Rolling Stability Control Based on Electronic Stability Program for In-Wheel-Motor Electric Vehicle

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EVS24 Stavanger, Norway, May 13 - 16, 2009

Rolling Stability Control Based on Electronic Stability Program for In-wheel-motor Electric Vehicle

Kiyotaka Kawashima, Toshiyuki Uchida, Yoichi Hori University of Tokyo, Tokyo, Japan, [email protected]

Abstract

In this paper, a novel robust rolling stability control (RSC) based on electronic stability program (ESP) for electric vehicle (EV) is proposed. Since EVs are driven by electric motors, they have the following four remarkable advantages: (1) motor torque generation is quick and accurate; (2) motor torque can be estimated precisely; (3) a motor can be attached to each wheel; and (4) motor can output negative torque as a brake actuator. These advantages en- able high performance three dimensional vehicle motion control with a distributed in-wheel-motor system. RSC is designed using two-degree-of-freedom control (2-DOF), which achieves tracking capability to reference value and disturbance suppression. Generally, RSC and YSC are incompatible. Therefore, ESP, which is composed of estimation system(S1) and integrated vehicle motion control system(S2) is proposed. A distribution ratio of RSC and YSC is deﬁned based on rollover index (RI) which is calculated in S1 from rolling state information. The effectiveness of proposed methods are shown by simulation and experimental results. Keywords:rolling stability control, electric vehicle, disturbance observer, two-degrees-of-freedom control, vehicle motion control, identiﬁcation

Nomenclature 1 Introduction

ax,ay:Longitudinal and lateral acceleration 1.1 In-wheel-Motor Electric Vehicle’s Advan- ayd:Lateral acceleration disturbance ayth:Critical lateral acceleration tages and Application to Vehicle Motion cf ,cr:Front and rear tire cornering stiffness Control Cr:Combined roll damping coefﬁcient d, df ,dr:Tread at CG, front and rear axle Electric vehicles (EVs) with distributed in-wheel-motor Fxfl,Fxfr,Fxrl,Fxrr:Tire longitudinal forces systems attract global attention not only from the en- Fyfl,Fyfr,Fyrl,Fyrr:Tire lateral forces vironmental point of view, but also from the vehicle Fzfl,Fzfr,Fzrl,Fzrr:Tire normal forces motion control. In-wheel-motor EVs can realize high g:Gravity acceleration performance vehicle motion control by utilizing advan- hc,hcr:Hight of CG and distance from CG to roll center tages of electric motors which internal combustion en- Ir:Moment of inertia about roll axis (before wheel-lift-off) gines do not have. The EV has the following four re- Ir2:Moment of inertia about roll axis (after wheel-lift-off) markable advantages [1]: Iy:Moment of inertia about yaw axis Kr:Combined roll stiffness coefﬁcient • Motor torque response is 10-100 times faster than l, lf ,lr:Wheelbase and distance from CG to front and rear internal combustion engine’s one. This property axle enables high performance adhesion control, skid M,Ms,Mu,:Vehicle, sprung and unsprung mass prevention and slip control. N:Yaw moment by differential torque • V,Vw:Vehicle and wheel speed Motor torque can be measured easily by observing β,γ:Body slip angle and yaw rate motor current. This property can be used for road δ:Tire steering angle condition estimation. ˙ φ, φ:Roll angle and roll rate • ˙ Since an electric motor is compact and inexpen- φth, φth:Threshold of roll angle and roll rate sive, it can be equipped in each wheel. This fea-

