1 Seoul 2000 FISITA World Automotive Congress F2000G341 June 12-15, 2000, Seoul, Korea Development of the Active Front Steering Control System Tokihiko Akita * , Katsuhiko Satoh, Masayuki Kurimoto, Tsuyoshi Yoshida AISIN SEIKI CO., LTD., 2-1 Asahi-Machi, Kariya, Aichi 448-8650, Japan For active front steering control systems that intervene in driver’s operation to assist in the control of the vehicle’s motion, the effect of the man-machine interface is much larger than for other conventional control systems. This paper focuses on human factors. The results of analysis regarding control effects and system design concerns are also described. The user benefits of this control system are improved vehicle stability and reduced driving workload. Both theoretical and experimental evaluations are described. Regarding the man-machine interface, the influence of the oversteer characteristic when braking and turning on driver’s steering operation, the influence of driver reaction in system failure and steering wheel reaction torque when driving with the actuator are also analyzed. Keywords: front steering control, human factor, variable gear ratio, vehicle motion control, failure analysis INTRODUCTION Recently, front steering control systems [1]-[4] such as the steer-by-wire system have been proposed to respond to the demand for improved handling for better safety and to aid our aging population. Front steering is most closely connected to the driver as the point of contact between the man and the vehicle. Therefore, large user benefits can be obtained by control intervention in this area. At the same time, there are some new challenges. These items, which are related to human factors, were analyzed theoretically and experimentally. SYSTEM CONFIGURATION A pure steer-by-wire system, which has no mechanical linkage between the tires and the steering wheel, is the ultimate steering control system. However, at the present time, a control system that is added to the conventional steering system and superimposes a controlled steering angle on the driver’s operation, is reasonable in terms of cost, reliability and compatibility with current vehicles. Thus, we developed the control system in Fig. 1 and installed it in an experimental vehicle. The test subjects were analyzed using this configuration. USER BENEFITS The functions of the front steering control system can be classified in two groups. One is the passive control such as variable gear ratio or lead steer. The other is active control such as yaw rate feedback control or cooperative control with the brake system. The latter can improve vehicle dynamics performance. However, it is not directly related to human factors, but to the vehicle motion characteristics. Thus, we will not described it here and concentrate on the results of analyzing and evaluating the passive control functions in this paper. VARIABLE GEAR RATIO EFFECT OF VEHICLE STABILITY IMPROVEMENT The effect of varying the steering gear ratio to improve vehicle stability is theoretically analyzed. Using the simple yaw rate feedback driver model in Fig. 2, the performance was analyzed by yaw rate convergence. Driver model: sTd1 Kd )s(Gd ⋅+ = Actuator model: Ga(s) = Ka Vehicle model: 2 s2Ts1T1 sTr1 0Grdf)s(Gv ⋅+⋅+ ⋅+ ⋅= The 1st order delay model for yaw rate feedback was adopted as a simplified driver model. The actuator was represented as a steering angle amplification model with a constant gain and no delay. The bicycle model was used for the vehicle. The transfer function of this closed loop system is calculated as follows: * Corresponding author. e-mail: akita@rd.aisin.co.jp Driver’s inputs ● Steering wheel angle ● Steering wheel torque ● Master cylinder pressure ● Throttle angle Vehicle motion ● Wheel’s velocity ● Yaw rate ● Lateral acceleration ● Longitudinal acceleration Tire Brush-less DC motor Steering Planetary gear sets ECU Current Steering angle Steering torque Tire angle Fig.1 AFS control system configuration Vehicle :Gv(s) Driver :Gd(s) AFS