Realization of Steer-by-Wire System for Electric Vehicles using Caster Wheels and Independent Driving Motors

Transcription

1 [ThD2-4] 8th International Conference on Power Electronics - ECCE Asia May 30-June 3, 2011, The Shilla Jeju, Korea Realization of Steer-by-Wire System for Electric ehicles using Caster Wheels and Independent Driving Motors Yunha Kim 1, Hiroshi Fujimoto 2, and Yoichi Hori 2 1 Department of Electrical Engineering, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo, Japan 2 Department of Advanced Energy, The University of Tokyo, Kashiwanoha, Kashiwa-shi, Chiba, Japan Abstract Recently many works have been done on electric vehicle motion control. Most of them, however, still remain in the horizon of the conventional vehicle chassis structure, which is waste of ability. This paper presents a novel steer-by-wire system for electric vehicles using caster wheels and independent driving motors, which maximizes degrees of freedom in E mobility and eventually distinguishes Es from the ICEs. A small-sized experimental vehicle is introduced and its basic dynamic characteristics are shown with actual experimental data. It is shown that the mobility of the vehicle can be improved by using caster wheels and independent driving motors at low speed, while it maintains stability at high speed. Feasibilities for future E applications are shown with mathematical modeling and analyses, and control strategies are proposed in the paper. Index Terms Caster Wheels, Electric ehicle, Independent Driving Motors, Motion Control I. INTRODUCTION Recent popularization of electric vehicles Es) is remarkable. Some of the leading automobile manufacturers are launching fully electrified vehicles to compete for the preoccupancy of the market, and many research groups around the world are working on the vehicle electrification and its related issues. Many of them are focusing on the energy storage system involving batteries, capacitors, or fuel cells for instance [1]. Some of them are into charging and power transfer techniques [2][3], and many others are focusing on the infrastructural studies. From the motion control point of view, it is widely known that, compared to conventional vehicles mounting internal combustion engines ICEs), Es have several significant advantages in vehicle dynamic performance such as: electric motors have very quick torque response 1ms or less); electric motors have highly accurate output torque; there is no difference between acceleration and decceleration i.e. electric motors act as both engine and brake); electric motors are compact so that they can be fitted in each wheel In-Wheel Motor, IWM); and the motor torque can be measured easily [4]. Among the advantages mentioned above, it is worth noting that, by using independent driving motors IDMs), the traction and braking force distribution can be easily controlled, and thus the vehicle mobility and stability can be drastically improved with the additional forces and moments given to the vehicle [5][6]. The aforementioned research works, however, are the ones assuming the four-wheeled vehicle frame, which remains unchanged from the beginning of the mass production of passenger vehicles. Meanwhile, a very few in literature have tried to address the chassis configuration with regard to the new powertrain system, although it is important and interesting from the view point of vehicle motion control. Focused on this property, the effects of wheel placement change on the vehicle dynamics were examined and evaluated by the author [7] as shown in Figure 1. It was shown that, some alternative wheel placements such as three-wheeled ones can show better performance in vehicle motion control while showing equivalent stability as that of conventional four-wheel configuration [8][9]. Which implies that more studies need to be done on this matter. In the same context, this paper proposes a novel steerby-wire system using caster wheels Fig. 2) and IDMs as one of the possible chassis configurations for the future Fig. 1. Yaw rate response to the direct yaw moment input from the driving motors. 3-wheeled 2 front driving wheels) in blue, 3-wheeled 2 rear driving wheels) in green, and 4-wheeled 2 rear driving wheels) vehicle in red were evaluated /11/$ IEEE

