Regenerative Brake and Slip Angle Control of Electric Vehicle with In-wheel Motor and Active Front Steering

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1 Regenerative Brake and Slip Angle Control o Electric Vehicle with Inwheel Motor and Active Front Steering Hiroshi Fujimoto 1) 1) The University o Tokyo, Graduate School o Frontier Sciences Transdisciplinary Sciences Bldg. 613, 515, Kashiwanoha, Kashiwa, Chiba, , Japan ujimoto@k.utokyo.ac.jp) Received on March 31st, 211 Presented at the JSAE Annual Congress on May 17th, 211 ABSTRACT: Electric vehicles EVs) have attractive potential not only or energy and environmental perormance but also or vehicle motion control because electric motors have quick and measurable torque response. Recently, the authors laboratory has developed a completely original EV which has active ront and rear steering systems and hightorque directdrive inwheel motors in the all wheels. In this paper, the main eatures o this vehicle are briely introduced and our recent studies on pitching control, slipratio control, and yawrate and slipangle control with lateral orce sensors are explained with experimental results. KEY WORDS: Electric vehicle, Inwheel motors, Pitching and Slip ratio Control, Active steering 1. Introduction As a solution o energy and environmental problems, electric vehicles EVs) is paid to attention. In addition, rom the point o view o control engineering, EVs including battery, uelcell, and plugin) hybrid vehicles have very attractive potential. Since electric motors and inverters are utilized in drive system, they have great advantages over internal combustion engine vehicles ICEVs). These advantages can be summarized as ollows, 1) Quick torque response The torque response o electric motors is 15 times as ast as that o ICEVs. 2) Measurable motor torque In ICEVs, it is diicult to accurately measure their output torque. On the other hand, the output torque o electric motor can be measured easily rom current. Thereore, the state o the road can be estimated precisely. 3) Individual wheels control By using inwheel motors, each wheel can be independently driven. Then, individual wheel control can enhance the vehicle stability. These advantages o electric motor enhance vehicle motion control in EVs 1)3). Our research group ocus the merits o motors and we are researching on the motion control or the electric vehicles to achieve saety and comort driving 4). In this paper, our recent researches on pitching control or comort braking 5) and slipratio control or emergent braking 6) are briely introduced by using the regenerative brake o inwheel motors. Finally, the advanced vehicle stability control method by active ront steering 7) is explained. Fig. 1 Experimental vehicle 2. Experimental vehicle To veriy the proposed control algorithm, an original electric vehicle FPEV2Kanon developed in our laboratory is used or the test vehicle. Fig. 1 and Fig. 2 show the test vehicle and its coniguration Inwheel motors The outer rotor type inwheel motors made by Toyo Denki Seizo K.K., Ltd. are installed in two rear wheels as driving powertrain. Table 1 shows the speciication o the inwheel motors. Because this motor adopts the direct drive system, the reaction orce rom the road is directly transered to the motor without gear reduction and backlash. Then it can be said that this vehicle is ideal to examine the proposed estimation and control methods. Fig. 3 shows inwheel motor and Fig. 4 shows motor coniguration. Recently, we installed inwheel motors with much higher torque into two ront wheels to develop control methods or 4WD EVs. However in this paper, only the results with rear inwheel motors will be introduced or 2 wheels individual drive EVs Energy Storage The Liion battery is used or the energy storage. In this Copyright c 21 Society o Automotive Engineers o Japan, Inc. All rights reserved

