2008:010 HIP
BACHE LO R’S TH ESIS
Vehicle dynamics
- optimization of Electronic Stability Program for sports cars
Johan Andersson
B.Sc PROGRAMME IN
AUTOMOTIVE ENGINEERING
Luleå University of Technology
Department of Applied Physics and Mechanical Engineering
Division of Computer Aided Design
Universitetstryckeriet, Luleå
2008:010 HIP • ISSN: 1404 - 5494 • ISRN: LTU - HIP - EX - - 08/010 - - SE
Abstract
This thesis was performed during the spring of 2008 at the Bosch test facility in Arjeplog. The
thesis describes how to optimize the intervention of an ESP system for a sports car. The
problem with ESP today is that it is very often defensively programmed and affects the feel
when the car is driven. What to be researched in this thesis is if an optimization of the
program can be done that allows greater body slip without affecting the vehicle dynamics and
stability in a negative way. The thesis describes programming and simulation of ESP, the
code for ABS, TCS and ESP has been written and then tested in the simulation environment
where after the parameters and code have been changed in attempt to achieve a ESP that
allows greater body slip without compromising the stability.
The ESP has been created with several setups depending on wanted behaviour and
intervention. The results from the simulations shows that greater body slip is possible without
affecting stability, the feel when driving is more or less similar as without ESP and TCS. The
measurements prove that the lap times are faster with ESP in race mode compared to only
ABS and TCS. Worth to be mentioned is that a simulation is a reproduction of a real
measurement, results and feel can differ from the reality when testing a vehicle.
Keywords: ABS, ESP, TCS, vehicle dynamics, oversteer, understeer, lateral acceleration,
yaw rate, steady-state cornering
Sammanfattning
Detta examensarbete genomfördes under våren 2008 i Arjeplog på Bosch testanläggning.
Arbetet beskriver hur ingripande av ett antisladdsystem kan optimeras för en sportbil.
Problemet med ESP idag är att det ofta är väldigt defensivt inställt och påverkar känslan i
körningen av bilar. Det som undersöks är om en optimering av ESP kan göras som tillåter
större driftvinklar utan att påverka stabiliteten. Examensarbetet behandlar programmering och
simulering av antisladdsystem, kod för ABS, TCS och ESP har skrivits som sedan testats i
simulatormiljö varefter parametrar och koden ändrats för att försöka uppnå ett stabilt system
som tillåter ökade driftvinklar jämfört med standard.
ESP har skapats med olika inställningar beroende på önskat uppträdande och ingrepp.
Resultaten från simuleringen visar att ökade driftvinklar är möjliga utan att påverka
fordonsstabiliteten, känslan i körningen är nästan densamma som utan ESP och TCS.
Mätningarna visar att varvtiderna är lägre med ESP i raceläge jämfört med endast ABS och
TCS, ESP i normalläge samt endast ABS. Dock skall nämnas att en simulering är en
simulation av en verklig mätning, resultat och känsla kan vara annorlunda vid test på ett
fordon.
Nyckelord: ABS, ESP, TCS, fordonsdynamik, överstyrning, understyrning, sidoacceleration,
girvinkelhastighet (yaw rate), stationär kurvtagning
Preface
This is the thesis and final course of my three years to Bachelor of Automotive Engineering at
Luleå University of Technology. One of my biggest interests is cars, it has first of all been
very interesting to perform the education in Luleå, but the best part has of course been to
finalize all the theoretic knowledge in a thesis in a subject that I feel is very interesting.
During my time in Arjeplog where I except from my thesis also have worked some for
Arjeplog Test Management AB and Bosch with testing and presentations, I have learned a lot.
It has been great to do my thesis at such an interesting company and facility, this has given
me great knowledge in how the testing and developing of a new production car is performed.
I would like to thank Lars Holmgren, executive manager of ATM for giving me this
possibility to do my thesis at the Bosch facility.
Thanks to Jean-Marc Jacquin who was my examiner at ATM and helped me whenever I had
problems I could not solve by myself.
Thanks to Ove Isaksson that has been my examiner at Luleå University of Technology and
helped me with all kind of questions and thoughts throughout the thesis.
As well thanks to Frederic Potdevin at ATM that helped me with some questions about
simulation. David Holmlund, Prashant Rana and Håkan Jonsson at ATM, thanks for the help
with the ABS code in the beginning.
Many thanks to Erik Hellström at Linköping University for all the help with the simulation
environment and the measurements.
Last of all, thanks to my girlfriend, my family and friends for being there for me all the time.
Umeå 08-06-03
Johan Andersson
Notation
Variables and parameters
Symbol
Description
Unit
ax
Lateral acceleration
[m/s2]
az
Longitudinal acceleration
[m/s2]
αf
Side slip angle front tire
[rad]
αr
Side slip angle rear tire
[rad]
β
Body slip angle
[rad]
cαf
Front tire cornering stiffness
[kN/rad]
cαr
Rear tire cornering stiffness
[kN/rad]
δf
Steering wheel angle
[rad]
fxf
Front tire longitudinal force
[N]
fxr
Rear tire longitudinal force
[N]
fzf
Front tire lateral force
[N]
fzr
Rear tire lateral force
[N]
g
Gravity
[9,82 m/s2]
k1
Body slip regulator coefficient
k2
Yaw rate regulator coefficient
Kus
Understeer coefficient
[rad]
L
Wheelbase
[m]
Lf
Distance from CoG to front axle
[m]
Lr
Distance from CoG to rear axle
[m]
m
Total vehicle weight
[kg]
mf
Weight front axle
[kg]
mr
Weight rear axle
[kg]
R
Turning radius
[m]
v1-4
Wheel speed
[rad/s]
v
Vehicle speed
[km/h]
vx
Lateral vehicle speed
[km/h]
vz
Vehicle longitudinal speed
[km/h]
Ψ
Yaw rate
[rad/s]
Glossary
ABS
Antilock Braking System
CoG
Centre of Gravity
ECU
Electronic Control Unit
ESP
Electronic Stability Program
NHTSA
National Highway Traffic Safety Administration
TCS
Traction Control System
VTI
Statens väg - och transportforskningsinstitut
Characteristic speed
The speed when the steer angle required to negotiate a turn is
equal to 2L/R, typical for an understeered vehicle.
Critical speed
The speed at which the steerangle required to negotiate any turn is
zero, typical for an oversteered vehicle.
Understeer
The front of the car slides towards the outside of the bend.
Oversteer
Describes the situation when the rear of the vehicle starts to slide
outwards, i.e. the car rotates faster round its vertical axis than
required to take corners it is supposed to make.
Table of Contents
1. Introduction ............................................................................................................................ 1
1.1
Background ....................................................................................................................... 1
1.2
Problem ............................................................................................................................. 1
1.3
Goal ................................................................................................................................... 2
1.4
Structure of thesis for the reader ....................................................................................... 2
2. Method ................................................................................................................................... 3
2.1
Basic motor-vehicle dynamics .......................................................................................... 3
2.1.1
2-Wheel bicycle model................................................................................................... 4
2.1.2
Friction circle ................................................................................................................. 7
2.2
The construction and function of the ESP system ............................................................. 8
2.3
Simulation software........................................................................................................... 9
2.4
Programming ..................................................................................................................... 9
2.4.1 Regulator shell............................................................................................................... 10
2.4.2 Measurement sampling ................................................................................................. 10
2.4.3 ABS ............................................................................................................................... 10
2.4.4 TCS................................................................................................................................ 11
2.4.5 ESP ................................................................................................................................ 11
2.5
Testing ............................................................................................................................. 12
2.6
Simulation ....................................................................................................................... 13
2.6.1 ABS ............................................................................................................................... 13
2.6.2 TCS................................................................................................................................ 14
2.6.3 ESP ................................................................................................................................ 14
3. Results .................................................................................................................................. 17
4. Conclusion ............................................................................................................................ 18
5. Discussion ............................................................................................................................ 19
References ................................................................................................................................ 20
Appendix A ................................................................................................................................ 1
ABS ............................................................................................................................................ 1
TCS............................................................................................................................................. 4
ESP ............................................................................................................................................. 6
Appendix B .............................................................................................................................. 10
Regulator shell.......................................................................................................................... 10
MATLAB measurement sampling ........................................................................................... 12
1. Introduction
This chapter gives a brief history about the ESP system. The problem and the goal
of the thesis is presented as well as the structure of the report.
