Stability Control of Electric Vehicles with In-wheel Motors

Stability Control of Electric Vehicles with In-wheel Motors
Stability Control of Electric Vehicles with
In-wheel Motors
by
Kiumars Jalali
A thesis
presented to the University of Waterloo
in fulfillment of the
thesis requirement for the degree of
Doctor of Philosophy
in
Mechanical Engineering
Waterloo, Ontario, Canada, 2010
© Kiumars Jalali 2010
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis,
including any required final revisions, as accepted by my examiners.
I understand that my thesis may be made electronically available to the public.
Kiumars Jalali
ii
Abstract
Recently, mostly due to global warming concerns and high oil prices, electric vehicles
have attracted a great deal of interest as an elegant solution to environmental and energy
problems. In addition to the fact that electric vehicles have no tailpipe emissions and are
more efficient than internal combustion engine vehicles, they represent more versatile
platforms on which to apply advanced motion control techniques, since motor torque and
speed can be generated and controlled quickly and precisely.
The chassis control systems developed today are distinguished by the way the
individual subsystems work in order to provide vehicle stability and control. However,
the optimum driving dynamics can only be achieved when the tire forces on all wheels
and in all three directions can be influenced and controlled precisely. This level of control
requires that the vehicle is equipped with various chassis control systems that are
integrated and networked together. Drive-by-wire electric vehicles with in-wheel motors
provide the ideal platform for developing the required control system in such a situation.
The focus of this thesis is to develop effective control strategies to improve
driving dynamics and safety based on the philosophy of individually monitoring and
controlling the tire forces on each wheel. A two-passenger electric all-wheel-drive urban
vehicle (AUTO21EV) with four direct-drive in-wheel motors and an active steering
system is designed and developed in this work. Based on this platform, an advanced
fuzzy slip control system, a genetic fuzzy yaw moment controller, an advanced torque
vectoring controller, and a genetic fuzzy active steering controller are developed, and the
performance and effectiveness of each is evaluated using some standard test maneuvers.
Finally, these control systems are integrated with each other by taking advantage of the
strengths of each chassis control system and by distributing the required control effort
between the in-wheel motors and the active steering system. The performance and
effectiveness of the integrated control approach is evaluated and compared to the
individual stability control systems, again based on some predefined standard test
maneuvers.
iii
Acknowledgements
This research has been carried out in the Motion Research Group at the University of
Waterloo, in Canada. I am pleased to acknowledge the financial support that I received
from AUTO21, a Canadian Network of Centres of Excellence, and the Natural Sciences
and Engineering Research Council of Canada (NSERC). The financial support from these
organizations allowed me to focus on my research and carry it out to completion.
There are a number of people to whom I would like to express my gratitude. First
of all, I owe a great deal of gratitude to my supervisors, Prof. Steve Lambert and Prof.
John McPhee, for giving me great freedom in selecting my research topics and who,
through a combination of patience and persistence, have enabled me to grow more than I
knew possible during the course of my Ph.D. This work is a result of their unlimited
support and encouragement, and the faith they put in me. It was a long journey that I‟m
happy to have experienced.
Special thanks go to the present (Tom Uchida, Matthew Millard, Sukhpreet
Sandhu, Ramin Masoudi, Willem Petersen, Joydeep Banerjee, Mohammad Sharif
Shourijeh, Mohammadreza Saeedi, and Mike Boos) and past (Kevin Morency, Mathieu
Léger, Mike Wybenga, Adel Izadbakhsh, William Bombardier, Akram Abdel-Rahman,
Dr. Nasser Azad, Dr. Yi Liu, and Dr. Chad Schmitke) lab mates at the Motion Research
Group. I have had a great time working with you guys and hope that we keep in touch in
the future.
Tom Uchida, I had a great time working with you and, without your enthusiasm,
patience, and constant support, this thesis would be neither half as good nor half as
finished by now. I hope I will be able to repay you soon.
Chad Schmitke, it was my honor to work with you on a variety of projects, and I
thank you for your support throughout my thesis.
Kevin Morency, thank you for the great support you provided me during your stay
in Waterloo. It was a great time having you as my lab mate and roommate at the same
time.
Last but not least, I would like to thank my parents, Robabeh Djalali and Amir
Hossein Jalali, for the unlimited love and support you provided me throughout my life. I
am who I am just because of you. Without your unconditional support, care, and belief in
iv
me, I would not have made it this far in life. You have been there for me every step of the
way and have aided me through all of my decisions.
Thank You!
Waterloo, April 2010
Kiumars Jalali
v
Dedication
This thesis is dedicated to my father, who has raised me to be the person I am today. You
have been with me every step of the way, through good times and bad. Thank you for all
the unconditional love, guidance, and support that you have always given me, helping me
to succeed and instilling in me the confidence that I am capable of doing anything I put
my mind to.
Thank you for everything. I love you!
vi
Table of Contents
List of Figures.............................................................................................................. x
List of Tables .......................................................................................................... xxiii
1
Introduction and Background .............................................................................. 1
1.1
1.1.1
Brake-by-wire systems.............................................................................................................5
1.1.2
Steer-by-wire systems .............................................................................................................7
1.2
Anti-lock braking system........................................................................................................10
1.2.2
Traction control system .........................................................................................................11
1.2.3
Methods of adjusting the tire slip ratio .................................................................................12
Conventional stability control systems ................................................................. 13
1.3.1
Braking-based electronic stability control system .................................................................15
1.3.2
Steering-based electronic stability control system ................................................................17
1.3.3
Torque vectoring control system ...........................................................................................20
1.4
Advanced stability control system through networked chassis .............................. 25
1.5
Thesis outline and contributions........................................................................... 29
Test Maneuvers and Analytical Driver Models.................................................... 31
2.1
Test maneuvers for evaluating vehicle handling and performance ......................... 33
2.1.1
Selection and evaluation of chosen test maneuvers .............................................................35
2.1.2
Comprehensive evaluation of chosen test maneuvers .........................................................41
2.2
Modelling the behaviour of a driver ..................................................................... 42
2.2.1
Development of a path-following driver model ....................................................................44
2.2.2
Development of a speed-control driver model .....................................................................50
2.3
3
Conventional slip control systems ..........................................................................9
1.2.1
1.3
2
State-of-the-art drive-by-wire technologies ............................................................4
Evaluation of the path-following and speed-control driver models ........................ 52
Advanced Fuzzy Slip Control System ................................................................... 60
3.1
Conventional slip control systems ........................................................................ 61
3.2
Development of an advanced fuzzy slip control system ......................................... 62
3.3
Evaluation of the advanced fuzzy slip control system ............................................ 71
vii
Table of Contents
3.4
4
Genetic Fuzzy Yaw Moment Controller ............................................................... 80
4.1
Simplified vehicle model with in-wheel motors..................................................... 81
4.2
Soft computing and hybrid techniques ................................................................. 83
4.3
Fuzzy yaw moment controller design .................................................................... 90
4.4
Evaluation of the fuzzy yaw moment controller .................................................... 98
4.5
Genetic tuning of the fuzzy yaw moment controller ............................................ 100
4.6
Evaluation of the genetic fuzzy yaw moment controller ...................................... 111
4.6.1
ISO double-lane-change maneuver .................................................................................... 111
4.6.2
Step-steer response maneuver........................................................................................... 115
4.6.3
Brake-in-turn maneuver ..................................................................................................... 116
4.6.4
Straight-line braking on a -split road ................................................................................ 119
4.7
5
Chapter summary .............................................................................................. 121
Advanced Torque Vectoring Controller ............................................................. 123
5.1
Control method for left-to-right torque vectoring distribution............................. 123
5.2
Calculation of tire adhesion potential ................................................................. 126
5.3
Control method for front-to-rear torque vectoring distribution ........................... 130
5.4
Evaluation of the advanced torque vectoring controller ...................................... 131
5.4.1
ISO double-lane-change maneuver .................................................................................... 131
5.4.2
Step-steer response maneuver........................................................................................... 137
5.4.3
Brake-in-turn maneuver ..................................................................................................... 139
5.4.4
Straight-line braking on a -split road ................................................................................ 142
5.5
6
Chapter summary ................................................................................................ 78
Chapter summary .............................................................................................. 146
Genetic Fuzzy Active Steering Controller .......................................................... 147
6.1
Fuzzy active steering controller design ................................................................ 148
6.2
Evaluation of the fuzzy active steering controller ................................................ 151
6.3
Genetic tuning of the fuzzy active steering controller .......................................... 153
6.4
Evaluation of the genetic fuzzy active steering controller .................................... 156
viii
Table of Contents
6.4.1
ISO double-lane-change maneuver .................................................................................... 156
6.4.2
Step-steer response maneuver........................................................................................... 161
6.4.3
Brake-in-turn maneuver ..................................................................................................... 163
6.4.4
Straight-line braking on a -split road ................................................................................ 166
6.5
7
Chapter summary .............................................................................................. 169
Integration of the Advanced Torque Vectoring and Genetic Fuzzy Active Steering
Controller ............................................................................................................... 171
7.1
Integration of chassis control systems using an activation function ..................... 171
7.2
Evaluation of the integrated control of the advanced torque vectoring and genetic
fuzzy active steering ....................................................................................................... 174
7.2.1
ISO double-lane-change maneuver .................................................................................... 174
7.2.2
Step-steer response maneuver........................................................................................... 180
7.2.3
Brake-in-turn maneuver ..................................................................................................... 181
7.2.4
Straight-line braking on a -split road ................................................................................ 187
7.3.
8
Chapter summary .............................................................................................. 192
Conclusions and Future Work ........................................................................... 194
References .............................................................................................................. 201
Appendices ............................................................................................................. 211
A
Design and Modelling of the AUTO21EV .......................................................... 211
A.1
Preliminary vehicle design .................................................................................. 212
A.1.1
Longitudinal dynamics ........................................................................................................ 212
A.1.2
Lateral dynamics ................................................................................................................. 216
A.1.3
Vertical dynamics ................................................................................................................ 218
A.2
Detailed suspension design ................................................................................ 220
A.3
Dynamic model of the AUTO21EV....................................................................... 225
A.4
Permanent magnet synchronous in-wheel motor................................................ 227
ix
List of Figures
Figure 1-1: American driving patterns [San05] .................................................................. 3
Figure 1-2: GM Hy-wire concept car with rolling and driving chassis [Elb04] ................. 4
Figure 1-3: Hazard severity of failures in drive-by-wire and higher-level control systems
[Rie99] ................................................................................................................................ 5
Figure 1-4: (a) Electro-hydraulic braking (EHB) and (b) electro-mechanical braking
(EMB) concepts for brake-by-wire technology [Ham03] ................................................... 7
Figure 1-5: (a) Electro-hydraulic actuation, (b) pure hydraulic actuation, and (c) electromechanical actuation concepts for steer-by-wire technology [JB04] ................................. 9
Figure 1-6: Characteristics of the tire longitudinal and lateral forces as a function of tire
slip ratio for constant tire slip angles; used for a slip control system with limited slip ratio
[Bei00] .............................................................................................................................. 12
Figure 1-7: Characteristics of the tire longitudinal and lateral forces as a function of tire
slip ratio for constant tire slip angles; used for a slip control system with adjustable slip
ratio [Bei00] ...................................................................................................................... 13
Figure 1-8: Braking intervention of an ESC system (a) in an oversteered vehicle and (b)
in an understeered vehicle (the ellipse on each tire demonstrates the adhesion potential of
that tire; a dotted ellipse indicates that the adhesion potential has been exceeded).......... 16
Figure 1-9: Design concept and mechanical layout of the BMW active steering system
[Koe04] ............................................................................................................................. 17
Figure 1-10: Variable steering ratio caused by an active steering system [Koe04] .......... 18
Figure 1-11: Generation of a corrective yaw moment through braking intervention using
an ESC system (left) and through steering intervention using an active steering system
(right) ................................................................................................................................ 19
Figure 1-12: An active powertrain system with active center and rear differentials [Jal04]
........................................................................................................................................... 22
Figure 1-13: Torque vectoring in an active powertrain to enhance the vehicle traction
[Jal04] ............................................................................................................................... 22
Figure 1-14: (a) Stability control of an oversteered vehicle through side-to-side torque
vectoring on the front axle, and (b) stability control of an understeered vehicle through
side-to-side torque vectoring on the rear axle ................................................................... 23
x
List of Figures
Figure 1-15: Front-to-rear torque vectoring (a) in an understeered vehicle, and (b) in an