2 Motor or SBW acceleration a x,a y sensor yawrate γ sensor steering angle δ sensor δ Controller AUTOBOX DS113 ) ω,treal Liion Battery 15V 1 15V 3V Chopper T* R inverter L inverter R motor L motor Motor or SBW Fig. 2 δr Coniguration o FPEV2Kanon Fig. 3 Inwheel motor Fig. 4 Motor coniguration Table 1 Speciication o inwheel motor Manuacturer TOYO DENKI Type Direct drive system Outer rotor type Rated torque 137[Nm] Maximum torque 34[Nm] Rated power 4.3[kW] Maximum power 1.7[kW] Maximum speed 15[rpm] Weight 26[kg] Cooling system Air cooling suix i =,r represents the ront wheel and rear wheel, respectively. The slip ratio λ is deined as V ω V λ = max V, 4) ω,v,ɛ) where the denominator o 4) is changed by the values o V ω and V. Because V ω is aster than V when the vehicle is driving V ω > V), the denominator becomes V ω. On the other hand, because V ω is slower than V on braking V ω <V), it becomes V. Here, ɛ 1) is a small constant in order to avoid zero denominator. V M!i Tbi V! i r Tmi Fi Fig. 5 Vehicle model Fig. 6 Two wheel model vehicle, ten batteries o 15V per module are installed and connected in series. In addition, the battery voltage 15V boosts to 3V by using chopper circuit, and it is ed to power to the inverter. 3. Vehicle modeling 8) 3.1. Longitudinal motion equation and slip ratio By assuming that the driving resistance o the vehicle is negligible, the longitudinal motion equations both o wheel and vehicle shown in Fig. 5 can be described as J ωi ω i = T mi T bi rf i 1) m V =2F 2F r 2) V ωi = rω i 3) where J ωi is the moment o inertia o wheel, ω i is the motor angular velocity, T mi is the motor torque, T bi is the brake torque, r is the tire radius, F i is the driving orce generated by the contact between tire and road, m is the vehicle mass, V is the vehicle velocity, and V ωi is the wheel velocity. The y α δ β V γ α r δ r x l l r 3.2. Cornering orce The orce in the orthogonal direction to the wheel sideslip angle is called the cornering orce. I the wheel sideslip angle is small, the cornering orce increases in proportion to the wheel sideslip angle. I the wheel sideslip angle is big, the cornering orce has nonlinear characteristic. Here, assuming that the wheel sideslip angle is small, the relationship between the cornering orce and the wheel sideslip angle can be described as F y Y = C α = C β l ) V γ δ 5) ) F yr Y r = C rα r = C r β lr V γ δr, 6) where F y and F yr are tire lateral orces, C and C r are the cornering stiness, α and α r are tire sideslip angles, β is the vehicle sideslip angle, γ is the vehicle yawrate, l and l r are the distance rom body center o gravity to steering knuckle spindle and rear wheel axle. Y and Y r are the cornering orce o ront and rear wheels which depend onthetirecharacteristics Twowheel vehicle model Fig. 6 shows the twowheel vehicle model. This model is assumed that the roll o vehicle is negligible and the vehicle speed is constant. From the twowheel vehicle model, the linearized dynamics o the lateral motion is derived as dβ ) mv dt γ =2Y 2Y r = 2C β l ) ) V γ δ 2C r β lr V γ, 7) I dγ dt =2l Y 2lrYr Nz = 2C β l ) ) V γ δ l 2C r β lr V γ l r N z,8) Copyright c 21 Society o Automotive Engineers o Japan, Inc. All rights reserved

3 P l M h lr θ Pr θ * Tmn axn θ C1 Axn Pns) s e Tb. ω Tb Tm ax Ax θ Ps) s θ. C2 θ. Fig. 7 Hal car model where I is the inertia around vehicle yawing axis, N z is yawmoment generated by the torque dierence between let and right inwheel motors. 4. Pitching control 5) This section ocus on the pitching motion o the vehicle to enhance the driving comort. The pitching motion occurs when the acceleration changes by the driving orce and the braking orce. We have studied on the control method o this pitching motion Modeling o the pitching motion The pitching motion is body attitude change around the y axis o Fig. 6. Because the pitching motion is the motion around the y axis, it is possible to model it by the hal car model, as shown in Fig. 7, which has only the ront and rear wheels. The transer unction o the hal car model can be described as θ M = 1 I ps 2 Cs K, 9) where I p is the pitching inertia, C is the damper coeicient, K is the spring constant, θ is the pitch angle, and M is