Seoul 2000 FISITA World Automotive Congress June 12-15, 2000, Seoul, Korea F2000G349 Analysis on Steering Gain and Vehicle Handling Performance with Variable Gear-ratio Steering System(VGS) Masato Abe 1) *, Yasuji Shibahata 2) and Yasuo Shimizu 2) 1) Kanagawa Institute of Technology, 1030 Shimo-ogino, Atsugi-shi 243-0292, JAPAN 2) Tochigi R&D Center, Honda R&D Co., Ltd., Haga-machi, Tochigi-ken 321-3393, JAPAN A change of vehicle handling characteristics due to increase of lateral acceleration as well as effects of the steering gain adaptation of VGS to that was analyzed by quasi-steady-state analysis to find out a basic strategy for the adaptive gain scheduling in the VGS. A study using a simple fixed base type of simulator showed the upper and lower limit of the appropriate gain of the steering system. A computer simulation study on lane-change response of the driver-vehicle-system gave us a view that there exists a suitable gain setting for the VGS from a view point of driver-vehicle-system stability. Key words : Handling Stability, Closed-loop System, Steering Gain, Adaptation, EPS INTRODUCTION Recently attentions are focused on electric power steering system. A primary advantage of the electric power steering system compared with hydraulic power steering system is that it is easy for us to change the control characteristics of the steering system. It is obvious that a vehicle widely changes its handling characteristics according to the changes of vehicle speed and lateral acceleration. Thus it is desirable for the steering system which is an interface part of the vehicle and human driver to adapt to the characteristic change of the vehicle handling because if the steering system has the adaptive function, the driver will be required less adaptive work and thus it will be easy for the human driver to drive the car. The electric power steering system is expected to be a suitable system to give an answer to such a requirement mentioned above. to the change of the vehicle response characteristics[3]. In the paper, the author proved the effect of the increase of the steering gain according to decrease of vehicle speed as well as increase of steering angle. However, it is easy to understand that too much high steering gain is liable to course unstable motion in driver-vehicle-system especially when the vehicle response characteristics is deteriorated. Therefore, special attentions are focused in this study on stability of driver-vehicle-system and ease of control in terms of the limit of high steering gain. In Figs.1 and 2, it is shown how the steering gains of two types of VGS considered in this study are changed according to increase of steering angle as well as vehicle speed. The steering gain equal to 1.0 corresponds to the steering gain of the conventional vehicle. VEHICLE RESPONSE AND VGS In this paper, a steering gain adaptation of the electric power steering system is dealt with. A vehicle response gain to steering input widely changes with vehicle speed therefore a driver has to control the vehicle with large steering angle at low speed and greatly reduce his(or her) steering gain according to the increase of the vehicle speed. Also as the response gain decreases with the lateral acceleration due to the saturation property of tire lateral force to side-slip angle, a driver feels less responsive to steering input during running with large lateral acceleration. Based upon the above view, one of the authors proposed an electric power steering system with adaptive gain characteristics called the variable gear-ratio steering (VGS) system in which the steering gain increases with decrease of vehicle speed as well as with increase of steering angle, which reflects lateral acceleration, to adapt Fig.1 Gain setting of VGS1 Fig.2 Gain setting of VGS2 In order to investigate the change of the vehicle characteristics according to lateral acceleration as well as to vehicle speed, the response characteristics of the conventional vehicle are analyzed by using nonlinear vehicle model of steady-state turning. In this analysis, equivalent tire cornering powers at each equilibrium point are calculated which eventually gives us the gain and the *Masato Abe. e-mail:abe@sd.kanagawa-it.ac.jp 1
equivalent response time of the vehicle response to steering input at each running condition. Fig.3 shows how the yaw rate gain and the time constant of yaw rate response change with the increase of lateral acceleration. Here the yaw rate response is approximated by the 1 st order lag to steering input in which the time constant is given by the inverse of the natural frequency of the yaw rate response. It is recommended that the optimum vehicle response parameters the yaw rate gain and the time constant from the view point of ease of control should exist at the particular region on the plane composed by the two parameters which is shown in Fig.4. The figure 5 shows the response parameters of the conventional vehicle on the plane. Fig.5 Response parameters of conventional vehicle Fig.3 Vehicle characteristics to lateral acceleration Fig.4 Optimum response parameters by Wier[4] Also this analysis method is used for the evaluation of the effect of the steering gain adaptation by calculating the vehicle response characteristics for the vehicle with the VGS. The results are shown in Figs.6 and 7. It is shown that the response characteristics of the vehicle with VGS2 remains within the recommended region even during turning with braking, on the other hand, the vehicle response parameters with VGS1 in some cases are fallen out of the region recommended as optimum. This results of the analysis gives us the basic strategy of the adaptive gain scheduling in the VGS to compensate for the Fig.6. Effects of VGS on vehicle response characteristics response characteristics change of the vehicle itself. The vehicle response deteriorates at high lateral acceleration with high vehicle speed which is due to the excessive increase of the equivalent time constant. It suggests that there should be a limit in the intentional increase of the steering gain according to the steering angle to compensate for the decrease of the vehicle response gain with the increase of the lateral acceleration. 2
