4ws on formula student racing car
TRANSCRIPT
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Four Wheel Steering (4WS) on a Formula Student Racing Car
IPG: CarMaker ® with formula student racing car model
Author (Allwright, Joshua) Swinburne University of Technology
Contact details:
Email: [email protected]
ABSTRACT
Formula Student is a student-based competition betweencompeting universities worldwide where students design,
fabricate and race a small open wheel racing car. This
challenging task leads to innovations to gain a completive
edge. 4WS vehicles have higher lateral acceleration
capability, which is an advantage for the formula student
competition. The aim of this research is to quantify theadvantages of 4WS on a formula student racing car. This has
been completed by simulating two different 4WS controllers
(Vehicle Speed Function and Improved Yaw DynamicsWith Feed-Forward Control). The two 4WS controllers were
simulated in IPG: CarMaker ®. Results show a formulastudent racing car in the skid-pan event can expect
approximately 1.30% to 1.36% reduction in lap times when
completing a loop of the track (left turn or right turn).Results show a formula student racing car in the auto-cross
and endurance event can expect 0.43% to 0.57% reduction
in lap times for an 800m track. Within the simulation of the
endurance event, a reduction of 6.6 to 8.8 seconds was seen
by the 4WS models when comparing the total time taken by
the Front Wheel Steering (FWS) model. This difference isenough to move a team ahead more than one position when
looking at 2014 Formula Student Germany endurance track
times. This presents 4WS on a formula student car isadvantageous. There are limitations on the findings. Driver
effort has been found to increase as larger rear wheelmovement is used. Results have only been established
within a simulated environment.
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1. INTRODUCTION
Improving vehicle dynamics is an endless pursuit that is
actively seen within racing. The student-based formula
student competition is an example of this. It is a challengingtask where innovations are constantly being developed to
gain a competitive edge. Advancements in integrated
control systems for vehicle dynamics has led to thedevelopment of electric formula student racing cars with
two wheel drive and four wheel drive systems that take
advantage of influencing lateral forces [1]. When designing
a race car for the formula student competition, it is
important to understand the significance of each design
parameter [2]. The formula student competition event is
made up of tracks with many tight corners, and best lap
times are achieved by maximizing the longitudinal and
lateral acceleration. Maximizing lateral acceleration willresult in faster times around the track due to higher average
velocities maintained during corning. Increase of the lateral
acceleration capability is achieved by reducing the lateral
load transfer [3]. 4WS can reduce the amount of lateral loadtransfer in a turn, when compared to FWS vehicle [4]. Thusa 4WS vehicle can turn with higher velocities compared to
FWS and stay within a controlled range. The advantages of
4WS have been established on commercial size vehicles [5].
From the literature; 4WS enhances performances [6],
improves agility [5], provides better handling [7, 8, 9, 10,
11], improves comfort [7, 11], creates easier
manoeuvrability [10, 11, 12], improves stability [7, 9, 11]
and reduces driver effort [9]. It is unknown whether 4WS is
a worthwhile pursuit in this context.
The aim of this report is to see if 4WS is applicable to a
formula student racing car and whether it provides a
competitive advantage. This will provide future formula
student teams with information regarding the advantages of
using 4WS. Beyond this report, findings will further
contribute to the knowledge of benefits and effects of 4WS.
Two 4WS controllers have been selected from the studied4WS controllers to run through a range simulation. Data
analysis from the results will provide a conclusion regarding
4WS in Formula Student.
2. LITERATURE REVIEW
Four areas of research were selected to fulfil the aim of this
investigation. Improvement Of Vehicle Dynamics covers thetheory behind 4WS and the established enhancements.
Design Approaches presents the concepts that 4WS systems
are designed around. Control Methods present a range of
different control methods and their controllers that achieve
4WS. 4WS Systems present the mechanical systems used to
steer the rear wheels in relation to control methods.
Together, these four topics will present the warrants and
knowledge to further investigate 4WS on a formula student
racing car.
2.1 Improvement Of Vehicle Dynamics
Vehicle behaviour during a turn can be broken down into
transient and steady state response. During the transition
from driving straight to turning, the steady state responses between FWS and 4WS are the same. However, the
transient response between going straight and reaching
steady state turning is different among FWS and 4WS (seeFigure 1 and Figure 2).
Figure 1: Transient response of FWS vehicle to steer ing
input [13]
F igure 2: Tr ansient response of 4WS vehicle to steeri ng
input [13]
In Figure 1, two phases of lateral force are generated beforeturning starts. The first lateral force is made by the front
wheels, which start the rotation around the centre of gravity,
and generates a yaw motion. The side-slip angle then builds
up creating the second lateral forces on the rear wheels,
which then starts turning the vehicle in the desired direction.
