Proposal of Driving Torque Control Method for Electric Vehicle with In-Wheel Motors Masataka Yoshimura (Yokohama National University) Hiroshi Fujimoto

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1 Propoal of Control Method for Electric ehicle with In-Wheel Motor Maataka Yohimura (Yokohama National Univerity) Hirohi Fujimoto (The Univerity of Tokyo) Abtract The anti-lip control or the lip ratio control of E can improve the tability of vehicle in low µ road. However, thee control method cannot control the driving torque. Then in thi paper we propoe the driving method for E with in-wheel motor. By uing thi method, we can control the driving torque directly. Simulation and experiment are carried out to demontrate the effectivene of the propoed method. (electric vehicle driving lip ratio driving torque oberver ). () () () (6) µ (7) M Fig.. J Fd T r Single wheel model. Fd Fig.. M Fd Two wheel model. µ µ. () () J = T rf d () M = F d () [rad/]: [m/]: T [Nm]: F d [N]: M[kg]: r[m]: J[Nm ]: () M M () M = M () λ = r () λ = max(,, ε) () ε

2 D (5) D = F d λ (5) µ λ Magic Formula (8) F d µ N = Mg/(g: ) (6) (7) F d = µn (6) T d = rf d (7). µ λ µ λ peak p λ peak n λ peak n λ λ peak p λ µ λ µ λ peak n λ λ peak p µ (6) (8) ( ) ( < ) { λ = ( ) ( < ) (8) (9) k k = (9) λ k () λ = λ k λ k k λ k { ( λ ) k = λ ( < ) () D () T d = rd λ () k λ () I friction coefficient µ λpeak_n λ peak_p Fig µ λ Typical µ λ curve k (= /) λ k Fig.. elationhip between λ and k. Fig. 5. initial value= 5 k * T* Wheel peed Oberver.5 ehicle Driving ytem. k k () = k () 5 k k max k min k k min k k max k max λ max λ min λ rd kmin < λmax <, < λmin < k max >, < k min < k k = (λ = ) () () ( = ) = = k () k min k k max (k min λ kmax k max ) ()

3 σ < σ = σ = (5) kσ * σ K = { k ( σ) kσ ( < σ) (5) < σ (6) k minσ k maxσ (6) < σ (k min k max ) k (7) (8) K (9) K K < σ Kσ = = = K = k (7) K min K K max (K min λ Kmax K max ) (8) = { K ( σ) Kσ ( < σ) (9) < σ () K min σ K max σ () Fig. 7. -ρ 7 initial value= 6 Kσ Fig. 6. ange of. K * T* Wheel peed Oberver t ehicle λ rd Driving ytem conidering tarting. K * T* Wheel peed ρ * initial value= -ρ ρ Fig uppreion. * ight eft initial value= K * Oberver Wheel peed Oberver T* ehicle λ λ rd rd Driving ytem with yaw-moment K min < < σ ( K min K max ) (5) (9) 6 K 7 7 K max K min K K min K K max K max K min λ max λ min < λ max <, < λ min < K max >, < K min < K K = (λ = ) µ µ 5 K = K max µ µ () () T d T ˆ d, Tˆ d ρ( ρ ) = ρ T ˆ d ( ρ) () = ρ T ˆ d ( ρ) () µ ρ 8 5 () 9

4 T 9 Fig. 9. PF J Jn Driving torque oberver. * * T* CPI r r J Fig.. initial value= Fig.. 6 Wheel peed control ytem. K λ* * T* Wheel peed τ ehicle Effect of driving torque oberver. λ rd () T T d () = J T () C P I () PI 7 K I K τ τ PF () T d = rd rdk I τ rdk I τ τ () (5) ± rdk τ τ p, p = I τ (5) D D max D min K I. D ehicle ver. (9) µ λ λ = µ λ = µ [rad/] [m] K I =.5 D max = D min = (5) e(p ),e(p ) = 6.7[rad/] λ max =, λ min = K max = 5, K min = σ σ =.5[m/] µ (a) (b) K (c) (d) µ t = [] µ t = 5.5[] µ µ µ ρ ρ =.5 (a) (b) (i) µ µ µ (c) (i) µ K K max = 5 µ ρ =.5 µ µ ρ 5. FPE- Kanon