Actuator :Ga(s) target yaw rate yaw rate + - Vehicle :Gv(s) Driver :Gd(s) AFS Actuator :Ga(s) target yaw rate yaw rate + - Fig.2 Stability analysis model including a driver 2 The characteristics of this system were theoretically analyzed by the pole location and step response of the above transfer function for various steering gain and driver characteristics. This steering gain is the reciprocal of the steering gear ratio, thus increasing the gain is the same as decreasing the gear ratio. In the case of the standard driver, shown in Fig. 3, yaw rate convergence is improved by increasing the steering gain, which means the stability of the vehicle can be improved. In Example 2 (Fig.4), the driver steers too quickly with the controller set at high gain. The imaginary parts of the poles get bigger, thus yaw rate overshoots more. Since this is a linear model, there is no divergence. The actual system tends to become unstable. This means that it’s more difficult for a driver who cannot adapt to different vehicle characteristics to operate the vehicle with an excessively large steering gain. This analysis illustrates the basic effect of the variable gear ratio function on the vehicle stability characteristics. The experimental results using the prototype system to verify these effects are shown in Figs. 6 to 10. A double lane change maneuver, shown in Fig.5, run on a low friction road, was used for these tests. The vehicle characteristics with steering gear ratios of 17 (Conventional), 10 and 6 were evaluated by a test driver. The experimental results are shown in Figs. 6 to 8, including Lissajous’s figures of steering angle and yaw rate. The average yaw rates for each gear ratio in the evaluation are shown in Fig. 9. The peak yaw rate when passing the last gate is shown in Fig.10. These results show that with a smaller gear ratio, the yaw rate is slower, thus vehicle stability can be improved. The system was also evaluated with a driver who was not familiar with driving on a low friction road. The results are shown in Figs. 11 to 13. Closed loop transfer function: 32 sTd2Ts)Td1T2T(s)TrKaKd0GrdfTd1T(KaKd0Grdf1 sTr1 KdKa)s(G ⋅⋅+⋅⋅++⋅⋅⋅⋅+++⋅⋅+ ⋅+ ⋅⋅=γ Zero-pole map Step response Fig.3 Ex.1: Yaw rate stability for standard driver (Td=0.5 sec, Kd=0.245 rad/(rad/sec), Ka=1,2,4,8) Zero-pole map Step response Fig.4 Ex.2: Yaw rate stability for quick and high gain driver (Td=0.2 sec, Kd=0.49 rad/(rad/sec), Ka=1,2,4,8) Fig.9 Average yaw rate Fig.10 Peak yaw rate •μ: 0.17 60 km/h Fig.5 Double lane change course on low friction road 0 1 2 3 4 5 6 -100 -50 0 50 100 steering/tire angle (deg) 0 1 2 3 4 5 6 -20 -10 0 10 20 20 time (sec) yaw rate (deg/sec) -100 -50 0 50 100 -20 -15 10 - 10 -5 0 5 10 15 20 Steering angle (deg) yaw rate (deg/sec) Fig.6 Yaw rate and steering angle at gear ratio 17 0 1 2 3 4 5 6 -100 -50 0 50 100 steering/tire angle (deg) 0 1 2 3 4 5 6 -20 -10 0 10 20 20 time (sec) yaw rate (deg/sec) -100 -50 0 50 100 -20 -15 10 - 10 -5 0 5 10 15 20 Steering angle (deg) yaw rate (deg/sec) Fig.7 Yaw rate and steering angle at gear ratio 10 0 1 2 3 4 5 6 -100 -50 0 50 100 steering/tire angle (deg) 0 1 2 3 4 5 6 -20 -10 0 10 20 20 time (sec) yaw rate (deg/sec) -100 -50 0 50 100 -20 -15 10 - 10 -5 0 5 10 15 20 Steering angle (deg) yaw rate (deg/sec) Fig.8 Yaw rate and steering angle at gear ratio 6 Real Axis Imag Axis -25 -20 -15 -10 -5 0 5 -20 -15 -10 -5 0 5 10 15 20 Ka=1 Ka=1 2 2 4 4 8 8 Real Axis Imag Axis -25 -20 -15 -10 -5 0 5 -20 -15 -10 -5 0 5 10 15 20 Ka=1 Ka=1 2 2 4 4 8 8 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 time (sec) yaw rate (rad/sec) 2 Ka=1 4 8 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 time (sec) yaw rate (rad/sec) 2 Ka=1 4 8 Real Axis Imag Axis -15 -10 -5 0 5 -50 0 50 Ka=1 4 8 2 Ka=1 4 8 2 Real Axis Imag Axis -15 -10 -5 0 5 -50 0 50 Ka=1 4 8 2 Ka=1 4 8 2 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 time (sec) yaw rate (rad/sec) Ka=1 4 8 2 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 time (sec) yaw rate (rad/sec) Ka=1 4 8 2 3.5 m 5 m 40 m 3.5 m 25 m 2.2 m 5 m IN 3.5 m 5 m 40 m 3.5 m 25 m 2.2 m 5 m IN Steering angle Tire angle Steering angle Tire angle 6.47 5.14 4.6 0 1 2 3 4 5 6 7 17 10 6 (deg/sec) Steering gear ratio 6.47 5.14 4.6 0 1 2 3 4 5 6 7 17 10 6 (deg/sec) Steering gear ratio 20.1 12.35 10.77 0 5 10 15 20 25 17 10 6 Steering gear ratio (deg/sec) 20.1 12.35 10.77 0 5 10 15 20 25 17 10 6 Steering gear ratio (deg/sec) 3 When the gear ratio was large, the vehicle spun off the course due to the delay in the steering operation as in Fig. 11. In contrast, when the gear ratio was too small, the vehicle ran off the course since the driver steered too much and too quickly, as in Fig. 13. Only when the proper gear ratio was selected did the driver successfully maneuver the course. These results match the aforementioned analysis. The appropriate gear ratio must be selected considering the compatibility with conventional vehicles for various drivers. EFFECT OF MITIGATION FOR OPERATION LOAD If a smaller gear ratio is selected, the driver’s workload can be reduced [1]. Steering operation with various gear ratios is shown in Fig. 15 when driving on the evaluation circuit course in Fig. 14. The steering operation energy is plotted in Fig. 16. The energy reduction corresponds to the lower gear ratio. However, if an excessively small gear ratio is selected, the energy reduction effect corresponding to the lower gear ratio cannot be obtained due to frequent steering corrections, as showing in Fig. 16. Furthermore, if a smaller gear ratio is selected, the high frequency part of the steering operation is increased, as in Fig. 17. This means the operation is not as smooth and the driver’s mental workload increases. It is important to select the appropriate gear ratio from this point of view as well. HUMAN FACTORS CONCERNS This system is closely connected to the driver’s operation compared to other control systems, so it is important to consider human factors issues. The main concerns regarding human factors were determined through our vehicle experiments, and then analyzed. OVERSTEER WHILE BRAKING AND TURNING For the variable gear ratio function, the gear ratio changes as a function of vehicle velocity. Thus, the vehicle quickly steers toward the inside of a turn when rapidly braking and turning due to the gear ratio change. A similar phenomenon occurs when accelerating and turning. However, the amount of under-steer is smaller than when braking and was not a problem in the vehicle tests. So the accelerating and turning condition was not analyzed and the braking while turning problem is the focus in this paper. By considering the required steering speed at maximum deceleration in a small, constant radius turn, it can be determined whether general drivers can easily operate the system. This value can be calculated by the following equation. Required steering angular velocity: dt/}fvgr(v) R l )vK1{(d 2 st ⋅⋅⋅+=ω at maxGdt/dv = 0 1 2 3 4 5 6 -200 -150 -100 -50 0 50 100 150 200 steering/tire angle (deg) 0 1 2 3 4 5 6 -20 -10 0 10 20 20 time (sec) yaw rate (deg/sec) -200 -100 0 100 200 -20 -15 10 - 10 -5 0 5 10 15 20 Steering angle (deg) yaw rate (deg/sec) Fig.11 Result with a beginner driver at gear ratio 17 0 1 2 3 4 5 6 -200 -150 -100 -50 0 50 100 150 200 steering/tire angle (deg) 0 1 2 3 4 5 6 -20 -10 0 10 20 20 time (sec) yaw rate (deg/sec) -200 -100 0 100 200 -20 -15 10 - 10 -5 0 5 10 15 20 Steering angle (deg) yaw rate (deg/sec) Fig.12 Result with a beginner driver at gear ratio 10 0 1 2 3 4 5 6 -200 -150 -100 -50 0 50 100 150 200 steering/tire angle (deg) 0 1 2 3 4 5 6 -20 -10 0 10 20 20 time (sec) yaw rate (deg/sec) -200 -100 0 100 200 -20 -15 10 - 10 -5 0 5 10 15 20 Steering angle (deg) yaw rate (deg/sec) Fig.13 Result with a beginner driver at gear ratio 6 Fig.14 Composite circuit course Fig.15 Steering operation with each gear ratio Fig.16 Operation energy Fig.17 Power spectrum of steering angle -540 -450 -360 -270 -180 -90 0 90 180 270 360 450 540 0 