1.1 Background
The ESP was invented and set in to serial production by Robert Bosch GmbH in 1995. The
system improves vehicle stability by intervening if the car gets into a skid and helps the driver
to maintain the vehicle in the desired direction. Whether the car becomes over- or under
steered during a corner, the ESP maintains the vehicle on its course by either braking one or
more wheels to correct it. Today ESP more and more becomes standard equipment in many
countries. In the USA all new production cars shall be equipped with ESP in 2012.
According to a study made by the University of Cologne shows that 4.000 lives can be saved
and 100.000 accidents avoided every year if all European cars have ESC. Data from Mercedes
shows that vehicles standard equipped with ESP has resulted in a 29 percent reduction in
single-vehicle crashes and 15 percent fewer crashes overall. Based on these figures, if ESP
was standard equipment on cars in the United States as many as 5,000 lives and nearly $35
billion in economic losses annually could be save every year. The Swedish VTI study
indicates that ESP was found to reduce accidents with personal injuries [1].
1.2 Problem
How can the Electronic Stability Program be optimized for a sports car?
Some people that use their cars with ESP at for example track days believe that the system
interferes and makes the driving less enjoyable and slower compared with the system of. They
do want the extra safety that the ESP gives them, but they prefer the system to allow more slip
and a softer more progressive intervene.
More slip might generate a hard intervene of the system to prevent a total loss of control, that
might be a problem that is tough to solve. This will be investigated throughout the thesis if it
is possible to solve this. This setup of the ESP may not be recommended for public roads,
only to track days and special occasions.
One more problem is that the ESP system heats the brakes if the driver pushes to the limit of
grip lap after lap on a track, the program can make the brake pads to almost melt because of
the heat. This can lead to brake failure with metal against metal because the brake pads are
worn out. In this case safety programs like ESP can become a danger. If you had a more
forgiving ESP that allows some extra slip and a softer intervene, this would lead the driver to
better learn to control the vehicle and to save the brake pads from wearing out prematurely.
With the type of method for this thesis it is though not possible to measure or calculate the
wear of the brake pads.
1
1.3 Goal
The goal was to create an ESP code that could be implemented and tested in a simulation
software. The main task was to define how to optimize ESP for a sports car. Depending on
surface, the friction coefficient mue varies from about 1,0 on asphalt to about 0,1 on polished
ice. Based from these conditions the ESP must have different setups for different friction
conditions.
In this thesis these subjects will be presented with programming and simulations for each
surface, asphalt and snow that will be used in the simulations, ESP will be programmed with
different settings depending on preferred characteristics:
Low mue
 Ice
 Snow
 Race
 Off
– zero slip, zero wheel spin
– little slip, little wheel spin
– moderate slip, moderate wheel spin
– ESP does not intervene
High mue
 Normal
 Sport
 Race
 Off
– zero slip, zero wheel spin
– little slip, little wheel spin
– moderate slip, moderate wheel spin
– ESP does not intervene
1.4 Structure of thesis for the reader
Chapter 2 presents basic vehicle dynamics to explain the physics that affects a car.
Physics is shown with the 2-wheel bicycle model and the friction circle.
The ESP system is shown in detail as well as the programming, testing and simulation
procedures of ABS, TCS and ESP are described in its context.
Chapter 3 presents the results that have been achieved about the subject.
Chapter 4 summarizes the conclusions that have been drawn upon the presented
results of the thesis.
Chapter 5 contains discussion about personal reflections of the work and possible
future work of the study in this thesis.
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2. Method
Basic vehicle dynamics is presented in this chapter to explain the physics that
affects a car. The ESP system is shown in detail as well as the testing, programming and
simulation procedures of the system are described in its context.
Vehicle handling concerns two basic issues, controlling the direction of motion of the vehicle
and to stabilize the direction of the vehicle against external disturbances. For the
understanding of vehicle dynamics it is critical to find out which forces that affects on the
vehicle. When accelerating, braking and turning a vehicle is under influence of forces in
longitudinal, transversal and vertical axes. A vehicle has six degrees of freedom, these three
translation axes mentioned before and also rotation about these axes [2].
2.1 Basic motor-vehicle dynamics
Yaw is the rotation around the vertical axis of the vehicle. Pitch is the rotation around the
transverse axis of the vehicle. Roll is the rotation of the vehicle around the longitudinal axis.
Pitch and control are controlled by the suspension of the vehicle. Each wheel is affected by a
vertical force, a motive force on the driven wheels and a braking force when braking on all
wheels that is affecting in the opposite direction to the motive force. If the car starts to slide
on any of the wheels, this means that the lateral, motive or braking force exceeds the force
that that wheel can handle and then slides in transverse and or longitudinal axis. See figure 1
below.
Figure 1. Forces affecting a vehicle.
During steering the response of the car depends on its characteristics and speed, the car can be
neutral, under or over-steered at the limit of friction. Understeer is when the vehicle wants to
go straight ahead in a corner, oversteer is when the car turns more than wanted, or more than
the angle of the curve that is taken, figure 2.
3
Figure 2. Oversteering and understeering.
2.1.1 2-Wheel bicycle model
For the analysis of transient motion and steady state handling the model of the car is
simplified as a bicycle model [2]. The axes are chosen according to axes in Racer simulation
for the figure below.
δf
z
αf
Fzf
x
δ - αf
αr
Fxf
v
α r + δ - αf = L/R
vz
Lf
β
R
vx
L
Fzr
αr
Lr
Fxr
Figure 3. Simplified bicycle model for transient motion analysis and steady state handling.
To a great extent, the vehicle characteristics depend on the relationship between the front tires
and their slip angles, αf and αr. The relationship for the steering angle 𝛿𝑓 , the turning radius
𝑅, the wheel base 𝐿, slip angles αf and αr is explained by (2.1). The equation explains that to
make a given curve the required steer angle 𝛿𝑓 is a function not only affected by the turning
radius 𝑅, also the slip angles αf and αr affects steering ability.
4
𝐿
𝛿𝑓 = 𝑅 + 𝛼𝑓 − 𝛼𝑟
(2.1)
To calculate the slip angles αf and αr, the side forces on the wheels and the cornering stiffness
must be known. For small steer angles, the cornering forces are given by
𝐹𝑥𝑓 =
𝐹𝑥𝑟 =
𝑚 𝑣 2 𝐿𝑓
𝑔 𝑅 𝐿
(2.2)
𝑚 𝑣 2 𝐿𝑟
(2.3)
𝑔 𝑅 𝐿
The total weight of the vehicle is 𝑚, 𝑔 is the acceleration due to gravity, 𝑣 is the velocity of
the vehicle. See figure 3 above for the other parameters. The load on each tire is expressed by
equation (2.4) and (2.5).
𝑚𝑓 =
𝑚𝑟 =
𝑚 𝑙𝑟
(2.4)
2𝐿
𝑚 𝑙𝑓
(2.5)
2𝐿
(2.2) and (2.3) can be rewritten as
𝑣2
𝐹𝑥𝑓 = 2𝑚𝑓 𝑔𝑅
(2.6)
𝑣2
𝐹𝑥𝑟 = 2𝑚𝑟 𝑔𝑅
(2.7)
The slip angles and cornering forces of the tires may within a certain range considered to be
linearly correlated with a constant tire cornering stiffness for front and rear tires, 𝐶𝛼𝑓 and 𝐶𝛼𝑟 .