oversteered vehicle [Wal06] ............................................................................................. 24
Figure 1-16: Domain structure of driveline and chassis systems [Sem06] ....................... 26
Figure 1-17: Interdependencies among longitudinal, lateral, and vertical dynamics ....... 27
Figure 1-18: Effective range of various control concepts based on the resulting tire-road
friction circle [Yam91] ..................................................................................................... 28
Figure 2-1: Graphical representation of the driver-vehicle-environment control loop..... 32
Figure 2-2: Different test maneuvers for evaluating vehicle handling and performance
characteristics [Roe77] (Y = yes and N = no)................................................................... 34
Figure 2-3: ISO 3888 double-lane-change maneuver test track design [Bau99] .............. 36
Figure 2-4: Important properties of the dynamic behaviour of the vehicle evaluated by
each test maneuver ............................................................................................................ 42
Figure 2-5: Linear bicycle model used for developing the driver model ......................... 45
Figure 2-6: Steady-state vehicle motion along a circular path of radius R ....................... 46
Figure 2-7: (a) Single-preview-point and (b) multiple-preview-point driver models....... 49
Figure 2-8: Block diagram of the gain scheduling speed controller ................................. 51
Figure 2-9: Path-following driver model concept in a double-lane-change maneuver .... 53
Figure 2-10: (a) Desired and actual vehicle trajectories, (b) driver‟s steering wheel input,
and (c) vehicle yaw rate with respect to the steering wheel angle when driving through a
double-lane-change maneuver at 40 km/h using the path-following driver model .......... 54
Figure 2-11: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when
driving through a double-lane-change maneuver at 40 km/h using the path-following
driver model ...................................................................................................................... 55
Figure 2-12: (a) Desired and actual vehicle trajectories, (b) driver‟s steering wheel input,
and (c) vehicle yaw rate with respect to the steering wheel angle when driving through a
double-lane-change maneuver at 75 km/h using the path-following driver model .......... 55
Figure 2-13: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when
driving through a double-lane-change maneuver at 75 km/h using the path-following
driver model ...................................................................................................................... 56
Figure 2-14: (a) Desired and actual vehicle trajectories, (b) required steering wheel angle
applied by the driver model, and (c) desired and actual vehicle longitudinal speeds when
xi
List of Figures
driving through the steady-state constant radius maneuver using the path-following and
speed-control driver models .............................................................................................. 56
Figure 2-15: (a) Driver‟s steering wheel input and (b) vehicle sideslip angle as functions
of vehicle lateral acceleration when driving through the steady-state constant radius
maneuver using the path-following and speed-control driver models .............................. 57
Figure 2-16: Stepwise speed request from the driver model and the actual speed of the
vehicle ............................................................................................................................... 58
Figure 2-17: Motor torques during the stepwise speed variation test when driving in a
straight line........................................................................................................................ 59
Figure 3-1: Typical adhesion coefficient characteristics as a function of tire slip ratio for
different road conditions ................................................................................................... 63
Figure 3-2: Planar two-track vehicle model...................................................................... 64
Figure 3-3: Block diagram of neural network sideslip estimator proposed by Durali and
Bahramzadeh [Dur03] ....................................................................................................... 66
Figure 3-4: Performance of the neural network sideslip angle estimator during a doublelane-change maneuver ...................................................................................................... 66
Figure 3-5: (a) Translational and (b) rotational tire motion .............................................. 67
Figure 3-6: Block diagram for calculating the actual slip ratio of the front-left tire ........ 68
Figure 3-7: Control rule base (left) and control surface (right) of the fuzzy slip control
system ............................................................................................................................... 70
Figure 3-8: Shape and distribution of membership functions for the input and output
variables of the fuzzy slip controller ................................................................................. 70
Figure 3-9: Block diagram of the advanced slip control system for the front-left tire ..... 71
Figure 3-10: (a) Vehicle speed and (b) vehicle longitudinal acceleration versus forward
speed during the straight-line acceleration maneuver ....................................................... 71
Figure 3-11: Tire slip ratios during the straight-line acceleration maneuver.................... 72
Figure 3-12: Motor torques during the straight-line acceleration maneuver .................... 73
Figure 3-13: (a) Braking distance, (b) vehicle speed, and (c) vehicle longitudinal
deceleration versus forward speed during the straight-line braking test........................... 74
Figure 3-14: Tire slip ratios during the straight-line braking maneuver ........................... 75
Figure 3-15: Motor torques during the straight-line braking maneuver ........................... 75
Figure 3-16: Vehicle trajectory when accelerating on a -split road................................ 75
xii
List of Figures
Figure 3-17: Tire slip ratios during the straight-line acceleration maneuver on a -split
road ................................................................................................................................... 76
Figure 3-18: Motor torques during the straight-line acceleration maneuver on a -split
road ................................................................................................................................... 76
Figure 3-19: Vehicle trajectory when braking on a -split road ....................................... 77
Figure 3-20: Tire slip ratios during the straight-line braking maneuver on a -split road 78
Figure 3-21: Motor torques during the straight-line braking maneuver on a -split road 78
Figure 4-1: AUTO21EV vehicle model implemented in DynaFlexPro ........................... 82
Figure 4-2: Advantages and disadvantages of soft computing techniques ....................... 84
Figure 4-3: Hybrid techniques possible through the combination of soft computing
paradigms .......................................................................................................................... 85
Figure 4-4: Block diagram of a fuzzy control systems ..................................................... 86
Figure 4-5: Block diagram of a genetic fuzzy control system .......................................... 89
Figure 4-6: Linear bicycle model [Wal05] ....................................................................... 92
Figure 4-7: Block diagram of the fuzzy yaw moment controller ...................................... 95
Figure 4-8: Three-dimensional rule base of the fuzzy YMC ............................................ 97
Figure 4-9: Initial shape and distribution of the membership functions for the input and
output variables of the fuzzy YMC ................................................................................... 98
Figure 4-10: Control surfaces of the fuzzy YMC ............................................................. 98
Figure 4-11: Desired and actual vehicle trajectories when driving through the doublelane-change maneuver with an initial speed of 75 km/h (a) using the driver model and (b)
using the driver model with the fuzzy YMC .................................................................... 99
Figure 4-12: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when
driving through the double-lane-change maneuver using the driver model, with and
without the fuzzy YMC (FYMC) ................................................................................... 100
Figure 4-13: (a) Lateral acceleration, (b) steering wheel angle, and (c) vehicle speed as
functions of time; and (d) vehicle yaw rate as a function of the steering wheel input when
driving through the double-lane-change maneuver with and without the fuzzy YMC
(FYMC)........................................................................................................................... 101
Figure 4-14: Corrective yaw moment generated by the fuzzy YMC .............................. 101
Figure 4-15: Curvature of the road in a two-dimensional plane using Cartesian coordinate
system ............................................................................................................................. 103
xiii
List of Figures
Figure 4-16: Desired fixed steering wheel input for driving through the double-lanechange maneuver ............................................................................................................ 104
Figure 4-17: Desired and actual vehicle trajectories (top), and yaw rate and sideslip angle
(bottom) when driving through the double-lane-change maneuver with a fixed steering
wheel input ...................................................................................................................... 105
Figure 4-18: The effects of linear and nonlinear scaling functions on a fixed set of
normalized membership functions .................................................................................. 107
Figure 4-19: Maximum fitness function value for each generation of the multi-criteria
genetic algorithm ............................................................................................................ 109
Figure 4-20: Block diagram of the multi-criteria genetic algorithm used for tuning the
fuzzy YMC...................................................................................................................... 109
Figure 4-21: Shape and distribution of the genetically-tuned membership functions for the
input and output variables of the fuzzy YMC ................................................................. 111
Figure 4-22: Control surfaces of the genetically-tuned fuzzy YMC .............................. 111
Figure 4-23: Desired and actual vehicle trajectories when driving through the doublelane-change maneuver with an initial speed of 75 km/h using the driver model and the
genetic fuzzy YMC ......................................................................................................... 112
Figure 4-24: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when
driving through the double-lane-change maneuver using the driver model, with and
without the genetic fuzzy YMC (GFYMC) .................................................................... 112
Figure 4-25: (a) Lateral acceleration, (b) steering wheel angle, and (c) vehicle speed as
functions of time; and (d) vehicle yaw rate as a function of the steering wheel input when
driving through the double-lane-change maneuver without a controller, with the fuzzy
YMC (FYMC), and with the genetic fuzzy YMC (GFYMC) ........................................ 113
Figure 4-26: Comparison of the corrective yaw moment generated by the fuzzy and
genetic fuzzy YMCs ....................................................................................................... 114
Figure 4-27: (a) Required steering wheel input and (b) lateral acceleration of the vehicle
when driving through the step-steer maneuver ............................................................... 115
Figure 4-28: Yaw rate (top) and sideslip angle (bottom) of the vehicle when driving
through the step-steer maneuver with and without the genetic fuzzy YMC (GFYMC) . 116
xiv
List of Figures
Figure 4-29: Desired and actual vehicle trajectories when braking in a turn using (a) the
driver model only, and (b) using the driver model with the genetic fuzzy YMC (GFYMC)
......................................................................................................................................... 117
Figure 4-30: (a) Required steering wheel input and (b) lateral acceleration of the vehicle
when braking in a turn with and without the genetic fuzzy YMC (GFYMC) ................ 118
Figure 4-31: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when
braking in a turn using the driver model with and without the genetic fuzzy YMC
(GFYMC) ........................................................................................................................ 118
Figure 4-32: (a) Vehicle speed as a function of time and (b) longitudinal acceleration as a
function of vehicle speed when braking in a turn using the driver model with and without
the genetic fuzzy YMC ................................................................................................... 118
Figure 4-33: Desired and actual vehicle trajectories when braking on a -split road
holding the steering wheel fixed with and without the genetic fuzzy YMC (GFYMC) . 120
Figure 4-34: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when
braking on a -split road holding the steering wheel fixed with and without the genetic
fuzzy YMC (GFYMC) .................................................................................................... 120
Figure 4-35: (a) Corrective yaw moment required to counteract the side-pushing effect of
the vehicle and (b) vehicle speed while braking on a -split road holding the steering
wheel fixed and using the genetic fuzzy YMC ............................................................... 121
Figure 5-1: Advanced torque vectoring strategy using couple generation on each axle (the
dash-dotted ellipse surrounding each tire indicates the adhesion potential of that tire; the
solid ellipse indicates the actual friction ellipse) ............................................................ 124
Figure 5-2: Torque balance at the tire-road contact patch .............................................. 125
Figure 5-3: (a) Longitudinal weight shift during acceleration and (b) lateral weight shift
during cornering .............................................................................................................. 128
Figure 5-4: Desired and actual vehicle trajectories when driving through the double-lanechange maneuver with an initial speed of 75 km/h using the path-following driver model
and the ATVC ................................................................................................................. 131
Figure 5-5: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when
driving through the double-lane-change maneuver using the driver model with and
without the ATVC........................................................................................................... 132
xv
List of Figures
Figure 5-6: (a) Lateral acceleration, (b) steering wheel angle, and (c) vehicle speed as
functions of time; and (d) vehicle yaw rate as a function of the steering wheel input when
driving through the double-lane-change maneuver without a controller, with the genetic
fuzzy YMC (GFYMC), and with the ATVC .................................................................. 133
Figure 5-7: Requested and actual motor torque at each wheel when driving through the
double-lane-change maneuver using the driver model with the ATVC ......................... 134
Figure 5-8: Front-to-rear torque vectoring ratios when driving through the double-lanechange maneuver using the driver model with the ATVC ............................................. 135
Figure 5-9: Traction potential of each tire when driving through the double-lane-change
maneuver using the driver model with the ATVC .......................................................... 136
Figure 5-10: Tire slip ratios when driving through the double-lane-change maneuver
using the driver model with the ATVC........................................................................... 136
Figure 5-11: (a) Required steering wheel input and (b) lateral acceleration of the vehicle
when driving through the step-steer maneuver using the ATVC ................................... 138
Figure 5-12: Yaw rate (top) and sideslip angle (bottom) of the vehicle when driving
through the step-steer maneuver using the ATVC .......................................................... 138
Figure 5-13: Desired and actual vehicle trajectories when braking in a turn using (a) the
driver model only and (b) the driver model with the advanced torque vectoring controller
(ATVC) ........................................................................................................................... 140
Figure 5-14: (a) Required steering wheel input and (b) lateral acceleration of the vehicle
when braking in a turn using the driver model without a controller, with the genetic fuzzy
YMC (GFYMC), and with the ATVC ............................................................................ 140
Figure 5-15: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when
braking in a turn using the driver model without a controller, with the genetic fuzzy YMC
(GFYMC), and with the ATVC ...................................................................................... 141
Figure 5-16: (a) Vehicle speed as a function of time using the driver model with the
ATVC and (b) longitudinal acceleration as a function of vehicle speed when braking in a
turn using the driver model without a controller, with the genetic fuzzy YMC (GFYMC),
and with the ATVC ......................................................................................................... 142
Figure 5-17: Desired and actual vehicle trajectories when braking on a -split road
holding the steering wheel fixed with and without the ATVC ....................................... 143
