Study on Cornering Stability Control Based on Pneumatic Trail Estimation by Using Dual Pitman Arm Type Steer-By-Wire on Electric Vehicle Ryo Minaki Yoichi Hori The University of Tokyo The University of Tokyo Department of Electrical Engineering Graduate School of Frontier Sciences Hongo, Bunkyo-ku, Japan Kashiwa, Chiba, Japan [email protected] [email protected] Abstract—This paper proposes novel high accuracy road margin). In addition, we propose a novel cornering stability condition estimation called Tire Grip Margin (TGM), and TGM control technique based on the tire grip margin with active is estimated by using dual pitman arm type steer-by-wire and front steering and in-wheel motor on electric vehicle. Finally, lateral force sensor and estimator. In addition, we propose we verify the technique by the vehicle dynamics simulator cornering stability control technique based on the TGM. It can CarSim. help driver and vehicle before unstable state. We verify our proposed system achieves robust vehicle dynamics control on the low friction road by CarSim. CarSim is simulator for the vehicle II. TIRE GRIP MARGIN (TGM) dynamics. A. Ground Contact Length of Tire and Lateral Keywords-active front steering; electric power steering; electric Displacement of Tire Tread Rubber vehicle; in-wheel motor; pitman arm; pneumatic trail; steer-by- A Tire has ground contact length caused by vehicle load, wire; tire grip margin; deflection because tire is made of hollow rubber. It is about 15- 20 [cm]. When a tire is rolled ground contact is started. After a I. INTRODUCTION few second, it is ended. The ground contact length is between In recent years, the demand for safer vehicles has increased. start position and end position. It is shown in Fig.1 (a). According to traffic accident reports prepared by Institute for Traffic Accident Research and Data Analysis (ITARDA) in Japan, almost all traffic accidents are caused by human errors such as driver negligence or operational mistakes. Therefore, future technologies need to precisely detect driver’s mistakes and adopt active control in order to increase vehicle safety. In the recent decade, reserch and development of automotive company and university have proposed vehicle dynamics control techniques equipped with advanced active control (a) Ground contact (b) Lateral displacement capability such as Intelligent Tutoring System (ITS) and Fig. 1. Lateral displacement of tire ground contact. everything else and verified the experimental efficacy. However, almost all of them are inefficient on the low friction On the other hand, when a tire is slid to lateral direction road and split-μ road had different friction on the right road and shown in Fig.1 (b) tread rubber of tire is displaced toward left road. In comparison, our proposed control technique will lateral position against wheel assumed rigid body. In this provide robust vehicle dynamics under any road friction regard, the lateral displacement is not a uniform state in the circumstance. There is a general knowledge that controlling the ground contact of tire. The ground contact added tire slip angle yaw rate on vehicle is stabilizing vehicle dynamics. However, α from above is shown in Fig.2. The center line x is direction it is a half of mistake. Because controlling friction between tire of the tire before turning a steering wheel. After turning it, the and road surface is most important and fundamental to control tire is slid to the lateral direction by the slip angle α. The point stable yaw rate. Before now, there are some technical paper A is starting ground contact. The point B is finishing it. From about tire friction control such as tire friction circle estimation point A to point C, the tire tread rubber is dragged by road [1] and slip μ estimation. However, they have enormous friction along with line α and is an adhesion state. From point calculation amount and model error because of using very C to point A, the tread between tire and road is slip state. The complicated model. In this paper, our proposed method lateral force of tire equation is shown in (1). estimate pneumatic trail with a very simple model. And we show that it is effective to estimate tire friction limit (tire grip 978-1-4244-8218-4/10/$26.00 ©2010 IEEE B SAT, Our technical papers [3], [4] propose to estimate it using the road reaction torque observer with an electric power Fy = Ks y dx (1) ∫ steering. The observer is shown in Fig. 6. In this regard, the A time constant value needs to be large to estimate SAT with Q filter design. TRTRS (SAT,Friction) Δθ* Power