2 Fig. 2. A caster wheel image source: passenger electric vehicles. The system consists of two independent driving wheels on the rear and two caster wheels on the front. A caster wheel is an undriven wheel that is free to move or rotate. By choosing caster wheels as steering wheels, the effect of traction and braking force distribution generated by driving wheels on the vehicle dynamics can be maximized. In addition to this, the unique dynamic characteristics of caster wheel itself can affect the vehicle motion, which allows the vehicle to have expanded mobility. Although caster wheels can be found in numerous applications, including shopping carts, chairs, mobile robots and even the aircraft landing gears, their dynamics has not been satisfatorily addressed yet with regard to the vehicle dynamics. For instance, it is sometimes neglected as in [10], being described as a point only exerting normal force from the ground to the vehicle body. In order to fully utilize the advantages of using independent driving motors in vehicle powertrain-chassis system, the caster behavior needs to be exained being linked to vehicle dynamics, which is done in the following section. II. EXPERIMENTAL EHICLE AND MODELING A. Experimental ehicle, CIME CIME Caster-wheeled Independent Motor-driven Electric ehicle) is designed to run unmanned. It is controlled by a digital signal processor S-BOX) with two input signals transmitted through a radio controller. The PWM signals interpreted by the receiver are sent into the DSP, where they are linearized to drive the motors both driving and steering to run the vehicle. Four independently controlled electric motors are used. Two are used for steering and the other two for driving. The vehicle is powered by a 24 Ni-MH battery. System configuration is shown in Fig. 4. Measured vehicle parameters are shown below in Table I, and the dimensions and the frame of reference are shown in Fig. 5. The specification of the driving and the steering motors are shown in Table II and Table III, respectively, and the DSP S-BOX) I/O setting is shown in Table I. The sampling time of DSP is set 1 ms. Four encoders are attached to each of motors to monitor the rotation of both the steering and the driving motors. Two encoders for the driving motors have the resolution of 3600pulse/rotation, and the others for the steering motors are with the resolution of 1024pulse/rotation. Fig. 3. Caster wheeled electric vehicle CIME: Two rear wheels are driven via belt and pulley by two independent driving motors 90 Watts each). Two front wheels are casters, connected via gears to two independent steering motors 60 Watts each). Fig. 4. System configuration of the experimental vehicle CIME: The vehicle is controlled by a digital signal processor S-BOX) with a remote controller. Its dynamic behavior is monitored and recorded through an acceleration sensor unit and four endcoders. Fig. 5. ehicle dimensions and the frame reference. Additionally, an acceleration sensor unit Fig. 6) is used to monitor the behavior of the vehicle.

3 TABLE I EHICLE PARAMETERS MEASURED) Parameters Meanings alues m ehicle mass 18.5 kg N f Normal force on each front wheel 39.2 N* N r Normal force on each rear wheel 51.5 N* I z Moment of inertia vehicle) kgm 2 ** I w Moment of inertia caster wheel) kgm 2 *** e Caster arm length m l f Distance, from C.G. to front axle m l r Distance, from C.G. to rear axle m L Wheel base m d Tire track m Fig. 6. Acceleration sensor unit used in the system. Yaw rate, x- directional, and y-directional accelerations can be measured. *g = 9.8m/s 2 **Measured by torsional pendulum method ***Calculated TABLE II SPECIFICATION OF DRIING MOTOR Parameters Meanings alues P rd Rated power 90 W K τd Torque coefficient N m/a K ed Back EMF coefficient /rad/s) R id Internal resistance 0.6 Ω N nd Rotational speed without load 2350 rpm I nd Current without load 0.6 A J md Moment of inertia of roter kgm 2 r rd Reduction ratio belt and pulley) 14:25 Fig. 7. Kinematic relations between parameters during cornering. TABLE III SPECIFICATION OF STEERING MOTOR Parameters Meanings alues P rs Rated power 60 W K τs Torque coefficient N m/a K es Back EMF coefficient /rad/s) R is Internal resistance 2.52 Ω N ns Rotational speed without load 8490 rpm I ns Current without load A J ms Moment of inertia of rotor kgm 2 r rs Reduction ratio gears) 18 : 120 TABLE I DSPS-BOX) I/O SETTINGS Channel Parameters Meanings CNT1 ω L Wheel Speed L) CNT2 ω R Wheel Speed R) CNT3 δ L Steering Angle L) CNT4 δ R Steering