xvi
List of Figures
Figure 5-18: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when
braking on a -split road holding the steering wheel fixed with and without the ATVC143
Figure 5-19: Tire slip ratios when braking on a -split road holding the steering wheel
fixed and using the ATVC .............................................................................................. 144
Figure 5-20: Requested and actual motor torque at each wheel when braking on a -split
road holding the steering wheel fixed and using the ATVC ........................................... 144
Figure 5-21: Front-to-rear torque vectoring activation when braking on a -split road
holding the steering wheel fixed and using the ATVC ................................................... 145
Figure 6-1: Block diagram of the fuzzy active steering controller ................................. 149
Figure 6-2: Initial shape and distribution of the membership functions for the input and
output variables of the fuzzy ASC .................................................................................. 150
Figure 6-3: Rule base (left) and control surface (right) of the proposed fuzzy active
steering controller ........................................................................................................... 150
Figure 6-4: Desired and actual vehicle trajectories when driving through the double-lanechange maneuver with an initial speed of 60 km/h (a) using the driver model and (b)
using the driver model with the fuzzy ASC .................................................................... 151
Figure 6-5: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when
driving through the double-lane-change maneuver using the driver model with and
without the fuzzy ASC (FASC) ...................................................................................... 152
Figure 6-6: (a) Lateral acceleration, (b) steering wheel angle, and (c) vehicle speed as
functions of time; and (d) vehicle yaw rate as a function of the steering wheel input when
driving through the double-lane-change maneuver with and without the fuzzy ASC
(FASC) ............................................................................................................................ 152
Figure 6-7: Maximum fitness function value for each generation of the multi-criteria
genetic algorithm ............................................................................................................ 155
Figure 6-8: Control surface of the genetically-tuned fuzzy ASC ................................... 155
Figure 6-9: Shape and distribution of the genetically-tuned membership functions for the
input and output variables of the fuzzy ASC .................................................................. 156
Figure 6-10: Desired and actual vehicle trajectories when driving through the doublelane-change maneuver with an initial speed of 60 km/h using the driver model and the
genetic fuzzy ASC .......................................................................................................... 156
xvii
List of Figures
Figure 6-11: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when
driving through the double-lane-change maneuver with an initial speed of 60 km/h using
the driver model, with and without the genetic fuzzy ASC (GFASC) ........................... 157
Figure 6-12: (a) Lateral acceleration, (b) steering wheel angle, and (c) vehicle speed as
functions of time; and (d) vehicle yaw rate as a function of the steering wheel input when
driving through the double-lane-change maneuver with an initial speed of 60 km/h
without a controller, with the fuzzy ASC (FASC), and with the genetic fuzzy ASC
(GFASC) ......................................................................................................................... 158
Figure 6-13: Desired and actual vehicle trajectories when driving through the doublelane-change maneuver with an initial speed of 75 km/h using the driver model and the
genetic fuzzy ASC .......................................................................................................... 159
Figure 6-14: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when
driving through the double-lane-change maneuver with an initial speed of 75 km/h using
the driver model, with and without the genetic fuzzy ASC (GFASC) ........................... 159
Figure 6-15: (a) Lateral acceleration, (b) steering wheel angle, and (c) vehicle speed as
functions of time; and (d) vehicle yaw rate as a function of the steering wheel input when
driving through the double-lane-change maneuver with an initial speed of 75 km/h
without a controller, with the genetic fuzzy YMC (GFYMC), with the ATVC, and with
the genetic fuzzy ASC (GFASC) .................................................................................... 160
Figure 6-16: (a) Required steering wheel input and (b) lateral acceleration of the vehicle
when driving through the step-steer maneuver using the genetic fuzzy ASC (GFASC) 162
Figure 6-17: Yaw rate (top) and sideslip angle (bottom) of the vehicle when driving
through the step-steer maneuver using the genetic fuzzy ASC (GFASC) ...................... 162
Figure 6-18: Desired and actual vehicle trajectories when braking in a turn using (a) the
driver model only and (b) the driver model with the genetic fuzzy ASC ....................... 163
Figure 6-19: (a) Required steering wheel input and (b) lateral acceleration of the vehicle
when braking in a turn using the driver model with the genetic fuzzy YMC (GFYMC),
with the ATVC, and with the genetic fuzzy ASC (GFASC) .......................................... 164
Figure 6-20: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when
braking in a turn using the driver model with the genetic fuzzy YMC (GFYMC), with the
ATVC, and with the genetic fuzzy ASC (GFASC) ........................................................ 165
xviii
List of Figures
Figure 6-21: (a) Vehicle speed as a function of time when braking in a turn using the
driver model with the genetic fuzzy ASC, and (b) longitudinal acceleration as a function
of vehicle speed when braking in a turn using the driver model without a controller, with
the genetic fuzzy YMC (GFYMC), with the ATVC, and with the genetic fuzzy ASC
(GFASC) ......................................................................................................................... 165
Figure 6-22: Desired and actual vehicle trajectories when braking on a -split road while
holding the steering wheel fixed, with and without the genetic fuzzy ASC (GFASC) .. 166
Figure 6-23: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when
braking on a -split road while holding the steering wheel fixed and using the genetic
fuzzy ASC (GFASC) ...................................................................................................... 167
Figure 6-24: Equivalent corrective steering wheel input applied by the genetic fuzzy ASC
(GFASC), augmenting the fixed steering input of the driver in order to correct the sidepushing effect of the vehicle when braking on a -split road ......................................... 168
Figure 6-25: Tire slip ratios when braking on a -split road while holding the steering
wheel fixed and using the genetic fuzzy ASC (GFASC) ................................................ 168
Figure 6-26: Requested and actual motor torque at each wheel when braking on a -split
road while holding the steering wheel fixed and using the genetic fuzzy ASC (GFASC)
......................................................................................................................................... 169
Figure 7-1: Subjective evaluation of the performance and effectiveness of the GFYMC,
ATVC, and GFASC based on different test maneuvers (3 = very effective, 2 = effective,
1 = effective to some extent, 0 = ineffective) ................................................................. 172
Figure 7-2: Activation function used for the integration of the ATVC and GFASC ..... 173
Figure 7-3: Desired and actual vehicle trajectories when driving through the double-lanechange maneuver with an initial speed of 75 km/h using the path-following driver model
and the integrated control of the ATVC and GFASC ..................................................... 174
Figure 7-4: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when
driving through the double-lane-change maneuver with an initial speed of 75 km/h using
the driver model and the integrated control of the ATVC and the GFASC ................... 175
Figure 7-5: (a) Lateral acceleration, (b) steering wheel angle, and (c) vehicle speed as
functions of time; and (d) vehicle yaw rate as a function of the steering wheel input when
driving through the double-lane-change maneuver with the GFYMC, the ATVC, the
GFASC, and the integrated control of the ATVC and GFASC ...................................... 176
xix
List of Figures
Figure 7-6: Requested and actual motor torque at each wheel when driving through the
double-lane-change maneuver using the driver model with the integrated control of the
ATVC and GFASC ......................................................................................................... 177
Figure 7-7: Front-to-rear torque vectoring ratios when driving through the double-lanechange maneuver using the driver model with the integrated control of the ATVC and
GFASC ............................................................................................................................ 177
Figure 7-8: Traction potential of each tire when driving through the double-lane-change
maneuver using the driver model with the integrated control of the ATVC and GFASC
......................................................................................................................................... 178
Figure 7-9: Tire slip ratios when driving through the double-lane-change maneuver using
the driver model with the integrated control of the ATVC and GFASC ........................ 179
Figure 7-10: (a) Required steering wheel input and (b) lateral acceleration of the vehicle
when driving through the step-steer maneuver using the integrated control of the ATVC
and GFASC ..................................................................................................................... 180
Figure 7-11: Yaw rate (top) and sideslip angle (bottom) of the vehicle when driving
through the step-steer maneuver using the integrated control of the ATVC and GFASC
......................................................................................................................................... 181
Figure 7-12: Desired and actual vehicle trajectories when braking in a turn using (a) the
driver model only and (b) the driver model with the integrated control of the ATVC and
GFASC ............................................................................................................................ 182
Figure 7-13: (a) Required steering wheel input and (b) lateral acceleration of the vehicle
when braking in a turn using the driver model with the GFYMC, the ATVC, the GFASC,
and the integrated control of the ATVC and GFASC ..................................................... 183
Figure 7-14: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when
braking in a turn using the driver model with the GFYMC, the ATVC, the GFASC, and
the integrated control of the ATVC and GFASC ............................................................ 183
Figure 7-15: Requested and actual motor torque at each wheel when braking in a turn
using the driver model with the integrated control of the ATVC and GFASC .............. 185
Figure 7-16: Tire slip ratios when braking in a turn using the driver model with the
integrated control of the ATVC and GFASC ................................................................. 185
Figure 7-17: Traction potential of each tire when braking in a turn using the driver model
with the integrated control of the ATVC and GFASC ................................................... 186
xx
List of Figures
Figure 7-18: Front-to-rear torque vectoring ratios when braking in a turn using the driver
model with the integrated control of the ATVC and GFASC ........................................ 186
Figure 7-19: (a) Vehicle speed as a function of time when braking in a turn using the
driver model with the integrated control of the ATVC and GFASC, and (b) longitudinal
acceleration as a function of vehicle speed when braking in a turn using the driver model
with the GFYMC, the ATVC, the GFASC, and the integrated control of the ATVC and
GFASC ............................................................................................................................ 186
Figure 7-20: Desired and actual vehicle trajectories when braking on a -split road while
holding the steering wheel fixed, with and without using the integrated control of the
ATVC and GFASC ......................................................................................................... 187
Figure 7-21: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when
braking on a -split road while holding the steering wheel fixed, using the integrated
control of the ATVC and GFASC .................................................................................. 188
Figure 7-22: Equivalent corrective steering wheel input applied by the GFASC when
using the integrated control of the ATVC and GFASC, augmenting the fixed steering
input in order to correct the side-pushing effect of the vehicle when braking on a -split
road ................................................................................................................................. 189
Figure 7-23: Requested and actual motor torque at each wheel when braking on a -split
road while holding the steering wheel fixed, using the integrated control of the ATVC
and GFASC ..................................................................................................................... 190
Figure 7-24: Tire slip ratios when braking on a -split road while holding the steering
wheel fixed, using the integrated control of the ATVC and GFASC ............................. 190
Figure 7-25: Traction potential of each tire when braking on a -split road while holding
the steering wheel fixed, using the integrated control of the ATVC and GFASC.......... 191
Figure 7-26: Front-to-rear torque vectoring ratios when braking on a -split road while
holding the steering wheel fixed, using the integrated control of the ATVC and GFASC
......................................................................................................................................... 191
Figure 7-27: Subjective evaluation of the performance and effectiveness of the GFYMC,
ATVC, GFASC, and integrated control of the ATVC and GFASC based on different test
maneuvers (3 = very effective, 2 = effective, 1 = effective to some extent, 0 = ineffective)
......................................................................................................................................... 193
xxi
List of Figures
Figure A-1: AUTO21EV concept car (left) and the commercially-available Smart fortwo
[Sma10] (right)................................................................................................................ 212
Figure A-2: AUTO21EV longitudinal traction effort characteristics ............................. 213
Figure A-3: Direct-drive PMDC in-wheel motor run-up characteristics ........................ 213
Figure A-4: AUTO21EV power requirements ............................................................... 214
Figure A-5: Ideal braking force distribution and a braking force limiter technique for
different CG heights ........................................................................................................ 215
Figure A-6: Self-steering characteristics of the bicycle model when the position of the
vehicle center of gravity varies and the tire lateral stiffnesses are the same on both axles
......................................................................................................................................... 216
Figure A-7: Typical range of yaw damping rate and natural frequency for available
passenger cars [Wal05] ................................................................................................... 217
Figure A-8: Yaw natural frequency (top) and damping rate (bottom) of the AUTO21EV
as functions of forward speed ......................................................................................... 218
Figure A-9: Half-car suspension model when assuming an equal static mass distribution
on the front and rear axles [Jal07]................................................................................... 219
Figure A-10: Optimization results for the AUTO21EV suspension system ................... 220
Figure A-11: Sign convention for camber, caster, and toe angle on a double-wishbone
suspension [Jal05] ........................................................................................................... 221
Figure A-12: Front and rear suspension systems of the AUTO21EV ............................ 222
Figure A-13: Illustration of kingpin inclination (), kingpin offset (r), caster angle (),
and caster trail (r,k) in front suspension of the AUTO21EV .......................................... 223
Figure A-14: (a) Pitch poles of the front and rear axles, and (b) AUTO21EV body pitch
motion for accelerating and braking with and without the anti-pitch mechanism .......... 223
Figure A-15: Roll understeering behaviour through toe angle changes on the front and
rear suspensions when driving in a curve ....................................................................... 224
Figure A-16: (a) Differential steering angle ( i - o,A > 0) according to Ackermann,
and (b) influence of steering rack position on differential steering angle ...................... 225
Figure A-17: (a) Kinematic and (b) dynamic models of the AUTO21EV ..................... 226
Figure A-18: Typical applications for ADAMS tire models [Aks06] ............................ 227
Figure A-19: PMSM in-wheel motor offered by L-3 Communications Magnet-Motor
GmbH [MMG10] (left) and TM4 Inc. [TM410] (right) ................................................. 228
xxii
List of Tables
Table 1-I: Operating efficiency of EVs and ICE vehicles [Gri98] ..................................... 2
Table 2-I: Criteria for desirable vehicle response during a double-lane-change maneuver