According to [3], the slip angles are given by
𝑚 𝑓 𝑣2
𝐹
𝛼𝑓 = 2𝐶𝑥𝑓 = 𝐶
𝛼𝑓
𝛼𝑓
𝑔𝑅
𝑚 𝑟 𝑣2
𝐹
𝛼𝑟 = 2𝐶𝑥𝑟 = 𝐶
𝛼𝑟
𝛼𝑟
𝑔𝑅
(2.8)
(2.9)
By substituting equation (2.8) and (2.9) into equation (2.1), the steer angle 𝛿𝑓 to take a given
curve is equation (2.10). 𝐾𝑢𝑠 is the understeer coefficient and 𝑎𝑥 is the lateral acceleration.
𝐿
𝛿𝑓 = 𝑅 + 𝐾𝑢𝑠
𝑎𝑥
𝑔
(2.10)
For the steady state handling behaviour of a vehicle equation (2.10) is fundamental. 𝐾𝑢𝑠 is a
function of the tire cornering stiffness and the weight distribution on the front and rear axle as
equation (2.11).
𝑚𝑓
𝐾𝑢𝑠 = 𝑐
𝛼𝑓
𝑚𝑟
−𝑐
𝛼𝑟
(2.11)
The understeer coefficient depends on the relationship between the front and rear slip angles,
depending on the value the steady state handling characteristics can be sorted into three types,
5
neutral steering, oversteer and understeer. The normal understeer coefficient value for a
passenger car is in the range of 0,3 radians, that means that most of the cars are designed so
that they understeer in the linear lateral acceleration range [3].
𝐾𝑢𝑠 = 0 = Neutral steering
𝐾𝑢𝑠 < 0 = Oversteered car
𝐾𝑢𝑠 > 0 = Understeered car
When the slip angles αf and αr for front and rear tires are equal the steer angle to take a given
curve is shown by equation (2.12) This means that the vehicle is neutral steered, when grip is
lost the vehicle slides as much front as rear.
𝐿
𝛿𝑓 = 𝑅
(2.12)
If the vehicle understeers, if 𝐾𝑢𝑠 > 0, it means that the slip angle αf is greater than αr. Typical
for an understeered vehicle is that the steering wheel angle must be increased when
accelerating in a turn with a constant radius, the vehicle wants to go straight ahead in a corner.
The term characteristic speed 𝑣𝑐𝑕𝑎𝑟 in equation (2.13) is used to describe the phenomenon of
a understeered vehicle, it is the speed at which the required steering wheel angle to perform a
curve is equal to 2L/R, according to [2].
𝑣𝑐𝑕𝑎𝑟 =
𝑔𝐿
(2.13)
𝐾𝑢𝑠
If a vehicle is oversteered, if 𝐾𝑢𝑠 < 0, it means that the slip angle of the rear wheel αr is
greater than the front wheel αf. This means that the rear end of the vehicle slides more than
the front, which demands the driver to countersteer in order to keep the vehicle in the desired
course. For an oversteered vehicle the term critical speed 𝑣𝑐𝑟𝑖𝑡 is used to describe the
behaviour at which the steering wheel angle is zero to take any turn (2.14).
𝑣𝑐𝑟𝑖𝑡 =
𝑔𝐿
(2.14)
−𝐾𝑢𝑠
The body slip of a vehicle can be calculated by equation (2.15), where 𝑣𝑥 is the lateral
velocity and 𝑣𝑧 is the longitudinal velocity. Body slip is one of two key parameters required to
create vehicle stability regulation.
𝑣
𝛽 = tan−1 𝑣𝑥
(2.15)
𝑧
Typical behaviour for ESP regulating a vehicle is a body slip close to zero.
𝛽𝑛𝑜𝑚 = 0
(2.16)
The yaw rate 𝛹 𝑛𝑜𝑚 can be calculated with equation (2.17) if the vehicle speed, understeer
coefficient, wheel base, gravity and steering wheel angle are known.
𝛹 𝑛𝑜𝑚 = 𝐿+𝐾
𝑣
𝑢𝑠 𝑣
2 /𝑔
𝛿𝑓
(2.17)
6
According to [2] and [4] the simplest method to create an ESP system is to proportionally
regulate 𝛽 and 𝛹, equation (2.18). k1 is the body slip regulator coefficient, k2 is the yaw rate
regulator coefficient, if k1 = 0 gives yaw control only, k2 = 0 gives only body slip control.
∆𝑀 = 𝑘1 𝛽 𝑛𝑜𝑚 − 𝛽 + 𝑘2 (𝛹 𝑛𝑜𝑚 − 𝛹)
(2.18)
If oversteer occurs, the ESP must create a straightening momentum by braking the outer
forward wheel. If understeer occurs, the ESP brakes the inner real wheel creating a turning
momentum.
By this simplified bicycle model it is now possible to create a ESP based on the equations that
where derived from the model.
2.1.2 Friction circle
The friction circle shows the lateral and longitudinal acceleration of a vehicle, when no
acceleration, braking or turning, there is no measurement, the pointer is in the cross section of
the cross [5]. It is a good example to show of how the ESP can be optimized. The interesting
part of the friction circle is the boundary area of the circle, i.e. on the limit of grip for the
vehicle. If the tires of the car lose the grip at 10 m/s2 on asphalt, this limit area is where the
optimization shall be done for the ESP system. Longitudinal acceleration is during braking
and acceleration and lateral acceleration is during cornering. When the acceleration exceeds
the limit of the grip ESP intervenes to stabilize the vehicle. The friction circle figure below
shows a typical plot of a car accelerating, braking and cornering on a race track.
Brake
10 m/s2
10 m/s2
10 m/s2
Acceleration
10 m/s2
Figure 4. Sampled measurement for friction circle
7
2.2 The construction and function of the ESP system
The key functions for the ESP are to improve directional stability and keeping the vehicle on
the track under all operating conditions. The ESP system is built into the brake system of the
vehicle. The hydraulic modulator is connected to the brake master cylinder and functions as
the central component of electronic brake systems. Control commands from the ECU are
converted by the hydraulic modulator and the solenoid valves are opened and closed to
control the pressures of the brakes in the vehicle. By braking individual wheels the stability of
the vehicle maintains as desired and keeping the vehicle in the given direction. Also by
accelerating the driven wheels, the ESP can regulate stability [3] [6].
As the ESP function is integrated with the ABS and TCS, the system uses the same
components as those systems. The parts of the ESP are:
 Hydraulic modulator with ESP ECU and integrated hydraulic valves (1)
 Wheel brakes and wheel-speed sensors (2)
 Steering wheel angle sensor (3)
 Yaw sensor with acceleration sensor (4)
 Engine management ECU (5)
 Brake master cylinder (6)
Figure 5. The components of the ESP.
The input parameters of the ESP system are:
 Longitudinal velocity
 Lateral acceleration
 Yaw rate
 Brake pressure
 Throttle pedal position
 Steering wheel angle
8
The output parameters that control the directional stability are:
 Individual wheel braking
 Engine management, acceleration or reducing output power
The ESP measures steering wheel angle, lateral acceleration and yaw rate. Based on these
inputs it records and calculates the estimated vehicle direction and behaviour, suppose an
intervention is needed, if the vehicle over or understeers for example one or more wheels are
braked to correct the directional stability according to the float schematics in figure 6.
ESP
Measurement of
steering wheel angle
and wheel speed
Measurement of
lateral acceleration
Recording of the intended
vehicle direction
Measurement of yaw
rate
Recording of the actual
vehicle behaviour
Calculation of the deviation of wanted
and actual vehicle behaviour
Decision if ESP intervention
is needed to stabilize vehicle
To counter oversteer brake
force is applied at the outer
front wheel
To counter understeer, brake
force is applied on inner rear
wheel
Figure 6. The function of the ESP
2.3 Simulation software
For the simulations in this thesis the software Racer release 0.5.0 has been used. This version
is free ware but not open source for commercial use, but the source code has possibilities to
be modified and to implement your own code for non commercial purposes [7]. The
simulation has realistic vehicle dynamics which was important to the decision of simulation
tool. The 0.5.0 version of Racer has to be run in Linux, which was done for the thesis.