the pitching moment around the center o gravity COG). When the vehicle accelerates or decelerates, the pitching motion is caused. As the braking torque is transered to the suspension through the brake unit, the antidive orce is generated to ront wheel and the antilit orce is generated to rear wheel when the vehicle is braking. By considering them, 9) can be rewritten as θ = 2mh mβl tanφ 1 β)l rtanφ r) a x,1) I ps 2 Cs K where the irst term o righthand side is generated by inertia orce, the second term is caused by braking orce which works at the contact point o tires, h is the height o COG, β is the ront wheel distribution o braking orce, and φ and φ r are the angle rom the contact point o tires to the instantaneous rotation centers o the suspension Control system design 1) Calculation o longitudinal acceleration Because the obtained pitching model is acceleration input, the calculation method o acceleration rom motor torque is considered. From 1) and 2), the acceleration is derived as ollows. a xn = 2Tmi 2Jω ω J ωr ω r) 4T bi 11) rm Fig. 8 Block diagram o pitching control This equation can be calculated rom motor torque, braking torque, and wheel acceleration. However, because it is generally diicult to measure the braking toque T b directly, an estimation method o T b is proposed. 2) Braking torque estimation By eliminating F i and V rom 1) to 4), the equation o T bi is derived as 12) when V > V ωr. Here, the wheel acceleration ω r is obtained rom the pseudoderivative with highpass ilter. The braking torque estimation can be achieved precisely to consider the road condition because the slip ratio is included in 12). Tˆ bi = 1 2 Tmi 1 2 Jωr ω r 1 2 Jω ω r2 m ω i 41 λ r2 mω i λi 12) i) 41 λ i) 2 3) 2DOF Pitching Controller Based on the identiied model o pitching motion and the estimation method o braking torque, pitching controller is proposed as shown in Fig. 8 which has twodegreeoreedom 2DOF) control structure. The blocks A x and A xn represent 11). In this control system, the required sensors are the encoder o motors to detect ω r and ω r) and gyroscope o pitchrate θ. It is not appropriate to use the inverse plant model as the eedorward FF) controller because the o pitchangle is zero θ = ) in this paper. Then, model ollowing control structure is applied. In the FF control part o Fig. 8, the nominal plant P ns) is controlled by the highgain controller C 1s). This C 1s) generates the acceleration a xn based on the braking torque estimation ˆT b. The calculated o motor torque T mn which can control pitchangle o nominal plant ideally is applied to the real plant P s) asff torque command. When the real plant coincides with the nominal model, the pitching motion can attenuate by this FF controller. When the modeling error or disturbance exists, the pitchrate error between nominal and real plants is appeared. This pitchrate error is attenuated by the eedback controller C 2s) with moderate gain. Then, robust pitching control perormance is achieved even when the modeling error exists. Both C 1s) andc 2s) are designed by the pole placement method. Because the input o C 1s) is pitchangle error, the Copyright c 21 Society o Automotive Engineers o Japan, Inc. All rights reserved

4 proportionalderivative PD) controller is adopted as C 1s). On the other hand, the proportionalintegral PI) controller is applied as C 2s) since the input o C 2s) ispitchrateerror. The poles o closedloop system with C 1s) canbe set high enough to control pitchangle o model ideally. However, those with C 2s) have limitation to keep the stability margin and noise attenuation o the actual closedloop system with P s). Pitch rate[rad/s] with ctr without ctr a)pitchrate Pitch angle[rad] with ctr without ctr b)pitchangle closeup) 4.3. Experiments The proposed control method is tested by experiments with FPEV2Kanon. The experiment is assumed that the vehicle is stopped by the mechanical brake while it is running about 9m/s on a lat dry road. When the vehicle speed becomes less than 1.5m/s, the pitching controller turns