10 20 30 40 50 time (sec) steering angle (degree) gear ratio : 17 (normal) 6 3 0 2 4 6 8 10 -80 -70 -60 -50 -40 -30 -20 -10 0 frequency (Hz) normalized signal power (dB) gear r atio : 3 6 17 (normal) steering energy (J) 17 6 3 gear ratio 0 200 400 600 800 1000 1200 1400 1600 Additional energy due to correction 5m 25R 15R 15 R 15R 15 R 15R Start line 160m White line Pylon 5m 25R 15R 15 R 15R 15 R 15R Start line 160m White line Pylon Off the course Steering angle Tire angle Off the course Steering angle Tire angle Spin out Spin out 4 When using the variable gear ratio characteristic shown in Fig. 19 [1] based on a limited steering wheel operation range, the required velocity is 260 deg/sec. Since the general driver’s fastest steering speed is about 200 to 1600 deg/sec, almost any driver should be able to operate the system. However, this maneuver is supposed to be difficult. An experimental evaluation using this gear ratio characteristic was done under the condition in Fig. 18. Fig. 20 shows the experimental results indicating that a rapid return steering operation is necessary even at a deceleration of 0.5G. For the modified gear ratio characteristic in Fig. 21, the gear ratio change gradient ( v/)v(fvgr ∂∂ ) is around 0.1 /(km/h). Using the above equation, the required steering operation speed is 50 deg/sec, which general drivers should easily be able to do. In the experiments, the driver could smoothly maneuver through the course as in Fig. 22. This is also a requirement for the variable gear ratio set up. EFFECT OF SYSTEM FAILURE The following 2 kinds of system failures can arise. 1. Sudden, unintended steering 2. System lock-up The failure analysis and countermeasures study that examined various failure detection mechanisms, sudden, unintended steering can never arise as long as the dual failure does not occur. Thus, the analysis for the system failure 1 is not considered in this paper. For this configuration, when the system locks up, the steering characteristic just returns to that of conventional system. However, if the change is large, it may affect to drive. The following analysis focuses on the variable gear ratio function due to the large characteristic change. To understand the phenomena with concrete value, the simple model in Fig. 23 was set up under the following assumptions. [Assumption] 1. At the beginning, the driver steers with a small gear ratio in the variable gear ratio function. 2. The system locks up and the gear ratio returns to the normal one that is large. 3. The driver notices the failure after some constant lag time and starts steering using a normal steering gain to return to the planned trajectory. For the driver model, a 1st order linear prediction model was used where the driver steers corresponding to the deviation between the planned trajectory and a point projected on straight line a set distance ahead of the car. This “preview distance” is a function of the vehicle speed. Then the corrective steering operation speed is limited to match the actual environment. The linear bicycle model with the Pacejka tire model is used as the vehicle model. The maximum deviation from the planned trajectory was used as the evaluation parameter. The simulation results for these rather severe conditions are shown in Fig. 24. The permissible value depends on the driving environment. The deviation is not so large with small steering gains, even under this severe condition. The vehicle experiments were done to verify these results. A severe double lane change course on a dry asphalt road in Fig. 25 was set up to evaluate the failure effect. The Active Front Steering Control System was locked up during the 1st or 2nd turn. The driver did not know in advance when the failure was to occur. Gear ratio values of 10 and 6 were chosen for the Active Front Steering Control. When the system locked up, it reverted to a gear ratio of 17. 