Sano et al. [13] expressed that there is a delay between thetwo lateral force generations and with higher vehicle speeds
DRIVER’S STEERING
SLIP ANGLE AT FRONT TIRES
LATERAL FORCE ON FRONTTIRES
START OF TURNING AROUND
VEHICLE C.G
VEHICLE SIDE-SLIP ANGLE
CENTRIPETAL FORCE BY FRONT& REAR TIRES RESULTING IN
VEHICLE TURN
SLIP ANGLE AT REAR TIRES
LATERAL FORCE ON REAR TIRES
ROTATION
AROUND C.G (YAW RESPONSE)
REVOLUTION
(LATERAL
ACCELERATION
RESPONSE)
DRIVER’S STEERING
SLIP ANGLE AT FRONT TIRES SLIP ANGLE AT REAR TIRES
LATERAL FORCE ON FRONTTIRES
LATERAL FORCE ON REARTIRES
REVOLUTIONCENTRIPETAL FORCE BY FRONT & REAR TIRES RESULTING IN
VEHICLE TURN
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this delay becomes larger due to greater side-slip angles.
Figure 2 shows the ideal case of 4WS. There is no delay in
generation of cornering forces between front and back, no
rotation around the centre of gravity and no side-slip angles.
Centripetal forces start the vehicle turning in a shorter time
compared to FWS.
2.1.1 Lap Time Improvements
There is little available literature published on 4WS withregards to the improvement on racing cars however there
has been literature on the improvement on lap times. In
1993, Benetton Formula 1 team added a hydraulically
operated rear steering rack to their Cosworth-powered B193
to test the improvements before the FIA banned ‘driver aids’
in 1994. Michael Schumacher and Riccardo Patrese tested
this racing car and concluded that it added nothing in terms
of lap times. No quantification of improvements was made
[14]. However, the 2014 Porsche 911 turbo has claimed that
active rear- axle steering (4WS) has played a significant role
in the improvement of lap times at the Nürburgring inGermany [15]. No quantification was made to express how
much active rear-axle steering improved lap times. Further
research is required to quantify the benefit of 4WS with
regards to reduced lap times.
2.2 Design Approach
Researchers have proposed a range of different strategies to
control the rear wheels with relation to normal input of front
wheel angle. Siahkalroudi and Naraghi [16] grouped these
strategies into three categories: zero side-slip, zero yaw rate
and reference model.
2.2.1 Zero Side-Slip
This strategy aims to not allow the vehicle to side sideways
during a turn. Turning the rear wheels out of phase of thefront wheels can achieve zero side-slip (see Figure 3). This
can reduce lateral motion, reduces the delay phase in lateral
acceleration which occurs in FWS [13] and improve
manoeuvrability by reducing the Turning Circle (TC) [13,
17, 18]. The negative side to this strategy is the increased
yaw-rate, which makes this strategy unsuitable at high
speeds.
2.2.2 Zero Yaw Rate
This strategy aims to reduce the rotational motion around
centre of gravity and increase the lateral motion; this is more
suitable for high speeds [16]. This strategy works in
opposition to a zero side-slip strategy. Turning the rear
wheels in phase of the front wheels can achieve zero yaw-
rate (see Figure 4).
2.2.3 Reference Model
This strategy aims to mathematically model the ideal
behaviour of the car to create a reference model which is
used by the 4WS controller [9]. The reference model is
compared with incoming signals which then evaluate the
correct rear wheels angles to keep the car as close as
possible to the ideal behaviour and prevent undesired
behaviour.
Figure 3: Rear Wheels Steered Out Of Phase [5]
Figure 4: Rear Wheels Steered In Phase [5]
These design approaches are combined to create control
methods. Sylvain [9] concluded in his thesis that a design
approach with more than one strategy is better for overallcontrol, recommending the use of yaw rate and derivative of
the lateral velocity strategy. A combined design approach
has been used by many researchers [4,5,6,7,19,20,21,22]
with results proving an improvement in stability over a
single strategy method.
2.3 Control MethodsThis section will look into the range of control methods used
to achieve 4WS. The control methods can be split into open-
loop and closed-loop controllers. Researchers have shown
significant improvement with the use of closed-loop
controllers [9, 21, 23, 24]; however, there is also evidence
that open-loop controllers can perform just as well [20]. The
main difference between the two methods is in open loop,
the rear wheel angles are moved by a function of the driver
inputs. In closed-loop, feedback from the controller output is
sent back to stabilize parameters and is added or subtract to
the driver inputs. Another control method reviewed is
independent rear wheel steering. Each rear wheel angle is picked and steered independently of each other.
