Proposal of a Range Extension Control System with Arbitrary Steering for In-Wheel Motor Electric Vehicle with Four Wheel Steering

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1 Proposal of a Range Extension Control System with Arbitrary Steering for In-Wheel Motor Electric Vehicle with Four Wheel Steering Toshihiro Yone and Hiroshi Fujimoto The University of Tokyo 5-1-5, Kashiwanoha, Kashiwa, Chiba, Japan Phone: Fax: yone@hflab.k.u-tokyo.ac.jp, fujimoto@k.u-tokyo.ac.jp Abstract In this paper, a range extension control system with vehicle dynamics control is. and rear active steering and torque difference between left and right in-wheel motors enable yaw rate and side-slip angle control with higher energy efficiency. The effectiveness of the method was verified by both simulations and experiments. I. INTRODUCTION Electric vehicles EVs are expected to be a drastic solution to the current environmental and energy problems by depriving internal combustion engine vehicles ICEVs of its position. Furthermore, EVs have advantages in motion control compared with ICEVs [1. Due to limited cruising range per charge, EVs have been prevented from wide spreading. In order to solve this problem, efficiency of motors [ and regenerative torque control [3 were studied. From the view point of motor efficiency improvement control, research of torque and angular velocity pattern that maximise efficiency during acceleration and deceleration was carried out [4. To decrease EV s energy consumption, torque distribution to traction motors with different charasteristics was studied [5. On the other hand, the authors research group range extension control systems RECSs [6, [7, [8. These systems do not involve changes of vehicle structure such as additional clutch [5 and motor type. RECS extends cruising range by motion control of vehicle. In article [8 consumed energy during cornering is decreased by making difference between torques of left and right motors. However, the system is only effective when the vehicle is traveling at a constant velocity and a constant radius of curvature. That is, the system could not be applied in case yaw rate is not constant. In this paper, to apply RECS to the normal steering situations, RECS that can be applied even when steering command changes arbitrarily is. This RECS not only minimises consumed energy, but also controls yaw rate and side slip angle to enable vehicle to follow a target trajectory by utilising four wheel steering and a moment that is created by torque differece between left and rear in-wheel motors. a FPEV-Kanon Fig. 1. Experimental vehicle II. EXPERIMENTAL VEHICLE b In-wheel motor In this research, an original electric vehicle FPEV Kanon, manufactured by the authors research group, is used. This vehicle has four outer-rotor type in-wheel motors. Therefore, driving and braking force distribution to each motor can be used to produce torque around the z-axis of the vehicle. and rear electric power steerings are equipped, which enable active control of both front and rear steering mechanisms. Power train of the vehicle consists of battery, chopper, inverters and motors. Input voltage V dc and currents I dc of inverters are measurable. III. DYNAMICS EQUATIONS AND TRAVELING RESISTANCE In this section, traveling resistance is calculated from dynamics equations. F x F xfl + F xfr + F xrl + F xrr 1 F y F yfl + F yfr + F yrl + F yrr F y β + γ 3 M z I γ F yfl l f + F yfr l f F yrl l r F yrr l r + N z 4 N z : d f F xfl + F yfr + d r F xrl + F yrr 5 F x is sum of driving or braking force, F y is total lateral force, M z is yaw moment applied to the vehicle, F xfl, F xfr, F xrl, F xrr are driving or braking forces of each tyre, F yfl, F yfr, F yrl, F yrr are lateral force of each tyre, M is mass of the vehicle, V is vehicle velocity, β is side slip

2 angle of the vehicle, γ is yaw-rate, I is inertia around z- axis, l f, l r are the distances to front and rear axles from the centre of gravitycg, d f, d r are front and rear treadwidth. N z represents moment by differencial torque of right and left motors and shown by Eq.5. Tyre slip angle is an angle between surface of the tyre and direction of movement of the vehicle and written as α fl, α fr, α rl, α rr. When front and rear steering written as δ f and δ r are small,approximations can be made as below. α fl α fr α f β + l f γ V δ f 6 α rl α rr α r β l rγ V δ r 7 Lateral forces are proportional to tyre slip angle and are approximated as below. F yfl F yfr F yf C f α f 8 F yfr F yrr F yr C r α r 9 Therefore, dynamics equations of lateral and yaw motions are established as below. Fig.. Bicycle model of Vehicle Dynamics ẋ Ax + Bu 1 [ a11 a A 1 a 1 a [ Cf +C r l f C f l r C r 1 11 B x l f C f l rc r I [ b11 b 1 b 13 b 1 b