........................................................................................................................................... 38
Table 2-II: Criteria for desirable vehicle response during a step-steer maneuver ............ 39
Table 2-III: Criteria for desirable vehicle response during a brake-in-turn maneuver ..... 40
Table 2-IV: Criteria for desirable vehicle response during a straight-line braking
maneuver on a -split road ............................................................................................... 41
Table 3-I: Definition of the input and output variables of the fuzzy slip controller ......... 69
Table 3-II: Linguistic variables used in the fuzzy rules .................................................... 70
Table 4-I: Definition of the input and output variables of the fuzzy yaw moment
controller ........................................................................................................................... 96
Table 4-II: Linguistic variables used in the fuzzy rules .................................................... 97
Table 4-III: Vehicle response during the double-lane-change maneuver using the driver
model with and without the genetic fuzzy YMC (GFYMC) .......................................... 114
Table 4-IV: Vehicle response during the step-steer maneuver using a fixed step-steer
input with and without the genetic fuzzy YMC (GFYMC) ............................................ 116
Table 4-V: Vehicle response during the brake-in-turn maneuver using the driver model
with and without the genetic fuzzy YMC (GFYMC) ..................................................... 119
Table 4-VI: Vehicle response during the straight-line braking on a -split road maneuver
holding the steering wheel fixed with and without the genetic fuzzy YMC (GFYMC) . 121
Table 4-VII: Subjective evaluation of the effectiveness of the genetic fuzzy YMC based
on different test maneuvers (3 = very effective, 2 = effective, 1 = effective to some
extent, 0 = ineffective) .................................................................................................... 122
Table 5-I: Vehicle response during the double-lane-change maneuver using the driver
model without a controller, with the genetic fuzzy YMC (GFYMC), and with the ATVC
......................................................................................................................................... 137
Table 5-II: Vehicle response during the step-steer maneuver using the driver model
without a controller, with the genetic fuzzy YMC (GFYMC), and with the ATVC ...... 139
Table 5-III: Vehicle response during the brake-in-turn maneuver using the driver model
without a controller, with the genetic fuzzy YMC (GFYMC), and with the ATVC ...... 142
xxiii
List of Tables
Table 5-IV: Vehicle response during the straight-line braking on a -split road maneuver
holding the steering wheel fixed without a controller, with the genetic fuzzy YMC
(GFYMC), and with the ATVC ...................................................................................... 146
Table 5-V: Subjective evaluation of the effectiveness of the ATVC based on different test
maneuvers (3 = very effective, 2 = effective, 1 = effective to some extent, 0 = ineffective)
......................................................................................................................................... 146
Table 6-I: Definition of the input and output variables of the fuzzy active steering
controller ......................................................................................................................... 149
Table 6-II: Vehicle response during the double-lane-change maneuver using the driver
model without a controller, with the genetic fuzzy YMC (GFYMC), with the ATVC, and
with the genetic fuzzy ASC (GFASC) ............................................................................ 161
Table 6-III: Vehicle response during the step-steer maneuver using the driver model
without a controller, with the genetic fuzzy YMC (GFYMC), with the ATVC, and with
the genetic fuzzy ASC (GFASC) .................................................................................... 163
Table 6-IV: Vehicle response during the brake-in-turn maneuver using the driver model
without a controller, with the genetic fuzzy YMC (GFYMC), with the ATVC, and with
the genetic fuzzy ASC (GFASC) .................................................................................... 166
Table 6-V: Vehicle response during the straight-line braking on a -split road maneuver
without a controller, with the genetic fuzzy YMC (GFYMC), with the ATVC, and with
the genetic fuzzy ASC (GFASC) .................................................................................... 169
Table 6-VI: Subjective evaluation of the effectiveness of the genetic fuzzy ASC based on
different test maneuvers (3 = very effective, 2 = effective, 1 = effective to some extent, 0
= ineffective) ................................................................................................................... 170
Table 7-I: Vehicle response during the double-lane-change maneuver using the driver
model without a controller, with the GFYMC, with the ATVC, with the GFASC, and
with the integrated control of the ATVC and GFASC ................................................... 180
Table 7-II: Vehicle response during the step-steer maneuver using the driver model
without a controller, with the GFYMC, with the ATVC, with the GFASC, and with the
integrated control of the ATVC and GFASC ................................................................. 181
Table 7-III: Vehicle response during the brake-in-turn maneuver using the driver model
without a controller, with the GFYMC, with the ATVC, with the GFASC, and with the
integrated control of the ATVC and GFASC ................................................................. 187
xxiv
List of Tables
Table 7-IV: Vehicle response during the straight-line braking on a -split road maneuver
while holding the steering wheel fixed without a controller, with the GFYMC, with the
ATVC, with the GFASC, and with the integrated control of the ATVC and GFASC ... 192
Table 7-V: Subjective evaluation of the effectiveness of the integrated control of the
ATVC and GFASC based on different test maneuvers (3 = very effective, 2 = effective, 1
= effective to some extent, 0 = ineffective) .................................................................... 192
Table A-I: PMDC motor characteristics ......................................................................... 214
Table A-II: PMSM in-wheel motor characteristics ........................................................ 231
xxv
1
Introduction and Background
During the last two decades, advances in electronics have revolutionized many aspects of
automobiles, especially in the areas of engine management and vehicle dynamics safety
systems such as the anti-lock braking system (ABS), traction control system (TCS), and
electronic stability control (ESC) system. In these cases, the signals generated by the
brake or accelerator pedal are modulated by an electronic control unit in order to control
the tire slip of individual wheels in emergency braking (ABS) or emergency acceleration
(TCS) situations, or to control the vehicle yaw rate through individual wheel braking
(ESC). It is important to note that the U.S. National Highway Traffic Safety
Administration (NHTSA) has passed a new Federal legislation that makes installation of
ESC mandatory on all passenger cars, multipurpose passenger vehicles, trucks, and buses
by 2012 [FMV07]. The move to improve the safety, comfort, and performance of
vehicles has led to an increase in the use of electronic control systems and the
introduction of drive-by-wire systems. Today, the value added to the modern vehicle by
electronic systems is approximately 20 percent. In luxury vehicles, for example, more
than 90 control systems are used to control a variety of actuators. It is expected that this
rate will consistently increase, reaching over 40 percent by the year 2015 [ATZ06].
Integrating various electronic control systems offers the potential to optimize
driving behaviour independently of the driving maneuver through the individual control
and allocation of traction, steering, and braking forces. These unique features open new
horizons for controlling the driving dynamics of a vehicle in a way that has never been
possible. For example, integrating the active braking and active steering systems can
avoid the vehicle side-pushing behaviour when braking on a -split road [Koe06]. In
addition, by integrating different chassis control systems, individual sensor signals can be
used by the entire system, thereby avoiding sensor redundancy and reducing costs.
Recently, electric vehicles (EVs) have attracted a great deal of interest as an
elegant solution to environmental and energy problems. Thanks to great improvements in
electric motor and battery technologies, EVs have achieved sufficient driving
performance and efficiency in comparison to conventional internal combustion engine
(ICE) vehicles. EVs have no tailpipe emissions because they have no fuel, combustion, or
exhaust systems. In fact, EVs are virtually maintenance-free because they never need oil
1
1
Introduction and Background
changes, air filters, tune-ups, mufflers, timing belts, or emission tests. Critics proclaim
that EVs are simply “elsewhere emission vehicles” because they transfer emissions from
the tailpipe to the smokestack. Although there are emissions associated with coal- and
oil-fired power plants, the smokestack emissions associated with charging EVs are very
low [Bra94]. However, in the ideal scenario, EVs would be charged from renewable
energy sources such as hydro, solar, and wind power, or even zero-emission nuclear
power.
Even EVs recharging from fossil-fuel power plants, such as those powered by
coal and oil, have unique efficiency advantages over ICE vehicles. As a system, EVs and
power plants are twice as efficient as ICE vehicles and the system that refines gasoline
(Table 1-I). At current U.S. energy prices, with the cost of gasoline at 3 dollars per gallon
and the national average cost of electricity at 8.5 cents per kilowatt per hour, a plug-in
EV runs on an equivalent of 75 cents per gallon. According to an interesting study
revealed in 2005, half the cars on U.S. roads are driven no more than 25 miles a day
(Figure 1-1). Therefore, an EV with just a 20-mile-range battery could reduce the national
fuel consumption by approximately 60 percent [Gri98]. In addition, EVs are the most
exciting platforms on which to apply advanced motion control techniques, since the
torque of an electric motor can be generated and controlled quickly and precisely in an
efficient way. Note that the torque response of an electric motor is several milliseconds
and, therefore, 10 to 100 times faster than that of the ICE, or even hydraulic braking
systems [Hor04]. Furthermore, the installation of small but powerful direct-drive inwheel motors into each wheel will produce a novel all-wheel-drive (AWD) system in
which even bidirectional torques on the left and right wheels can be generated. This
flexibility can be used to support the driver‟s steering wheel movements and reduce
response times in tight cornering and lane-change maneuvers.
EVs and Power Plants
ICE and Fuel Refining
39% (Electricity Generation)
92% (Fuel Refining)
Transmission Lines
95%
–
Charging
88%
–
Vehicle Efficiency
88%
15%
Overall Efficiency
29%
14%
Processing
Table 1-I: Operating efficiency of EVs and ICE vehicles [Gri98]
2
1
Introduction and Background
Figure 1-1: American driving patterns [San05]
This novel powertrain concept represents a very advanced torque vectoring
system, enabling any desired torque distribution between all four wheels, and allowing
the realization of many advanced stability control systems. Moreover, such a powertrain
concept can support a very advanced AWD system, ensuring the optimal traction of each
wheel by controlling the motor torque in all driving conditions. Further benefits of such
an EV include a reduction of noise pollution and the minimization of the noise, vibration,
and harshness (NVH) of the vehicle due to the elimination of the ICE and other
powertrain components.
In summary, replacing the ICE and the entire conventional powertrain system
with two or four electric motors and batteries will bring entirely new perspectives to the
discipline of vehicle design. The batteries can be placed into the chassis as a modular
package which, likewise, can be built as a modular unit. This concept will allow the
designer to combine the modular chassis with different body frames to realize different
vehicle types. The Hy-wire concept car developed by GM is an example of this type of
chassis, where the vehicle structure is classified into two separate groups. The first group
is designed with the vehicle bodywork and chassis together, and is called the rolling
chassis. The second group is the driving chassis, which is a functional module that houses
the electric motors, power source, steering, and suspension systems (Figure 1-2).
This research focuses on the development and verification of innovative vehicle
stability control strategies for an electric all-wheel-drive drive-by-wire vehicle. The
3
1
Introduction and Background
vehicle is being designed as part of an AUTO21 research project to examine the use and
development of collaborative design tools.
Figure 1-2: GM Hy-wire concept car with rolling and driving chassis [Elb04]
1.1
State-of-the-art drive-by-wire technologies
Since 1986, an increasing number of vehicle engines have been manipulated by an
electronic pedal and an electrically-driven throttle or injection, which represent the first
drive-by-wire components [Jur06]. Such systems are equipped with a fail-safe function
whereby the throttle spring system automatically closes the throttle in the event of
electronic failure. Other mechatronic units have been developed to allow an automatic
transmission to control a hydraulic torque converter as well as gear shifting functions.
The successful use of fly-by-wire technology in the aviation industry, positive experience
with the throttle-by-wire and electronically-controlled transmissions in automobiles, and
various electronic driver assistance systems for braking and power steering are the
incentives for the future development of complete drive-by-wire systems without
mechanical backup. Such a scheme is usually not fail-safe but, rather, has fault-tolerant
properties [Ise02]. The lower reliability and different fault behaviour inherent in the
electronic and electrical components used in drive-by-wire systems without mechanical
backup have made the transition from systems with mechanical backup extremely
challenging. Nevertheless, fault-tolerant electronic systems must be incorporated to meet
the high safety requirements set by governments, especially in the developed countries.
Figure 1-3 illustrates the hazard severity of failures for different electronic and electrical
driving systems [Rie99]. As shown, the hazard severity increases considerably when
drive-by-wire systems are used. Note that the brake and steering systems in a vehicle are
safety-critical systems that must continue to operate in the event of a failure, without
4
1
Introduction and Background
endangering human life. However, the hazard severity of the steer-by-wire system is the
highest among the drive-by-wire systems simply because, in contrast to the braking
system, it consists of only a single unit, so a malfunction causes the driver to lose all
steering control of the vehicle. In contrast, if a single braking actuator fails, three
alternate units remain, providing the driver with 75 percent of the normal braking force.
Moreover, new functions such as collision avoidance, autonomous driving, lane-keeping
assistance, and advanced stability control systems require vehicles to be equipped with
full by-wire systems, where all actuators can be controlled through electronic control
units to enable the application of driver-independent signals to the system. Therefore, the
hazard severity of such systems is equally elevated.
Figure 1-3: Hazard severity of failures in drive-by-wire and higher-level control systems [Rie99]
1.1.1
Brake-by-wire systems
With the exception of the electronic parking brake (EPB), brake-by-wire systems can be
divided into two classes: electro-hydraulic brakes (EHB) and electro-mechanical brakes
(EMB). Although EPB and EHB systems are already standard features for many car
manufacturers, EMB systems are still in the development stage [Elb04].
In EHB systems, the input from the brake pedal is replaced with an electronically
controlled actuator. This actuation is attainable using a hydraulic system, where control is
5
1
Introduction and Background
achieved by operating the pump and various control valves (Figure 1-4-a). The input
from the driver would be provided by a position sensor, taking any form required (e.g., a
traditional pedal or even a joystick) [Ham03]. The sensor converts the braking request of
the driver into an electrical signal and sends it to an EHB unit at each wheel. The brake
unit consists of an electric motor, a pump, and a hydraulic tank. In the event of a failure, a
standard hydraulic brake system is activated as a fail-safe system, which provides the
minimum braking power prescribed by legal braking regulations [Elb04]. In EMB
systems, the hydraulic system is completely removed and the braking force is generated
at each wheel by a high-power electric actuator. All electric motors are controlled
through an electronic control unit (ECU), where the driver input would, again, come from
a suitable sensor similar to those used in EHB systems. A feedback actuator at the brake
pedal provides force feedback to the driver (Figure 1-4-b). Note that an EMB system
fully decouples the driver from the braking system. The ECU plays a central role,
converting the brake request of the driver into an electrical signal and adopting tasks such
as ABS control. Since each wheel has its own electronic module that controls the
respective brake independently of the others, the system can maintain 75 percent of its
total potential even after an actuator fails whereas, in a typical dual-circuit hydraulic
brake system, a failure will cause half of the brakes to become ineffective. For safety
reasons, an EMB system has a backup power circuit and a backup ECU. Both types of
brake-by-wire system have the following advantages over their conventional counterparts
[Elb04]:

