traction and yaw-rate control of electric vehicle with slip-ratio and cornering stiffness estimation

1、Proceedings of the 2007 American Control Conference Marriott Marquis Hotel at Times SquareNew York City, USA, July 11-13, 2007FrC06.5Traction and Yaw-rate Control of Electric Vehicle with Slip-ratio and Cornering Stiffness EstimationHiroshi Fujimoto, Kiyoshi Fujii, and Naoki TakahashiVAbstract In tr

2、action control systems of vehicles, it is gener- ally required to detect vehicle speed in order to obtain the slip- ratio. However, it is hard to measure vehicle speed directly. In the first part of this paper, novel estimation method of slip-ratio is proposed without detecting the vehicle speed. Ba

3、sed on this estimation, a slip-ratio controller is developed with feedback linearization. In the second part, a novel DYC is proposed with the adaptive observer which can identify the front and rear cornering stiffness independently as well as it can estimate the body side-slip angle. The advantages

4、 of proposed methods are verified by simulations and experiments with an electric vehicle which has two in-wheel motors.ZM VWT r FdFig. 1. Vehicle poses the slip-ratio estimation method without vehicle speed detection. Next, this method is applied to slip-ratio control with feedback lineari

5、zation.In the second part of this paper, a novel estimation method of the cornering stiffness coefficients is proposed. These unknown parameters which depend on the road condition are important in lateral dynamics of vehicles. Authors have proposed an adaptive direct yaw control (DYC) based on the c

6、ornering stiffness estimation in 6. This method had good control performance on dry and snowy road in experiments. However, it was assumed that cornering stiffness coefficients of front and rear wheels are identical. By this assumption, the parameter identification problem became much simpler becaus

7、e yawing dynamics can be decoupled from the side- slip angle. In this paper, the above assumption is relaxed to develop an independent identification method of front and rear cornering stiffness. This method also enables the precise estimation of side-slip angle by an adaptive observer. Moreover, th

8、e observability of system is enhanced by the lateral acceleration measurement. Experiments of yaw-rate control are performed to show the advantages of proposed methods. The estimation and control technologies of vehicle side-slip and yaw-rate are very important components for the vehicle stability a

9、nd safety driving 7, 8.II. SLIP-RATIO ESTIMATION AND CONTROL WITHOUT VEHICLE SPEED DETECTIONA. Longitudinal motion dynamicsAs shown in Fig. 1, the longitudinal motion equations both of wheel and vehicle can be described asI. INTRODUCTIONFrom the point of view of control engineering, Electric vehicle

10、s (EVs) including battery, fuel-cell, and hybrid vehi- cles have very attractive potential. Since electric motors and inverters are utilized in drive system, they have great advan- tages over internal combustion engine vehicles (ICVs) such as quick and comprehensible torque response and individual c

11、ontrol of each wheel 1. Although several control methods have already been proposed using these merits 2, 3, their controllers require some immeasurable parameters such as vehicle velocity, slip angle, or cornering stiffness.Authors have proposed simple controllers for EVs with in- wheel motors base

12、d on double disturbance observers (DOB) in 4. The proposed control algorithm never required these parameters. First, new anti-skid control was proposed with inner-loop DOB to control longitudinal motion. The stability robustness was theoretically guaranteed by modeling the road condition change as i

13、nertia variation with dead-time. Second, as outer-loop lateral controller, robust direct yaw-moment control (DYC) was proposed based on yaw-moment observer (YMO). The observer tried to nominalize the yawing dynam- ics by compensating the unknown nonlinear lateral force and disturbance yaw-moment as

14、lumped disturbance.In the first part of this paper, a novel traction control system is proposed based on slip-ratio estimation. In order to calculate slip-ratio, the vehicle speed have to be detected. In the conventional slip-ratio controller, it is measured from the speed of non-driven wheel 5. How

15、ever, this method is not applicable when the vehicles decelerate by brakes in all wheels or accelerate by 4WD systems. The speed detection through accelerometer cannot avoid the problem of speed offset by the long-time integral calculation. Then, this paperJ = T rFd, M V = Fd,where J is the wheel in