TC-2
TC-1
TC-2
TC-1
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-1.5
-1
-0.5
0
0.5
1
0 20 40 60 80 100 120 k s
Speed (Km/h )
Speed vs K(ratio)
speed vs K(ratio)
2.3.1 Open Loop Controllers
Two well-known open-loop controllers developed for 4WSare; Vehicle Speed Function Based and Steering Angle
Function Based [13]. However, these two controllers are
limited around 0.6g in lateral acceleration before coming
unstable [25]. Formula student racing cars will operate
under large lateral forces; these two methods might not besuitable, further research is required to determine whetherthese type controllers are suitable.
2.3.1.1 Vehicle Speed Function
Sano et al. [13] developed an open loop algorithm to keep
the side-slip angle to zero at slow speeds and zero yaw at
high speeds, see Figure 5. This controller was used by
Honda and in 1987 was the first 4WS system to be
integrated into mass production vehicles [26]. At low
speeds, the rear wheels are turned out of phase to the front
wheels, which reduces wheel base length and improvemanoeuvrability. At high speeds, the rear wheels are turned
in phase of the front wheels which increases the effective
wheel base and improves stability. Whether this open-loop
algorithm is suitable for a small wheel base racing car
requires further research.
Figur e 5a: A lgori thm presenting the relationship between
fr ont and rear steeri ng angle [13] where;k s : r atio of rear wheel angle over f ront
S 1 , S 2 : f ront/r ear wheel angle (rad)
a, b: distance fr om fr ont/rear axle to c.g (m)
M : vehicle mass (kg) L: Wheel Base (m)
C r , C f : f ront/r ear cornering stif fness (N/r ad)
F igur e 5b: graph of algori thm seen in 5a
2.3.1.2 Improved Yaw Dynamics Wi th Feed-
Forward Control
Besselink et al [20] developed a closed-loop, see Figure 6.
However, due to the velocity of the vehicle being considered
external to the steering subsystem, controllers that use the
forward vehicle velocity as an input are classified and
analysed as open-loop controllers. This controller maps the
inputs of the front steering angle and forward vehicle
velocity to a given rear wheels angle. The controller is
designed to output the same signal as a zero yaw rate
strategy controller, without the need of a yaw rate sensor.
Besselink et al [20] summarised from previous work that a
very accurate yaw rate signal should be available when
applying zero yaw rate strategy. The use of a transfer
function might be a viable and robust solution without theneed of very accurate signals; however further research
needs to be conducted.
Figur e 6: Improved Yaw Dynamics Wi th Feed-Forward
control [20] where;
V :vehicle speed (m/s)
S 1 , S 2 : f ront/r ear wheel angle (rad)K: 0.7
τ 1 : 0.5
τ 2 : 0.1
2.3.2 Closed Loop Controllers
Closed-loop controllers have been strongly recommended as
the primary 4WS control method. Fahimi [8] produced a
summary of the research on closed-loop methods which
showed a range of approaches. Fahimi [8] concluded from
this summary that each method was tested with longitudinal
speed of the vehicle be kept constant. This approach is
limited as the increasing or decreasing of speed will affectyaw and lateral motion. A more suitable simulation should
take into account longitudinal dynamics, lateral dynamics
and yaw motion.
2.3.2.1 Direct Yaw-moment contr ol
Wang and Li [22] added a yaw-moment control to the
Vehicle Speed Function; see Figure 7 (see Figure 5a for Ks
function). The aim of this controller is to keep 4WS benefits
but also keep yaw rate to the maximum level that would be
seen in a FWS vehicle to preserve driver feeling andhandling. The results of this method showed a significant
improvement in stability. However no quantification was
made.
k s=S2
S1=
-b+V2 Ma
CrL
a+V2Mb
Cf L
Hs2,s1(s)=K(τ1 − τ2)s
(τ1+1)(τ2+1)
VehicleS 1 Input
S 2
V
S 1 Input S 2 ActualVehicle
Model
M 2
M ff M fb
k s
Proportional
Feed-forward
Controller Gain
Feed-forwardCompensation
Controller K ff
Feed-backController K fb
+M 1 M
ⱷr
+
+
+
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Figur e 7: Structure of the integrated optimal control logic
[22] where;
S 1 , S 2 : f ront/r ear wheel angle (rad)
β: side-sli p angle (rad)
ⱷ: yaw rate (rad/s)
M : momentum (Ns)
2.3.2.2 Yaw-moment Control vs. Deri vative ofLateral Velocity
In the thesis of Sylvain [9], 4WS was investigated via a
comparison to an Active FWS system on a commercial size
vehicle. The thesis investigated the improvements in
stability and handling. The two controllers used were yaw-
rate control (Figure 8) and derivative of the lateral velocity
control (Figure 9). Quantification was made through acomparison of yaw rate, lateral acceleration, roll angle and
side-slip angle. The results showed that no strategy was
better but both showed improvement.