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ture realizes high performance three dimensional 2 Electronic Stability Program for vehicle motion control. Electric Vehicle • There is no difference between acceleration and deceleration control. This actuator advantage enables high performance braking control. 2.1 Introduction of Electronic Stability Pro- gram Slip prevention control is proposed utilizing fast torque response [1]. Road condition and skid detection meth- Fig. 1 shows concept of ESP for EV. ESP consists ods are developed utilizing the advantage that torque of two systems; vehicle/road state estimation system can be measured easily [1]. Yawing stability control, (S1) and integrated vehicle motion control system (S2). side slip angle estimation and control methods are also S1 integrates information from sensors (accelerome- proposed by utilizing a distributed in-wheel-motor sys- ter, gyro, GPS, suspension stroke and steering angle tem [2] - [4]. sensors) and estimates unknown vehicle parameters (mass), vehicle state variables (yaw rate, lateral acceleration, roll angle, roll rate and normal forces on tires) 1.2 Background and Purpose of the Research and environmental state variables [7] [12]. According to the information from S1, S2 controls ve- The purpose of this paper is to propose integrated hicle dynamics using RSC and YSC, pitching stability rolling and yawing stability control (RSC and YSC). control (PSC) and anti-slip control (ASC). According to Rollover stability is important for all classes of light- RI, which is calculated by S1, a proper stability control vehicles such as light trucks, vans, SUVs and espe- strategy (YSC, RSC or mixed) is determined. cially, for EVs which have narrow tread and high CG RSC is based on DOB and nominal vehicle state is cal- because EV is suitable for relatively small vehicle and culated by a controller. If there are errors between cal- human height does not change. According to the data culated and actual dynamics, it is compensated by dif- from NHTSA, ratio of rollover accidents of pick ups’ ferential torque. and vans’ crashes in 2002 was only 3% against whole accidents. However, nearly 33% of all deaths from pas- Electronic stability program on EV senger vehicle crashes are due to rollover accidents [5]. Human Therefore, RSC is very important not only for ride qual- S1 S2 maneuver ity but also for safety. Estimation Motion control Vehicle dynamics The RSC system has been developed by several auto- Vehicle parameter motive makers and universities [6] [7]. Rollover detec- mass YSC A tion systems, such as rollover index (RI) [8] and Time- Vehicle state variables RSC S to-rollover (TTR) [9] are proposed for mitigating criti- yaw rate, ay, roll angle, roll rate, RI, Fz cal rolling motion. Environmental state variables PSC C Sensors Every system controls braking force on each wheel in- bank angle, mu dependently and suppresses sudden increase of lateral PSC operates only before vehicle stops acceleration or roll angle. However, since braking force is the average value by pulse width modulation con- Figure 1: ESP based on DOB trol of brake pad, brake system cannot generate precise torque or positive torque. In the case of in-wheel-motor, both traction and braking force can be realized quickly and precisely. In addition to actuator advantages, RSC is designed by utilizing two-degrees-of-freedom (2-DOF) control 2.2 A Scheme of Integrated Vehicle Motion based on disturbance observer (DOB) [10]. For the vehicle motion control ﬁeld, DOB is applied to vehicle Control yaw/pitch rate control [2] [3] and 2-DOF control is applied to the electric power steering control [11]. There Lateral acceleration is composed of vehicle side slip, are three reasons to utilize DOB: 1)disturbance suppres- yaw rate and longitudinal speed. sion, 2)nominalize lateral vehicle model and 3)tracking ˙ capability to reference value. DOB loop that suppresses a =(β + γ)V (1) the effect of disturbance, is faster than outer loop that y achieves tracking capability. Designing DOB for traction force is not applicable for ICEV, because engine If constant vehicle speed is assumed and lateral acceler- torque is not accurately known and long time delay ex- ation is suppressed, yaw rate is also suppressed as long ists. Therefore, DOB is applicable only in case of EVs. as differentiation of side slip is not controlled. This The tracking capability and robustness for lateral accel- physical constraint makes RSC and YSC incompatible. eration disturbance against such as side blast are real- Therefore, rollover detection is necessary for integrated ized by the proposed method. control. In order to detect rollover, Yi proposed RI However, roll and yaw stabilities are incompatible. (0