easy incorporation with anti-lock braking and traction control systems,

faster response and improved performance,

disturbance-independent pedal force characteristics,

improved package and NVH performance,

improvement of ergonomics and crash behaviour,

modular structure, and

environmental friendliness and improved maintenance for the EMB due to the
elimination of hydraulic fluid.
6
1
Introduction and Background
Figure 1-4: (a) Electro-hydraulic braking (EHB) and (b) electro-mechanical braking (EMB) concepts for
brake-by-wire technology [Ham03]
Brake-by-wire technology can be used to realize anti-lock braking (ABS), traction
control (TCS), and stability control (ESC) systems by controlling the longitudinal slip of
the tires. Note that an ABS system only uses braking intervention to control the
longitudinal dynamics of the vehicle, whereas TCS and ESC systems use both motor
management and braking intervention to control, respectively, the longitudinal and lateral
dynamics of the vehicle.
1.1.2 Steer-by-wire systems
Automotive steering systems have evolved from mechanical steering systems to
hydraulic power steering assist systems and, recently, to electric power steering systems.
Electro-hydraulic power steering is becoming more popular than hydraulic power
steering since, due to the electronically-controlled operation of the power pack, energy
consumption is reduced by 70 percent in comparison to conventional hydraulic steering
systems. Electro-mechanical power steering systems have recently been introduced to the
market, and have the benefit of eliminating all the hydraulic components and the
environmentally unfriendly hydraulic fluid. Electro-mechanical power steering systems
consume 85 percent less energy than conventional hydraulic systems, because the
electrical systems only operate when steering, and are lighter and more compact than
their hydraulic counterparts [Elb04].
The next step in steering evolution is the complete elimination of the mechanical
linkage between the steering wheel and the rest of the steering system. Since torque
feedback and the self-centering effect are important characteristics that a driver expects to
experience when steering a vehicle, force feedback actuators must be installed at the
steering wheel to generate an artificial steering torque based on the actual aligning
7
1
Introduction and Background
moment on the tires. Torque feedback is essential to the driver for estimating the driving
conditions, and the self-centering effect should occur when the driver releases the
steering wheel while exiting a turn. Electronics allow the amount of feedback steering
torque to be set independently of the actual aligning moment, and can be tuned for
different driving styles. Furthermore, the absence of the steering column greatly
simplifies the interior design of the car, since the steering wheel can then be assembled
modularly into the dashboard on either the left or right side. Removal of the steering
column also frees up space in the engine compartment and improves the frontal crash
behaviour of the vehicle. Additionally, the elimination of the steering column prevents
the transmission of NVH from the road to the driver through the steering wheel [Yih05].
The steer-by-wire system has the ability to electronically augment the steering
input of the driver and, thus, is capable of providing variable steering ratio and active
steering functionalities during normal driving situations as well as emergency maneuvers.
The following three architectures have been applied in concept cars to realize a steer-bywire system [JB04]:

electro-hydraulic actuation (Figure 1-5-a),

purely hydraulic actuation (Figure 1-5-b), and

electro-mechanical actuation (Figure 1-5-c).
One method of realizing a steer-by-wire system is to replace the input from the
steering column to the steering rack with an electric motor attached to the rack and
pinion, adding an additional force feedback actuator on the steering wheel, and retaining
all other conventional steering system components (Figure 1-5-a). Although this solution
provides a relatively easy method of converting a conventional vehicle into a steer-bywire vehicle, it suffers from packaging and weight issues. The purely hydraulic method,
shown in Figure 1-5-b, enables steering actuation by adding a series of hydraulic control
valves to the power-assisted steering rack, thereby providing control over the rack
position; however, this solution still suffers from packaging and weight issues due to the
retention of the conventional power steering system. The most sensible way to achieve a
steer-by-wire system is to completely remove the hydraulic system and replace it with a
powerful direct-drive electric motor. The wheel actuation can be accomplished with one
8
1
Introduction and Background
motor controlling both wheels through a steering rack or with one motor controlling each
wheel, the latter of which allows the independent control of each wheel (Figure 1-5-c).
Figure 1-5: (a) Electro-hydraulic actuation, (b) pure hydraulic actuation, and (c) electro-mechanical
actuation concepts for steer-by-wire technology [JB04]
1.2
Conventional slip control systems
In the last 30 years, advances in electronics have revolutionized many aspects of the
automobile industry. Thanks to the advancements in automotive braking technologies,
drivers now rely on electronic support to help them not only to decelerate and accelerate,
but also to stabilize their vehicles while in motion. In this regard, slip control systems,
such as anti-lock braking systems (ABS) and traction control systems (TCS), have
received particular attention. These safety systems involve the use of electronic control
units to modulate the brake and accelerator pedal inputs provided by the driver in order to
control the slip of individual tires during emergency braking (ABS) or acceleration
(TCS). The primary task of a slip control system is to influence the longitudinal dynamics
of a vehicle by preventing the tires from locking up when braking and spinning out when
accelerating, thereby enhancing the stability and steerability of the vehicle. A
comprehensive overview of the history, operation, and types of slip control systems can
be found in [Bow93, Bur93, Pen96, Mit82].
9
1
Introduction and Background
According to a study conducted by the Monash University Accident Research
Centre, ABS has reduced the risk of multiple vehicle crashes by 18 percent and the risk of
run-off-road crashes by 35 percent [Bur04]. Another study conducted by the National
Highway Traffic Safety Administration (NHTSA) confirms that a statistically significant
decrease in multi-vehicle crashes and fatal pedestrian strikes is achievable using an ABS
system [Maz01]. As a result, the European Automobile Manufacturers Association has
been committed to equipping all new vehicles with ABS since 2003 [Bur04]. Figures also
indicate that about 95 percent of all-new vehicles in the United States have been equipped
with ABS since 2003 [Vel01].
1.2.1 Anti-lock braking system
ABS is by no means a new innovation, and its development and acceptance has occurred
over a number of decades. The first ABS system was developed by Dunlop Maxaret in
1952, and was used on aircraft landing systems [Vel01]. In 1978, Robert Bosch GmbH
introduced the modern anti-lock braking system for passenger vehicles [Mar02-a,
Mar02-b]. By the 1990s, ABS was a common option on many vehicles, and is now a
standard feature on nearly all new vehicles.
An ABS system detects the onset of wheel lock-up due to a high braking force,
and then limits the braking pressure to prevent wheel lock-up. An ABS system is
considered a stand-alone system (i.e., it can be installed independently of other control
systems), and consists of a wheel speed sensor, a hydraulic modulator, and an electronic
control unit (ECU) for signal processing, control, and triggering the actuators in the
hydraulic modulator [Bos07]. The ECU recognizes wheel lock-up by detecting sharp
increases in wheel deceleration, and reduces the braking force in a closed-loop process
until the lock-up situation vanishes. The cyclic application and reduction of the braking
force ensures that the brakes operate at or near their most efficient operating point and the
vehicle maintains steering control. This cyclic application is also responsible for the
pulsation that a driver feels through the brake pedal when the system is activated. Note
that the driver can be isolated from this pulsation in a brake-by-wire system.
In general, when a driver presses the brake pedal, the brake slip increases until the
point of maximum friction between the tire and the road surface is reached, which is the
limit between the stable and unstable regions. At this point, any increase in brake
pressure will reduce the friction between the tire and the road surface, and the wheel will
10
1
Introduction and Background
tend towards skidding. In a vehicle with a conventional braking system, as the wheels
tend towards lock-up, the lateral force potential of the tires (which enables steering) is
greatly reduced, and approaches zero when the wheels are fully locked. By preventing
wheel lock-up, the lateral force potential of the tires is maintained at a high level,
allowing the driver to retain steering control during emergency braking. Thus, the task of
an ABS system is to use the friction coefficient between the tires and the road surface in
an optimal fashion in order to minimize the braking distance while retaining steerability.
1.2.2 Traction control system
In 1971, the Buick division of GM introduced MaxTrac as the first TCS, which was used
to detect rear wheel spin and modulate the engine power delivered to those wheels in
order to provide the most traction possible. Since then, more sophisticated TCS systems
have been developed by different companies, such as Cadillac and Robert Bosch GmbH,
and involve an engine management controller that cooperates with the brake system in
order to prevent the driven wheels from spinning out.
Tire slip can also be controlled in an acceleration mode using a combination of
the hydraulic brake system and the engine management controller to prevent tire spin-out.
This task is accomplished by a TCS system, which is a constructive add-on to an existing
ABS system and cannot be installed alone. In a TCS, the ECU recognizes wheel spin-out
by detecting sharp increases in wheel acceleration. The ECU then reduces the engine
torque through the engine management controller in a closed-loop process to reduce the
traction force on the driven wheels. If the ECU is unable to prevent a spin-out situation
using this first method of intervention, it applies the brakes in order to stop the wheels
from spinning out. The closed-loop control process and the cooperation between the
engine management controller and the brake system together ensure that the friction
coefficient between the tires on the driven wheels and the road surface is used in an
optimal fashion, maximizing the traction force while retaining stability and steerability.
Note that the aim of a TCS system is defined based on the vehicle configuration. In a
front-wheel-drive (FWD) vehicle, TCS aims to maximize the traction force while
retaining steerability, whereas in a rear-wheel-drive (RWD) vehicle, TCS intends to
maintain vehicle stability while maximizing the traction force.
11
1
Introduction and Background
1.2.3 Methods of adjusting the tire slip ratio
One method of adjusting the tire slip ratio in a slip control system is to limit the
maximum possible slip ratio to a fixed amount. This strategy is shown in Figure 1-6,
where the longitudinal force (Fx) and lateral force (Fy) of the tire are plotted as functions
of the longitudinal slip ratio of the tire [Bei00]. The bold vertical line in Figure 1-6
highlights the limited slip ratio control strategy. The advantage of this method is that the
tire slip angle () reasonably controls the relation between the longitudinal and lateral tire
forces. In other words, at a fixed slip ratio, when the tire slip angle increases, the
longitudinal tire force decreases and, at the same time, the lateral force potential of the
tire increases, which improves the lateral stability of the vehicle (Figure 1-6).
Figure 1-6: Characteristics of the tire longitudinal and lateral forces as a function of tire slip ratio for
constant tire slip angles; used for a slip control system with limited slip ratio [Bei00]
An alternative approach is to adjust the tire slip ratio such that the maximum
possible traction force can be generated at all slip angles. This method prioritizes the
longitudinal tire force over the lateral tire force and ensures that the maximum possible
traction force is attained at every sideslip angle [Bei00]. In other words, if the tire slip
ratio is adjusted such that the maximum longitudinal force can be generated when the tire
slip angle increases, the lateral force potential will not always increase. This situation is
shown in Figure 1-7, where the upper bold-dashed line indicates the peak tire forces in
the longitudinal direction at every slip angle, and the lower bold-dashed line indicates the
corresponding lateral force of the tire.
12
1
Introduction and Background
Figure 1-7: Characteristics of the tire longitudinal and lateral forces as a function of tire slip ratio for
constant tire slip angles; used for a slip control system with adjustable slip ratio [Bei00]
1.3
Conventional stability control systems
Electronic stability control systems represent another breakthrough technology that has
evolved and incorporated the slip control systems. These stability enhancement systems
are designed to improve the lateral stability of the vehicle by electronically monitoring
vehicle states and automatically assisting drivers in dangerous situations and under
slippery road conditions. In general, most drivers are used to operating a vehicle with
their “linear range” skills, the range of lateral acceleration in which a given steering
wheel angle produces a proportional change in the heading of the vehicle [FMV07]. In
this range, heading adjustments are easy to achieve because the response of the vehicle is
proportional to the driver‟s steering input, and the lag time between the input and the
response is very small. Therefore, the driver feels that he is in control and the vehicle
travels in the direction in which it is pointed. However, when driving an ordinary vehicle
at higher lateral accelerations (above 0.4g on a dry road), the relationship between the
driver‟s steering input and the response of the vehicle changes, and the lag time of the
vehicle response can lengthen [Wal05]. As a result, when an average driver encounters
these changes in a panic situation, it is more likely that he will lose control and crash
because the familiar actions learned when driving in the linear range are no longer valid.
Electronic stability control systems augment the driver‟s inputs so that actions learned in
13
1
Introduction and Background
linear-range driving remain the correct actions for controlling the vehicle in panic
situations [FMV07].
Electronic stability control systems use sensors that monitor the speed of each
wheel, the steering wheel angle, and the overall yaw rate and lateral acceleration of the
vehicle. Data from the sensors are used to estimate the intended course of the driver by
monitoring the yaw rate and sideslip angle of the vehicle using a reference bicycle model
and comparing that to the actual motion of the vehicle. Comparing the desired and actual
data, an electronic stability control system can intervene early in the impending loss-ofcontrol situation, generating a corrective yaw moment and restoring yaw stability before
the driver has the opportunity to make an overcorrection or other error. In this way, an
electronic stability control system prevents a vehicle from changing its heading from the
desired path in a way that would induce further panic in a driver facing a critical situation
[Lie05]. Different types of electronic stability control systems exist for generating a
corrective yaw moment. For example, a corrective yaw moment can be generated by
braking individual wheels using an electronic stability control (ESC) system, by
superimposing the steering angle of the driver with a correction using an active steering
control (ASC) system, by modifying the steering angles on an axle using a four-wheelsteering (4WS) system, or by varying the available drive torques on the driven wheels
using a torque vectoring control (TVC) system [Zan00, Alb96, And06, Ack99, Rey03].
Several studies from around the world have confirmed that ESC is highly
effective at preventing crashes. The following list summarizes some results from these
global studies:

Germany: ESC would prevent 80 percent of skidding crashes and 35 percent of all
vehicle fatalities [Rie05].

Sweden: ESC would prevent 16.7 percent of all injury crashes, excluding rear-end
collisions, and 21.6 percent of serious and fatal crashes [Lib05].

Japan: ESC would prevent 35 percent of single-vehicle crashes and 50 percent of
fatal single-vehicle crashes. In addition, ESC would prevent 30 percent of head-on
crashes and 40 percent of fatal head-on crashes [Aga03].