2.4 Programming
The language that is used in Racer is C++ [8]. The programming has been created in different
libraries for each program. In the development of active safety systems in cars as ABS, TCS
and ESP, the first that was set into serial production was ABS in 1978 by Bosch [6]. For the
thesis the first code to be implemented was ABS. Each code is independent, but ABS & TCS
are integrated into the ESP. Therefore ABS and TCS had to be created first in order and then
ESP.
9
2.4.1 Regulator shell
The Racer simulation software has been used at the Linköping University and through them
the foundation for the regulator was given, with the input and output signals that was required
to implement code for ABS, TCS and ESP.
Input signals
PedalLevel
BrakeLevel
SteerAngle
Time
A_x
YawRate
// Accelerator pedal level [0, 1000]
// Brake pedal level [0, 1000]
// Steer angle [rad]
// Time [ms]
// Lateral acceleration [m/s2]
// Yaw rate [rad/s]
// The rotational speed of the wheels [rad/s]
omega_1
// 1 - FrontLeft wheel
omega_2
// 2 - FrontRight wheel
omega_3
// 3 - RearLeft wheel
omega_4
// 4 - RearRight wheel
Output signals
PedalLevel
BrakeLevel
BrakeFactors (0, 0, 0, 0)
// Accelerator pedal level [0, 1000]
// Brake pedal level [0, 1000]
// Brake scaling (FrontLeft, FrontRight, RearLeft, RearRight) [%]
2.4.2 Measurement sampling
All simulations have been logged with MATLAB, the measurements have been sampled and
visualized with MATLAB m-files for the specific measurement. All this MATLAB data
acquisition for the Racer Simulation was created by Erik Hellström, Linköping University.
See appendix B for m-file.
For all measurements, [km/h] was chosen as the unit for velocity instead of SI-units, as it is
often used as the unit for speed when referring to vehicles, also [ ̊ ] was chosen as the unit for
the steering wheel angle.
2.4.3 ABS
For the code of ABS the important input signals are wheel speed and brake level. For output
brake factors are the key parameters. By measuring the speed of the wheels and the velocity
of the car, if any of the wheels go below a value of speed for the other wheels the brake factor
for that wheel is reduced in order to avoid locking the wheel. In reality on a vehicle the wheel
speed are measured wheel by wheel, if the derivative for the wheel speed is too steep the
brake pressure is reduced [6].
10
if FrontLeft < RearLeft
BrakePressure FrontLeft = 0%
else FrontLeft > RearLeft
BrakePressure FrontLeft = 100%
If FrontRight < RearRight
BrakePressure FrontRight = 0%
else FrontRight > RearRight
BrakePressure FrontRight = 100%
if RearLeft < FrontLeft
BrakePressure RearLeft = 0%
else RearLeft > FrontLeft
BrakePressure RearLeft = 100%
if RearRight < FrontRight
BrakePressure RearRight = 0%
else RearRight > FrontRight
BrakePressure RearRight = 100%
if Brake
Figure 7. Float schematics ABS code.
2.4.4 TCS
The code for the TCS only intervenes with engine management to regulate the driven wheels
when accelerating. If brakes are used as well on TCS some noise occurs when the system is
activated. For this part the goal was to see if a TCS could work with expected results even
without brake intervention in the code. The TCS was programmed with several setups with 235% slip depending on conditions and preferred behaviour.
if Throttle
if RearLeft > FrontLeft X 1,02-1,35
Throttle = 20-50%
if RearRight > FrontRight X 1,02-1,35
Throttle = 20-50%
else RearLeft < FrontLeft X 1,02-1,35
Throttle = PedalLevel
else RearRight < FrontRight X 1,02-1,35
Throttle = PedalLevel
Figure 8. Float schematics TCS code.
2.4.5 ESP
The code for ESP has understeer and oversteer control. The important input signals for ESP
are A_x, YawRate and SteerAngle. Based on the input, if it goes above a certain threshold the
output signals BrakeLevel and PedalLevel corrects the direction and stability of the vehicle. If
the vehicle oversteers, by braking outside front wheel it will help the car to maintain on the
preferred course. If understeer occurs, correction will be done by braking inside rear wheel.
The code is created with several settings, ice and snow, race and off for low friction surfaces,
normal, sport, race and off for high friction surfaces.
11
All parameters are set based on testing, for optimal performance, the parameters could have
been chosen according to physical formulas in 2.1.1, but instead tested values for ESP worked
better than calculated. The code more or less works mainly on yaw rate, because lateral
velocity could not be used in the regulator, but it regulates based on maximal possible yaw
rate and lateral acceleration.
if Oversteer
Brake FrontLeft
if Understeer
Brake RearRight
if RightTurn
ESP
else no Intervention
if Oversteer
Brake FrontRight
if Understeer
Brake RearLeft
if LeftTurn
Figure 9. Float schematics ESP code.
2.5 Testing
Under the development of new production cars several manoeuvres must be performed to
analyse the performance and characteristics of the car. Among these tests the skid pad shows
the characteristics of the car and understeer gradient, characteristic speed and or critical speed
can be verified. The skid pad is a big circle with a constant radius from 50 meters to 500
meters. The lane change manoeuvre shows the vehicle response in a critical situation, where
the driver has to avoid from obstacles in the lane. Even a well balanced car can easily go into
a spin when performing the lane change, therefore it is a good test to make when calibrating
the ESP for a car. The test was performed to as similar conditions as possible as the ISO
3888-2 double lane change according to [6] and [9] see figure below.
Figure 10. Detailed figure of the double lane change.
12
The slalom test track is valuable to perform, in order to find out how the vehicle behaves on a
pendulum effect when turning from left to right repeatedly. The cones for the slalom test are
on a straight line with a distance of 15 m between every cone, a total of 5 cones. For ESP a
handling track with curves of different radius and shape, s-curve combination clearly shows
how the car and the system are behaving.
For ABS and TCS split friction surfaces are used to develop the systems, this is great to
optimize the stability with one side of the car on slippery surface and the other on a surface
with higher friction. These split friction test were not possible to perform in the simulation
software, all ABS and TCS tests were performed on either high friction or low friction
surfaces.
2.6 Simulation
The simulation has been done with a steering wheel, equipped with throttle and brake pedal to
achieve such a realistic environment as possible. The car that has been used is the Porsche
997 Carrera S, which is a rear engine real wheel drive car with manual gearbox. Maximum
steering angle is +/- 29 ̊, with the specific steering wheel gear ratio for the vehicle. The car has
the same setup on the different surfaces, summer tires are used both on high and low friction.
2.6.1 ABS
Braking tests from 100km/h to 0 km/h was performed at conditions similar to packed snow
with a friction coefficient set to 0,4. This condition is more interesting to analyse compared to
a surface as asphalt and a friction coefficient about 1,0, which would lead to smaller
differences when comparing the results. The tests were done with and without ABS, the speed
was 100 km/h +/- 4 km/h, in neutral, second and fourth gear and with full brake pressure.
The brake distance is longer with ABS than without in neutral gear, the distance with ABS
was 100 m compared to 85 m without ABS. The longitudinal acceleration goes up to 5 m/s2
without ABS and only just above 4,5 m/s2 with ABS. In second gear, the brake distance is
longer without ABS, 88 m compared to only 73 m with ABS. Maximal retardation is 5,8 m/s2
without ABS and 5,7 m/s2 with ABS. In fourth gear, with ABS the brake distance is shorter,
73 m compared to 79 m without. With ABS, maximal retardation is 5,5 m/s2 compared to
5,2 m/s2 without ABS. See appendix A for graphs A1-6 for the table below.