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Yawing motion: ∗ ˙ =( + ) − ( + ) N =f(RI, NRSC,NYSC,NDOB) Iyγ Fyfl Fyrl lf Fyfr Fyrr lr =RI ∗ N +(1− RI) ∗ N + N (2) lf lr RSC YSC DOB =−2c (β + γ − δ)l +2c (β − γ)l + N (4) f V f r V r

Rolling motion:

γ [ N Pγ Pγ N [ F K n YSC = ¨ + ˙ + − yfb PNγ a M h a I φ C φ K φ M gh sinφ Pa P yN N (5) y s cr y r r r s cr V N [ RI N [ ζ=f( , RSC, ay N N Kyff YSC, DOB) (φ<φ − − ) ayd wheel lift off K N rff RSC ¨ d n = − + PMa Q 2 n N y Mshcray Ir φ Msghcrsinφ Msg cosφ (6) Fay Krfb PNa DOB > 2 y ayd V n n ( ) a a φ>φ − − [P y P yN] wheel lift off Here, these motion equations need to be expressed as Figure 2: Block diagram of integrated vehicle motion control state equations to design observer. Observer gain matrix, however, becomes 2 × 4 matrix if whole equations are combined. To reduce redundancy of designing gain matrix, tire dynamics and rolling dynamics are sepa- rated. A matrix, Art connects two state equations. From eq.(3) and eq.(4), state equation is expressed as, 3 Estimation System ˙xt = Atxt + Btu, (7) y = C x + D u. (8) S1 is composed of vehicle parameters, state variables t t t t and environmental state variables estimation system. In It is noted that there is feedforward term in the transfer this section, vehicle state variable estimation system is function from u to y . Therefore, to eliminate feedfor- mainly introduced. According to the estimated state t ward term and design stable observer, xt vector is de- variables, RI, a distribution ratio of RSC and YSC is ﬁned using differential torque and steering angle as the determined. following equations, where, ˙ T xt = a − c2δ a˙ − c2δ − b1N − c1δ , y y T 3.1 Lateral Acceleration and Roll Angle Ob- yt = ay, u = Nδ , server Fig. 3 shows four wheel model and rolling model of 01 At = , electric vehicle. −a0 −a1 b1 c1 fl Bt = , l Z + + lf a1b1 b0 a1c1 c0

df 1 lr = 10 = 0 Ffl Ct ,Dt c2 . fr M rl V s Ir Cr Kr 2 y 3 Pc Frl Center of gravity

hcr hc 2 Ffr 4cf crl 2(cf lf − crlr) 4 rr = − dr a0 2 , Mu MI V I Frr y y 2 2 Pr 2 ( + )+2 ( + ) Rotational center M cf lf crlr Iy cf cr a1 = , (a)Four wheel model and (b)Rolling model MIyV rotational direction 2(cf + cr) 2(cf lf − crlr) b0 = ,b1 = − , Figure 3: Vehicle model MIy MIyV 4cf crl 4cf crlrl 2cf c0 = ,c1 = ,c2 = , Vehicle motion is expressed as the following three lin- MIy MIyV N ear equations. c0 = c − a0c2,c1 = c − a1c2 Lateral motion: 0 1 ˙ From eq.(7), state space equation is, MV(β + γ)=Fyfl + Fyfr + Fyrl + Fyrr ˙x = A x + A y , (9) lf lf r r r rt t =−2cf (β + γ − δ) − 2cr(β − γ) (3) y = C xr, V V r r (10)

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˙ T ˙ 1.5 where, xr = φ φ ,yr = φ, d 01 00 2 h A = r− s cr ,A = , 1 r K M gh Cr rt Mshcr Rollover threshold − − 0 ayth Ir Ir Ir (wheels lift off) Cr = 01. 0.5 These parameters are based on the experiment vehicle Lateral acceleration(m/s/s) ay=K ”Capacitor-COMS1” developed in our research group. -12 h The method to evaluate the values of cf ,cr are referred tan d 0 to the paper [13], and rolling parameters to the paper 0 0.2 0.4 0.6 0.8 1 [10] Roll angle(rad) It should be noted that lateral acceleration dynamics ex- Figure 4: Equilibrium lateral acceleration in rollover of a sus- pressed as eq.(8) is a linear time varying system de- pending on vehicle speed. The states are observable at pended vehicle various longitudinal speed except for a very low speed. In the following sections, for repeatability reason, experiment has been done under constant speed control. 150 Observer gains are deﬁned by pole assignment.

