外文翻譯--利用輪胎側(cè)向力傳感器并使用最小二乘法和卡爾曼濾波方法估計電動汽車的側(cè)滑角和側(cè)傾角（英文）

1、988 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 3, MARCH 2013Estimation of Sideslip and Roll Angles of Electric Vehicles Using Lateral Tire Force Sensors Through RLS and Kalman Filter ApproachesKanghyun Nam

2、, Student Member, IEEE, Sehoon Oh, Member, IEEE, Hiroshi Fujimoto, Member, IEEE, and Yoichi Hori, Fellow, IEEEAbstract—Robust estimation of vehicle states (e.g., vehicle sideslip angle and roll angle) is essential for ve

3、hicle stability control applications such as yaw stability control and roll stability control. This paper proposes novel methods for estimating sideslip angle and roll angle using real-time lateral tire force measurement

4、s, obtained from the multisensing hub units, for practical applica- tions to vehicle control systems of in-wheel-motor-driven electric vehicles. In vehicle sideslip estimation, a recursive least squares (RLS) algorithm w

5、ith a forgetting factor is utilized based on a linear vehicle model and sensor measurements. In roll angle estimation, the Kalman filter is designed by integrating available sensor measurements and roll dynamics. The pro

6、posed estimation methods, RLS-based sideslip angle estimator, and the Kalman filter are evaluated through field tests on an experimental electric vehicle. The experimental results show that the proposed estimator can acc

7、urately estimate the vehicle sideslip angle and roll angle. It is experimentally confirmed that the estimation accuracy is improved by more than 50% comparing to conventional method’s one (see rms error shown in Fig. 4).

8、 Moreover, the feasibility of practical applications of the lateral tire force sensors to vehicle state estimation is verified through various test results.Index Terms—Electric vehicles, Kalman filter, multisensing hub (

9、MSHub) unit, recursive least squares (RLS), roll angle, sideslip angle.NOMENCLATUREax Longitudinal acceleration at center of gravity (CG) (m/s2). ay Lateral acceleration at CG (m/s2). aym Sensor measurement of lateral ac

10、celeration (m/s2). d Track width = 1.3 m. g Acceleration due to gravity = 9.81 m/s2. hroll Height of the center of sprung mass above roll center (RC) = 0.32 m.Manuscript received May 10, 2011; revised November 23, 2011;

11、accepted January 27, 2012. Date of publication February 24, 2012; date of current version October 16, 2012. This work was supported in part by the Industrial Technology Research Grant Program from the New Energy and Indu

12、strial Technology Development Organization (NEDO) of Japan. K. Nam and S. Oh are with the Department of Electrical Engineering, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan (e-mail: nam@

13、hori.k.u-tokyo.ac.jp; sehoon@hori.k.u-tokyo.ac.jp). H. Fujimoto and Y. Hori are with the Department of Advanced Energy, Graduate School of Frontier Sciences, The University of Tokyo, Chiba 277- 8561, Japan (e-mail: fujim

14、oto@k.u-tokyo.ac.jp; hori@k.u-tokyo.ac.jp). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2012.2188874hRC Height of t

15、he RC above the ground = 0.21 m. i 1, 2, 3, and 4 corresponding to front left, front right, rear left, and rear right (= fl,fr,rl,rr). lf Distance from CG to front axle = 1.013 m. lr Distance from CG to rear axle = 0.702

16、 m. vx Longitudinal velocity at CG of vehicle (m/s). vy Lateral velocity at CG of vehicle (m/s). ? vy Estimated lateral vehicle velocity (m/s). m Total mass of vehicle = 875 kg. ms Sprung mass = 670 kg. Ci Tire cornering

17、 stiffness at the ith tire (N/rad). Cf Front tire cornering stiffness = 11 200 N/rad. Cr Rear tire cornering stiffness = 31 600 N/rad. Croll Roll damping coefficient = 3200 N · m · s/rad. F x i Longitudinal tir

18、e force at the ith tire (N). F y i Lateral tire force at the ith tire (N). F y left Lateral tire force on the left track wheels (= F y fl +F y rl) (N). F y right Lateral tire force on the right track wheels (= F y fr + F

19、 y rr) (N). Ix Roll moment of inertia = 250 kg · m2. Iz Yaw moment of inertia = 617 kg · m2. Kroll Roll stiffness coefficient = 12 000 N · m/rad. L Observer gain matrix. Mx Roll moment (N · m). Mz Yaw