16、ertia, is the wheel speed, T is(1)(2)the motor torque, r is the radius of tire, Fd is the driving force, M is the vehicle mass, and V is the vehicle speed. The slip-ratio is defined asH. Fujimoto, K. Fujii and N. Takahashi are with Department of Electrical and Computer Engineering, Yokohama National

17、 University, Yokohama 240- 8501, Japan Vw V := max(V , V, ) ,Vw := r(3)w1-4244-0989-6/07/$25.00 2007 IEEE.5742FrC06.5T*+ 1 w Vehicle Model VwrT* -JwsVrZ ZNOm-lFig. 3.Proposed slip-ratio estimator (SRE). FdMsP(s)DFig. 2. Block diagram of vehicle model.1Jns+T*w+where V is the wheel speed

18、 and 1 is the small constantwto avoid zero denominator. Because this paper deals with+-Jnsacceleration only, we assume that max(V ,V ) = V all thewwtime. In the following simulations, Magic Formula is adopted as the model between friction coefficient and slip-ratio . With this and normal force N , t

19、he block diagram of plant is obtained as Fig. 2.By differentiating (3) and substituting (1) and (2), the new non-linear model is obtained as d lFig. 4.Slip-ratio estimation by disturbance observer.T + r2MJ + r2M (1 )T + r2M J() =.(4)C. Slip-ratio estimation with DOB (for comparison)In order to compa

20、re the proposed method with another method which does not consider the second term of (4), the slip-ratio is estimated by disturbance observer (DOB). When the second term is neglected as = 0, the dynamics of (4) becomesB. Slip-ratio estimator (proposed method)The second term of (4) appears only when

21、 is varied. Because it becomes zero in steady-state condition, this term is missed in previous works such as 1. Then in this section, novel estimation method is proposed based on this newJn = T + r2M T d,(8):= J + r2M (1 n) is the nominal value ofmodel. From (4), the state equation on is obtainedasw

22、here JnJ(). From DOB shown in Fig. 4, the disturbance term d = = Jr2M can be estimated. Therefore, the slip-ratio can be estimated byTr2M r2M . +1+ (5)d r2M = ,(9)The right-hand side can be obtained from sensorsignals except for although it has nonlinearity. Then, asshown in Fig. 3, this paper propo

23、ses the slip-ratio estimator (SRE) as follows.where is calculated from pseudo-derivative by high-pass filter with time constant . The “calculator” in Fig. 4 means(9) and represents the variation of J() from Jn 6.= + J TJn J() J()1+ (6)=(10)r2Mr2MIII. VERIFICATION OF SLIP-RATIO ESTIMATION ANDCONTROLA

24、. Simulation of slip-ratio estimationIn this section, the slip-ratio estimation methods both of Fig. 4 and Fig. 3 are verified through simulations. From experiments, the simulation parameters are determined toJ = 1.0Nms2, Jn = 20.3Nms2, M = 420kg, r =0.22m. The road condition is assumed to be low ro

25、adIn order to analyze the convergence, the estimation error is defined as e(t) = . By subtracting (6) from (5), it can be described asd e(t)= e(t).(7)dtThen, the error converges to zero when 0. Because thispaper assumes 0, this estimator should turn on only when 0. However, when the vehicle is accel

26、erating, is positive almost all the time. becomes negative only when the vehicle recovers adhesion after the skid. If the error converges to zero during the skid with 0, (7) indicates that the error keeps zero even when re-adhesion with 0. Thus, the SRE is activated all the time in this paper.max= 0

27、.2 from t = 0 to 3s and high surface withmax= 1.0 from t = 3 s. The torqueroad surface withcommand T =100Nm is given as step-type function. The sampling frequency is 10kHz.Fig. 5 shows estimated slip-ratio by DOB and SRE. As shown in Fig. 5(a), DOB can not estimate the slip-ratio5743calculator 1ts+1

28、 sts+1estimatorfunctionSlip Ratio1VmlVw-VVwFrC06.5noise which causes the big ripple of by the division of 1/in (9).On the other hand, the proposed SRE does not need to have the slow filter because is obtained from the integral of the right-hand side of (6). Then, the cutoff of the high- pass filter