3.2 Rollover Index 100

RI is a dimensionless number which indicates a danger th

of vehicle rollover. RI is defined using the following Roll rate (deg/s) 50 three vehicle rolling state variables; 1)present state of roll angle and roll rate of the vehicle, 2)present lateral acceleration of the vehicle and 3)time-to-wheel lift. RI 0 is expressed as eq. (11), th −5 0 5 10 Roll angle (deg) | | ˙ + | ˙| | | = φ φth φ φth + ay Figure 5: Phase plane plot of roll dynamics RI C1 ˙ C2 , φ φ ayc th th |φ| ˙ +(1−C1 −C2) , if φ(φ − k1φ) > 0, φ2 + φ˙2 4.1.1 Lateral acceleration disturbance observer ˙ RI =0, else if φ(φ − k1φ) ≤ 0, (11) Based on fig. 6, transfer function from reference lateral acceleration u, δ and ayd to ay is expressed as the fol- where, C1,C2 and k1 are positive constants (0 < lowing equation. Roll moment is applied by differential C1,C2 < 1). torque N ∗ by right and left in-wheel-motors. Reference ayth is defined by vehicle geometry. Fig. 4 shows equi- value of lateral acceleration is given by steering angle librium lateral acceleration in rollover of a suspended and vehicle speed. vehicle. It shows the relation between vehicle geom- etrysuchash, d and K and vehicle states such as φ r n ( + ) and ay. From the static rollover analysis, critical lateral PayN PNay Kff Kfb Payδ a = u + δ acceleration ayth which induces rollover, is defined. y 1+P P n K 1+P P n K Phase plane analysis is conducted using a and roll ayN Nay fb ayN Nay fb yth 1 dynamics (eq. 7). Fig. 5 shows phase plane plot under + a . ˙ 1+ n yd (12) several initial condition (φ, φ) at critical lateral accel- PayN P Kfb ˙ Nay eration. Consequently, φth and φth are definedbythe analysis. Tracking capability and disturbance suppression are two important performances in dynamics system control and can be controlled independently. On the other hand, one-degree-of-freedom (1-DOF) control such as 4 Integrated Motion Control System PID controller loses important information at subtract- ing actual value from reference one. In the control, 4.1 Rolling Stability Control Based on Two- there is only one way to set feedback gain as high to im- prove disturbance suppression performance, however Degrees-of-Freedom Control the gain makes the system unstable. In this section, RSC based on 2-DOF control which Hence 2-DOF control in terms of tracking capability achieves tracking capability to reference value and dis- and disturbance suppression is applied to RSC. Pro- turbance suppression is introduced. posed lateral acceleration DOB estimates external dis- For RSC, lateral acceleration is selected as controlling turbance to the system using information; V , δ, N and parameter because roll angle information is relatively ay. Fig. 6 shows the block diagram of lateral accelera- slow due to roll dynamics (about 100ms). tion DOB.

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a yd Disturbance, which is lower than the cut-off frequency Kff a* * of Q and vehicle dynamics, is suppressed by DOB. In y n N ay Pa Pa N PNa [ y y ] F u Kfb y addition to the function of disturbance rejection, the V plant is nearly equal to nominal model in lower fre-