Assist AFS_Reference_angle Motor 1 P（ ）= s J s2+C s+K + θ * Tf + f f f + Steering θs f * Front Ts PD θ Wheel + + + Wheel f Tr − − Position Feedback Reactive Torque Motor + − Pn ^ Reaction TRTRS -1 Fig. 2. Lateral displacement added slip angle. Pn Q Torque Control Road Reaction Torque Observer Firstly, the force is given by multiplying the lateral stiffness TGM Ks of the tread rubber by the area of the lateral deflection Fig. 4. Road reaction torque observer. integrated form A to B. To the next, it is necessary to consider the center of the lateral force area. That is to say, it is a center The electric power steering is shown in Fig. 5. This motor position of the triangle area. The position is expected to be attached to the steering wheel axle is used for reactive torque behind center of the tire ground contact. The distance between control for a driver. The system uses other two motors to the center of the lateral force area and the center of the tire control the front tires independently. In addition, it estimates ground contact is known as pneumatic trail. TGMs with these motors and the observer. The system can control optimal vehicle dynamics estimating four TGMs. It has B. Tire Grip Margin (TGM) Difinition potential advantage to stabilize vehicle motion under any road condition. A pneumatic trail as a moment arm, a lateral force and a self aligning torque are shown in the Fig. 3 and the following Steering Wheel equation (2). When the pneumatic trail become zero or minus ･ Vehicle Velocity value, the tire experience slip phenomenon. We define the state ･ TGM Torque Controller variation of the pneumatic trail as the tire grip margin Δt. Sensor Reactive Torque Electric Motor Δt = TSAT Fy (2) Signal Line Controller Right wheel Light wheel motor motor Right Tire Left Tire Fig. 5. Dual Pitman arm type steer-by-wire. D. Road Reaction Torque Observer (RTOB) As mentioned above, the reactive torque must be measured or estimated to transmit this information to the driver. In this study, we estimated the torque using an assist motor attached to the front axle wheel and an observer. The block diagram of the reactive torque observer is shown in Fig. 4. The reaction torque TRTRS from the road surface is Fig. 3. Lateral force and self aligning torque. an unknown state variable to be estimated. First, the estimated ˆ C. Tire Grip Margin (TGM) Estimation angle of the front axle wheel, θ f , is calculated using the SAT and the lateral force need to be measured or estimated nominal model Pn (s) of plant P(s) and the reference torque to calculate TGM. First, the lateral force can be measured using * of the front axle wheel, T f , which are known state variables. the tire hub sensor produced by NSK in Japan. The technical Second, Δθ is calculated as the difference between the paper [2] proposes to estimate it using a resolver signal. About ˆ ˆ estimated value θ f and the measured value θ f . TRTRS is ⎛V ∗ β − l f ∗γ ⎞ −1 Fr = FrL = FrR = −K r ∗⎜ ⎟ (8) calculated by means of the inverse model Pn of the plant. ⎜ V ⎟ −1 ˆ ⎝ ⎠ Since Pn is not a proper function, TRTRS is calculated using a low-pass filterＱ. The formula is shown below. 2) Lateral Motion Equation * ˆ * ⎛ dβ ⎞ θ f = (T f + TRTRS )P(s) , θ f = T f ⋅P(s) (3) M z ∗V ∗ ⎜ + γ ⎟ = (F fL + F fR ) + (FrL + FrR ) (9) ⎝ dt ⎠ ˆ ˆ −1 = 2 ∗ F f − 2 ∗ Fr (10) TRTRS = (θ f −θ f )Pn (s)⋅Ｑ(s) (4) The lateral forces Ff and Fr generate yaw moment γ around If the nominal model Pn (s) is confirmed to be identical to center of gravity on a vehicle. plant P(s) , Tˆ is calculated by the following formula. RTRS 3) Rotational Motion Equation ˆ Ｑ dγ TRTRS = TRTRS ⋅ (s) (5) I ∗ = l ∗ (F + F ) − l ∗ (F + F ) + M (11) z dt r fL fR f rL rR P(s) is identified using the Prediction Error Method based on the Maximum-Likelihood Method. = 2 ∗ lr ∗ F f − 2 ∗ l f ∗ Fr + M (12) Low pass filter Ｑ reduces higher frequency gain than cut- off frequency 1/τq. τq is time constant value. If the reaction M is yaw moment by differential torque. In this study, the ˆ torque TRTRS estimated by the observer were to be directly torque is directly generated with two In-wheel motors on transmitted to the driver, the control would cause steering electric vehicle. interference in the same manner as the differential angle control, as shown in Fig. 8. Therefore, it is necessary to adjust 4) State Equation for Vehicle Dynamics the gain and frequency of Tˆ with the low-pass filterＱ. In RTRS t this regard, the time constant value needs to be large to x& = A x + BM + Hδ f , x = []β γ (13) estimate SAT with Q filter design.