b 3 [ β γ, u δ f δ r N z l f C f +l r Cr IV [ Cf C r l f C f l r C r 1 I I I 1 For the vertical direction of the vehicle, when the vehicle travels at a constant speed, driving force F x equals to traveling friction F r. Traveling friction consists of cornering drag force F cd, rolling friction and air resistance, which is shown as below. µ is the coefficient of the rolling friction, normal forces of front and rear tyres are N f and N r, and other disturbances are F dis. F r F cd + µ N f cos δ f + µ N r cos δ r + F dis 13 Cornering drag force F cd is the sum of cornering drag forces F cr work on each tyres as Fig. 3. When, tyre slipping angles α are small, cornering drag forces are calculated as below. F cr F y sin α 14 F cd F crf cos β + F crr cos β 15 Thus, from the fact that tyre side slip angles and steering angles are small and N f + N r Mg, by substituting Eq. 6, Eq.7 and Eq.15 into Eq.13, the following approximations is derived. F r C f α f + C r α r + µ Mg 16 Fig. 3. Cornering Drag on each tyres IV. DISTRIBUTION LAW FOR RECS A. Consumed electrical power In this paper, only front in-wheel motors are utilised. Consumed electrical power P is treated as an evaluation function and front and rear steering angles δ f, δ r, as well as differential torque N z are calculated to minimise the consumed electrical power. Consumed electrical power consists of motor output P m, copper loss P c and iron loss P i. P P m + P c + P i 17 At first, motor output P m is examined. Motor output is expressed by wheel angular velocity ω fl, ω fr and wheel torque T fl, T fr. P m ω fl T fl + ω fr T fr 18 On the assumption that slip does not occur between tyres and road, wheel angular velocity is calcurated as below. ω fl 1 V d r r γ 19 ω fr 1 V + d r r γ

3 r is radius of the tyres. When each wheel angular acceleration is small, torque T i is proportional to driving force. T i rf xi 1 Driving force and differential torque are distributed to left and right motors evenly. [ [ 1 [ Fxfl 1 d f Fr F xfr N z 1 Motor output P m is able to be expressed as follows by traveling resistance F r, longitudinal vehicle velocity V x, yaw rate γ and differential torque N z. By substituting Eq. to Eq. into Eq.18, motor output P m is calculated as follows [8. 1 d f P m V x F r + γn z 3 Secondary, copper loss is discussed as following. copper loss is proportional to square of current and under d-axis current i d control, torque T i are proportional to q-axis currents i qrl, i qrr. P c R a i qfl + i qfr 4 i qi T i T i P n ϕ a K t 5 Here, Coeffients of right and left motors are equal. R a is resistance value of armature windings, P n is number of magnetic pole pairs of a stator, ϕ a is interlinkage flux, K t is coefficient of torque. Thus, copper loss is expressed from Eq. as P c R ar 1 Kt F r + d Nz 6 f For the last, iron loss P i is ignored. Because the velocity of the vehicle in this paper is low, the iron loss is small enough to be ignored. By substituting Eqs.16, 3 and 6 into Eq.17, cosumed electrical power P is calculated as follows. For α f and α r, the terms that have order larger than are ignored. Ra r P C f µ Mg + V x αf K t Ra r +C r Kt µ Mg + V x αr +N z γ + R ar Kt d Nz + µ MG 7 r B. Distribution law to minimise the consumed electrical power Dynamic equations of lateral and yaw-motions are expressed as [ Cf C r α [ f α C f l f C r l r 1 r Fy 8 M N z z X is defined as the coefficient matrix in the left side of the equation, z is defined as a column vector of tyre slip angles and differential torque [α f α r N z T and column vector on the right side of the equation is defined as b. When W is defined as weighting matrix, solution of the method of weighted least squares is z opt and expressed as P z T W z 9 z opt W 1 X T XW 1 X T 1 b 3 C w 11 f C W : w r 31 C f C r R a r Kt d r Ra r w 11 : C f µ Mg + V x K t Ra r w : C r µ Mg + V x K t Treating lateral force and yaw-moment as commands, tyre side slip angles and differential torque that minimise the consumed electrical power are calculated from Eq.3. V. CONTROL SYSTEM DESIGN When the velocity of the vehicle is constant, the dynamics of the vehicle is expressed by side slip angle and yaw-rate. In this article, side slip angle and yaw rate are controlled by total yaw-moment M z and lateral force F y. Side slip angle is difficult to be measured directly, therefore, different kinds of algorithms were studied [1. Here, side slip angle is observed by a side slip angle observer SAO [11 and yaw rate is acquired by a gyro sensor that placed at the centre of gravity. Lateral force observer LFO and yaw-moment observer YMO are designed to control side slip angle and yaw rate [1. Observers are designed to nominal the plant including the destribution law, which decouple controls of side