on. The parameters used in the experiment are the vehicle mass m = 71kg, the wheel radius r =.32m, the wheel inertia o the each rontrear wheel J ωr =1.26Nms 2 and J ω = 1.Nms 2. As or the controllers C 1 and C 2, the poles o each closedloop system are set to 14rad/s and 8rad/s, respectively. Fig. 9 shows the experimental results. Fig. 9a) and b) show the pitchrate and the pitchangle which is obtained by the integral calculation o pitchrate. Both the pitchrate and the pitchangle are suppressed compared with the case without control. From this results, it can be said that the comortable braking is realized by the proposed control. Fig. 9c) shows the estimated braking torque and the motor torque. The estimated braking torque is inluenced by the sensor noise because the equations o braking torque estimation 12) include the wheel acceleration ω. The derivative calculation o the sensor signal ampliies the noise. Even though that, this noise does not damage the control perormance o pitching motion severally as shown in Fig. 9a) and b). Moreover, Fig. 9d) shows the distance rom beginning point o the breaking to the stop point with several experiments. This is obtained by the integral calculation o the vehicle speed. As the result, it can be said that the distance does not become longer by this control. This is very important or the application to the commercial products. 5. Slip ratio control on deceleration 6) Authors group proposed the slip ratio estimation method and the control method without the detection o the vehicle velocity at accelerating and decelerating in the s 4) and 9). In this paper, the slip ratio estimation and the control method without detection both o the vehicle velocity and the acceleration are extended to the twodimensional motion when the vehicle is decelerating. As or the riction coeicient between tire and road, the slip ratio becomes minimum value in near.2 asshownin Torque [Nm] motor torque braking torque Fig. 9 Coeicient o Friction µ c)torque.5.5 Distance[m] without ctr with ctr d)distance Experiment results o pitching control 1 Hi µ Low µ Slip Ratio λ Fig. 1 µ λ curve Fig. 1, and the maximum brake torque is obtained. Thereore, it can be said that the braking distance with control is shorter than the case without control i the wheel velocities are controlled to take the optimum slip ratio. However when the slip ratio approaches to, the vehicle motion becomes unstable and there are risks o side slip and spin. First, estimation method o slip ratio without vehicle velocity is derived. Next, slip ratio control system is introduced Slip ratio estimation By substituting rom 1) to 3) into the time derivative o 4), the state equation on λ is obtained as ) λ i = ωi Tm T b J ω ω 1 λ i) 1 λ i) 2 13) ω i r 2 Mω i where T m, T b and J ω ω are as ollows. T m =2T m 2T mr 14) T b =2T b 2T br 15) J ω ω =2J ω ω 2J ωr ω r 16) Motor torque, brake torque and rotation speed o motor are obtained rom motor current, pressure o brake line and resolver attached to motor, respectively. Moreover, the convergence o estimation error o the slip ratio is discussed in the 1). Copyright c 21 Society o Automotive Engineers o Japan, Inc. All rights reserved

5 Λ ^V r1 Λ ) ^V! Λ r! 1 ^ C s) ^ T Λ Vehicle Slip Ratio Estimator! C s) C s) c G G 1 2 Nc Nz Fig. 11 Block diagram o slip ratio control a) Decoupling control Slip Ratio λ.5.5 Velocity [m/sec] Vehicle Wheel * in C s) γ* C s) in c s c Mn Vn s 2Cn z γ Slip Ratio λ a) Slip ratio b) Vehicle & wheel velocity Fig. 12 Experiment results o slipratio control without control).5.5 λ λ^ a) Slip ratio b) Vehicle & wheel velocity Fig. 13 Experiment results o slipratio control with control) 5.2. Slip ratio control Velocity [m/sec] Vehicle Wheel Next, the slip ratio control with the wheel speed control is designed. Because the wheel speeds can be detected with the resolver, the estimation o the slip ratio is equivalent to the estimation o the vehicle velocity. The estimated vehicle velocity can be calculated rom 4) based on the estimated slip ratio. The value o