Fi gure 8: Yaw-Moment Controller Structure [9] where:
V : vehicl e speed (m/s)
S 1 , S 2 : f ront/r ear wheel angle (rad)
ⱷ: yaw rate (rad/s)
Figur e 9: Derivative of the Lateral Velocity Controll er
Structure [9] where:
V : vehicl e speed (m/s)S 1 , S 2 : f ront/r ear wheel angle (rad)
2.3.3 Four Wheel Independent Steering
Sang-Ho, Un-Koo, Sung-Kyu & Chang-Soo [27] described
a controller that steers the rear wheels independently from
each other. They claimed that cornering force at the outer
wheel is higher than the cornering force at the inner wheel
and therefore it is not appropriate to steer each rear wheel
with the same magnitudes. Independent control of both
wheels can enable the toe angle to be optimized. Dependingon the manoeuvre, the rear wheels can move selectively or
simultaneously, see Figure 10a and 10b. Their results
showed this method did not give better handling
performance in comparison to the standard 4WS model, but
it did offer better power utilisation. The theoretical
consumption of power is strongly decreased in comparison
with the standard 4WS system. Reduction of power
consumption is critical for both electric and petrol formula
student teams. This type of controller has been used by the
car manufacture Porsche on the 2014 911 models [15] and2014-2015 918 Spyder [28].
2.4 4WS Systems
The control method is only half of the design, the system
used to move the rear wheels in relation to the controller are
equally important. In this section, a review of the 4WS
systems and the related parameters is provided.
2.4.1 Hydraulic actuators
Hydraulic actuators have been used to steer the rear wheels
since 1985 [29]. This system uses constant power to keep
the pressure in hydraulic systems. As constant power
consumption would not be suitable for any formula student
racing car, further research is required to see the amount of
power a 4WS system needs in the context of a formula
student racing car.
2.4.2 Electromechanical Actuators
The use of electromechanical actuators is the current state of
the art with 4WS. These systems use less power than
hydraulic systems [5] and the removal of hydraulic fluidreduces the weight of the vehicle. Porsche has introduced
independent actuators in its 2014 911 models and 2014-
2015 918 Spyder. These actuators add a total of 7kg to the
vehicle. The low power consumption of electromechanical
actuators makes them ideal for application in a formula
student racing car.
2.4.3 Actuator Parameters
Counteracting the delays in actuators are critical todelivering the advantages of 4WS. Sylvain [9] integrated an
Controller Actuator
S 2
ⱷ
Error
ⱷ
V
Reference
ⱷ
V Input
+
S 1 Input
Reference
Model
_ Vehicle
Controller Actuator
S 2
Derivative
of the Lateral
VelocityError
V Input
+
S 1 Input
_ Vehicle
Constant
0
Fi gure 10a: I ndividual
Wheel Turni ng
Fi gure 10b: Both
Wheel Turni ng
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97
97.5
98
98.5
99
99.5
100
0 3 6 9 12 15
E f f i c i e n c y ( % )
Bending angle (degree)
CV Joint effciency
actuator model in to his controllers to simulate the delays
and limits that could occur, see Figure 11. A first order lag
is used to represent the signal lag that occurs and saturation
is added to the actuator model to limit the rear steering
angle. Yamanaka, Taneda, and Tanizaki [30] claim a
movement of ±2° of the rear wheels would be sufficient for
4WS system. Whether an estimate from track/wheelbase
ratio can be used to determine the required movement willneed further investigation. The movement needed for a
formula student racing car is unknown.
Fi gure 11: Actuator T ransfer Function
2.4.4 CV Limits
Constant Velocity (CV) joints are commonly used in
formula student racing cars to deliver the torque of the
motor to the wheels. Jan-Welm Biermann [31] investigated
CV joint efficiency. As shown in Figure 12 below, as theangle of the CV joint moves away from zero its efficiency
drops. The angles limits chosen for 4WS will need to take
efficiency reductions into consideration.
Fi gure 12: Ef fi ciency of CV joint at a given angle
2.5 L iterature Closing Comments
There are several important observations and conclusions to
be made. First, the effect of 4WS can improve vehicle
dynamics, however there is no research regarding whether
this improvement applies to a formula student racing car.Second, as a result of the knowledge gap with 4WS and
Formula Student, there has been no research done on control
methods in the context of a formula student racing car.