Brake test Speed [km/h] Max retardation [m/s2]
Braking distance [m] Gear [R, N, 1-6]
no ABS
101
-5
85
N
no ABS
no ABS
103
98
-5,8
-5,2
88
79
2
4
ABS
104
-4,5
100
N
ABS
97
-5,7
73
2
4
73
ABS
97
-5,5
Table 2.1. Brake test 100-0 km/h with and without ABS in neutral, second and fourth gear.
Brake balance is the same with and without ABS in order not to change any conditions of the
testing. Without ABS the front wheels lock immediately when the brakes are applied, with
ABS the wheels are braked and released repeatedly in order to not lock the wheels, until the
vehicle has stopped or the brake pedal is released.
13
When braking the distance becomes shorter if a gear is engaged but it can also lead to
instability on a rear wheel driven car due to the fact that the engine helps to reduce the speed
of the rear wheels because of motor torque.
2.6.2 TCS
For these 0-100 km/h tests, acceleration was done with a standing start. For the test without
TCS, the throttle was regulated by the driver and the test with TCS full throttle was engaged
and regulated by the TCS code. The conditions was the same as the braking measurements,
the surface is packed snow and the friction coefficient 0,4.
Measurements were performed on asphalt as well, but in that case TCS is more or less not
necessary, there were small or non difference when comparing with and without TCS.
The start is done in first gear on idle, accelerating as hard as possible, second gear is engaged
just above 60 km/h. The acceleration from 0-100 km/h were performed in 11,33 seconds
without TCS and 8,93 seconds with TCS with 10 % slip. In this case, TCS with a slip of 10 %
gives optimal acceleration. For better stability, a slip between 5-10 % is recommended. For
table 2.2, see appendix A for graphs A7-10.
Acceleration
2
Longitudinal acceleration [m/s ]
Time [s]
no TCS
2
11,33
TCS 5% slip
3
9,98
3,2
8,93
TCS 10% slip
TCS 15% slip
3,1
9,05
Table 2.2. Acceleration test 0-100 km/h with TCS 1,05, TCS 1,1, TCS 1,15 and without TCS.
2.6.3 ESP
The key parameters for ESP are yaw rate and lateral acceleration, if the values of yaw rate and
or lateral acceleration are too high, makes the vehicle unstable. By setting the maximum
limits of the lateral acceleration and the yaw rate the stability of the car is maintained with
ESP, without ESP the car goes into a skid or a spin with counter steering and losing control as
result, with ESP the car is easy to maintain on the preferred course with some slip.
To find out the characteristics during steady state cornering of a vehicle, the skid pad is a
great test to perform. On the limit of friction, this test shows if the car is under or oversteered,
how it behaves during load transfer when lifting of throttle or when braking. The skid pad
with a constant radius of 200 m has a friction coefficient of 0,4 for the tests below.
One lap is performed for each measurement, one with ABS and TCS, one with ESP in race
mode. The lap is done with standing start and braking in the end, with attempt to keep as high
speed as possible during the lap. For both test runs the TCS was programmed with a slip of
25 %, more slip on the driven wheels results in greater body slip angles, but also the counter
momentum of the ESP during under- or oversteer must be bigger due to bigger side slip on
the driven wheels.
14
With ABS and TCS, the car goes into a skid after three quarters of the circle is performed,
when the driver countersteers, the car goes into a spin and the control is lost. With ESP, the
driver does not have to steer as much due to greater stability as with ABS and TCS only, also
the speed is higher. For table 2.3, graphs for each test are figures A11 and A12 in appendix A.
Skid pad
ABS and TCS
2
Max lateral acceleration [m/s ]
ESP
1,5
1,26
-0,75
0,85
Max yaw rate [rad/s]
0,92
0,16
Min yaw rate [rad/s]
-1,9
-0,35
Max steering wheel angle [ ̊ ]
29
8
Min steering wheel angle [ ̊ ]
-29
-8
Max body slip [ ̊ ]
89
25
Min body slip [ ̊ ]
-88
0
Max speed [km/h]
124
129
2
Min lateral acceleration [m/s ]
Min speed [km/h]
-58
106
Table 2.3. Skid pad with ABS and TCS 1,25, skid pad with ESP in race mode.
The lane change is performed according to the ISO 3888-2 standard procedure, but the entry
speed is below 90 km/h in third gear. The surface friction for the test was set to 0,4. Without
ESP the car spins, with ESP in race mode the car maintains stable and avoids the obstacle and
is easy to handle. TCS was set with 5 % slip for straight ahead stability, during steering in the
lane change test the throttle pedal is disengaged according to test procedure ISO 3888-2.
Table 2.4 show the results of the measurements of the lane change in appendix A, figure A1314.
Lane change
ABS and TCS
2
Max lateral acceleration [m/s ]
ESP
5
2,02
-6
-1,43
Max yaw rate [rad/s]
0,98
1,01
Min yaw rate [rad/s]
-1,42
-0,66
Max steering wheel angle [ ̊ ]
29
28
Min steering wheel angle [ ̊ ]
-29
-14
Max body slip [ ̊ ]
61
14
Min body slip [ ̊ ]
-26
-12
88
85
2
Min lateral acceleration [m/s ]
Max speed [km/h]
Min speed [km/h]
-10
0
Table 2.4. Lane change with ABS and TCS 1,05, lane change with ESP in race mode.
For the slalom test the entry speed is just below 90 km/h in third gear, the surface on the
slalom track has a friction coefficient of 0,4. Without ESP only two cones were possible to
make, the first cone is no problem but when turning it creates a pendulum affect that makes
the car spin when coming to the second cone. With ESP all five cones were passed easily.
15
For both runs throttle is engaged through the cones, otherwise speed would have been lost,
which would result in, that the limit of the friction would not be passed other than for the first
or the second cone, then ESP would not be engaged to regulate the stability of the vehicle and
the outcome of the test would be different. Table 2.5 show the results of the measurements of
the slalom in appendix A, figure A15-16.
Slalom
ABS and TCS
2
Max lateral acceleration [m/s ]
ESP
0,83
1,15
-1,01
-1,32
Max yaw rate [rad/s]
0,65
1,02
Min yaw rate [rad/s]
-1,45
-0,98
2
Min lateral acceleration [m/s ]
Max steering wheel angle [ ̊ ]
29
29
Min steering wheel angle [ ̊ ]
-27
-29
Max body slip [ ̊ ]
88
14
Min body slip [ ̊ ]
-89
-20
86
89
Max speed [km/h]
Min speed [km/h]
-12
0
Table 2.5. Slalom with ABS and TCS 1,05, slalom with ESP in race mode.
The race track has a high friction surface, the friction coefficient is 1,0. The track has big
altitude variations and a rather uneven and bumpy surface which is perfect for dynamic tests.
As seen below in table 2.6, from the results of the measurements in figure A17-18 in appendix
A, there are no bigger differences with only ABS and TCS compared to with ESP, here the
ESP is setup in race mode.
But the ESP in this setup still makes the car more forgiving, which allows the driver to push
harder without losing control. Driving without the ESP feels less stable and demands faster
reactions from the driver when grip is suddenly lost. Especially in tight low speed corners and
s-curve sections it is more confident driving with ESP.
Race track
ABS and TCS
2
Max lateral acceleration [m/s ]
ESP
7,6
7,5
-11,6
-6,6
Max yaw rate [rad/s]
1,4
1,64
Min yaw rate [rad/s]
-1,31
-1,36
Max steering wheel angle [ ̊ ]
27
26
Min steering wheel angle [ ̊ ]
2
Min lateral acceleration [m/s ]
-29
-29
Max body slip [ ̊ ]
14
18
Min body slip [ ̊ ]
-25
-18
Max speed [km/h]
190
190
Min speed [km/h]
0
0
Time [s]
1,30,012 1,28,480
Table 2.6. Race track with ABS and TCS 1,25, race track with ESP in race mode.
16
3. Results
Chapter 3 presents the results that have been achieved about the subject.