wheel angular velocity at the optimum slip ratio is calculated rom 17) and 18). Slip ratio is controlled by the wheel speed control, as shown in Fig. 11. ˆV = rω 17) ω = 1λ ˆV 18) 1ˆλ r As the controller o the wheel velocity control, the simple PIcontroller was used and the plant was assumed as ω = 1 T, 19) J ωs where the pole was located at 3rad/sec with the pole placement method and target slip ratio was.2. Experiments are carried out in playground o university. The vehicle decelerated only with the rear wheels both without control and with control because inwheel motors were installed only rear wheel. Fig. 12 and Fig. 13 show experimental results. From Fig. 12, it can be conirmed that the wheels lock immediately with strong mechanical brakes and the slip ratio becomes without control. From Fig. 13, wheels do not lock and the slip ratio converge to.2. Fig. 14 c s c Ins b) LFOYMO Block diagram o control system 6. Yawrate and slipslip angle control 7) 6.1. Decoupling control method The vehicle sideslip angle and yawrate can be described as ollows [ 8). ] [ ][ ] β P 1s) P 2s) δ = γ P 3s) P 4s) N z 2) From this matrix, it is understood that two control inputs aect both the vehicle sideslip angle and yawrate. This intererence inluences the vehicle motion control. Then, the controller which takes into consideration this intererence is designed. The control laws o the two control inputs aregiveas δ = δ c G 1s)N z, 21) N z = N c G 2s)δ, 22) where δ c is the control steering angle, N c is the control moment, G 1s) andg 2s) are the controllers. By substituting 21) and 22) or 2), we obtain β = P 1s)δ c P 2s) P 1s)G 1s))N z, γ = P 4s)N c P 3s) P 4s)G 2s))δ. Then the controller G 1s) andg 2s) canbedesigned as ollows G 1s) =P 1 s)p 2s), 23) G 2s) =P 4 s)p 3s). 24) The inluence o the coupling terms are canceled. Fig. 14a) is the block diagram o the control method Yawmoment observerymo) 11) By considering the disturbance moment N d, 8) is rewritten as I dγ dt =2l Y 2l ry r N d N z. 25) Here N d is the disturbance moment such as the road condition variation and the eect o crosswind. By deining the moment caused by lateral orces as N t := 2l Y 2l ry r Copyright c 21 Society o Automotive Engineers o Japan, Inc. All rights reserved

6 and the lumped disturbance moment as N td := N t N d, 25) is simpliied as I dγ dt = N dt N z. 26) By using the moment N z as control input and yawrate γ as measured signal, the disturbance observer can be designed as Fig. 14b). The authors named this speciic disturbance observer as yawmoment observer YMO) in the 11). This YMO can compensate the lumped disturbance and nominalize the system as γ = 1 Nin. 27) I ns 27) is valid in the requency band less than the cuto requency ω c o YMO Lateral orce observer LFO) By considering the disturbance lateral orce, the lateral motion equation 7) is described as dβ ) mv dt γ =2Y 2Y r Y d = 2C β l ) ) V γ δ 2C r β lr V γ Y d,28) where Y d is the disturbance lateral orce caused by road condition variation and crosswind. Here, Y td is deined as Y td = 2C β l ) ) V γ 2C r β lr V γ mv γ Y d. Then, 28) is rewritten as mv β =2C δ Y td. 29) By using the ront steering δ as control input and β as measured signal, the disturbance observer can be designed as Fig. 14b). The authors named this speciic disturbance observer as lateral orce observer LFO). This LFO can nominalize the dynamics as 2C n β = m nv ns 6.4. Experimental veriication The control method shown in Fig. 14a) and the proposed control method combined YMO and LFO shown in Fig. 14b) are compared by experiments. In the proposed method, the controller C β s) issimply designed by proportional control in which the pole o the closed loop is placed to 2.rad/s or nominal plant 3). The controller C γs) is also designed by proportional controller in which the pole o the closed loop is placed to.rad/s or nominal plant 27). The cut o requency o LFO and YMO is set to 1rad/s. In the control, C β s) is designed by PID controller in which the poles o the closed loop are placed to 6.5rad/s or transer