Existing data and results are inconclusive due to other
commercial enhancements. Pure quantification of 4WS isnot identifiable. Third, the advantages in independent rearwheel steering are in power consumption over other 4WS
systems where the rear wheels are steered together. Fourth,
for an accurate control model, the parameters of an actuator
should be considered into the control method and integrated
into simulations. Finally when picking actuator limits, the
CV joints must be taken into consideration as efficiency is
reduced with greater angles used as well as the added
displaced of angles from suspension motion during
cornering.
3. RESEARCH QUESTION
The literature demonstrates there are enhancements with
4WS but there is a knowledge gap for these enhancements
on a formula student racing car. It is inconclusive whether
4WS is beneficial in the context of Formula Student. The
research question becomes:
Is it advantageous to use a 4WS system on a formula student
racing car?
4. METHODOLOGY
To determine the possible benefits of 4WS on a formula
student racing car, controllers need to be developed andtested. The first objective, developing controllers, is reliant
on literature. The literature does not identify the best control
method; however, all methods have offered improvements.
Open-loop controllers can be implemented with
less development compared to closed-loop controllers. The
found open-loop controllers will only require commonsignals that are available in a formula student racing car;
front steering angle and vehicle forward velocity.
Consequently open-loop controllers have been used todetermine if 4WS is advantageous.
To quantify the advantages of 4WS, the controllers need to
be tested. With the current level of knowledge, physical
testing would be too early with high expense. Building a
virtual model is a cost effective way of evaluating the
controllers and finding any issues which are not currently
known. Safety is an important aspect and robust controllersare required. Therefore, the two open-loops controllers were
developed in a MATLAB®/Simulink model and then
simulated with the software IPG: CarMaker ®. Wang and Li
[22] showed two degree of freedom simulators are only
acuate when the vehicle is in a non-emergency state (lateralacceleration is less than 0.4g). Greater degrees of freedomare therefore needed to simulate a racing environment. IPG:
CarMaker ® has been picked as the simulator due to many
degrees of freedom in the models used. In IPG: CarMaker ®
the skid-pan, Auto-cross and endurance events was
simulated.
The quantifications used for an evaluation are based around
the lap times recorded from a conventional FWS formula
student racing car completing the skid-pan, auto-cross and
endurance event. Besides lap times, other parameters have
been monitored including: lateral acceleration, yaw rate and
front steering angles to analyse whether lateral accelerationlimits can be extended and at what costs to driver effort.
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4.1 IPG CarMaker®
IPG: CarMaker ® is an advanced vehicle dynamics
simulatior. A realistic model of a vehicle is simulated with
all sub-components. The steering system, tires, braking
system, drive train and aerodynamics are fully integrated in
one multi-body model. All of this is also connected into a
simulink model to allow the testing of new controllers. This
flexible model is then complimented by three-dimensionalroad models and a robust fully parameterized driver model
(IPG: Racing Driver) allowing the tests of developing
controllers under relatively realistic conditions. A realistic
model of a formula student racing car will be used which
IPG: CarMaker ® has provided, basic car setup can be seen
in section 4.1.1. This model has a standard setup of aformula student racing car and the only change will be 7kg
added to the rear to simulate the weight actuators as found in
section 2.4.2. In justifying the advantageous of 4WS, the
4WS model must be able overcome the extra weight and
still be quicker.
4.1.1 Vehicle Parameters
4.2 4WS Controllers
From the literature review the two open-loop controllers,
Vehicle Speed Function and Improved Yaw Dynamics withFeed-Forward Control are picked as a starting point to
evaluate 4WS on a formula student racing car.
4.2.1 Controller 1: Vehicle Speed Function
Sano et al.[13] developed an open-loop controller to keep
the side-slip angle to zero. Only the front steering angle and
vehicle forward velocity are needed. Figure 14 shows the
Simulink model created for the use with IPG:CarMaker ®
including actuator lag and moment limits.
Figur e 14: CarMaker Vehicle Speed Function
4.2.2 Controller 2: Improved Yaw Dynamics
With Feed-Forward Control
Besselink et al. [20] designed a controller that only requires
the front steer angle and vehicle forward velocity. As stated
in the literature this controller could be a robust solution
because it does not rely upon very accurate signals such as
yaw rate. Figure 15 shows the Simulink model created for
use with IPG:CarMaker ® including actuator lag and
moment limits.
Figur e 15: CarMaker I mproved Yaw Dynamics with F eed-
Forward Control
4.3 Sensitivity Analysis
A sensitivity analysis was used to optimise parameters
influencing the controllers. In the skid-pan event, lateralacceleration is expected to increase and lap times reduced
with the use of 4WS controllers. Control parameters were
manually tuned via observations from simulations results
until satisfactory values were found.
4.4 Skid-Pan Track Test
The track model is based on the skid-pan layout [32]. Figure16 below is a bird’s eye view of the skid-pan track. Two
right loops and two left loops have to be completed to finish
the event.