The goal for this thesis was to create an optimized ESP for a sports car, which have been
done. The results from the simulations show that the code for ABS, TCS and ESP works well.
The ABS works with equal or better brake distances compared without ABS, with increased
stability and manoeuvrability.
During acceleration tests the differences with and without TCS are almost 2,5 seconds from
0-100 km/h to the benefit of TCS. A better driver might decrease that difference but it is hard
to feel have much throttle that can be given by the pedal for optimal acceleration.
All tests with ESP indicate that the subject for this thesis is possible, more slip and later
intervention is possible without compromising stability and comfort. The skid pad test can be
done without ESP, but if the car skids and the driver countersteers it is easy to lose stability
and control. With ESP the driver can steer and countersteer more than necessary without
losing control. On the lane change and slalom manoeuvres the importance of the ESP is
clearly shown, without ESP it is not possible to make the track in the same speed as with ESP.
On low mue friction surfaces it is evident that ESP is important for vehicle stability. On high
mue friction it is not as clear cause is it harder to pass the limit, but once the limit of grip is
exceeded the ESP will be needed for most drivers in order not to lose control of the vehicle.
On the race track the lap time is 1,5 seconds faster with ESP than without. Even though the
race mode setting for ESP on high friction is very permitting it still helps the driver just
enough without feeling intervening or unstable, although on this setting the driver must
countersteer some to maintain on the preferred course, but will not spin.
17
4. Conclusion
The conclusions that have been drawn upon the presented results
of the thesis is summarized in this chapter.
The simulation of the ESP has worked well when the code for each system and library
behaved as preferred. In most cases the Racer Simulation has been realistic and useful for the
conditions of the performed tests. Although some measurements indicate that the values for
longitudinal and especially lateral acceleration are below the values that should be reachable
in reality for the specific surfaces and frictions. This must depend on vehicle and or tire
parameters in Racer simulation. Due to this phenomenon yaw rate was more important to
focus on when creating ESP code.
For all the measurements it is possible to have a higher speed with ESP than without on low
friction surfaces. On high mue friction the speed is more or less the same, here it is much
easier for the driver to control the car up to the limit of friction. It is much harder to pass the
limit of friction on high mue surfaces and therefore the differences are smaller compared to
low mue conditions. But once the limit of friction is passed, whether the surface has low or
high friction, the function of the ESP is clearly shown, it works as required.
The ESP works exceptional with body slip up to 25 degrees or more without compromising
stability, when it activates and regulates the intervention is smooth and comfortable. Still, all
tests were performed with simulations, if the tests could have been performed on a vehicle the
test results could have been different, this was though not possible due to confidentiality
agreement issues.
18
5. Discussion
Chapter 5 contains discussion about personal reflections of the work and possible
future work of the study in this thesis.
During simulation and programming the biggest problem was to achieve an ABS that was
stable. In the beginning there were problems with bugs, for example one front wheel
sometimes locked completely without reason, this could change from side to side as well
which made it hard to understand why it did behave like this. Also the engine creates braking
torque when throttle pedal is released, which makes the driven wheels brake harder than the
undriven, which results in an unstable vehicle. Especially on a rear wheel drive car this
creates instability.
One problem was that if lateral velocity was used in the regulator shell, the wheel speed for
each wheel did not work correctly, which lead to the fact that lateral velocity of the vehicle in
the simulation could not be used. Lateral velocity is achieved by integrating the signal of
lateral acceleration. It could strangely though be sampled and measured in the log-file for
MATLAB. Due to this, code to regulate body slip was created empirically.
For the simulation it would have been preferable if the Force Feedback for the steering wheel
would have worked, unfortunately it did not. This would have done the simulation more
realistic with more feedback to the driver. The steering wheel has a support for 900 (+/-450)
degrees of rotation but that does not include Linux, so all measurement were done with 200
(+/-100) degrees of rotation of the steering wheel as it is by default in Linux.
Body slip only measures up to +/- 90 degrees in MATLAB, the calculation according to the
equation [2.1] does not result in higher values even if the car spins 360 degrees.
The ABS regulation code would not work as well in the reality on a car, because reducing
brake pressure to zero would create a slow, unsafe and inefficient brake system. This would
have been changed, if more time could have been spent on the ABS code.
Further work could be to optimize the code and research the possibilities of implementing P1regulation, or PI2-regulation even PID3-regulation [10].
Last of all, I have learned a lot about how ABS, TCS and ESP work and how they can be
optimized for the specific behaviour that is required.
1
proportional.
proportional and integrating.
3
proportional, integrating and derivating.
2
19
References
[1] ChooseESC, http://www.chooseesc.eu/en/facts_about_electronic_stability_control/
general_ information_about_esc/ 080516
[2] WONG, J. Y., Theory of Ground Vehicles. John Wiley & Sons Ltd, 3rd Edition, 2001.
[3] Robert Bosch GmbH, Automotive Handbook. Bentley Publishers, 6th Edition, 2004.
[4] Linköping University TSFS02, http://www.fs.isy.liu.se/~jaasl/Fordonsdynamik/F8.pdf
080521
[5] Lopez, C, Going Faster! Mastering the Art of Race Driving. Bentley Publishers, 2001.
[6] Robert Bosch GmbH, Safety, Comfort and Convenience Systems. John Wiley & Sons Ltd,
2006.
[7] www.racer.nl 080516
[8] C++ Reference, http://www.cppreference.com/ 080516
[9]NHTSA, http://www-nrd.nhtsa.dot.gov/pdf/nrd-01/esv/esv19/05-0221-O.pdf 080521
[10] Thomas, B, Modern Reglerteknik. Liber AB, 3rd Edition, 2003.
20
Appendix A
ABS
Brake test with and without ABS from 100-0 km/h. The velocity of the car is the blue line, the
speed of the rear wheels are the red lines and the speed of the front wheels are the purple
lines. As seen on the graphs the front wheels lock immediately without ABS when braking.
Longitudinal acceleration
Position
550
500
Velocity
2
Path start
Plot start
End
120
1
450
100
0
80
Z [m]
350
300
250
-1
60
Velocity [km/h]
Longitudinal acceleration [m/s²]
400
-2
40
-3
20
-4
200
100
-50
0
-5
150
0
X [m]
50
-6
300
350
400
Distance [m]
450
-20
300
350
400
Distance [m]
450
Figure A.1. Brake test 100-0 km/h without ABS in neutral gear.
Position
400
Longitudinal acceleration
Velocity
6
Path start
Plot start
End
350
4
300
2
120
100
250
200
Velocity [km/h]
Longitudinal acceleration [m/s²]
Z [m]
80
0
60
40
-2
20
150
100
-50
-4
0
X [m]
50
-6
150
0
200
250
Distance [m]
300
-20
150
200
250
Distance [m]
300
Figure A.2. Brake test 100-0 km/h without ABS in second gear.
1
Position
800
Longitudinal acceleration
Path start
Plot start
End
700
Velocity
6
100
4
80
2
60
Z [m]
500
400
Velocity [km/h]
Longitudinal acceleration [m/s²]
600
0
40
-2
20
-4
0
300
200
100
-50
0
X [m]
-6
500
50
520
540
560
Distance [m]
580
-20
500
600
520
540
560
Distance [m]
580
600
Figure A.3. Brake test 100-0 km/h without ABS in fourth gear.
Position
500
Longitudinal acceleration
Path start
Plot start
End
450
Velocity
2
120
1
100
0
80
-1
60
Z [m]
350
300
250
Velocity [km/h]
Longitudinal acceleration [m/s²]
400
-2
40
-3
20
-4
0
200
150
100
-50
0
X [m]
50
-5
200
250
300
Distance [m]
350
-20
200
250
300
Distance [m]
350
Figure A.4. Brake test 100-0 km/h with ABS in neutral gear.