unction P 1s). C γs) is also designed by PID controller with 5.5rad/s closedloop pole or transer unction P 4s). The parameters are set to vehicle speed is 12km/h, o vehicle sideslip angle is.35rad, and o yawrate is.15rad/s in experiments. In this paper, experiment vehicle runs on nonpavement road where the grip is lower than the asphalt road at V =12 δin. 3) km/h. The vehicle sideslip angle is measured with optical sensor CORREVIT S4 o the DATRON Co., Ltd. Fig. 15 shows the experimental results without parameter error in cornering stiness CS). Fig. 16 is the case with the 7 % parameter error. As shown in Fig. 15, both the conventional method control) and the proposed method LFOYMO) track the s o yawrate and sideslip angle in the case without parameter variation. On the other hand, in the case with parameter error the conventional method becomes highly oscillatory because the controllers 23) and 24) highly depend on the values o CS. On the other hand, the proposed controllers do not depend on these values except or C n in 3), almost same response with Fig. 15 is obtained even with the parameter variation, as shown in Fig. 16. The small vibration is caused by the roughness o the nonpavement road. Thereore, it can be said that the proposed method achieves higher robustness to the CS variation than the conventional method. 7. Conclusion In this paper, our original EV is explained, which has direct drive inwheel motors and active steering systems. Moreover, our recent studies on pitching, braking, yawing, and sideslip are introduced with experimental results. Acknowledgment Finally, this research was partly supported by Industrial Technology Research Grant Program rom New Energy and Industrial Technology Development Organization NEDO) o Japan and the author would like to thank his ormer students, S.Sato, T.Suzuki, Y.Yamauchi, to help experiments in this paper and H.Sumiya or the help to make the drat o this paper. Reerences 1 ) Y.Hori: Future Vehicle Driven by Electricity and Control Research on FourWheelMotored: UOT Electric March II, IEEE Trans. IE, Vol.51, No. 5, 24 2 ) M.Kamachi, K.Walters: A Research o Direct YawMoment Control on Skippery Road or InWheel Motor Vehicle, EVS22 Yokohama, JAPAN, Oct.2328, pp , 26 3 ) H.Sugai, S.Murata: Inluence o Inwheelmotor to vehicle structure and suspension, JSAE Annual Congress, No , 21 4 ) H.Fujimoto, K.Fujii, N.Takahashi: Road Condition Estimation and Motion Control o Electric Vehicle with Inwheel Motors, JSAE Annual Congress, pp. 2528, 26 5 ) H.Fujimoto, S.Sato: Pitching Control Method Based on Quick Torque Response or Electric Vehicle, in Proc. International Power Electronics Conerence ECCE ASIA, pp , 21 6 ) T.Suzuki, H.Fujimoto: Slip Ratio Estimation and Regenerative Brake Control without Detection o Vehicle Velocity and Acceleration or Electric Vehicle at Urgent Braketurning, in Proc. 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7 LFOYMO LFOYMO a)yawrate LFOYMO). b)sideslip angle LFOYMO). c)yawrate ctr). Fig. 15 Experiment results CS with true value). d)sideslip angle ctr) LFOYMO LFOYMO a)yawrate LFOYMO). b)sideslip angle LFOYMO). c)yawrate ctr). Fig. 16 Experiment results CS with parameter error). d)sideslip angle ctr). on Industrial Electronics 21 Proceedings, Bari, Italy, pp , ) R. Rajamani: Vehicle Dynamics and Control, Springer Science & Business Media, Inc., 26 9 ) K.Fujii, H.Fujimoto: Traction Control based on slip ratio estimation or Electric Vehicle, in Proc. The Fourth Power Conversion Conerence, Nagoya, pp , 27 1) T.Suzuki, H.Fujimoto: Proposal o Slip Ratio Estimation Method without Detection o Vehicle Speed or Electric Vehicle on Deceleration, IEE o Japan Technical Meeting Record, VT724, pp. 7782, 27 in Japanese) 11) H.Fujimoto, T.Saito, T.Noguchi: Motion Stabilization Control o Electric Vehicle under Snowy Conditions Based on YawMoment Observer, in Proc. 8th IEEE International Workshop on Advanced Motion Control AMC 4), Kawasaki, pp.354, 24 Copyright c 21 Society o Automotive Engineers o Japan, Inc. All rights reserved