4WS on Formula Student Racing Car

8/17/2019 4WS on Formula Student Racing Car

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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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SAE-A Vehicle Technology Engineer – Journal (VTE-J) 2Copyright The Society of Automotive Engineers-Australasia (SAE-A)

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;


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)


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.

4WS on Formula Student Racing Car

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Transcript of 4WS on Formula Student Racing Car