29、is set to 500rad/sec for detection in Fig. 3.As shown in Fig. 6(b), the smooth and exact estimation is obtained by the proposed SRE even in the transient of re- adhesion.C. Slip-ratio control without vehicle speed detectionIn 6, the authors have proposed anti-skid control without vehicle speed detec

30、tion. In this method, disturbance estima- tion dof Fig. 4 is fed back to torque command T in orderto reduce the torque when the vehicle loses its adhesion. Although this method can prevent skid with simple control structure, it is not able to achieve the maximum acceleration because it does not cont

31、rol slip-ratio directly.In this section, a novel slip-ratio control without vehicle speed detection is proposed based on the proposed SRE. By applying the feedback linearization control (11) to the nonlinear plant (5) as shown in the minor-loop of Fig. 8,the dynamics from new control input to the sl

32、ip-ratio is linearized as = .0 l ll1.510.5 0-0.5-100.5 1 1.5 2 2.5 3 3.5 4 4.5 5Timesec(a) DOB0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5Timesec(b) SREFig. 5.Simulation results of slip-ratio estimation.22llll1.51.5110.50.500-0.5-0.5-10-1 00.5 1 1.5 22.5 3 3.5 4 4.5 50.5 1 1.5 2 2.5

33、3 3.5 44.5 5TimesecTimesec(a) DOB(b) SREFig. 6. Experimental results of slip-ratio estimation.steering angle sensordnote PCProgramLRcontroller controllerlogging data JqLqRBattery 12V 6T = r2M + 1+ (11)2Rr MLinverterinverterLmotorRmotor =Then, by using the linear proportionalcontrollerKp( ) as outer-

34、loop controller C(s), the closed-loop transfer function becomes 1st-order system as Kp Fig. 7. Experimental setup.correctly when is varied by the re-adhesion because the term of is not considered. On the other hand, the proposed method which considers can estimateslip-ratio preciselyeven in the tran

35、sient. Although / becomes negative during =(12)s + KpWhen the slip-ratio can not be measured directly, of the outer-loop controller is replaced to the estimated slip- ratiowhich is obtained from SRE. In Fig. 8, of (11) can be obtained by pseudo-derivative with high-pass filter if the resolution of e

36、ncoder is high enough. However, we approximately calculate it with feedforward manner as 3.2s by re-adhesion, the estimation error keepst = 3zero since it converges before t = 3s. After that, / isgetting positive which satisfies convergence condition.B. Experiment of slip-ratio estimationTo verify t

37、he proposed control algorithm, an experimental setup was constructed based on a commercial EV “QUNO” made by CQ Motors Co., Ltd. which has two in-wheel motors (Fig. 7). We built motor controllers and inverters with Myway Labs. Co., Ltd. The torque controller with current vector control, slip-ratio e

38、stimation, and slip-ratio controller are implemented as software in two DSPs. The switching frequency of PWM inverters is 10 kHz. The vehicle speed is obtained by the integral calculation of accelerometer only for the evaluation although it is not required in the proposed method.In experiments, the

39、vehicle runs on a slippery board before t = 3s and dry road thereafter with constant torque command T =80Nm. Fig. 6 shows the experimental results both of DOB and SRE. In the case of DOB, the bandwidth offilter had to set narrow as 10rad/sec to detect from low- resolution encoder. Even with this fil

40、ter, includes remainedTJ + r2M (1 ) =(13)because our experimental setup has low-resolution encoder.Fig. 9 shows the simulation results on low road surface with max = 0.2. From t = 0, the constant torque reference is given as T = 80Nm. When the slip-ratio controller turns of at t = 0.03 with Kp = 70,

41、 the slip-ratio quickly converges to its reference = 0.2.In the experiment, the slip-ratio controller turns on at t =2.2 s. As shown in Fig. 10, the slip-ratio converges to =0.2 although it still has small ripple.IV. DYC WITH CORNERING STIFFNESS AND SIDE-SLIPANGLE ESTIMATIONA. Lateral motion dynamic

42、sAs shown in Fig. 11, the lateral motion dynamics of vehi- cle is modeled as the equivalent two-wheel model 9 which5744Slip Ratio l,lSlip Ratio l,lSlip Ratio l,lSlip Ratio l,lacceleration andyaw-rate sensorax ,ay, glFrC06.5xlv* +rM2 +PlantPVNC(s)?N&-+T*2Yf.wPQPNKPGTEQORGPUCVKQPHPFlfN?Slip Ratio Esti