Angle R) DI1 Radio Controller CH1 DI2 Radio Controller CH2 DI3 Radio Controller CH3 DI4 Radio Controller CH4 AD1 T L Driving Motor Torque L) AD2 T R Driving Motor Torque R) AD3 T ml Steering Motor Torque L) AD4 T mr Steering Motor Torque R) AD5 γ Yaw Rate AD6 a y Lateral Acceleration DA1 T L Driving Torque Reference L) DA2 T R Driving Torque Reference R) DA3 T ml Steering Torque Reference L) DA4 T mr Steering Torque Reference R) B. Mathematical Modeling In literature, most of the studies regarding the caster wheel dynamics are provided by those who are making mobile robots or aircrafts. The latter are concerned with the vibration of an aircraft landing gear during taxiing, thus they are focused on attenuating the phenomenon at high operation speed [11]. Meanwhile, the former are more into the kinematics of the system, and more likely to neglect the transient dynamics. Caster wheels are not seen in vehicle dynamics for passenger vehicles so far. To establish a simple but accurate mathematical model of the system, it is reasonable to start with the caster dynamics and its modelling. For the mathematical models, the parameters provided in the previous section are used. Here, it is assumed that the casters are free to rotate only under the effect of the stiffness K and the damping D about the king pin. In this model, the vehicle s cornering is controlled merely by the direct yaw moment input. Among the dynamic models provided by the aforementioned research groups, the model suggested by G. Somieski [11] seems to be compatible for our system. The system is modelled neglecting the existance of steering motors. The governing equations are written as: I w δ + D δ + Kδ = Msa α)+ef y α) D t ) δ 1) ) α = y +l f γ δ 2) x ± d 2 γ where, α: side slip angle of the wheels; K: spring constant about the king pin;

4 D: damping constant about the king pin; M sa : self aligning torque; F y : lateral force at the tire-road interface; and D t : damping moment due to tread width. At constant vehicle speed, limiting the side slip angle α to 5 degrees where it can be linearized, and using the Dugoff s tire model, and from the kinematic relations indicated in Fig. 7, we can rewrite the equation 1) as [12][13][14][15]: Iw s 2 +D + D t )s + K ) δ L ) ) = C y +l f γ sa δ x d 2 γ L + ec y +l f γ F δ x d 2 γ L for left wheel and Iw s 2 +D + D t )s + K ) δ R ) ) = C y +l f γ sa δ x + d 2 γ R + ec y +l f γ F δ x + d 2 γ R for right wheel, where, C sa : coefficient for self aligning torque; C F : coefficient for lateral force. We can rewrite equation 3) and 4) as below: δ L = δ R = C sa +ec F I w s 2 +D+D t )s+k+c sa +ec F ) C sa +ec F I w s 2 +D+D t )s+k+c sa +ec F ) y +l f γ x d 2 γ ) ) y +l f γ x + d 2 γ Moreover, the caster wheels, in relation with the vehicle body, are exerting moments through/about the king pin on the vehicle body, which are noted as: M L =Ds + K)δ L 7) M R =Ds + K)δ R 8) These moments can be written in the equivalent form of cornering force, whose direction is along with y axis, as: ) Y FL = M L e cos y + l f γ x d 2 γ 9) ) Y FR = M R e cos y + l f γ x + d 2 γ 10) When the vehicle speed is low parking lot maneuvers), the transient caster dynamics can be ignored as in [10]. Thus here we investigate the cater-vehicle dynamics assuming that the vehicle speed is high enough. By adding some modifications to the bicycle model, the vehicle dynamics can be written as: 3) 4) 5) 6) si z γ = l f Y FL + l f Y FR 2l r Y R + M z 11) m sβ + γ)=y FL +Y FR + 2Y R 12) where, M z : direct yaw moment input from driving wheels; β: side slip angle of the vehicle body; Y R : cornering force acting on the rear wheels. When the vehicle speed is high enough, i.e.: y + l f γ x d 2 γ y + l f γ x + d 2 γ β + l f γ 13) y l r γ x d 2 γ y l r γ x + d 2 γ β l rγ 14) By substituting 5) 10) into equation 11) and 12) and using parameters above, we get: Gs) Mz γ = γ = Ps) 15) M z Qs) where, Ps) is 4th order polynomial and Qs) is 5th order polynomial of s, which can be computed from the equations and the parameters defined above. Note that the torque input of the steering motors is not considered here. i.e. Caster wheels are free to rotate under influence of K and D only. The steering angle δ is a state variable. For active steering motor control, if we consider the motor torque inputs, and put K = 0 and D = 0, we can rewrite the equations 3), 4), 7), and 8) as: Iw + I m )s 2 + D t