slip angle and yaw rate, and strengthen the controls against disturbance and parameter errors. In addition, two degree of freedom control is constructed to control side slip angle and yaw-rate. The block diagram is shown in Fig. 4. A. Side-slip angle observer Not only yaw rate γ, δ f and δ r, but also lateral acceleration a y is utilised to construct a robust and linear observer. From Eqs.3 and 13, lateral acceleration a y is expressed as a y V a 11 β + a 1 γ + b 11 δ f + b 1 δ r + γ 3 Here a 11 a, b 11 b 3 are the components of the matrixes A, B. x, u are utilised to express the output equation as below. y Cx + Du 33 [ 1 C 34 V a 11 V a [ [ γ D, y, V b 11 V b 1 By utilising these output equations, an observer is designed as below to observe side slip angle β for control. ˆx Aˆx + Bu Kŷ y 35 ŷ C ˆx + Du 36 a y

4 trajectory, to compare method with method, a sinusoidal input in utilised as follows. u δf A sin ωt δr Nz 43 ẋ Ax + Bu 44 Fig. 4. B. Yaw-moment Observer Block Diagram of proposal method Considering the control inputs and disturbances to the vehicle, dynamics equation of yaw motion is described as below. I dγ dt M z + N td 37 Where N td is disturbance yaw-moment. By constructing a disturbance observer, disturbance yaw-moment is suppressed and Eq.37 is nominalised as following. C. Lateral Force Observer γ 1 I n s M z P γ sm z 38 Lateral dynamic equations with disturbance Y d included is given as dβ dt + γ F y + Y td 39 Eq.39 is transformed into β F y + Y td 4 Y td : γ + Y d 41 Eq. 41 is nominalised by disturbance observer into β D. degree of freedom control 1 M n V n s F y P β sf y 4 To control the nominalised plant by YMO and LFO, degree of freedom control is utilised. Cut off frequencies of low-pass filters G β s and G γ s to proper the inverse system in feedfoward control are 1 rad/s. When commands are compared with output in feedback control, commands are filtered by the same low pass filter as the feedfoward control. The yaw rate is controlled by P control and the side slip angle is controlled by PI control. VI. SIMULATION For vehicle dynamics evaluation, sinusoidal input to steering is a effective and widely used methodology [13. In this research, although this proposal RECS can be applied to any Target trajectory is designed as a trajectory that the vehicle travel by steering front steer in sinusoidal input, without rear steering and differential torque as is shown in Eq.43. Side slip angle and yaw rate calculated by the bicycle model that shown in Eq.44, are treated as command. A travel that steered only by front steering is defined as method and compared with proposal method. The front steering in method are settled as amplitude A is.1 rad and angular velocity ω is 1. rad/s. The constant velocity of the vehicle is 15 km/h. Cut off frequency of SAO is 3 rad/s and that of LFO and YMO are 1 rad/s. Feed back gains of yaw-rateγ and side slip angle β are determined by the pole placement method and the poles are placed at 6 rad/s. The results of the simulation for 4π seconds are shown in Fig. 5. Only output of and loss at the motors are considered so that efficiency of chopper and inverters are 1 %. Fig. 5a, Fig. 5b show that the vehicle is following the yaw rate and side slip angle commands. The steering angles of and proposal methods are shown in Fig. 5d and Fig. 5e and the differential torque in Fig. 5c. Fig. 5f shows consumed energy in 4π seconds. This consumed energy is integration of consumed electrical power. By the proposal method, consumed energy decreased for 9.1 %. The consumed energy converted into traveling distance per 1 kwh of energy is shown on Table I. Table I shows that traveling distance increased for.8 km per 1 kwh of energy stored in batteries. VII. EXPERIMENTS Experiments were conducted in the same conditions as the simulations. The experiments were held in experimental area in the university and the vehicle expressed in section was utilised. Vehicle velocity was controlled by PI controller and its feedback gains were designed by pole assignment method to place the pole at 1 rad/s. On the experiment, consumed energy was calculated from products of input voltages and currents of inverters. Thus, inverter loss and iron loss were included. Experiments were performed for 4 times each of convention and proposal method. The average of consumed energy and standard deviation as errorbar are shown in Fig. 6f. Fig. 6a, Fig. 6b, Fig. 6d, Fig. 6e shows that side slip angle and yaw rate are corresponding. The front and rear steering angles and differential torque are shown in Fig. 6c, Fig. 6g, Fig. 6h. Fig. 6f shows that consumed energy is decreasing for 13.4 %. On tableii traveling distance per 1 kwh is shown. 8 m increase of traveling distance is able to be confirmed.