United States: ESC would prevent 41 percent of single-vehicle crashes and 56
percent of fatal single-vehicle crashes [Far04]. In addition, ESC would reduce the
14
1
Introduction and Background
rates of fatal single-SUV crashes by 50 percent and fatal single-passenger-car
crashes by 30 percent. Corresponding reductions for non-fatal single-vehicle
crashes are 70 percent for SUVs and 55 percent for passenger cars [Gre06].
As a result of these studies, in March 2007, the U.S. National Highway Traffic
Safety Administration (NHTSA) passed a new Federal Motor Vehicle Safety Standard
(FMVSS No. 126) that makes the installation of ESC mandatory on all passenger cars,
multipurpose passenger vehicles, trucks, and buses with a gross vehicle weight rating of
4,536 kg or less by 2012 [FMV07]. Note that ESC was equipped on about 29 percent of
model year 2006 light vehicles sold in the U.S., and manufacturers intend to increase this
amount to 71 percent by 2011.
1.3.1 Braking-based electronic stability control system
Although electronic stability control (ESC) systems have been known by a number of
different trade names, such as Dynamic Stability Control (DSC), Dynamic Stability and
Traction Control (DSTC), Electronic Stability Program (ESP), Vehicle Dynamic Control
(VDC), Vehicle Stability Assist (VSA), Vehicle Stability Control (VSC), Vehicle Skid
Control (VSC), Vehicle Stability Enhancement (VSE), and Porsche Stability
Management (PSM), their function and performance are similar. All these systems use
computers to control individual wheel brakes, thereby helping the driver maintain control
of the vehicle during extreme maneuvers, keeping the vehicle headed in the intended
direction even when the vehicle nears or reaches the limits of road traction.
When a driver attempts a sudden maneuver (for instance, to avoid an obstacle or
crash, or due to misjudgment of the severity of a curve), the driver may lose control if the
vehicle responds differently as it nears the limits of its handling than it does in ordinary
driving situations. The driver‟s loss of control may be the result of the vehicle spinning
out (oversteering) or plowing out (understeering). As long as there is sufficient traction
between the tires and the road, a professional driver can maintain control of an unstable
vehicle (oversteered or understeered) by using counter-steering and by performing a
sequence of corrections based on the vehicle response. An average driver, on the other
hand, tends to correct the spinning motion of an unstable vehicle through inappropriate
steering inputs that, in most cases, make the situation even worse [FMV07]. An ESC
system automatically applies braking torques to individual wheels to generate a corrective
15
1
Introduction and Background
yaw moment, adjusting the heading of the vehicle if it departs from the direction in which
the driver is steering. Thus, ESC prevents the heading from changing too quickly
(oversteering) or not quickly enough (understeering). Although ESC cannot increase the
available traction, it supports the driver in his efforts to keep the vehicle under control
and on the road in an emergency maneuver, using only the driver‟s ordinary driving
actions learned in linear-range driving. Note that keeping the vehicle on the road prevents
single-vehicle crashes, and roadway departure is the situation that leads to most rollovers
[Dan04]. However, the activation of an ESC system is often at the expense of reducing
the vehicle speed which, in general, is perceived by the driver as being annoying.
Figure 1-8-a illustrates the operation of an ESC system during a left-hand turn in
order to stabilize an oversteered vehicle, where the rear of the vehicle begins to slide. In a
vehicle equipped with ESC, the system immediately detects that the heading of the
vehicle is changing more quickly than is appropriate given the driver‟s intended path, and
it momentarily applies the front outside brake to generate a corrective yaw moment that
turns the heading of the vehicle back to the intended path. In addition, braking the front
outside tire simultaneously reduces the lateral force potential of that tire, which also helps
to generate the required corrective yaw moment. Note that braking the rear outside tire is
not an appropriate action in this situation because, in an oversteered vehicle, reducing the
lateral force potential on the rear axle will lead to further instability.
Figure 1-8: Braking intervention of an ESC system (a) in an oversteered vehicle and (b) in an understeered
vehicle (the ellipse on each tire demonstrates the adhesion potential of that tire; a dotted ellipse indicates
that the adhesion potential has been exceeded)
16
1
Introduction and Background
Figure 1-8-b illustrates an understeered vehicle during a left-hand turn, whose
response as it nears the limits of road traction involves sliding at the front and plowing
out. In this situation, the ESC system detects that the heading of the vehicle is changing
less quickly than is appropriate given the driver‟s intended path, and immediately applies
the left inside brake to turn the heading of the vehicle back to the desired path. Once
again, the braking force and the reduced lateral force potential on the rear inside tire are
both used to generate the corrective yaw moment that is required to stabilize the vehicle.
Note that braking intervention using the front inside tire is not an appropriate action
since, in an understeered vehicle, the adhesion potential has already been exceeded on the
front axle.
1.3.2 Steering-based electronic stability control system
In 2004, BMW introduced its first commercial active steering system in its 5-series class
of vehicles. Active steering fills the gap between conventional steering system and steerby-wire technologies. Although an active steering system allows driver-independent
steering intervention, the mechanical linkage between the steering wheel and the rackand-pinion system on the front axle remains in place, acting as a fail-safe mechanism.
Figure 1-9 illustrates the active steering system developed by BMW, which is comprised
of a rack-and-pinion steering system, a double planetary gear, and an electric motor as the
actuator. An active steering system facilitates the implementation of two major functions:
a variable steering ratio, and maintaining vehicle stability and maneuverability during
emergency maneuvers or when driving conditions call for a change in the steering
response [Koe04].
Figure 1-9: Design concept and mechanical layout of the BMW active steering system [Koe04]
17
1
Introduction and Background
The basic design trade-off associated with conventional steering systems involves
choosing a suitable geometric steering ratio, which affects not only the steering effort
required during low-speed maneuvering, but also has a significant influence on the
vehicle dynamics at higher speeds. An active steering system resolves this conflict by
increasing the steering ratio at higher speeds to enhance the responsiveness of the vehicle,
and decreasing it at lower speeds to enhance the maneuverability. This adjustment is
accomplished using a double planetary gear and an electric motor. The active steering
system adds a slight steering angle to the driver‟s input at low speeds and counter-steers
slightly at higher speeds, thereby avoiding hand-over-hand steering when parking while
ensuring an essentially constant steering effort in the medium- and high-speed ranges,
where a more conservative steering system is required. The variable steering ratio of the
active steering system developed by BMW is illustrated in Figure 1-10. As can be seen,
the active steering system reduces the steering ratio to 1:10 at lower speeds to provide the
driver with a more direct steering feel, and increases the ratio to 1:20 in the high-speed
range to support the driver with a more sensitive steering system. Note that conventional
steering systems can only offer fixed steering ratios, which are typically between 1:14
and 1:18.
Figure 1-10: Variable steering ratio caused by an active steering system [Koe04]
Another significant advantage of an active steering system is its ability to
electronically augment the driver‟s steering input to stabilize the vehicle. In general,
steering intervention is faster than braking individual wheels, as is done in an ESC
system, since a certain amount of time is required to build up hydraulic brake pressure. In
18
1
Introduction and Background
comparison to braking intervention, modifying the reaction of the vehicle using steering
intervention is generally a continuous process and is not perceived by the driver – or, at
least, is not perceived as being annoying [Koe04]. Figure 1-11 compares the effectiveness
of ESC and active steering systems for correcting an oversteered vehicle, where the rear
tires have reached their limit of adhesion during a left turn. In such a situation, an ESC
system applies a braking force (FB) to the front outside tire to generate the required
corrective yaw moment (Mz), which is calculated as follows [Yih05]:
M z  FB 
tf
(1.1)
2
where tf is the front track-width of the vehicle. An active steering system, on the other
hand, applies a counter-steering angle in order to generate the same corrective yaw
moment (Mz) but, in this case, the moment is generated using the lateral forces (Fy) of the
front tires:
M z  2Fy  a
(1.2)
where a is the distance between the front axle and the vehicle center of mass. Assuming
that the same corrective yaw moment is generated by these two systems, and knowing
that the track-width of most passenger cars is very close to the distance between the
vehicle center of mass and the front axle, the required lateral force on the front tires is
only one-fourth of the required braking force:
Fy 
FB
4
(1.3)
Figure 1-11: Generation of a corrective yaw moment through braking intervention using an ESC system
(left) and through steering intervention using an active steering system (right)
19
1
Introduction and Background
Therefore, it is actually advantageous to use steering intervention rather than
braking intervention to generate a corrective yaw moment when controlling a vehicle on
slippery surfaces, where the limits of adhesion are easily reached. In addition, active
steering can also be used when driving on a -split road in order to correct the sidepushing effect that appears due to the different traction forces on the two sides of a
vehicle. However, the effectiveness range of the active steering system is very restricted
due to the actuator range limit. For instance, the active steering system developed by
BMW is only able to apply up to 3o of steering angle on the front wheels [Koe04].
1.3.3 Torque vectoring control system
In conventional four-wheel-drive (4WD) vehicles, either all the wheels of the vehicle are
permanently driven, which is referred to as an all-wheel-drive (AWD) vehicle, or one of
the two axles is always linked to the engine and the second can be engaged manually or
automatically when needed. In both cases, in order to transmit the available engine torque
to the wheels, inter-axle differentials or clutches must be installed on the propshaft,
between the front and rear axles, and on both drive axles in order to split the torque
between the left and right wheels. A comprehensive overview of the drivelines and
differentials available for 4WD and AWD vehicles can be found in [Whe02, Whe05].
Although these powertrain configurations can enhance the traction and driving dynamics
on various road conditions, they suffer from higher costs, weight, and power
consumption, as well as inefficiency.
In recent years, the market for AWD vehicles has evolved and expanded, and
customer expectations of the driving dynamics and stability of such vehicles have
increased drastically. In addition, consumers are increasingly willing to request AWD on
their new cars at extra cost [Pel05]. In order to meet these requirements and remain
competitive in the market, active differentials for driveline systems are being introduced,
which are able to distribute the engine torque to the front and rear axles, as well as to the
left and right wheels of each axle, depending on the driving maneuver or road conditions.
The possibility of actively influencing the distribution of the available engine torque
based on the driving situation and traction conditions has led to an upheaval of the AWD
market [Wun05]. However, the pressure to reduce CO2 emissions and increase fuel
efficiency standards force the weight, cost, and power requirements of these actuators to
be minimized.
20
1
Introduction and Background
Torque vectoring is the term introduced by the Ricardo Company [Whe05] to
describe a means of varying the distribution of engine torque between two outputs of a
differential unit by controlling the torque over a relatively small speed difference between
the outputs. Torque is directed in proportion to the relative shaft speeds, and can be
biased seamlessly from one output to the other. Later on, active torque vectoring systems
were introduced into the powertrain system, presenting torque-on-demand capabilities,
where a center differential distributes the available engine torque to the front and rear
axle differentials. Each axle differential can be equipped with an active torque vectoring
system as well, which can be used to distribute the torque between the left and right
wheels. An active center differential apportions the torque depending on the driving
dynamics and the traction potentials on each axle, whereas an active axle differential
distributes the torque based on the vehicle dynamics and the traction potential on each
wheel of a single axle.
The benefits of active torque vectoring technology are twofold: the enhancement
of vehicle traction and the enhancement of vehicle stability. On the one hand, torque
vectoring can be used to modulate the individual wheel speeds to keep each tire operating
in its optimal longitudinal slip range for the best traction. On the other hand, torque
vectoring can be used to enhance the vehicle handling response by generating a corrective
yaw moment to influence the vehicle yaw behaviour [Rey03]. For instance, Figure 1-12
illustrates an active powertrain with an active center differential, an active rear
differential, and an open front differential [Jal04]. In normal driving conditions, where
the differential actuators are not active, the center differential splits the torque generated
by the engine by a fixed ratio of 40:60 percent to the front and rear axles, respectively,
using a planetary gear. This fixed torque distribution ratio can be established based on the
axle-load ratios, the design philosophy of the vehicle, or the desired handling
characteristics of the vehicle [Rei02]. In addition, the front and rear differentials split
their received torques in half using open differentials. Using torque vectoring technology
for traction enhancement, the torque vectoring ratios on the center and rear differentials
can vary depending on the traction potentials available on each axle or tire, such that the
highest traction force on each wheel is attained. Figure 1-13 illustrates the case where the
front tires are on ice with almost no traction, and more traction is available on the rear
right tire than the rear left tire. As can be seen, the active center differential is capable of
21
1
Introduction and Background
sending 90 percent of the available engine torque to the rear axle, where more traction is
available. The active rear differential, on the other hand, splits the torque received from
the center differential asymmetrically by a ratio of 20:80 percent for the left and right
wheels of the rear axle, respectively.
Figure 1-12: An active powertrain system with active center and rear differentials [Jal04]
Figure 1-13: Torque vectoring in an active powertrain to enhance the vehicle traction [Jal04]
Torque vectoring can also be used as a stability control system, where the
available drive torque is distributed among the wheels in order to generate a corrective
yaw moment about the vertical axis of the vehicle. The corrective yaw moment can be