Fi gure 16 : Bird’s eyes view of Skid -Pan modell ed in IPG:
CarMaker®
No actuators
Mass: 332.9 kg
Wheelbase: 1.6 m
Front Track: 1.2 m
Rear Track: 1.15m
Front axle distance from
C.G: 0.814 m
Rear axle distance from
With 2x 3.5kg actuators
Mass: 339.9 kg
Wheelbase: 1.6 m
Front Track: 1.2 m
Rear Track: 1.15m
Front axle distance from
C.G: 0.83 m
Rear axle distance from
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4.5 Auto-Cross And Endurance
These two events will be based around a simulation of the
2006 Formula Student Germany auto-cross and endurance
track. The model of the track is provided by IPG: CarMaker,
see Figure 17. This track is approximately 800 meters long
which is the required length stated by the competition rules
[32]. For the sake of this investigation, both events will run
on the same track and in the same direction. Due to the
simulated environment, it is not required to run a fullendurance event to produce the total race times. Single lap
times will be taken from the auto-cross event and multiplied
by 27.5 to estimate the time it will take to complete the
endurance event (27.5 x 0.800 km =22 km).
Fi gure 17 : Bird’s eyes view of 2006 Formula student Auto-
Cross/Endur ance modell ed in IPG: CarMaker®
5. RESULTS
In this section, the results of skid-pan, auto-cross and
endurance simulations will be shown. The major focus has
been the investigation around the skid-pan event in
developing the controllers. The skid-pan track geometry
presented large and fast corning situations which are ideal torecord maximum lateral acceleration as well as a quick test
due to the length of the track. Different integrations of
controller models could be tested quickly and compare with
the FWS model.
5.1 Skid-Pan Simulation
Lap times of the event are recorded in Table 1 and 2. Duringsimulation, IPG: Racing Driver is cutting the corner in the
right turn 1 and left turn 1 in all three controller models. If
this did occur in a formula student competition, penalty
points would be given due to the shorter distance travelled.
Therefore quantification is based on right turn 2 and left turn
2 as no corner cutting was present. An average has beentaken to quantify the improvement. Results show a formula
student racing car can benefit from the 4WS controllers by
approximately 1.30% to 1.36%.
Table 1: % of improvement in lap times with Vehicle Speed
Function (VSF)
Table 2: % of improvement in lap times with Improved
Yaw Dynamics with Feed-Forward control (I YD)
5.2 Auto-Cross Simulation
The auto-cross event results can be seen in Table 3. Each
model completed one lap which was equal to a distance of
approximately 800 meters. Results show a formula student
racing car can expect improvements of approximately
0.43% to 0.57% reduction in lap times within the simulated
track. In the case of this simulation, that is a reduction of
0.24 seconds with Vehicle Speed Function and 0.32 seconds
with Improved Yaw Dynamics With Feed-Forward Control.
Table 3: % of improvement in lap times around 800m
Auto-Cross track
5.3 Endurance Simulation
The endurance event results can be seen in Table 4. Results
show a formula student racing car can expect 0.43% to
0.57% off one lap in the endurance event. In the case of this
simulation, that is a reduction of 6.6 seconds with Vehicle
Speed Function and 8.8 seconds with Improved Yaw
Dynamics With Feed-Forward Control.
Loop
direction/
No.
FWS (s) 4WS - VSF % of improvement
Righ t 1 4.913 4.819 1.91
Righ t 2 5.326 5.257 1.30
Lef t 1 5.218 5.109 2.09
Lef t 2 5.229 5.161 1.30
Average % of improvement 1.30
Loop
direction/
No.
FWS
(s)4WS - IYD
% of
improvement
Righ t 1 4.913 4.723 3.87
Righ t 2 5.326 5.249 1.45
Lef t 1 5.218 5.116 1.95
Lef t 2 5.229 5.163 1.26
Average % of improvement 1.36
Model
Lap
time
(s)
% of
improvement
over FWS
Time
reduction
(s)
FWS 55.71 - -
4WS – VSF 55.47 0.43 0.24
4WS – IYD 55.39 0.57 0.32
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Table 4: % of improvement in lap times around 22km
endurance track
6. ANALYSIS & DISCUSSION
In this section, the results from the simulation will be
examined. The 4WS on a formula student racing car will be
discussed in relation to the research question and literature.The two controllers will be evaluated and furthermore the
problems during the implementation and testing of the
controllers.