4 people including professional and beginner drivers were evaluated. [Calculation parameters] •R: 15 •Gmax: 1 G •v: 5 to 150 km/h Fig.18 "Braking and turning" evaluation method and calculation parameters Fig.21 Adjusted gear ratio Fig.22 Driver’s operation characteristic Fig.19 Proposed gear ratio Fig.20 Driver’s operation characteristic Fig.23 System fail model •Vehicle velocity: 40km/h •Maximum corrective steering speed: 200 deg/sec •Planned turning radius: 20 m •Driver preview time: 2 sec Fig.24 Maximum deviation in system failure Steering gain Maximum deviation (m) Recognition time=0.5 sec 0.2 sec 0 1 2 3 4 1 1.5 2 2.5 3 0.1 sec Steering gain Maximum deviation (m) Recognition time=0.5 sec 0.2 sec 0 1 2 3 4 1 1.5 2 2.5 3 0.1 sec 60km/h Braking Pyron 4 m 15R stop line 0 5 10 15 20 25 0 50 100 150 velocity (km/h) Steering gear ratio 0 5 10 15 20 25 0 50 100 150 velocity (km/h) Steering gear ratio -200 -150 -100 -50 0 50 100 velocity (km/h) yaw rate (deg/sec) steering angle (deg) time (sec) 0 1 2 3 4 -200 -150 -100 -50 0 50 100 velocity (km/h) yaw rate (deg/sec) steering angle (deg) time (sec) 0 1 2 3 4 0 50 100 150 10 20 30 40 50 velocity (km/h) Steering gear ratio 0 50 100 150 10 20 30 40 50 velocity (km/h) Steering gear ratio -200 -150 -100 -50 0 50 100 0 1 2 3 4 velocity (km/h) yaw rate (deg/sec) steering angle (deg) time (sec) -200 -150 -100 -50 0 50 100 0 1 2 3 4 velocity (km/h) yaw rate (deg/sec) steering angle (deg) time (sec) Trajectory with AFS Recognize failure, then start correcting Preview point Maximum deviation Trajectory in failure Bicycle model with Pacejka tire model 5 The test results showed that each driver could successfully pass through the course in all cases. The recognition lag time was 0.1 to 0.3 sec and the maximum steering speed was about 300 deg/sec in most cases. Figs. 26 to 28 show the results when using a gear ratio of 6. These simulations and experiments show that the driver can manage a lock-up failure under these conditions when using the gear ratio characteristic in Fig.21. A problem with this experiment is that the drivers knew a failure was supposed to occur, even though they didn’t know when, and quickly responded without panic. It is necessary to evaluate the performance of general drivers under actual conditions to improve the reliability of the experiments. A driving simulator would be useful for this purpose. This is one of our future research tasks. EFFECT OF REACTION STEERING TORQUE Reaction torque is applied by the actuator to not only the tires, but also the steering wheel. Thus, the effect of the reaction torque for driver’s operation was analyzed. This analysis was also classified into 2 functions. One is the passive function where the system follows driver’s intension and operation. The other is the active function where the system automatically activates based on the vehicle condition. Passive function The fundamental mechanism regarding the reaction torque is described using a simple model in Fig. 29. The difference between the system with and without the AFS system can be described as: Steering torque without AFS: swItITsw α⋅=α⋅= Steering torque with AFS: mIswItITm'Tsw α⋅+α⋅=α⋅== This means that the torque generated by the AFS motor is not additional torque but same torque that is actuating the tire. Therefore, since the actuator follows the driver’s steering operation, the driver should not feel any unexpected steering wheel torque. However, the control system has some delay. The effect of the delay and the level that is acceptable was analyzed. The driver’s haptic evaluation of the steering operation when the vehicle was stationary was done using the Significant Difference Method. Various amounts of lag time after the target signal was generated by the steering wheel angle, were added to the AFS actuator command signal. As shown in Fig. 30, the driver feels uncomfortable with more than 0.1 sec of lag time. This is the system delay limit. • swsw , αω : Steering velocity, acceleration • mm , αω : Motor velocity, acceleration • tt , αω : Tire velocity, acceleration •Tsw’: Steering torque •Tm: Motor torque