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1 338 電気自動車における旋回を考慮した速度軌道最適化による航続距離延長自動運転制御の基礎検討 Fundamental Research on Range Extension Autonomous Driving for Electric ehicle Based on Optimal ehicle elocity Profile in Consideration of Cornering 池澤佑太東京大学藤本博志東京大学川野大輔交通安全環境研究所後藤雄一交通安全環境研究所槌本みさき小野測器佐藤宏治小野測器 Yuta Ikezawa, Hiroshi Fujimoto, The University of Tokyo, 5--5 Kashiwanoha, Kashiwa, Chiba Daisuke Kawano, Yuichi Goto, National Traﬃc Safety and Environment Laboratory Misaki Tsuchimoto, Koji Sato, Ono Sokki Co.,Ltd. Electric vehicle (E) has been intensively studied in the last decade due to their environment friendly characteristics. However, the miles-per-charge of E is shorter than that of internal combustion engine vehicles. To improve miles-per-charge, the authors group has proposed Range Extension Autonomous Driving (READ) system which minimizes consumption energy by optimizing velocity profile. But conventional system can be applied to only straight driving. Therefore this paper extends READ to be applied to not only straight driving but also curvy road. The eﬀectiveness of the proposed method is verified by simulations and experiments. Key Words: electric vehicle, range extension autonomous driving, cornering resistance, optimization of velocity profile, motor loss, nonlinear optimal control はじめに近年地球温暖化や化石燃料の枯渇などの環境問題が顕在化してきているがこれらの問題を解決するために様々な研究が行われている解決策の一つとして環境負荷の少ない電気自動車 Electric ehicle: E に注目が集まっている環境面だけでなく E は従来の内燃機関を有する自動車と比べて以下の 4 つの優位点を持つ (). 従来の内燃機関を有する自動車と比較してトルク応答が桁速い Fig. FPE Kanon.. モータに流れる電流を測定することでトルクを正確に把握 3 3. 小型高出力であるため分散配置が可能である 4. 力行だけでなく回生が可能である以上のように多くの利点がある E だが一充電走行距離 Wheel velocity[km/h] チョッパを用いたドライブシステムにおける高効率化を図った研路面から車体へワイヤレスで給電を行う研究 5 解決するために損失の少ないモータの設計に関する研究 () や究 7 5 が短いという課題のため普及が妨げられているこの課題を (4) 6 5 Torque[Nm] Torque[Nm] できる (3) (a) Front motor Wheel velocity[km/h] (b) Rear motor. Fig. Eﬃciency maps of front and rear motors. などが行われている従来の航続距離延長自動運転制御は何れも直線走行のみを考慮し一方で高度道路交通システム (Intelligent Transport Sys- ており旋回を含んだコースに適用することはできない tems: ITS)(5) を活用して交通流を改善することでエネルギー本稿では車両の旋回運動その際に生じるコーナリング抵抗問題を解決しようとする研究もある前後の車の情報を利用したをモデル化することで航続距離延長自動運転制御を旋回を含ん隊列走行 (6) や仮想的な信号 (7) を導入することによって交通流だコースで適用できるように拡張するシミュレーション及び実の改善が図られている ITS がさらに進展していけば全ての験によって提案法の有効性を示す車両が自動運転に移行していき車両の速度はドライバーではなく ITS が決定するようになると考えられるこれによって目的地まで安全に到達するだけでなく速度軌道を最適化すること実験車両と車両モデル本章では実験車両について紹介するまた車両の運動モデで消費エネルギーを削減することも可能となる著者らのグルール消費電力モデルについて説明するプでは ITS から停止位置や勾配情報を取得できるという仮定の. 実験車両本稿では著者らのグループが作成した実験車両 FPE-Kanon を使用した車両の外観を図車両諸元を表に示すこの車両は 4 輪に東洋電機製造製アウターロータ型インホイールモータ (IWM) を搭載しているそのため各輪下速度軌道を最適化することで消費エネルギーを最小化し航続距離を延長する航続距離延長自動運転制御 (Range Extension Autonomous Driving: READ) を提案してきた (8, 9) しかし

