaned the elation of the slip atio is altenatively used. The contol input y i fo diving foce is epesented by y i = V wi. (28) V When vehicle acceleates, the contol input y i with espect to the slip atio λ i is epsented by y i = λ i λ i. (29) Fd A quantity of contol input y i is the almost the same as that of slip atio in the vicinity of λ i =. Moeove the slip atio is vey small since the tie is adhesive. Theefoe, in this pepe, it is assumed that the the contol input y i is equal to the slip atio λ i. Fom (28), the wheel velocity efeence is epesented by { Vwi V + yi V (V δ), = (3) V + y i δ (V < δ), whee δ is minute constant value. At vehicle stat (V = ), the vehicle velocity is assumed to be constant value δ in the ange of V < δ to avoid the wheel velocity efeence to be always zeo. B. Optimum diving foce efeence In this subsection, the optimum diving foce distibution contol system is explained. The diving foce efeences fo font and ea wheel fulfilled the optimum diving distibution atio is geneated. These efeences ae given by feedfowad. ( l F df = l h ) g lg a x F ef (3) ( lf F d = + h ) g l lg a x F ef (32) The system of optimum diving foce distibution contol is shown in Fig. 7. In (3), (32), the cofficient of vehicle diving foce efeence F ef ae equivalent to k opt and k opt in Fig. 7. C. Diving foce obseve In this subsection, the diving foce obseve is explained. Fom (), the diving foce obseve is designed fom the infomation of the moto toque and the wheel velocity. The system of diving foce obseve is shown in Fig. 8. In Fig. 8, eal value of the wheel inetia is taken as the nominal value of wheel inetia. The moto toque efeence is used as the infomation of the moto toque since the system of moto toque can follow the efeence immediately. The wheel velocity senso is used fo mesuing the wheel velocity. D. Wheel velocity contol In this subsection, the system of wheel velocity contol which is the inne loop of the system of diving foce contol in Fig. 7 is explained. In this pepe, massive diving foce is caused on tie, so that it is necessay to conside an influence of diving foce to the nominal plant of wheel. By diffeentiating (6) with espect to the time and substituting (), (2), and (3), the following equation is obtained. ω i = T i + 2 Mω i λ i 2 (33) M( λ i ) + J wi Fom (33), the nominal plant of wheel contol that ignoed λ is obtained. ω i = T i ( 2 M( λ n ) + J wi )s, (34) whee λ n is the nominal slip atio fo the diving foce. PI contolle which is designed by pole assignment is implemented.
E. Diving foce contol In this subsection, the system of diving foce contol in Fig. 7 is explained. The nominal plant of diving foce is epesented by F di λ i = D si. (35) PI contolle which is designed by pole assignment is implemented. The tansfe function fom the efeence to the diving foce is epesented by F di K P D si s + K I D si Fdi =, (36) ( + K P D si )s + K I D si whee K P is popotional gain, K I is integal gain. VI. SIMULATION In this section, the simulation was pefomed to confim the loss eduction fo optimum diving foce distibution contol. In the simulation, the vehicle specifications, shown in the Table. I, ae used. The vehicle model consideing a vaiation of nomal foce shown in Fig. 5 is used. The efeence of diving foce was set fo vehicle acceleation to be a x =. [m/s 2 ]. The poles both of diving foce contolle and wheel velocity contolle was set to -4.3 [ad/s] and -2 [ad/s], espectively. The time esponse of optimum diving distibution is shown in Fig. 9. In Fig. 9(a), massive diving foce at vehicle stat was geneated momentaily because a minute constant δ is used instead of the infomation of wheel velocity. The slip atios in font and ea wheel is the same as esults shown in Fig. 9(b). The time esponse of moto toque is simila to the esponse of diving foce as shown in Fig. 9(c). The moto toque is dominated by diving foce when the wheel is adhesive. The wheel velocity in font and ea is the same as shown in Fig. 9(d) because these slip atios is the same. Fom these esults, the moto output is shown in Fig. 9(e). In ode to evaluate the loss eduction, the moto output o the enegy fulfilled the optimum distibution atio is compaed with diving foce that filled only in font wheel (k f = ) o ea wheel (k f =.). The emakable diffeence is not easy to confim the loss eduction in the moto output. Theefoe, the enegy which is a integation value of the moto output, is compaed with these distibution atio in a cetain speed egion. The simulation esult is shown in Table. II. Fom Table. II, it is confimed that the enegy loss is mimimum in the optimum distibution atio. In a speed