s ) δ L ) ) = C y +l f γ sa δ x d 2 γ L + ec y +l f γ F δ x d 2 γ L + T ml 16) for left wheel and Iw + I m )s 2 + D t s ) δ R ) ) = C y +l f γ sa δ x d 2 γ R + ec y +l f γ F δ x d 2 γ R + T mr 17) for right wheel, where, I m : moment of inertia of the steering motor; T ml,t mr : steering motor torque. Equations 7) and 8) become: M L = T ml 18) M R = T mr 19) III. STABILITY ANALYSIS Using equation 15), simulations are done to see the system response and to determine the system stability. From Fig. 8 10, we can see that the open loop system is unstable with any stiffness or damping coefficient at any speed. As we know from our experiences of using shopping carts, the system should be under a feedback control by a human controller. As it turned out that the open loop system is unstable, it is plausible to see if the closed loop system is stable. First,

5 Fig. 11. A simple feedback controller to check the closed loop stability with a constant gain C. Fig. 8. Poles of the open loop system according to varying stiffness K 0 to 10Nm/rad), at D=0.1Nm/rad/sec), =10m/s. It is seen that there always exist a pole in the RHP marked with red circle) which makes the system unstable. Fig. 12. Closed loop system poles with varying K 0 to 10Nm/rad) at D=0.1Nm/rad/sec) and =10m/s. K does not have much effect on system stability. Fig. 9. Poles of the open loop system according to varying damping coefficient D 0 to 10Nm/rad/sec)), at K=0.1Nm/rad, =10m/s. It is seen that there always exist a pole in the RHP marked with red circle) which makes the system unstable. Fig. 13. Closed loop system poles with varying D 0 to 10Nm/rad/sec)) at K=0.1Nm/rad and =10m/s. D seems to have the dominant effect on system stability. Fig. 10. Poles of the open loop system according to varying vehicle speed 1 to 20 m/s), at K=0.1, D=0.1. It is seen that there always exist a pole in the RHP marked with red circle) which makes the system unstable. a simple feedback control loop is considered as shown in Fig. 11. With this structure, the root-locus of the closed loop system is plotted to obtain stability perspective. By using a feedback controller, the system poles are moved to LHP: the system is stabilized. As seen in Fig , the stiffness K does not have much effect on the system stability while the damping D has the dominant effect. And as the vehicle speed increases, the system poles moves to the fast side, where the system is more stable. Thus it is inferred that the vehicle can be stabilized with a simple feedback controller in certain speed range. From the analyses, however, it can be seen that with only passive control system, the range of control is restricted. Due to the existence of the limit in force that a tire-road interface can produce, the direct yaw moment also has limited value, which results in undesirably low understeer gradient. To have sufficient means of motion control, the experimental vehicle CIME is provided with two steering motors as shown in Fig. 15. I. CONTROL STRATEGIES By using caster wheels and independent driving motors, we can expect the vehicle to have mainly two

6 Fig. 14. Closed loop system poles with varying 0 to 20 m/s) at K=0.1Nm/rad and D=0.1Nm/rad/sec). It can be seen that the system becomes more stable as the vehicle speed increases. Fig. 15. Caster wheel with steering motor. merits: freer vehicle movement at low speed, and the application of controlled lateral forces at high speed. Using properly designed controllers with accordance with the speed range, these advantages can be maximized in their effects. A. Low Speed Range Control At low speed parking lot maneuvers) the tires do not develop lateral forces. They roll without any slip angle, and thus the vehicle turning is determined only by the geometrical relations. As shown in the Fig. 16, the instant center of rotaion ICR) of the vehicle, which is a criterion evaluating the vehicle mobility, can be placed at any point on the line passing through the rear axle by using caster wheels and independent driving motors, while that of the conventional vehicle cannot. The minimum turning radus of a vehicle with normal steering configuration is usually around five meters, on the other hand, that of the caster wheeled vehicle is zero. For this case, we can use the target ICR location determining process defined by Lam et al. [16]. In low speed range, the steering motors do not need to work