5 TABLE I TRAVELING DISTANCE PER 1 KWHSIMULATION Battery Capacity Without RECS With RECS 1 kwh 5.14 km 5.65 km 5 kwh 5.7 km 8.3 km 16 kwh 8. km 9.4 km TABLE II TRAVELING DISTANCE PER 1 KWHEXPERIMENTS Battery Capacity Without RECS With RECS 1 kwh 5.18 km 5.98 km 5 kwh 5.9 km 9.9 km 16 kwh 8.9 km 95.7 km [1 Y. Wang, B.M. Nguyen, H. Fujimoto, Y. Hori; Multirate Estimation and Control of Body Slip Angle for Electric Vehicles Based on Onboard Vision System, Industrial Electronics, IEEE Transactions on, vol.61, no., pp ,14 [11 Y. Aoki, Z.Li, Y. Hori: Robust design of body slip angle observer with cornering power identification at each tire for vehicle motion stabilization, Advanced Motion Control,6. 9th IEEE International Workshop on pp [1 Y. Yamauchi, H. Fujimoto: Proposal of Lateral Force Observer with Active Steering for Electric Vehicle, in Proc. SICE Annual Conference 8, Japan, pp , 8. [13 C. Fu, R. Hoseinnezhad, R. Jazar, A. Bab-Hadiashar, S. Watkin: Electronic Differential Design for Vehicle Side-Slip Control, Control, Automation and Information Sciences ICCAIS, 1 International Conference on, pp.36-31, 1 VIII. CONCLUSION In this article, a range extension control system is and its effect is confirmed by both simulations and experiments. Future works include consistent of range extension and controllability especially considering safety. In addition, yaw rate and side slip angle can be changed to achieve higher efficiency. ACKNOWLEDGEMENT This research was partly supported by Industrial Technology Research Grant Program from New Energy and Industrial Technology Development OrganizationNEDO of Japan number 5A4871d, and by the Ministry of Education, Culture, Sports, Science and Technology grant number REFERENCES [1 Y. Hori: Future Vehicle Driven by Electricity and Control Research on Four Wheel Motored: UOT Electric March II, IEEE Trans. IE, Vol. 51, No. 5, pp [ H. Toda, Y. Oda, M. Kohno, M. Ishida and Y. Zaizen: A New High Flux Density Non Oriented Electrical Steel Sheet and its Motor Performance, IEEE Trans. MAGNETICS, Vol. 48, No. 11, pp [3 K. Oh, M. Takeda and A. Kawamura: A Study on Control of Regenerative Braking System in Electric Vehicle h, in Proc. IEE of Japan Technical Meeting Record, IIC in Japanese [4 K. Kotera, K. Inoue, and T. Kato: Derivation and Verification of Optimal Trajectories in Induction Motor Drive System under Rotating Speed and Torque Limit, in Proc. IEE of Japan Technical Meeting Record, HCA in Japanese [5 X. Yuan and J. Wang: Torque Distribution Strategy for a and Wheel Driven Electric Vehicle, IEEE Trans. Veh. Technol., Vol. 61, No. 8, pp [6 T. Suzuki and H. Fujimoto: Proposal of Range Extension Control System by Drive and Regeneration Distribution Based on Efficiency Characteristic of Motors for Electric Vehicle, in Proc. IEE of Japan Technical Meeting Record, IIC 1 19, pp in Japanese [7 H. Fujimoto, S. Egami, J. Saito, and K. Handa: Range Extension Control System for Electric Vehicle Based on Searching Algorithm of Optimal and Driving Force Distribution, in Proc. the 11th IEEE International Workshop on Advanced Motion Control 1 [8 H. Sumiya, H. Fujimoto: Distribution Method of / Wheel Side Slip Angles and Left/Right Motor Torques for Range Extension Control System of Electric Vehicle on Curving Road, in Proc. 1st International Electric Vehicle Technology Conference 11 [9 S. E. Shladover: Cooperative rather than autonomous Vehicle- Highway Automation Systems, Intelligent Transportation Systems Magazine, IEEE, Vol. 1, No. 1, pp

6 Side slip angle [rad a Side-slip angle Yawrate [rad/s b Yaw Rate Yaw moment [Nm c Differencial Torque d Steering angle e Steering angle f Electricity Consumed Fig. 5. Simulation Side slip angle [rad Side slip angle [rad Yaw moment [Nm 4 Yawrate [rad/s a Side slip angle d Yaw Rate.15.1 Yawrate [rad/s b Side slip angle e Yaw Rate Electricity Consumption [kws c Differencial Torque f Electricity Consumption g Steering angle h Steering angle Fig. 6. Experimental Results