2 F yr F yf l r γ r γ β l f γ δ f Y X Fig.3 Bicycle model of vehicle dynamics. Table. ehicle specification. ehicle mass M 854 kg Wheelbase l.7 m Distance from center gravity l f :. m to front and rear axle l f,l r l r :.7 m Gravity height h g.5 m Front wheel inertia J ωf.4 kg m Rear wheel inertia J ωr.6 kg m Wheel radius r.3 m Front cornering stiffness C f.5 kn/rad Rear cornering stiffness C r 8. kn/rad Table. Specification of in wheel motors. Front Rear Manufacturer TOYO DENKI SEIZO K.K. Type Direct Drive System Rated torque Nm 7 Nm Maximum torque 5 Nm 53 Nm Rated power 6. kw 6. kw Maximum power. kw 5. kw Rated speed 38 rpm 45 rpm Maximum speed rpm rpm () () F all (3) (4) (5) J ωj ω j = T j rf j () M = F all sgn( )(F DR + F CR ) () F f = F r = 4 F all (3) Ma y = M ( β + γ) = Y f Y r (4) I γ = ( l f Y f + l ry r) (5) J ωj ω j T j r F j M sgn F DR F CR a y β γ Y f Y r I l f l r j f r F DR F DR ( ) = µ Mg + b + ρc da (6) µ b ρ C d A.. λ j ωj = rω j (7) λ j = ωj max( ωj,, ϵ) ϵ λ j 4 µ j λ j () D s F j (8) (7) F j = µ j N j D s N j λ j (8) N j F all (9) () N f (, F all ) = [ lr l Mg h g l {F all sgn( )(F DR( ) + F CR)}] (9) N r(, F all ) = [ lf hg Mg + l l {F all sgn( )(F DR ( ) + F CR )}] () h g..3 5 F yj = C jα j () C j α j Y j Y j F yj = C jα j ()

3 friction coefficient [ ].5.5 µ D λ s.5.5 slip ratio [ ] 車輪の進行方向 F CR ' F yf Y f l f γ 車体の進行方向 Fig.4 µ λ Curve ()., F CR F CR Y f sinα f Y rsinα r (3) C f α f + C r α r (4) x F CR F CR C f α f cosδ f + C rα r cosδ r C f α f + C rα r (5) α f α r α f (, β, γ, δ f ) = β + l f γ δ f (6) α r (, β, γ) = β l rγ δ f (7) R ( β = γ = ) R β = ( B ) l R γ = R δ f = ( + A ) l R α f = A l R B l r R α r = B l r R A B (8) (9) () () () A = M l l f C f l r C r C f C r (3) B = M l l f l rc r (4) () () (5) R F CR (, R) M ( lr + l ) f 4 (5) l C f R.3 P in (6) () C r P in = P out + P c + P i (6) P out P c P i Fig.5 Cornering resistance of front tyre. λ j T j ω j T j rf j (7) ω j r ( + λ j) (8) P out (9) P out = ω j T j F all ( ) F all + 4D s N j (, F all ) (9) q d P c P c = R j i qj r 8 F all R j K tj (3) R j i qj q K tj d λ j P i P i = = r v odj + v oqj R cj ω ej R cj { (Ldj i odj + Ψ j ) + (L qj i oqj ) } P nj R cj { ( ) rlqj F all + Ψ } j 4K tj (3) v odj v oqj dq R cj ω ej L dj d L qj q i odj i oqj dq dq P nj Ψ j R cj (3) R cj (ω ej ) = + R cj R cj ω ej (3) P in F all P in(, F all ) = P out(, F all ) + P c(f all ) + P i(, F all ) (33) 3

4 3 W in (t) tf min. W in = P in(x(t), u(t))dt (34) t s.t. ẋ = f(x(t), u(t)) [F M all sgn( )(F DR( ) + F CR(, R))] [ (t) ] = (C f +C r) (lf C β f l rc r) γ + C f δ M M M f (l f C f +l r C r ) β (l f Cf +l r Cr ) γ + l f C f δ I I I f (35) χ(x(t )) = x(t ) x (t ) = X(t ) X β(t ) β = (36) γ(t ) γ ψ(x(t f )) = x(t f ) x f (t f ) f = X(t f ) X f β(t f ) β f = (37) γ(t f ) γ f (t) x(t) = X(t) β(t) (38) γ(t) [ ] Fall (t) u(t) = (39) δ f (t) x x f δ f () () t f 35. s 3 a x max a x (4) + a xt (t < t < t ) (t) = max (t < t < t ) max a x t (t < t < t f ) t = (4) max a x + t (4) t = t f max f a x (4) Fig.6 Driving course. a x max (43) + a x t (t < t < t ) max (t < t < t ) (t) = max t M t (F DR( ) (43) +F CR(, R))dt (t < t < t 3) (t 3 t) (t 3 < t < t f ) t = max + t (44) a x t = t + ) (L max (45) max a x t 3 = t f + t (46) 3 4. (47)- (5) P out P M P J P DR P CR P S P out = P M + P J + P DR + P CR + P S (47) P M = d ( ) dt M (48) P J = ( ) d dt Jω j ωj (49) P DR = F DR (5) P CR = F CR (5) P S = F all λ j (5) W X = tf t P X (x(t), u(t))dt (53) X M J DR CR S c i (g) W CR 3. %.45 % 4