20、 moment (N · m). αi Slip angle at the ith tire (rad). αf Front tire slip angle (rad). αr Rear tire slip angle (rad). β Vehicle sideslip angle (rad). ? βcom Estimated sideslip angle from combined method (rad). ? βkin

21、 Estimated sideslip angle from kinematics-based esti- mation method (rad). ? βmod Estimated sideslip angle from model-based estimation method (rad). δf Front steering angle (rad). φ Roll angle (rad). ˙ φ Roll rate (rad/s

22、). ¨ φ Roll acceleration (rad/s2). γ Yaw rate (rad/s). λ Forgetting factor in recursive least squares (RLS) algorithm. µ Road friction coefficient.0278-0046/$31.00 © 2012 IEEE990 IEEE TRANSACTIONS ON INDUS

23、TRIAL ELECTRONICS, VOL. 60, NO. 3, MARCH 2013Fig. 1. Three-DOF yaw plane vehicle model.The governing equations for longitudinal and lateral motions are given bymax = F x r + F x f cos δf ? F y f sin δf (1)may = F y r + F

24、 x f sin δf + F y f cos δf (2)where the steering angles of front left and right wheels are assumed to be the same (i.e., = δf), front longitudinal tire force F x f is the sum of the front left and right longitudinal tire

25、 forces (i.e., F x f = F x fl + F x fr), rear longitudinal tire force F x r is the sum of the rear left and right longitudinal tire forces (i.e., F x r = F x rl + F x rr), front lateral tire force F y f is the sum of the

26、front left and right lateral tire forces (i.e., F y f = F y fl + F y fr), and rear lateral tire force F y r is the sum of the rear left and right lateral tire forces (i.e., F y r = F y rl + F y rr). The yaw moment balanc

27、e equation with respect to point CG isIz ˙ γ = lfF x f sin δf + lfF y f cos δf ? lrF y r + Mz (3)where the yaw moment Mz indicates a direct yaw moment control input, which is generated by the independent torque control o

28、f in-wheel motors. During yaw motion control, Mz is the control law to stabilize the vehicle motion and plays a role as an additional input to the vehicle. Therefore, Mz is included in yaw moment balance equation and can

29、 be calculated as follows:Mz = d2 (F x rr ? F x rl) + d2? F x fr ? F x fl ? cos δf. (4)Here, longitudinal tire forces can be obtained from a driving force observer which is designed based on wheel dynamics [32]. The tire

30、 slip angles are calculated based on geometric deriva- tion using wheel velocity vectors. If the velocities at wheel ground contact points are known, the tire slip angles can be easily derived geometrically and are given

31、 by [33]αfl = ? δf + tan?1 ? vy + γlfvx ? γd/2?(5)αfr = ? δf + tan?1 ? vy + γlfvx + γd/2?(6)αrl = tan?1 ? vy ? γlrvx ? γd/2?(7)αrr = tan?1 ? vy ? γlrvx + γd/2?. (8)Fig. 2. Vehicle coordinates and tire slip angle. (a) Bod

32、y fixed to global coordinates. (b) Tire slip angle.For design simplicity, the single-track vehicle model (also called the bicycle model) is usually used in estimator design. By assuming that δf is relatively small, the l

33、ateral and yaw rate dynamics, including a yaw moment control input, are obtained as follows [17]:may = mvx( ˙ β + γ) = F y f + F y r (9)Iz ˙ γ = lfF y f ? lrF y r + Mz. (10)For small tire slip angles, the lateral tire fo

34、rces can be linearly approximated as follows:F y f = ? 2Cfαf = ?2Cf?β + γlfvx ? δf?(11)F y r = ? 2Crαr = ?2Cr?β ? γlrvx?. (12)III. DESIGN OF ROBUST SIDESLIP ANGLE ESTIMATORThe vehicle sideslip angle is defined as the ang

35、le between the longitudinal axis of the vehicle and the orientation of vehicle velocity vector [33]. The vehicle sideslip angle, shown in Fig. 2, is obtained asβ = tan?1 ?vyvx?. (13)A. Review on Conventional Sideslip Ang

36、le Estimation MethodsThe conventional estimation methods of sideslip angle were proposed based on model-based observer design and direct sensor integration [11]. The model-based estimation method has the advantages of hi

37、gh accuracy in linear tire region and ro- bustness against sensor bias. However, the estimation accuracy is dominantly dependent on vehicle parameters, tire parameters, and driving conditions. Since it is difficult to co

38、rrectly identify the vehicle parameters (e.g., mass) and tire parameters (e.g., tire cornering stiffness) in real time, a model-based estimation method cannot provide reliable estimation over all driving conditions. In t