2
Position
550
Longitudinal acceleration
Path start
Plot start
End
500
Velocity
2
120
1
100
450
0
80
Z [m]
350
300
250
-1
Velocity [km/h]
Longitudinal acceleration [m/s²]
400
-2
60
40
-3
20
-4
200
100
-50
0
-5
150
0
X [m]
-6
300
50
350
400
450
Distance [m]
-20
300
500
350
400
450
Distance [m]
500
Figure A.5. Brake test 100-0 km/h with ABS in second gear.
Position
600
Longitudinal acceleration
Path start
Plot start
End
550
Velocity
1
120
0
100
-1
80
-2
60
Longitudinal acceleration [m/s²]
450
Z [m]
400
350
300
250
Velocity [km/h]
500
-3
40
-4
20
-5
0
200
150
100
-50
0
X [m]
50
-6
300
350
400
450
Distance [m]
500
-20
300
350
400
450
Distance [m]
500
Figure A.6. Brake test 100-0 km/h with ABS in fourth gear.
3
TCS
Acceleration 0-100 km/h with and without TCS. The velocity of the car is the blue line, the
speed of the rear wheels are the red lines and the speed of the front wheels are the purple
lines. As seen in figure A.7, that under these conditions it is hard to regulate the throttle for
the driver for an optimal acceleration without TCS, the speed of the rear wheels are much
higher than for the car.
Position
Velocity
450
120
Path start
Plot start
End
400
100
Velocity [km/h]
350
Z [m]
300
250
200
80
60
40
20
150
0
100
-100
-80
-60
-40
-20
-20
0
0
50
100
150
Distance [m]
X [m]
Longitudinal acceleration
250
300
Time / Velocity
3.5
120
3
Longitudinal acceleration [m/s²]
200
100
Velocity [km/h]
2.5
2
1.5
1
80
60
40
0.5
20
0
-0.5
0
50
100
150
Distance [m]
200
250
0
300
15
25
25
Time [s]
30
Figure A.7. Acceleration test 0-100 km/h without TCS.
Velocity
Position
450
400
100
Velocity [km/h]
350
Z [m]
120
Path start
Plot start
End
300
250
200
60
40
20
150
100
-80
80
-70
-60
-50
X [m]
-40
-30
0
-20
0
50
150
Time / Velocity
120
3
100
Velocity [km/h]
Longitudinal acceleration [m/s²]
Longitudinal acceleration
4
2
1
0
-1
100
Distance [m]
80
60
40
20
0
50
100
150
Distance [m]
200
250
300
0
14
16
18
Time [s]
20
22
24
Figure A.8. Acceleration test 0-100 km/h with TCS 5 % slip.
4
Velocity
Position
450
400
100
Velocity [km/h]
350
Z [m]
120
Path start
Plot start
End
300
250
200
80
60
40
20
150
100
-80
-70
-60
-50
X [m]
-40
-30
0
-20
0
50
100
120
3
100
2
1
0
-1
200
250
300
Time / Velocity
4
Velocity [km/h]
Longitudinal acceleration [m/s²]
Longitudinal acceleration
150
Distance [m]
80
60
40
20
0
50
100
150
Distance [m]
200
250
0
300
15
20
Time [s]
25
30
Figure A.9. Acceleration test 0-100 km/h with TCS 10 % slip.
Position
Velocity
450
120
Path start
Plot start
End
400
100
Velocity [km/h]
Z [m]
350
300
250
80
60
40
20
200
150
-80
-70
-60
-50
X [m]
-40
-30
0
-20
0
20
40
Longitudinal acceleration
120
120
100
3
Velocity [km/h]
Longitudinal acceleration [m/s²]
100
Time / Velocity
4
2
1
0
-1
60
80
Distance [m]
80
60
40
20
0
20
40
60
80
Distance [m]
100
120
0
13
14
15
16
17
18
Time [s]
19
20
21
22
Figure A.10. Acceleration test 0-100 km/h with TCS 15 % slip.
5
ESP
Skid pad with and without ESP.
Position
Velocity
200
0
-100
50
0
-50
-200
-300
-200
-100
0
X [m]
100
-100
200
0
500
1000
Distance [m]
10
0
-10
-20
-30
1500
0
Lateral acceleration
2
0.5
1.5
0
-0.5
-1
-1.5
500
1000
Distance [m]
1500
Body slip
50
1
0.5
0
0
-50
-0.5
-1
1500
500
1000
Distance [m]
100
Body slip [ ]
Lateral acceleration [m/s²]
Yaw rate [rad/s]
Yaw rate
1
0
20
Steering wheel angle [ ]
Path start
Plot start
End
Velocity [km/h]
Z [m]
30
100
100
-2
Steering wheel angle
150
0
500
1000
Distance [m]
1500
-100
0
500
1000
Distance [m]
1500
Figure A.11. Skid pad with ABS and TCS.
Position
Velocity
Steering wheel angle
150
10
0
Velocity [km/h]
Z [m]
100
Path start
Plot start
End
100
Steering wheel angle [ ]
200
-100
50
0
5
0
-5
-200
-200
-100
0
X [m]
100
-50
200
0
Yaw rate
0
-0.1
-0.2
-0.3
500
1000
Distance [m]
1500
500
1000
Distance [m]
1500
30
25
1
20
Body slip [ ]
Lateral acceleration [m/s²]
0.1
0
0
Body slip
1.5
0.2
Yaw rate [rad/s]
-10
1500
Lateral acceleration
0.3
-0.4
500
1000
Distance [m]
0.5
0
15
10
5
-0.5
-1
0
0
500
1000
Distance [m]
1500
-5
0
500
1000
Distance [m]
1500
Figure A.12. Skid pad with ESP in race mode.
6
Lane change with and without ESP.
Position
Velocity
Path start
Plot start
End
350
30
80
20
60
Velocity [km/h]
Z [m]
300
250
200
40
20
150
0
100
-100
-80
-60
-40
X [m]
-20
-20
0
0
Yaw rate
0
-10
-20
-30
300
0
100
200
Distance [m]
0
-0.5
-1
100
200
Distance [m]
80
4
60
2
0
-2
-4
300
40
20
0
-20
-6
-8
300
Body slip
6
Body slip [ ]
Lateral acceleration [m/s²]
Yaw rate [rad/s]
0.5
0
100
200
Distance [m]
10
Lateral acceleration
1
-1.5
Steering wheel angle
100
Steering wheel angle [ ]
400
0
100
200
Distance [m]
-40
300
0
100
200
Distance [m]
300
Figure A.13. Lane change with ABS and TCS.
Position
Velocity
400
300
250
200
30
80
Velocity [km/h]
Z [m]
350
60
40
20
0
150
100
-100
-80
-60
-40
X [m]
-20
-20
0
0
Yaw rate
200
300
Distance [m]
0
-0.5
100
0
-10
0
100
200
300
Distance [m]
400
400
Body slip
10
2
1
0
-1
-2
200
300
Distance [m]
15
Body slip [ ]
Lateral acceleration [m/s²]
0.5
0
10
-20
400
3
1
Yaw rate [rad/s]
100
20
Lateral acceleration
1.5
-1
Steering wheel angle
100
Path start
Plot start
End
Steering wheel angle [ ]
450
5
0
-5
-10
0
100
200
300
Distance [m]
400
-15
0
100
200
300
Distance [m]
400
Figure A.14. Lane change with ESP in race mode.
7
Slalom with and without ESP.
Position
Velocity
Path start
Plot start
End
350
Velocity [km/h]
Z [m]
300
250
200
150
30
80
20
60
40
20
0
100
-100
-80
-60
-40
X [m]
-20
-20
0
0
Yaw rate
-20
0
100
200
Distance [m]
-0.5
-1
100
200
Distance [m]
Body slip
0.5
50
0
-0.5
0
-50
-1
-1.5
300
300
100
Body slip [ ]
Lateral acceleration [m/s²]
0
0
0
-10
-30
300
1
0.5
Yaw rate [rad/s]
100
200
Distance [m]
10
Lateral acceleration
1
-1.5
Steering wheel angle
100
Steering wheel angle [ ]
400
0
100
200
Distance [m]
300
-100
0
100
200
Distance [m]
300
Figure A.15. Slalom with ABS and TCS.