43、matorVOyFig. 8.Slip-ratio control without vehicle speed detection.N N?2YrlrV10.40.35 llWheel Speed Vehicle Speed0.80.6Fig. 11. Equivalent two-wheel vehicle model.0.40.2Fig. 12 shows the block diagram of DYC with YMO. By using the moment Nz as control input and yaw-rate as measur

44、edsignal, this YMOcancompensatetheyaw-moment Nt and nominalize the inner-loop system as00000.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5Timesec(a) Slip-ratio.Timesec(b) Wheel & vehicle speed.Fig. 9.Simulation results of slip-ratio control.1(s) Nin(s).(18)14

45、.543.532.521.510.500InsWheel Speed Vehicle Speedl l0.8(18) is valid within the cut-off frequency of YMO c 10.0.6B. Cornering-stiffness and Slip-angle EstimationIn 6, the authors have proposed an adaptive DYC with cornering stiffness estimation. In this method, we assumed that lf = lr = l and Cf = Cr

46、 = C in order to simplify the model and neglect the terms on side-slip angle from (16)as0.40.200 0.5 1 1.5 2 2.5 3 3.5 40.5 1 1.5 2 2.5 3 3.5 4 4.5 5TimesecTimesec(a) Slip-ratio.(b) Wheel & vehicle speed.Fig. 10. Experimental results of slip-ratio control.4l2V 2l . (19)Nt(t) = (t), = C, (s) = F (s)i

47、s sometimes called as half vehicle model. The linearized dynamics of the lateral motion is derived asThe cornering stiffness is estimated by recursive least-square (RLS) algorithm. Fig. 13 shows the block diagram of DYC with this cornering stiffness estimation. In the block ofd dt+ = 2(Yf + Yr)MV(14

48、)“NTE”, Nt(t) is calculated on-line from estimatedand the measured (t) by (19).However, the front and rear cornering stiffness coefficientsCdI= N N ,(15)I is to beztdtwhere is the side-slip angle, is the yaw-rate,the vehicle inertia. The vehicle speed V is assumedCf and Cr sometimes have different v

49、alues. If we try to estimate Cf and Cr independently, the terms on cannot be neglected. Then, the authorshave proposedthe simultaneous estimation methods of Cf, Cr and in 11, 12. From (16),(17) can be written asconstant. Nz is the control moment which is generated by theforce difference between the

50、left and right in-wheel motors. Nt := 2lrYr 2lf Yf is the moment generated by tire and road contact, where Yf and Yr are the lateral force of frontand rear wheels, respectively. lf and between the center of mass and wheels. The Nt in (15) can be modeled aslrarethedistanceNt(t) = T (t),T= Cf,C r,(20)

51、2 + l lf(s)= F (s)Vf.(21)ll r 2 lN = 2C + f l 2C lr, (16)lrrtffrVVVBased on the above model, the cornering stiffness coeffi- cients Cf and Cr are adaptively identified by RLS algorithm aswhere Cf and Cr are the front and rear cornering stiffnesses, respectively 9. From (15), Nt can be estimated by y

52、aw- moment observer (YMO) 6 as (k 1)(k)(k) = (k 1) Nt = F (s)(Nz I )(17) + T (k)(k 1)(k)T (k)(k 1) y(k)where F (s) = c/(s + c) is a filter to calculate .(22)5745Slip Ratio lSlip Ratio lWheel, Vehicle Speedm/sWheel, Vehicle Speedm/sT*Jw+r2M(1-l*)FrC06.5dddgaygaygNinNgggNKNzPin-+KNzPf+-*inNzPIft s+1P+

53、PI+-t s+1f+PIfobserver-CSIDg+ -NVbCNTECSIDInnsgNVNt gCf CrNTE wc s+wcP: PlantCSID: Cornering Stiffness Identification NTE: Nt EstimationP: PlantCSID: Cornering Stiffness Identification NTE: Nt EstimationFig. 12. Yaw-moment observer (YMO).Fig. 13. Cornering-stiffness estimation (CSE).Fig. 14.Proposed adaptive