n n quency region than the cut-off frequency. Therefore the Pa Pa N [ y y ] proposed RSC has the function of model following control. ^ ayd 4.2 Yawing Stability Control Figure 6: Block diagram of lateral acceleration DOB As fig. 2 shows, YSC is yaw rate control. Yaw rate reference value is defined by steering angle and longitudinal vehicle speed. Transfer function from yaw rate ayd reference and steering angle is expressed as the follow- Kff ing equation. * n N ay a a PNa [P yP yN] F u Kfb y v n V P P (K + K ) = γN Nγ ff fb + Pγδ n n γ u δ.(19) a a n n [P yP yN] 1+ 1+ PγNPNγKfb PγNPNγKfb Q a > yd 5 Simulation Results Figure 7: Block diagram of 2-DOF for RSC based on DOB Three dimensional vehicle motion simulations have been conducted with combination software of Car- Sim7.1.1 and MATLAB R2006b/Simulink. At first, the effectiveness of RSC is verified. Lat- Estimated lateral acceleration disturbance aˆ and a eral acceleration disturbance is generated by differen- yd y tial torque for repeatability reason of experiments. In are expressed as the simulation, lateral blast is generated at straight and ∗ aˆ = a − P n N − P n δ, (13) curve road driving, the proposed DOB suppresses the yd y ayN ayδ disturbance effectively. = ∗ + + ay PayN N Payδδ ayd. (14) To show the effectiveness of ESP, lateral acceleration response and trajectory at curving are compared. It is shown that lateral acceleration is unnecessarily sup- P n P pressed only with RSC, however, tracking capability to ˆ = Nay Nay − 1 +( − n ) + yaw rate reference is achieved by ESP. ayd n ay Payδ Payδ δ ayd . (15) PNay PNay In eq. (15), the first and the second terms are modeling 5.1 Effectiveness of RSC errors and the third term is lateral disturbance. If modeling error is small enough, ayth is approximately equal 5.1.1 Vehicle Stability under Crosswind Distur- to actual lateral acceleration disturbance. bance Vehicle stability of RSC under crosswind disturbance is 4.1.2 Disturbance suppression and normalize of demonstrated. At first, the vehicle goes straight and a roll model driver holds steering angle (holding steering wheel as 0 deg). Under 20 km/h vehicle speed control, crosswind Fig. 7 shows the proposed 2-DOF control for RSC. is applied during 3-6 sec. Fig. 8 shows the simulation Estimated lateral acceleration disturbance is fedback to results. lateral acceleration reference multiplied by filter Q.

1 0.3 ∗ Disturbance No RSC Disturbance No RSC = − ˆ roll moment With RSC roll moment With RSC ay v Qayd. (16) 0.2 0.5

Filter Q is low pass ﬁlter and expressed as the following 0.1 equation [14]. In this study, the cut-off frequency is set 0 as 63 rad/s. 0 Yaw rate (rad) Lateral acceleration(m/s/s) -0.5 N−r k 1+ =1 a (τs) -0.1 Q = k k , (17) N -1 1+ ( )k 2 4 Time(s) 6 8 10 -0.2 k=1 ak τs 2 4 Time(s) 6 8 10 (a)Lateral acceleration where r must be equal or greater than relative order of (b)Yaw rate the transfer function of the nominal plant. Substituting eq. (16) to eq. (13), the following equation is deﬁned. Figure 8: Simulation result of RSC: Disturbance suppression = + n +(1− )ˆ at straight road drive ay v Payδδ Q ayd. (18)

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When proposed RSC is activated, the proposed lateral 6

acceleration DOB detects the lateral acceleration distur- 4 bance and suppresses it. Then, disturbance is applied at curve road driving. Un- 2 der 20km/h constant speed control as well, 180 deg step steering is applied with roll moment disturbance dur- 0 ing 3-6 sec. Fig. 9 shows decrease of lateral accelera- -2

tion since disturbance is rejected perfectly by differen- Lateral acceelration(m/s/s) tial torque with RSC. The robustness of RSC is veriﬁed -4 No RSC with simulation results. With RSC RSC reference -6 3 1 4 6 8 Time(s)10 12 14 Disturbance Disturbance 2.5 roll moment roll moment 0.8 2 Figure 10: Simulation result of RSC: tracking capability to