Position
Velocity
Path start
450
Plot start
350
Z [m]
30
80
20
End
Velocity [km/h]
400
Steering wheel angle
100
Steering wheel angle [ ]
500
300
250
60
40
20
200
0
150
100
-100
-80
-60
-40
X [m]
-20
-20
0
0
Yaw rate
0.5
0
-0.5
100
-10
-20
-30
400
0
100
200
300
Distance [m]
400
15
1
10
400
5
0.5
0
-0.5
0
-5
-10
-1
-1.5
200
300
Distance [m]
Body slip
1.5
Body slip [ ]
Lateral acceleration [m/s²]
Yaw rate [rad/s]
1
0
200
300
Distance [m]
0
Lateral acceleration
1.5
-1
100
10
-15
0
100
200
300
Distance [m]
400
-20
0
100
200
300
Distance [m]
400
Figure A.16. Slalom change with ESP in race mode.
8
Race track with and without ESP.
Path start
Plot start
End
Position
100
0
-300
-400
Steering wheel angle [ ]
Velocity [km/h]
-200
100
50
0
-500
-600
-600
-400
-200
0
X [m]
200
-50
400
0
Yaw rate
10
0
-10
-20
-30
3000
0
0.5
0
-0.5
-1
1000
2000
Distance [m]
20
5
10
0
-5
-10
-15
3000
1000
2000
Distance [m]
3000
Body slip
10
Body slip [ ]
Lateral acceleration [m/s²]
Yaw rate [rad/s]
1
0
1000
2000
Distance [m]
20
Lateral acceleration
1.5
-1.5
Steering wheel angle
30
150
-100
Z [m]
Velocity
200
0
-10
-20
0
1000
2000
Distance [m]
-30
3000
0
1000
2000
Distance [m]
3000
Figure A.17. Race track with ABS and TCS.
Path start
Plot start
End
Position
100
0
-300
-400
Steering wheel angle [ ]
Velocity [km/h]
-200
100
50
0
-500
-600
-600
-400
-200
0
X [m]
200
-50
400
0
Yaw rate
10
0
-10
-20
-30
3000
0
1
0.5
0
-0.5
-1
1000
2000
Distance [m]
3000
20
5
10
0
-5
-10
1000
2000
Distance [m]
3000
Body slip
10
Body slip [ ]
Lateral acceleration [m/s²]
Yaw rate [rad/s]
1.5
0
1000
2000
Distance [m]
20
Lateral acceleration
2
-1.5
Steering wheel angle
30
150
-100
Z [m]
Velocity
200
0
-10
0
1000
2000
Distance [m]
3000
-20
0
1000
2000
Distance [m]
3000
Figure A.18. Race track with ESP in race mode.
9
Appendix B
Regulator shell
//
// controller.cpp: implementation of a controller
//
//
// Erik H, 20070213.
//
// Johan Andersson, 20080404
//
#include
#include
#include
#include
#include
#include
<math.h>
<control.h>
<iostream.h>
<abs.h>
<tcs1.25slip.h>
<esphighrace997.h>
//
// Controller main function
//
void Controller(const ControlInput& In, ControlOutput& Out) {
//
// Declare work variables
//
float dt;
//
// The keyword static causes a variable that is defined within a
// function to be preserved in subsequent calls to the function.
// It is thus suitable for keeping state variables.
//
// States
static int t0
= 0;
// Last time stamp [ms]
//
// ESP Parameters
//
//
// Retrieve inputs
//
const int PedalLevel
= In.PedalLevel; // Accelerator pedal level [0,1000]
const int BrakeLevel
= In.BrakeLevel; // Brake pedal level [0,1000]
const float SteerAngle = In.SteerAngle; // Steer angle [rad]
const int t1
= In.Time;
// Time [ms]
const float A_x
= In.A_x;
// Lateral acceleration [m/s^2]
const float YawRate
= In.YawRate;
// Yaw rate [rad/s]
// The rotational speed of the respective wheels [rad/s]
// 1 - Front left wheel
3 - Rear left wheel
// 2 - Front right wheel 4 - Rear right wheel
const float omega_1
= In.FrontLeft().AngVel;
const float omega_2
= In.FrontRight().AngVel;
const float omega_3
= In.RearLeft().AngVel;
const float omega_4
= In.RearRight().AngVel;
// Velocity of Car [m/s]
const float V_y
= (((omega_1+omega_2+omega_3+omega_4)/4)*0.331);
//
10
// Update states
//
dt = t1-t0; // Time difference since last call [ms]
if(t0 > 0) {
// Update
}
else {t0 = t1;
// Reset
}
// Update time stamp
//
// Default output values
//
Out.SetPedalLevel(PedalLevel);
Out.SetBrakeLevel(BrakeLevel);
Out.SetBrakeFactors(0,0,0,0);
Out.State = ON;
Out.Monitor = 1;
// Accelerator pedal level [0,1000]
// Brake pedal level [0,1000]
// Brake scaling [%]
// Controller state {OFF,ON}
// Monitor variable
//
// Controller implementation
//
// For ABS
abs(omega_1, omega_2, omega_3, omega_4, V_y, BrakeLevel, YawRate, &Out);
// For TCS
tcs(omega_1, omega_2, omega_3, omega_4, V_y, PedalLevel, BrakeLevel, &Out);
// For ESP
esp(omega_1, omega_2, omega_3, omega_4, V_y, BrakeLevel, PedalLevel, SteerAngle,
A_x, YawRate, &In, &Out);
}
11
MATLAB measurement sampling
% LoadRacerData.m
%
% Erik H, 20061214.
%
% modified by Johan Andersson, 20080414
%
% Load data from last run
load /tmp/logger.mat
%
% EXTRACT DATA
%
%
% Definition of axes:
%
% X: Out of the front door
% Y: Up through the roof
% Z: Out of the front windshield
%
%
X
%
^
%
|
%
|---.---| -> Z
%
Y
%
Rear
Front
%
%
% Static properties
%
% Radius of the wheels [m]
r_FL = RacerStatic.FrontLeftRadius;
r_FR = RacerStatic.FrontRightRadius;
r_RL = RacerStatic.RearLeftRadius;
r_RR = RacerStatic.RearRightRadius;
%
% Dynamic data
%
% Information
Time = 1e-3*RacerInfo(:,1);
Dist = RacerInfo(:,2);
State = RacerInfo(:,3);
N = length(Time);
%
X
Y
Z
%
%
%
%
Time [s]
Driven meters [m]
Controller status flag
Number of samples
Position of the car (in world orientation) [m]
= RacerPosition(:,1);
= RacerPosition(:,2);
= RacerPosition(:,3);
% Velocity of the car (in car orientation) [km/h]
V_x = RacerVelocity(:,1);
V_y = RacerVelocity(:,2);
V_z = RacerVelocity(:,3);
% Acceleration of the car (in car orientation) [m/s^2]
A_x = RacerAcceleration(:,1);
A_y = RacerAcceleration(:,2);
A_z = RacerAcceleration(:,3);
% Rotational velocity of the car (in car orientation) [rad/s]
R_x = RacerRotVelocity(:,1);
R_y = RacerRotVelocity(:,2);
R_z = RacerRotVelocity(:,3);
12
% Angular velocities of the wheels [rad/s]
a_FL = RacerWheel(:,1);
a_FR = RacerWheel(:,2);
a_RL = RacerWheel(:,3);
a_RR = RacerWheel(:,4);
% Controls
Pedal = RacerControl(:,1); % Pedal
Brake = RacerControl(:,2); % Brake
Angle = RacerControl(:,3); % Steer
BrakeFactor = RacerControl(:,4:7);
level [0,1000] [-]
level [0,1000] [-]
angle [rad]
% Brake factor [0,100] [%]
13