egion of -3 [km/h], the diffeence of the enegy between optimum distibution atio and font only efeence (k f = ), o ea only efeence (k f =.) ae about 36 [Ws], 2 [Ws]. Futhemoe, the moto output in a high-speed egion can be deceased in Table. II. VII. EXPERIMENT In this section, the expeiment esults ae shown. The expeiment is pefomed on the high fiction oad. The time esponse of optimum diving foce distibution contol is shown in Fig.. The esponse of diving foce has oveshoot since TABLE II SIMULATION RESULT Dive System RECS Dive Dive Range Enegy[kWs] Enegy[kWs] Enegy[kWs] -3[km/h] 29.7 3.6 29.82 -[km/h] 367.4 37.8 369. a minute constant value δ is used instead of the infomation of wheel velocity at vehicle stat. The expeiment of acceleation was done to veify the loss eduction fo given optimum distibution atio. The vehicle acceleation is set to be a x =. [m/s 2 ]. It is difficult to measue pecise moto output when the vehicle unning. Theefoe, the loss evaluation is pefomed indiectly by measuing the input powe of invetes. The electic loss of invete and moto is ignoed in the evaluation. The evaluation equation is epesented by V dc I dc = V dc (I dcf + I dc ), (37) whee V dc is the dc-bus voltage of invetes, I dcf, I dc is the cuent that flows to invetes fo font and ea wheels. The enegy loss is measued five times. Table. III and Fig. shows each aveages of that expeiment esults and the eo ba. The enegy loss fo optimum diving foce atio is minimum. Meanwhile, the supeioity of esults distibuted only to font wheel and ea wheel have evesed. This is why that the loss of the moto and invete ae included in the esult. TABLE III EXPERIMENTAL RESULT Dive System RECS Dive Dive Range Enegy[kWs] Enegy[kWs] Enegy[kWs] -3[km/h] 6. 62.27 75.36 VIII. CONCLUSION In this pape, a ange extension contol system based on load tansfe is poposed. The effectiveness of the poposed method was veified by the simulation and the expeiment. Meanwhile, the supeioity between font only efeence (k f = ) and ea only efeence (k f =.) diffe fom the simulation. This poblem could be due to the electic loss and the mechanical loss. The futue wok will be the pecise evaluation of the moto output. Futhemoe, the novel poposal of ange extension contol system consideing the efficiency of moto, choppe, o invete, should be studied. ACKNOWLEDGMENT Finally, this eseach was patly suppoted by Industial Technology Reseach Gant Pogam fom New Enegy and Industial Technology Development Oganization (NEDO) of Japan and in pat by the Ministy of Education, Cultue, Spots, Science and Technology gant numbe 2224657.
Diving foce [N] 5 4 3 2 Slip atio.2.5..5 Moto toque [Nm] 3 25 2 5 5 2 4 6 8 (a) Diving foce Wheel velocity [km/h] 3 25 2 5 5 2 4 6 8 (b) Slip atio 8 6 4 2 2 4 6 8 (c) Moto toque Diving foce [N] 5 4 3 2 2 4 6 8 Fig. 9. (d) Wheel velocity 2 4 6 8 (e) Moto output Simulations - Optimal Diving Foce Distibution Contol Slip atio.2.5..5 Moto toque [Nm] 3 25 2 5 5 2 4 6 8 (a) Diving foce Wheel velocity [km/h] 3 25 2 5 5 2 4 6 8 (b) Slip atio 5 5 2 4 6 8 (c) Moto toque Fig.. 2 4 6 8 (d) Wheel velocity 2 4 6 8 (e) Moto output Expeimental Results - Optimal Diving Foce Distibution Contol Enegy [kws] 8 7 6 5 4 3 2 Optimal. Diving Foce Distibution Ratio k f Fig.. Expeimental Result REFERENCES [] Y.Hoi: Futue Vehicle by Electicity and Contol-Resech on Fou- Wheel-Motoed: UOT Electic Mach II, IEEE Tans. IE, Vol.5, No.5, 24 [2] H.Sado, S.Sakai, and Y. Hoi: Road Condition Estimation fo Taction Contol in Electic Vehicle, In Poc. 999 IEEE IntenationalSymposium on Industial Electonics, pp.973-978, 999 [3] K.Fuji and H.Fujimoto: Taction Contol based on Slip Ratio Estimation Without Detecting Vehicle Speed fo Electic Vehicle, in Poc. The Fouth Powe Convesion Confeence, Nagoya, pp.688-693, 27 [4] M.Yoshimua, H.Fujimoto: Diving toque contol method fo electic vehicle with in-wheel motos, IEEJ Tans. on Industy Applications, Vol.3, No.5, pp.-8, 2 (in Japanese) [5] H.Sumiya, H.Fujimoto: Range Extension Contol System fo Electic Vehicle with Active Steeing and Diving/Baking Foce Distibution on Cuving Road, in Poc. 36th Annual Confeence of the IEEE Industial Electonics Society, Aizona, pp.2346-235, 2 [6] T.Suzuki, H.Fujimoto: Poposal of Range Extension Contol System by Dive and Regeneation Distibution Based on Efficiency Chaacteistic of Motos fo Electic Vehicle, IEEJ Techinical Meeting Recod, IIC- -9, 2 (in Japanese) [7] H. B. Pacejka, and E.Bakke: The Magic Fomula Tye Model, Tye model fo vehicle dynamic analysis:poceeding of thest Intenational Colloquium on Tye Models fo Vehicle Dynamics Analysis, held in Delft, The Nethelands, 99