6.1 4WS On A Formula Student Racing
Car
Two 4WS open-loop controllers have been considered to
investigate the advantageous of 4WS systems on a formula
student racing car. The literature review showed 4WS can
enhance a number of vehicle characteristics, but did not
apply the findings to a small wheel-based vehicle. The
results do show it is advantageous to use a 4WS system on a
formula student racing car within the simulated
environment. With 7kg added to the model, lap times arestill faster. The quantified amount of improvement seen in
this research is not large, but formula student competitions
record lap times down to 0.001 of a second. The results of
lap times in endurance are where the strongest benefits are
shown. 0.43% to 0.57% off lap times is small, however
applying this to the time taken by a FWS model; a drop of6.6 to 8.8 seconds is seen. That is possibly enough to jump
ahead more than one position, as shown in Table 5.
Table 5: 2014 Formula Student Germany endurance track
times
To explain why lap times are faster, we can look at the
lateral acceleration. In Figures 18, we see the lateral
acceleration recorded from the skid-pan event. In that figure
we can determine that the controllers 1 and 2 are producing
larger lateral acceleration displacements over the FWS
model at different times. The increased lateral acceleration
increases in the transient state response during turning.
Greater velocity can be carried into the corner which in turncreates the larger lateral acceleration as the vehicle changes
its trajectory. Once the trajectory path is constant, the
vehicle falls into a steady state turn and lateral acceleration
displacements are the same as the FWS model. This
observation from the lateral acceleration results is close to
what was found in the literature on 4WS (section 2.1).
Figur e 18: Lateral Acceleration around Skid-Pan event inthe fi rst corner
Beside lateral acceleration and lap times, it is important to
analyse the effects on handling behaviour. To measure
handling behaviour, yaw rate and driver steering angle were
recorded. Decreased yaw rate will reduce driver effort in
counter steering. Decreased driver steering angle will also
reduce driver effort. From the results, only one of these
important variables is aided by 4WS. Figure 19 on the next
page shows the yaw rate is reduced, but the driver steering
angle is increased as shown in Figure 20. This is due to afew factors. One being the limits set on the rear wheel
actuators. It is not common for the rear wheels to be steeredgreater then ±3°. With the angle kept low, it can reduce the
required steering angle input by the driver. In this research
paper, the limits of the actuator have been set to a maximum
of ±8°, which has required larger driver efforts. Theadvantage found with larger rear wheel angles was reduced
lap times. However, power steering systems and/or changing
rack ratios might be needed in 4WS to make it more
advantageous. However, the formula student competition
rules ban power steering systems. Drivers of formula student
racings cars might need higher levels of fitness toexperience 4WS benefits and keep within the rules.
-16
-15
-14
-13
-12
-11
-10
0 2 4 6 8 10
L a t e r a l A c c e l e r a t i o n ( m
/ s ^ 2 )
Time (s)
Lateral Acceleration
FWS
4WS - VSF
4WS - IYD
Model
Single
Lap
time
(s)
Endurance
event
complete
time (s)
Time
reduction
(s)
FWS 55.71 1532.025 -
4WS – VSF 55.47 1525.425 6.6
4WS – IYD 55.39 1523.225 8.8
CAR Uni versity Time (s)1 Corvallis OSU 1301.74
4 Göteborg Chalmers 1412.41
2 Stuttgart U 1412.80
49 Erlangen U 1414.27
17 Pomona CSU 1414.37
30 Prague CTU 1416.42
80 Coburg UAS 1428.25
60 Weingarten UAS 1431.68
55 Geißen UAS THM 1445.13
108 Karlsruhe UAS 1454.66
7 Seattle U Washington 1463,34
12 Thessaloniki U 1470.40
28 Kassel U 1482.49
131 Regensburg UAS 1487.11
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Figur e 19: Yaw Rate around Skid-Pan event in the fi rst
corner
Figur e 20: D ri ver steeri ng angle around Skid-Pan event
6.2 Controller 1: Vehicle Speed Function
The results show this controller has the potential to reduce
lap times on the skid-pan event by 1.3% and reduce laptimes on auto-cross by 0.43%. Increased benefits are seen in
high speed turns which are shown in the skid-pan event.
Auto-cross event results aren’t the strongest for 4WS;
however, this could be a result of the driver model. IPG:
Racing Driver could not stay on the track in some cornerswhen the parameters of maximum lateral and longitudinal
acceleration were set too high. Therefore lower limits of
maximum lateral and longitudinal acceleration were set to
prevent the driver model going off track in some corners.
This created a slower pace around the track but was still able
to present the advantages of 4WS.