actively; only with the direct yaw moment input and passive caster wheels, the vehicle movement can be managed satisfactorily. Fig. 17 shows the experimental result of the vehicle yaw rate responses to the direct yaw Fig. 16. Possible location of ICR, colored blue. Caster wheeled vehicle upper) and conventional one lower). ehicle with normal steering has usually 5 meters of turning radius, while with caster wheels it is zero. Fig. 17. Yaw rate responses to the direct yaw moment input versus the conventional steering maneuver at 90 degrees cornering. ehicle speed is 2m/s in all cases. The steering angle is 30 degrees at inner wheel for the conventional steering case. Direct yaw moment is given by wheel speed controller. moment input versus the conventional steering maneuver at 90 degrees cornering. For the conventional steering case, the steering angle was given at 30 degrees which is usually the maximum for passenger vehicles. It is shown that the yaw rate can go over the maximum rate of the conventional one, by applying direct yaw moment to the driving wheels. B. High Speed Range Control At high speed, tires produce lateral forces in accordance with the tire slip angle. These lateral forces are crucial because they provide the vehicle with the centripetal force during cornering. Thus, in passenger vehicle applications, the steering motors should be actively controlled for safety and stability reasons. Since CIME is equipped with two independent steering motors, it is possible to control the lateral force vectors by controlling the steering angle of each steering wheel. If we put: Td = Csa y + l f γ δ x ± d2 γ + ecf y + l f γ δ x ± d2 γ 20)

7 Fig. 18. Lateral forces calculated by using disturbance observer versus the one calculated by using lateral acceleration sensor during a steady state circle running. ehicle speed was 4m/s, and the steering angle was 15 degrees at inner wheel. Fig. 19. Controller configuration where, T d is the disturbance torque, the lateral force ) y + l f γ C F x ± d 2 γ δ 21) can be instantaneously calculated C sa, C F are known values.) by using a disturbance observer [17], and moreover, by controlling the steering angles independently, the vehicle is allowed the controlled lateral forces, which have never been controlled in the conventional steering systems. Fig. 18 shows the lateral forces which were calculated by using disturbance observer and acceleration sensor. Since it is a steady state circle running, i.e. γ = 0 and M z = 0, equations 11) and 12) become: 0 = l f Y FL + l f Y FR 2l r Y R 22) ma y = Y FL +Y FR + 2Y R 23) Using these equations, disturbance torques were converted into lateral forces red and blue dashed lines in Fig. 18), and the lateral acceleration was converted into the necessary net lateral force to make the turn black solid line in Fig. 18). Experimental result shows that the lateral force estimation by using disturbance observer has reliable accuracy as compared with the calculation using acceleration sensor. The controller configuration is shown in Fig CONCLUSION AND FUTURE WORKS In this paper, a novel steer-by-wire system is proposed using caster wheels and independent driving motors. An actual experimental vehicle is introduced, and its system configuration is shown. The mathematical model is discussed with simulations, and the system stability is analyzed. The open loop system turned out to be unstable. However it is shown that, with feedback controller and additional actuators, the system can be more powerful than the conventional one. Feasibility of the system is shown with experiment results in the low and high speed ranges. By using various control strategies including cost function minimization, it is possible to contorl the vehicle motion in a certain desired fashion such as: yaw stabilizing control, energy saving control [18], and etc.. Utilizing the high degrees of freedom of CIME, many possible control applications will be examined. I. ACKNOWLEDGMENT The authors would like to thank Dr. Sehoon Oh, Mr. Toshiyuki Uchida, and other research group members for their sincere academic and technical supports. Also they would like to send sincere condolences to the victims of the earthquake and the tsunami, and believe that Japan will recover soon from the tragic disaster vibrantly. REFERENCES [1] S. M. Lukic, R. C. Bansal, and A. 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