Fig.29 Principle model for reaction torque generation mechanism 40 km/h Fig.25 Evaluation course for system failure 0 1 2 3 4 5 6 -200 -150 -100 -50 0 50 100 150 200 steering/tire angle (deg) 0 0 0 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 -20 -10 0 10 20 yaw rate (deg/sec) 0 1 2 3 4 5 6 -300 -200 -100 0 100 200 300 time(se ) time (se c ) Steering speed (deg/sec) 0 1 2 3 4 5 6 -200 -150 -100 -50 0 50 100 150 200 steering/tire angle (deg) 0 0 0 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 -20 -10 0 10 20 yaw rate (deg/sec) 0 1 2 3 4 5 6 -300 -200 -100 0 100 200 300 time(se ) time (se c ) Steering speed (deg/sec) 0 1 2 3 4 5 6 -200 -150 -100 -50 0 50 100 150 200 steering/tire angle (deg) 0 0 0 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 -20 -10 0 10 20 yaw rate (deg/sec) 0 1 2 3 4 5 6 -300 -200 -100 0 100 200 300 time(se ) time (se c ) Steering speed (deg/sec) Fig.26 Without system failure Fig.27 Failure in the 1st turn Fig.28 Failure in the 2nd turn •Surface: Dry asphalt •Vehicle velocity: 0km/h •Steering input: Random (Various pattern) Fig.30 Haptic evaluation for the system lag time 3.5 m 5 m 20 m 3.5 m 15 m 2.2 m 5 m IN 3.5 m 5 m 20 m 3.5 m 15 m 2.2 m 5 m IN Steering angle Tire angle Superimposed angle Failure 1 2 3 4 5 0 0.05 0.1 0.15 0.2 System lag time (sec.) Evaluation grade Standard level = no incompatibility Steering angle Tire angle Failure I T m T sw’ swsw ,αω mm ,αω tt ,αω Steering wheel Tire Motor I T m T sw’ swsw ,αω mm ,αω tt ,αω Steering wheel Tire Motor Steering angle Tire angle Superimposed angle Superimposed angle 6 The required response of the system was analyzed. It can be calculated from the driver’s maximum steering operation speed, operation range at that speed and permissible lag time using the following equation. Required system functioning speed: Rnorm: Normal gear ratio Rvgr: Gear ratio in variable gear ratio function θmax: Steering operation range ωswmax: Driver’s maximum steering operation speed Tlag: Acceptable system lag time The results from 2 example calculations for severe driving conditions are shown in Fig. 31. One condition is for high speed steering with a narrow range such as in case of a collision avoidance maneuver. The other is for slow speed operation with a wide steering angle range like when parking. The haptic evaluation using the experimental vehicle with gear ratios of 6 and 10 was done. The maximum driving speed of the prototype system was 32 deg/sec at the tire angle. As the results of the haptic evaluation, the drivers didn’t notice the system delay with a gear ratio of 10, but felt it with a gear ratio of 6. This experimental result matches the calculation results. Active function When the system with active functions is triggered such as when the vehicle starts to become unstable, the motor angle is superimposed to the driver’s steering operation to compensate the vehicle’s motion. This operation generates additional reaction torque. This influence was analyzed through vehicle experiments using the aforementioned course on an artificially low friction road with 4 drivers, including professionals and beginners. The following simple yaw rate feedback control algorithm was adopted. Target tire angle: dt/dKrd)t(Krp0tt γ⋅−γ−γ⋅+θ=θ θt0: Target tire angle calculated from the steering angle γ t: Target yaw rate calculated using the bicycle vehicle model with the Pacejka tire model Krp, Krd: Proportional gain, Differential gain All drivers were able to pass through the test course without any negative influences from the AFS system. Fig. 32 shows the results from one of these experiments. Fig.33 shows the relationship between the reaction torque when the correction control was applied and the steering angle fluctuation at that time. It shows that very little steering angle fluctuations occurred, even when rather high reaction torque was applied. This is likely due to the fact that the direction of the correction control coincides with the driver’s intention, thus the driver didn’t feel large unintended motions. It can be concluded from these experiments that the system does not generate any negative effects to the driver. CONCLUSION The following facts were verified when the appropriate gear ratio was selected. 