5 5 5 etimated driving force hat [Nm] 5 5 K,K K K vehicle velocity [m/] time [] (a) Etimated driving torque. 5 5 time [] (b) K. Fig time [] (c) Slip ratio. µ Simulation reult high-µ road. 5 5 time [] (d) ehicle velocity. etimated driving force hat [Nm] etimated driving force hat [Nm] K,K K K time [] time [] time [] time [] time [] (a) Etimated driving torque: Torque (b) Slip ratio: Torque (c) Etimated driving torque: Driving torque (d) K: Driving torque (e) Slip ratio: torque Driving etimated driving force hat [Nm] K,K K K yaw rate [rad/] driving uppreion vehicle velocity [m/] 6 5 driving uppreion time [] (f) Etimated driving torque: uppreion time [] (g) K: uppreion. Fig time [] (h) Slip ratio: with yaw moment uppreion time [] (i) Yaw rate. µ µ Simulation reult low-µ road plit-µ road time [] (j) ehicle velocity. Table. Parameter of experimental vehicle. Wheel Inertia J. Nm Wheel adiu r. m ehicle Ma M 85 kg Tread l p. m ehicle Inertia I 6 Nm σ σ =.[m/] µ K [m/] [m/] [m/] µ t = [] µ t = 5.5[] µ µ µ 5 µ µ µ µ µ 6.

6 5 5 etimated driving torque hat [Nm] 5 5 K,K K K... vehicle velocity [m/] 6 5 time [] 5 5 time []. 5 5 time [] 5 5 time [] (a) Etimated driving torque. (b) K. (c) Slip ratio. µ Fig.. Experimental reult high-µ road. (d) ehicle velocity. etimated driving torque hat [Nm] etimated driving torque hat [Nm] K,K K K time [] 5 6 time [] 5 6 time [] 5 6 time [] 5 6 time [] (a) Etimated driving torque: Torque (b) Slip ratio: Torque (c) Etimated driving torque: Driving torque (d) K: Driving torque (e) Slip ratio: torque Driving etimated driving torque hat [Nm] K,K K K yaw rate [rad/] driving uppreion vehicle velocity [m/] 5 driving DTC uppreion 5 6 time [] (f) Etimated driving torque: uppreion. 5 6 time [] (g) K: uppreion. Fig time [] (h) Slip ratio: with yaw moment uppreion. µ µ 5 6 time [] (i) Yaw rate. Experimental reult low-µ road plit-µ road. 5 6 time [] (j) ehicle velocity. NEDO ( ID: 5A87d) A Nagae K Hoomi S Yamamoto M Ooba Y Takahira T Ihikawa: Development of Active-Traction Control Sytem TOYOTA Technical eview ol 5 No pp 68-7 (in Japanee) Y Turuoka Y Toyoda and Y Hori: Baic Study on Traction Control of Electric ehicle Tran IEE of Japan ol 8-D No pp (in Japanee) H Sado S Sakai and Y Hori: oad Condition Etimation for Traction Control in Electric ehicle In Proc 999 IEEE International Sympoium on Indutrial Electronic pp K Fujii H Fujimoto: Slip atio Control Baed on Wheel Speed Control without Detection ehicle Speed for Electric ehicle T-7-5 pp 7-7 (in Japanee) 5 K Nakamura H Fujimoto: Propoal of Slip atio Control for Electric ehicle with Inverter Control Baed on PWM Hold IIC-8-6, pp 75-8, 8 (in Japanee) 6 M Yohimura H Fujimoto: Slip atio Control of Electric ehicle with Singlerate PWM Conidering Driving Force in Proc. Proc. The th IEEE International Workhop on Advanced Motion Control pp K Kanou H Fujimoto: Yaw-rate Control Baed on Slip-ratio Control with Driving Stiffne Identification for Electric ehicle CCS SY//8/-6 8(in Japanee) 8 H B Pacejka and E.Bakker The Magic Formula Tyre Model Tyre model for vehicle dynamic analyi:proceeding of the t International Colloquium on Tyre Model for ehicle Dynamic Analyi held in Delft The Netherland 99 9 S. Sakai: D-Tire Model ver. a.ac.jp/index j.html,.

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