1.5 0.6 reference 1

0.4Yaw rate 0.5

Lateral acceleration 0 6 0.2 0.04 -0.5 No RSC No RSC With RSC With RSC 5 -1 0 0.03 0 2 4 Time(s) 6 8 10 0 2 4 Time(s) 6 8 10 4 (a)Lateral acceleration (b)Yaw rate 0.02 3

0.01 Figure 9: Simulation result of RSC: Disturbance suppression Roll angle (rad) at curving 2 Lateral acceleration (ms/s/s) 0 1 Without control Without control With ESP With ESP With RSC only With RSC only -0.01 0 2 4 6 Time(s) 8 10 12 2 4 6 Time(s) 8 10 12 (a)Lateral acceleration (b)Roll angle 5.1.2 Tracking capability to reference value 2 14 12

In this section, tracking capability of RSC to reference 1.5 value is verified with simulation results. Under 20km/h 10 8 vehicle speed control, 180 deg sinusoidal steering is ap- 1 plied and reference value of lateral acceleration is 80% Y (m) 6 Yaw rate (rad/s) 4 of nominal value. Fig. 10 shows that lateral accelera- 0.5 Without control Without control tion follows reference value with RSC. 2 With ESP With ESP With RSC only With RSC only 0 0 2 4 6 Time(s) 8 10 12 0 5 10 X (m) 15 20 5.2 Effectiveness of ESP (c)Yaw rate (d)Trajectory Rollover experiment can not be achieved because of Figure 11: Simulation result of ESP: Step steering maneuver safety reason. Under 20km/h constant speed control, 240 deg step steering is applied. From fig. 16, with only RSC case, even though the danger of rollover is not so high, lateral acceleration is strongly suppressed At first, disturbance suppression performance and and trajectory of the vehicle is far off the road. On the tracking capability to reference value are verified with other hand, with ESP case, the rise of lateral accelera- experimental results. Then, effectiveness of ESP is tion is recovered and steady state yaw rate is controlled demonstrated. In the experiment, since vehicle rollover so that it becomes close to no control case. experiment is not possible due to safety reason, step response of lateral acceleration and yaw rate are evalu- ated. 6 Experimental Results 6.2 Effectiveness of RSC 6.1 Experimental setup 6.2.1 Vehicle Stability under Crosswind Distur- A novel one seater micro EV named ”Capacitor bance COMS1” is developed for vehicle motion control experiments. The vehicle equips two in-wheel motors in the For repeatability reason, roll moment disturbance is rear tires, a steering sensor, an acceleration sensor and generated by differential torque. Under 20 km/h con- gyro sensors to detect roll and yaw motion. An upper stant speed control, roll moment disturbance is applied micro controller collects sensor information with A/D from 1 sec. The disturbance is detected by DOB and converters, calculates reference torques and outputs to compensated by differential torque of right and left in- the inverter with DA converter. In this system, sampling wheel motors. Here, the cut-off frequency of the low time is 1 (msec). pass filter is 63 rad/s. Fig. 12 shows the vehicle control system and TABLE I Fig. 13 shows disturbance suppression during straight shows the specifications of the experimental vehicle. road driving. Step disturbance roll moment (equivalent

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1.5 0.2 Disturbance roll moment Disturbance roll moment 0.15 1

0.1 0.5 0.05

0 0

Shift SW D/R

Lateral acceleration(m/s/s) -0.05

Acc/Run/Start SW -0.5 Yaw rate(rad/s) -0.1 D N R -1 Without control Without control -0.15 three-phase With FB With FB 200V ECU With FB+DOB With FB+DOB 6channel -0.2 -1.5 0.5 1 1.5 2 2.5 0.5 1 1.5 2 2.5 Time(s)

DI Time(s) Charger keypad PC/104 Monitor CCN (b)Yaw rate Super 8channel (a)Lateral acceleration

AD LINUX Capacitor PC Figure 13: Experimental result of RSC: Disturbance suppres-