1. User benefits 1-1. Vehicle stability can be improved. 1-2. Steering operation workload can be mitigated. 2. Concerns for human factor 2-1. The driver can manage the oversteer and understeer characteristic caused by the variable gear ratio. 2-2. The driver can control the vehicle, even when the control system suddenly locks up. 2-3. The reaction torque doesn’t affect the driver’s operation. These are preliminarily results since it is difficult to generalize these effects over the entire driving public, many of whom have different driving styles and preferences. Further research using a wider range of drivers is necessary to refine this system for the market. Fig.32 The influence of reaction torque Fig.31 Required system functioning speed 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 0 5 10 15 20 25 Reaction steering torque (Nm) Steering angle fluctuation (deg) Fig.33 Influence of reaction torque Tlag maxsw max max )1 Rvgr Rnorm (vsr + ω θ θ ⋅−= 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -100 -50 0 50 100 t (s e c) steer/tire angle (deg) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -20 -10 0 10 20 t (s e c) yaw rate (deg/sec) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -20 -10 0 10 20 t (s e c) to rq ue (N m ) Steering wheel torque Reaction torque Steering angle Tire angle Compensation by the system 10 6 Steering gear ratio Required system angular velocity (tire angle, deg/sec) 0 10 20 30 40 50 60 70 80 Prototype performance High speed, narrow range (1600deg/sec, 90deg) Low speed, wide range (540deg/sec, 1080deg) 10 6 Steering gear ratio Required system angular velocity (tire angle, deg/sec) 0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 80 Prototype performance High speed, narrow range (1600deg/sec, 90deg) Low speed, wide range (540deg/sec, 1080deg) 7 NOMENCLATURE p.1 Kd : Driver’s steering gain Td : Time constant of driver’s operation Ka : Actuator gain Grdf0 : Vehicle yaw rate gain [ ))v+K1(l(= v/ ⋅ ] Tr : Parameter of Gv(s) [ v)lCr(lf/=m ⋅⋅⋅ ] T1 : Parameter of Gv(s) [ = lr/v ] T2 : Parameter of Gv(s) [ )lCr(= Iz/ ⋅ ] M : Vehicle mass Iz : Yaw moment of inertia v : Velocity of vehicle body Cf, Cr : Cornering power lf, lr : Length between center of gravity and tire contact point l : Wheel base K : Stability factor p.3 R : turning radius Gmax : maximum deceleration fvgr : VGR steering gear ratio function vt : vehicle velocity at t sec γ : yaw rate ACKNOWLEDGMENT The advice of Dr. Y. Amano of TOYOTA CENTRAL R&D LABS., INC. in the ergonomic analysis is gratefully acknowledged. REFERENCES [1] Akita, T., Yoshida, T., et al. 1999. User Benefits of Active Front Steering Control System: Steer-by-Wire: FISITA 99SF013 [2] Shimizu, Y., Kawai, T., Yuzuriha, J. 1999 Improvement in driver-vehicle system performance by varying steering gain with vehicle speed and steering angle: VGS (Variable Gear-ratio Steering system): SAE 1999-01-0395 [3] Wolfgang, K., Matthias, H. 1996 Potential Functions And Benefits Of Electronic Steering Assistance: FISITA B0304 [4] Karnopp, D. 1992 Active Steering Systems: Report of Department of Mechanical, Aeronautical and Materials Engineering, The University of California, Davis . experimentally. SYSTEM CONFIGURATION A pure steer-by-wire system, which has no mechanical linkage between the tires and the steering wheel, is the ultimate steering control system. However,. 5 -20 -10 0 10 20 t (s e c) to rq ue (N m ) Steering wheel torque Reaction torque Steering angle Tire angle Compensation by the system 10 6 Steering gear ratio Required system angular velocity (tire. Benefits of Active Front Steering Control System: Steer-by-Wire: FISITA 99SF013 [2] Shimizu, Y., Kawai, T., Yuzuriha, J. 1999 Improvement in driver-vehicle system performance by varying steering