polynomial of side-slip angle. Both of them are two degree of freedom vehicle plane model with constant speed. A task to follow random lane change commands during turning curved path with constant radius of curvature with constant speed as shown in Fig.9 is imposed upon the operator of the simulator. The vehicle previewed position and the target path is displayed on the screen. The time integral of square error between the vehicle previewed position and the target path is adopted as the performance index to evaluate the driver-vehicle-system. The results are shown in Fig.10. It is shown that the driver-vehicle-system performance is deteriorated with increase of the lateral acceleration during turning in which the lane change task is imposed on the driver. This is due to the deterioration of vehicle response characteristics coursed by tire nonlinear characteristics to side-slip angle. The performance is worse when the nonlinear vehicle model is used for the simulator. This is because of unsymmetrical steering responses between right and left directions at high lateral acceleration in addition to the deterioration of the response characteristics itself. It is found that there exist upper and lower limits of the steering gain and the optimum range of it becomes narrow with the deterioration of the vehicle response characteristics caused by lateral acceleration during turning. This aspect is more clear especially in the results with the nonlinear model and the upper limit of the steering gain is more sensitive to the deterioration of the vehicle response characteristics. The above result suggests that there exists an upper limit of the steering gain for VGS as well from a view point of ease-of-control for human driver especially during turning with high lateral acceleration under which the vehicle response characteristics deteriorates significantly. Taking this aspect into account, the optimum adjustment of the adaptive gain control should be considered in VGS. Fig.7 Characteristics during turning with 0.2G braking LIMIT OF STEERING GAIN For the purpose of proving general aspects of the effect of the steering gain on human drivers under the deterioration of vehicle response characteristics due to turning with high lateral acceleration, the experimental study is conducted with a simple fixed base type of simulator as shown in Fig.8 for investigating typical control characteristics of human operators. The response characteristics of the simple simulator to the steering input is set as that of a vehicle turning along a circular path with constant lateral acceleration. The two types of vehicle model are adopted. One is a linearized model at the trim point of the circular turning. Another is a nonlinear one using a nonlinear tire model in which lateral force is described by second order Fig.8 Fixed base type of simple simulator 3
Fig.9 Lane change during circular turning with and without VGS during circular turning with constant lateral acceleration is carried out. The computer simulation model consists of 14 degrees of freedom vehicle nonlinear model with combined slip type of tire model. The tire model is a brush type one in which the combined lateral and longitudinal forces are obtained by integrating the distributed tire deformations in the contact-patch. A small size passenger cars equipped with VGS1 and VGS2 respectively are considered and the 1 st -order preview model is adopted for a human driver in the simulation. The simulated lane change responses during circular turnings with lateral accelerations of 0.3G and 0.7G are shown in Figs.11 and 12. It is found that the vehicle responses with VGS1 become oscillatory with the increase of the lateral acceleration from 0.3G to 0.7G as is pointed out in the simulator study. However, the vehicle responses with VGS2 still remains almost the same responses as that of the conventional vehicle even under circular turning with high lateral acceleration. Fig.10 Results of simulator study COMPUTER SIMULATION In order to show the effects and the limit of the gain adjustment of VGS, a computer simulation of the lane change response of a closed-loop driver-vehicle-system Fig.11 Lane change responses in turning with 0.3G lat.acc. The yaw rate response of the vehicle with VGS1 compared with the response of the other vehicles in Fig. 13 shows unsymmetrical aspect between the lane changes to inner and outer lanes especially during turning with 4
high lateral acceleration. This also corresponds to one of the results obtained in the former simulator study. On the other hand, there is no such aspect in the response of the vehicle with VGS2, which suggests the view that the gain setting of VGS2 is within a limit of the optimum steering gain discussed above. The experimental investigation using a prototype vehicle with the VGS system proves the results obtained in the simulation study mentioned above. Fig.13 Lane changes to inner and outer lanes CONCLUSIONS The followings are summarized. Fig.12 Lane change responses in turning with 0.7G lat.acc. (1) The vehicle response parameters with and without VGS depending on the lateral acceleration during turning as well as on vehicle speed were calculated by using nonlinear vehicle model of quasi-steady-state turning and it is shown that the response characteristics of the vehicle with VGS2 remains within the recommended region. (2) The simulator study shows that there exists upper and lower limit of the vehicle steering gain and the range of the optimum gain becomes narrow with the deterioration of vehicle response characteristics. The upper limit is more sensitive to the deterioration, 5
which is due to the tire nonlinear characteristics. (3) The computer simulation study proves the results of the simulator study and shows that the gain setting of VGS2 is within a limit of the optimum steering gain from the view point of stability and control of driver-vehicle-system. (4) It is conclusively found that the proposed electric power steering system with the adaptive steering gain characteristics is significantly effective for improving driver-vehicle-system performance ACKNOWLEDGEMENTS The authors are deeply indebted to Mr. Y. Kano, Kanagawa Institute of Technology and Mr. Y. Okada, Graduate Student of Kanagawa Institute of Technology for their cooperation with the simulator study. REFERENCES [1] S. Takimoto et al. A Study of Drivers Behavior in Turning a Curve Proceedings of JSAE Spring Convention 9732748, 1997 [2] J. Tajima et al. Research on Effect of Steering Characteristics on Control Performance of Driver-Vehicle System from a Viewpoint of Steer-by-Wire System Design Proceedings of AVEC 98, Nagoya, September, 1998 [3] Y. Shimizu et al. Improvement in Driver-Vehicle System Performance by Varying Steering Gain with Vehicle Speed and Steering Angle : VGS(Variable Gear-ratio Steering System) SAE Paper99PC-480, March, 1999 [4] D.H.Wier et al. Correlation and Evaluation of Driver-Vehicle Directional Handling Data SAE Paper 780010 6