Analysis on Steering Gain and Vehicle Handling Performance with ...

Seoul 2000 FISITA World Automotive Congress
June 12-15, 2000, Seoul, Korea
F2000G349
<strong>Analysis</strong> 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.
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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
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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
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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,
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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
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