I,V I,V 25F counter DA DO sion at straight road drive 2channel 2channel

DSP DSP 5channel Controller Controller

2 2 Disturbance Disturbance roll moment roll moment HL DI AD 2channel Torque 1.5 1.5 11channel PIC Phase Run/Stop

ErrReset 1 1

0.5 0.5

Figure 12: Control system of experimental vehicle Normalized yaw rate

No Dist with RSC No Dist with RSC Normalized lateral acceleration 0 Dist with RSC 0 Dist with RSC Dist without RSC Dist without RSC

0 2 4 Time(s) 6 8 0 2 4 Time(s) 6 8 Table 1: Drive train specification of experimental vehicle (a)Lateral acceleration (b)Yaw rate Motor Figure 14: Experimental result of RSC: Disturbance suppression at curve road driving Category IPMSM Phase/Pole 3/12 Rating power/Max 0.29kW/2kW shows that in the case with RSC, tracking capability to Max torque 100Nm reference value is achieved. Max velocity 50km/h Inverter 6.3 Effectiveness of ESP Switching Hardware MOS FET Effectiveness of ESP is demonstrated by experiments. Control method PWM vector control For safety reason, rollover experiment is impossible. Therefore, experimental condition is the same as 5.2. Under 20km/h constant speed control, 180 deg step steering is applied. to 0.5m/s2 ∗ h r) is applied around 1 sec. In the case Fig. 16 shows that in the case with only RSC, lateral c acceleration and yaw rate are strongly suppressed. On without any control and only with FB control of RSC, the other hand, in the case with ESP, yaw rate is recov- lateral acceleration is not eliminated and vehicle trajec- ered close to reference value. In addition, the rise of tory is shifted in a wide range. On the other hand, in the lateral acceleration is also recovered and stable corner- case with DOB, disturbance is suppressed and vehicle ing is achieved with ESP. trajectory is maintained. Fig. 14 shows the experimental results of disturbance suppression at curve road driving. Under 20 km/h con- 7 Conclusion stant speed control, 240 deg steering is applied and disturbance is applied at around 2.5 sec. In this case, data In this paper, a novel RSC based on ESP utilizing dif- is normalized by maximum lateral acceleration. In the ferential torque of in-wheel-motor EV is proposed. Ef- case with RSC DOB, whole effect of disturbance is sup- fectiveness of novel RSC designed by 2-DOF control is pressed as no disturbance case. In the case without verified with simulation and experimental results. Then RSC, lateral acceleration decreases about 25% and ve- incompatibility of RSC and YSC is described and ESP hicle behavior becomes unstable. is proposed to solve the problem utilizing RI which is calculated using estimated value of estimation system of ESP. Experimental results validates the proposed 6.2.2 Tracking capability to reference value ESP. In the previous section, since it was assured that the in- ner DOB loop is designed properly, tracking capability to reference value is verified with experimental results. Acknowledgments 180 deg sinusoidal steering is applied and reference lateral acceleration is 80% of nominal value. The outer The author and the work are supported by Japan Society loop is designed with pole root loci method. Fig. 15 for the Promotion of Science.

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6 Without RSC [6] E. K. Liebemann, ”Safety and Performance Enhancement: With RSC Reference The Bosch Electronic Stability Control(ESP)”, SAE Techni- 4 cal Paper Series, 2004-21-0060, 2004.10 2 [7] Hongtei E. Tseng, et al, ”Estimation of land vehicle roll and pitch angles”, Vehicle System Dynamics, Vol.45, No.5, 0 pp.433-443, 2007.05 2 [8] Kyongsu Yi, et al, ”Uniﬁed Chassis Control for Rollover Pre-

4 vention, Maneuverability and Lateral Stability”, AVEC2008, Lateral acceleration(m/s/s) pp.708-713, 2008.10 6 [9] Bo-Chiuan Chen, Huei Peng,”Differential-Braking-Based