6.3 Controller 2: Improved Yaw
Dynamics With Feed-Forward Control
The results show this controller has the potential to reduce
lap times on the skid-pan event by 1.36% and reduce laptimes on auto-cross by 0.57%. The same driving problems
occurred as discussed in 6.2. What is different with this
controller though, is it was more capable of reducing lap
times then controller 1. This is a result of being able to pull
larger lateral acceleration, see Figure 18. Conversely there
are some undesirable effects. In Figure 18, the lateral
acceleration throughout the skid-pan event shows the lateral
acceleration dropping. This is the result of the controller and
not loss of traction. As the rear wheels turn from out of
phase to in phase with the front wheels it creates adisturbance in the lateral acceleration. This effect is
undesirable if stability is compromised, and further research
is required to understand the full effects it will have before
being a potential control method.
6.4 Problems With Implementation Of
Controllers And Simulation
The first problem to overcome was developing the
controllers to aid the performance of the FWS formula
model. A sensitivity analysis was used to achieve the
desired performance out of the chosen controllers. Secondwas the driver model and corner cutting. For the skid-pan
event, it is important that no corner is ever cut. The setup of
the driver model’s ability to never cut corners could be set;however, much slower lap times were seen over all as a
result. A percentage of cornering cutting was set which
resulted in first corner being cut in the skid-pan event but
the rest of the event was driven at a faster pace. The
controllers could be tested at the maximum speeds and
present their lateral acceleration limits. The results were
only quantified on laps that did not cut corners to maintain
relevancies of the findings back to formula student;
however, the other laps were not ignored. These other laps
still present relevant data proving the advantages of 4WS. Ifthese lap times were counted, greater reductions may have
been found.
7. SUMMARY
The results suggest it is advantageous to use a 4WS system
on a formula student racing car. The research question has
been answered; however, the optimum control method will
require further research. In this research, two approaches tocontrolling a 4WS system have been investigated as a
starting point. The two open-loop controllers have shown
advantages and can reduce lap times. Though, driver effortneeds to be kept within suitable ranges to avoid the need of
aided front wheel steering systems. Furthermore the rear
steering angle limits needs to be taken into consideration, as
a large steering angle will lead to increased driver effort;
however, faster lap times are the result. This trade off must
be consider during the application of 4WS in Formula
Student.
8. FUTURE WORK
This research project was just the start in developing 4WSsystems for formula student racing car. It is now clear
further research efforts should be spent on this topic.
Literature shows closed-loop systems with references
-150
-100
-50
0
50
100
150
0 0.1 0.2
D r i v e r s t e e r i n g a n g l e ( d e g )
Time (s)
Driver Steering Angle - Skid Pan
FWS
4WS - VSF
4WS - IYD
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0 1 2 3 4 5 6
Y a w R a t e (
r a d / s )
Time (s)
Yaw Rate - Skid Pan
FWS
4WS - VSF4WS - IYD
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models of desired trajectories are better than open-loop
controllers; however, they are more complex to implement.
Open-loop controllers have shown an improvement and
therefore validate the next stage to develop closed-loop
controllers. The use of closed-loop controllers will add the
benefit of stability to the controller. Safety is an important
aspect and robust controllers are required.
Another area requiring attention is the 4WS system that
would be used. 7kg was used as the weight of the system in
this investigation and was picked due to the findings in the
literature. A formula student racing car is significantly
lighter than a Porsche 911 and so the weight of the system
could be reduced. The amount of force needed to move therear wheels will reduce the mechanical design specifications
and weight loss of the system should be expected. 5kg
system could be used in the next round of simulations.
Development of a rear wheel system that meets the
constraints of formula student rules as well as the
requirements demanded by the controllers is an open
research question that requires further investigation.
In further work with simulations of the next generation of
4WS controllers, the introduction of slalom tests should be
added. Slalom are common in formula student tracks and as
well as being good test of vehicle agility.
Acknowledgements
The author would like to gratefully acknowledge the
following for their support.
Professor Geoffrey Brooks for his support assisting with
controller development and guidance.
IPG: CarMaker ® for supplying their software and IPG:
CarMaker ® Service Team for their assistance and their
continual support with IPG: CarMaker ®.
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PUBLISHED REVIEWS
David G N Clark, MEng(Mech) CPEng(Ret) MIEAust
Senior Lecturer (Retired) Mechanical Engineering,
Swinburne University of Technology
This paper outlines simulations that show some minor
potential improvement in lap times of Formula Student
racing cars when four wheel steering is applied, compared to
front wheel steering. It is considered worthwhile to design
and build a four wheel steered Formula Student racer and
confirm that it performs better in all applications of skid-
pan, auto-cross and endurance events. The controllers for
the four wheel steering system will need to be carefully
implemented.
Clint Steele
Swinburne University of Technology
The most striking outcome of this paper is the revelation of
the compromise between the use of 4WS and the extra
driver effort required. This is unlikely to be of practical
consequence to industry due to the option of power, but it
does raise an area of research that is of academic value – thedevelopment of an ergonomically viable control system that provides 4WS benefit without power assistance.