5 elocity [km/h] 3 Conv. 5 5 Total driving force [N] Conv Cornering resistance [N] Conv. 5 5 Inverter input power [kw] Conv. 5 5 Side slip angle [rad].4. (a) elocity. Conv Yaw rate [rad/s] (b) Total driving force F all Conv (c) Cornering resistance F CR. Consumption energy [kws] 5 5 Conv. W i W c W S W CR W DR (d) Inverter input power P in. Y position [m] 3 Reference Conventional Conventional Proposed X position [m] (e) Side slip angle β. (f) Yaw rate γ. (g) Consumption energy W in. Fig.7 Simulation results (t f = 35. s). (h) XY position. s M r (+λ j ) Jωj Driving + C force PI r distribution + F all F j T j ehicle Fig.8 ehicle speed control system. 7(g) W CR 49. % 5. % W c.53 % 6. % W DR.57 % 5.63 % F all F all (3) F j T j T j = rf j + Jω j ( + λ j ) (54) r λ j.5 ( > ) λ j = ( = ).5 ( < ) (55) C PI(s) PI 5 rad/s = F all Ms (56) P in P in = dc I dcj (57) dc I dcj 4 9(b) F all 9(c) 9(e).58 %.33 % 5

6 elocity [km/h] 3 Conv. 5 5 Total driving force [N] 3 Conv. Conv. 5 5 Distance traveled [m] Inverter input power [kw] 3 Conv. Conv. 5 5 Distance traveled [m] (a) elocity. Yaw rate [rad/s] Distance traveled [m] (b) Total driving force F all. Conv. Conv. Consumption energy [kws] (d) Yaw rate γ. (e) Consumption energy W in. Fig.9 Experimental results (t f = 35. s) (c) Inverter input power P in. Conv. 6 (READ).33 % NEDO ID:5A487d : () Y. Hori, Future vehicle driven by electricity and control - research on four-wheel-motored UOT Electric March II, IEEE Trans. on Industrial Electronics, ol. 5, No. 5, pp (4). (),,, D, ol. 35, No., pp (4). (3) M. Takeda, N. Motoi, G. Guidi, Y. Tsuruta, and A. Kawamura, Driving Range Extension by Series Chopper Power Train of E with Optimized dc oltage Profile, Proceedings of the 38th Annual Conference of the IEEE Industrial Electronics Society (), pp (4) T. E. Stamati and P. Bauer, On-road charging of Electric ehicles, Transportation Electrification Conference and Expo, ol. 5, No. (3), pp. 8. (5) J. Zhang, F. Y. Wang, K. Wang, W. H. Lin, X. Xu, and C. Chen, Data-Driven Intelligent Transportation Systems:A Survey, IEEE Trans. on Intelligent Transportation Systems, ol., No. 4 (), pp (6) J. W. Kwon and D. Ghwa, Adaptive Bidirectional Platoon Control Using a Coupled Sliding Mode Control Method, IEEE Trans. on Intelligent Transport Systems, ol. 5, No. 5 (4), pp (7) M. Ferreira and P. M. d Orey, On the Impact of irtual Traffic Lights on Carbon Emissions Mitigation, IEEE Trans. on Intelligent Transport Systems, ol. 3, No. (), pp (8) Y. Ikezawa, H. Fujimoto, and Y. Hori, Range Extension Autonomous Driving for Electric ehicles Based on Optimal ehicle elocity Trajectory Generation and Front-Rear Driving-Braking Force Distribution with Time Constraint, The st IEEJ International Workshop on Sensing, Actuation, and Motion Control (5). (9) H. Yoshida and H. Fujimoto, Range Extension Autonomous Driving for Electric ehicles Based on an Optimal ehicle elocity Trajectory Considering Road Gradient Information, The st IEEJ International Workshop on Sensing, Actuation, and Motion Control (5). () H. B. Pacejka and E. Bakker, The Magic Formula Tyre Model, ehicle System Dynamics: International Journal of ehicle Mechanics and Mobility, ol., No. (99), pp. 8. (),,, (4). (),, (). 6

IIC Proposal of Range Extension Control System by Drive and Regeneration Distribution Based on Efficiency Characteristic of Motors for Electric

IIC Proposal of Range Extension Control System by Drive and Regeneration Distribution Based on Efficiency Characteristic of Motors for Electric IIC-1-19 Proposal of Range Extension Control System by Drive and Regeneration Distribution Based on Efficiency Characteristic of Motors for Electric Vehicle Toru Suzuki, Hiroshi Fujimoto (Yokohama National