6 8 10 12 Rollover Prevention for Sport Utility Vehicles with Human- Time(s) in-the-loop Evaluations”, Vehicle System Dynamics, Vol.36, Figure 15: Experimental result of RSC: tracking capability No.4-5, pp359-389, 2001. to reference [10] Kiyotaka Kawashima, Toshiyuki Uchida, Yoichi Hori, ”Rolling Stability Control of In-wheel Electric Vehicle Based on Two-Degree-of-Freedom Control”, The 10th International Workshop on Advanced Motion Control, pp. 751-756, Trento 5 0.1 Italy, 2008.03

4 0.08 [11] Bilin Aksun Guvenc, Tilman Bunte, Dirk Odenthal and Lev- ent Guvenc, ”Robust Two Degree-of-Freedom Vehicle Steer- 0.06 3 ing Controller Design”, IEEE Transaction on Control Sys- 0.04 2 tems Technology, Vol. 12, No. 4, pp.627-636, 2004.07 Roll angle(rad) 0.02 [12] A. Hac, et. al, ”Detection of Vehicle Rollover”, SAE Techni- Lateral acceleration(m/s/s) 1 Without control Without control cal Paper Series, 2004-01-1757, SAE World Congress, 2004. With ESP 0 With ESP With RSC only With RSC only 0 0 2 4 Time(s) 6 8 10 2 4 Time(s) 6 8 10 [13] N. Takahashi, et. al, ”Consideration on Yaw Rate Control for (a)Lateral acceleration (b)Roll angle Electric Vehicle Based on Cornering Stiffness and Body Slip 20 Angle Estimation”, IEE Japan, IIC-06-04, pp.17-22, 2006

[14] Takaji Umeno, Yoichi Hori, ”Robust Speed Control of DC 15 Servomotors Using Modern Two Degrees-of-Freedom Con- 0.8 troller Design”, IEEE Transaction Industrial Electronics,

0.6 10 Vol.38, No. 5, pp.363-368, 1991.10

0.4 Y (m) 5

Yaw rate(rad/s) 0.2

0 Without control 0 With ESP Without control With RSC only -0.2 With ESP Authors 0 2 4 6 8 10 Time(s) With RSC only -5 (c)Yaw rate -5 0 5 X (m) 10 15 20 He received B.C. and M.S. degrees (d)Trajectory in E.E. department, the University of Figure 16: Experimental result of ESP: Step steering maneu- Tokyo in 2004 and 2006, and pro- ver ceeded to Ph.D. course, the University of Tokyo. He is now researching the motion control of electric vehicle. References

[1] Yoichi Hori, ”Future Vehicle driven by Electricity and Control-Research on Four Wheel Motored UOT Electric March II”, IEEE Transaction on Industrial Electronics, He is working as a engineering official Vol.51, No.5, pp.954-962, 2004.10 in E.E. department, the University of [2] Hiroshi Fujimoto, Akio Tsumasaka, Toshihiko Noguchi, Tokyo ”Vehicle Stability Control of Small Electric Vehicle on Snowy Road”, JSAE Review of Automotive Engineers, Vol. He received Ph.D degree in E.E. from 27, No. 2, pp. 279-286, 2006.04 the UT in 1983 and became a Profes- [3] Shinsuke Satou, Hiroshi Fujimoto, ”Proposal of Pitching sor in 2000. IEEE Fellow. He is now Control for Electric Vehicle with In-Wheel Motor”, IIC-07- 81 IEE Japan, pp.65-70, 2007.03 (in Japanese). an AdCom member of IEEE-IES. He is [4] Peng He, Yoichi Hori, ”Improvement of EV Maneuverability the President of IEE-Japan IAS in 08’- and Safety by Dynamic Force Distribution with Disturbance 09’. His research fields are control the- Observer”, WEVA-Journal, Vol.1, pp.258-263, 2007.05 ory and its industrial application to EV, [5] National highway traffic safety administration, Safercar pro- mechatronics, robotics, etc. gram, http://www.nhtsa.gov/

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