22
1
Introduction and Background
generated in a left-to-right torque vectoring mode, where the available drive torque is
distributed asymmetrically to the left and right wheels of an axle, or in a front-to-rear
mode, where the available engine torque is distributed asymmetrically to the front and
rear axles. For instance, an oversteering situation, in which the adhesion potential has
been reached at the rear axle, can be corrected using left-to-right torque vectoring on the
front axle, where more torque is transmitted to the front inside tire (Figure 1-14-a).
Conversely, an understeering situation, in which the adhesion potential has been
exceeded on the front axle, can be corrected by using left-to-right torque vectoring on the
rear axle, in which a higher percentage of the available axle torque is transmitted to the
rear outside tire in order to generate the required corrective yaw moment (Figure 1-14-b).
Figure 1-14: (a) Stability control of an oversteered vehicle through side-to-side torque vectoring on the
front axle, and (b) stability control of an understeered vehicle through side-to-side torque vectoring on the
rear axle
The driving dynamics of a vehicle can also be influenced by varying the front-torear torque distribution. The front-to-rear torque vectoring mode takes advantage of the
interconnection between the longitudinal and lateral tire forces, where changing one force
will automatically influence the other. For instance, an understeered vehicle can be
controlled by transmitting more of the engine torque to the rear axle than the front axle.
This strategy not only increases the lateral force potential at the front axle and,
simultaneously, enhances the steerability of the vehicle, but it also reduces the lateral
force potential of the rear axle by increasing the longitudinal traction force. The lateral
force difference between the two axles generates the required corrective yaw moment
about the vertical axis of the vehicle, helping the vehicle to travel in the direction in
which it is pointed (Figure 1-15-a). Conversely, an oversteered vehicle can be controlled
by transmitting more of the available engine torque to the front axle, thereby increasing
23
1
Introduction and Background
the essential lateral force potential on the rear axle. At the same time, this strategy will
reduce the lateral force potential on the front axle by elevating its longitudinal force, thus
helping the vehicle to develop more understeering behaviour (Figure 1-15-b).
Figure 1-15: Front-to-rear torque vectoring (a) in an understeered vehicle, and (b) in an oversteered vehicle
[Wal06]
Although the theory behind the torque vectoring technique is similar to that used
for an ESC system, torque vectoring is more effective, especially for generating a
corrective yaw moment at higher vehicle speeds and during emergency maneuvers near
the handling limits of the vehicle [Rey03]. In general, torque vectoring can affect the
vehicle driving dynamics and traction while causing almost no change in the total driving
force of the vehicle. Active braking, on the other hand, is hampered by a net braking
effect and drive torque reduction, which not only increases the inefficiency of the vehicle
by eliminating power that has already been produced, but it has also been reported by
drivers as being disruptive due to the unexpected speed reduction. Moreover, in contrast
to active braking, which is allowed only a limited operation time to ensure a safe reserve
of fade-free braking performance, torque vectoring can be employed much more actively
to enhance driving dynamics and vehicle traction even in normal driving conditions and
everyday driving experience. However, it is important to note that a torque vectoring
system can only be effective when a driving torque exists in the first place. In other
words, torque vectoring is not able to intervene when the driver releases the throttle or
brakes the vehicle. In such cases, an ESC system must maintain the stability of the
vehicle. Therefore, torque vectoring and active braking should be considered to be
complementary technologies whose full potential can only be realized if a holistic
approach is used to operate both systems under a common supervisory controller.
In summary, to control the vehicle traction and driving dynamics during both
braking and acceleration maneuvers, the vehicle should be equipped with ABS, TCS,
24
1
Introduction and Background
ESC, and torque vectoring control systems, and all of these systems should be networked
together in an integrated fashion. However, equipping a vehicle with all the
aforementioned control systems and actuators is a very expensive and complex task. It is
for this reason that such a degree of vehicle control is only available in luxury-class
vehicles, where the customer is prepared to pay for the required technologies.
1.4
Advanced stability control system through networked chassis
Until the 1980s, chassis technology, which directly determines the dynamic performance
of a vehicle, advanced exclusively within the mechanical engineering framework. After
the mid-1980s invention and practical application of the four-wheel-steering system
(4WS), the vehicle dynamics performance field became a main stream of research and
development for control technology. Since then, research and development of vehicle
dynamics performance has been carried out as a collaborative technology of mechanical
engineering and control engineering.
Current chassis control systems are distinguished by the way the individual
subsystems work. Each individual subsystem can generally be assigned to an individual
dynamic domain, such as longitudinal, lateral, or vertical dynamics. However, individual
subsystems often influence two of the three domains, as illustrated in Figure 1-16. For
instance, a torque vectoring system can influence both the longitudinal and lateral
dynamics of a vehicle. Furthermore, the influences of individual subsystems, especially
during extreme maneuvers, are interconnected and coupled through the tire-road
characteristics. Thus, the optimum driving dynamics can only be achieved when the tire
forces on all four wheels and in all three directions can be influenced and controlled
precisely. In order to achieve this level of control, the vehicle must not only be equipped
with various active chassis subsystems, but these subsystems must be networked together
in order to control the tire forces and meet the instantaneous driving dynamics, safety,
and comfort requirements [Sem06].
Taking advantage of the benefits and strengths of each subsystem, the ideal
stability control system can be obtained by activating the most effective subsystem or
subsystems based on the driving maneuver and road conditions. For example, an ESP
system uses braking intervention of individual wheels in order to influence the
longitudinal forces on the tires and, ultimately, the yaw behaviour of the vehicle.
25
1
Introduction and Background
However, in order to obtain stabilization, vehicle braking is not necessary in all
situations. In particular, if the vehicle speed must be maintained at the same level while
turning in a curve, torque vectoring techniques can be used to affect the driving
dynamics. Furthermore, the influences of individual subsystems, especially during
extreme maneuvers, are interconnected and coupled through the tire-road characteristics.
Figure 1-17 demonstrates the interdependencies of longitudinal, lateral, and vertical
dynamics. For example, a friction ellipse couples the lateral and longitudinal tire forces,
whereas a “longitudinal friction coefficient versus slip ratio” relationship couples the
longitudinal and vertical tire forces, and a “lateral friction coefficient versus slip angle”
relationship couples the lateral and vertical forces of a tire. Thus, most vehicle control
principles can be related to the linear and nonlinear characteristics of the tire-road
contacts. The factors influencing the nature of this contact can be summarized as direct
effects of the steering angle, slip angle, and camber angle of the tires on lateral forces,
and direct effects of traction and braking intervention on longitudinal forces. The wheel
vertical load, however, influences both longitudinal and lateral forces directly by defining
the maximum possible adhesion potential.
Longitudinal
Dynamics
Braking
System
Transmission
Torque
Vectoring
All Wheel
Drive
Lateral
Dynamics
Vertical
Dynamics
Steering
System
Active
Steering
Variable
Damping
Active
Anti-Roll Bar
Active Axle
Kinematics
Leveling
System
Figure 1-16: Domain structure of driveline and chassis systems [Sem06]
The fundamental question of which configurations are both effective and feasible
given a specific set of driving conditions can only be answered if the strengths and
limitations of each active chassis subsystem have been identified. A popular method of
addressing such issues is by presenting the effects of each subsystem on the resulting tireroad friction ellipse or circle. Since the driver is limited by the friction constraints of the
tires, the vehicle controls are expected to provide the driver with predictable authority
26
1
Introduction and Background
over longitudinal and lateral accelerations, within the physical constraints of the vehicle
“friction circle”, and subject to perceived customer acceptability of the frequency and
amplitude dependence of the vehicle responses [Gor03]. Therefore, given that friction
limits change with speed, road surface conditions, and so forth, these vehicle control
systems are required to provide adequate feedback of such changes. The concepts
illustrated in Figure 1-18, presented by Toyota [Yam91], indicate the domain of operation
of some typical vehicle control systems. Although the diagrams should not be taken too
literally, they clearly underline the fact that integrated control can enlarge the dynamic
response domain of the vehicle by taking advantage of the control system with the most
effectiveness for a particular driving maneuver and set of road conditions.
Figure 1-17: Interdependencies among longitudinal, lateral, and vertical dynamics
The majority of the stability control systems currently on the market stabilize the
vehicle in critical driving situations by intervening with only one type of active chassis
subsystem at a time, which limits the performance of the vehicle. Recently, there has
been a move towards networking the individual subsystems in order to take advantage of
synergies and increase the performance of the vehicle. Until very recently, however,
27
1
Introduction and Background
mainly due to marketing strategies, chassis subsystems have been treated as stand-alone
systems in a so-called “coexistence” architecture, which requires no overhead but still
suffers from suboptimal performance. This architecture can lead to a situation in which,
for instance, a vehicle with four active chassis subsystems is equipped with as many as
four independent sets of sensors, state estimators, reference models, and state controllers
[Sem06, Koe06]. Since the simultaneous actuation of these subsystems may affect the
same degrees-of-freedom of the vehicle and have counterproductive results, the
overlapping of actuator effort must be addressed in a more coordinated way. One solution
to this problem is a “hierarchical coexistence” of the subsystems with a unidirectional
information flow, where one system acts independently and the others adapt as necessary.
Figure 1-18: Effective range of various control concepts based on the resulting tire-road friction circle
[Yam91]
An “integrated approach” is a more sophisticated means of addressing the
coordination of several actuators [And06, Gor03]. In this approach, each of the chassis
subsystems has one basic function. In contrast to the coexistence approach, there is only
one set of sensors, one state estimator, one reference model, and one state controller.
Based on the desired and actual behaviour of the vehicle, the system can calculate the
required generalized forces and moments to maintain the course desired by the driver.
These generalized forces and moments are then applied by the actuators based on their
effectiveness, ensuring the best overall safety, ride quality, and driving pleasure.
28
1
1.5
Introduction and Background
Thesis outline and contributions
In order to investigate effective and feasible control configurations given a specific set of
driving conditions, the performance and limitations of several active chassis subsystems
have been analyzed and evaluated. These subsystems have been specifically designed for
the AUTO21EV, which is equipped with four direct-drive in-wheel motors and an active
steering system on the front axle.
To this end, a set of test maneuvers is developed in Chapter 2 for evaluating
vehicle handling and performance. In addition, path-following and speed-control driver
models are developed and implemented, which allow the simulation of closed-loop test
maneuvers.
In Chapter 3, an advanced fuzzy slip controller is developed for the AUTO21EV
that combines the functionalities of an ABS, a TCS, and the brake system of the vehicle.
Furthermore, the performance and functionalities of the developed fuzzy slip control
system are evaluated using four test maneuvers.
In Chapter 4, a 14-degree-of-freedom (DOF) vehicle model is developed to allow
for the testing of different control strategies, and for applying a genetic tuning algorithm
to the development of the fuzzy yaw moment controller. The genetic tuning procedure is
applied to the developed fuzzy yaw moment controller to improve its performance. The
genetic fuzzy yaw moment controller determines the corrective yaw moment that is
required to stabilize the vehicle and applies a virtual yaw moment around the vertical axis
of the vehicle. The effectiveness and performance of the genetic fuzzy yaw moment
controller is evaluated using a variety of test maneuvers.
Chapter 5 describes the development of an advanced torque vectoring controller
based on the previously developed genetic fuzzy yaw moment controller. The objective
of the advanced torque vectoring controller is to generate the required corrective yaw
moment through the torque intervention of the individual in-wheel motors to stabilize the
vehicle during normal and emergency driving maneuvers. A novel algorithm is developed
for the left-to-right torque vectoring control on each axle, and a PD controller is
introduced for the front-to-rear torque vectoring distribution action. Several maneuvers
are simulated to demonstrate the performance and effectiveness of the advanced torque
vectoring controller, and the results are compared to those obtained using the genetic
fuzzy yaw moment controller.
29
1
Introduction and Background
In Chapter 6, the simplified 14-DOF vehicle model introduced in Chapter 4 is
used to develop a fuzzy active steering controller. Use of this simplified vehicle model
facilitates the testing of different control strategies and the application of a genetic
algorithm procedure to the development of the fuzzy active steering controller. The
performance of the fuzzy active steering controller is improved by tuning the membership
functions of the fuzzy controller using a genetic tuning procedure. The performance and
effectiveness of the genetic fuzzy active steering controller are confirmed by simulating a
variety of maneuvers, and the results are compared to those obtained using the genetic
fuzzy yaw moment controller and the advanced torque vectoring controller.
Chapter 7 presents an activation function that integrates the control efforts of the
advanced torque vectoring and genetic fuzzy active steering controllers. Several test
maneuvers are simulated to demonstrate the performance and effectiveness of this
integrated control approach. It is confirmed that the integrated control approach produces
better results than all of the individual control systems.
Finally, Chapter 8 summarizes the work, highlights the contributions, and
discusses directions for future work in this thesis.
30
2
Test Maneuvers and Analytical Driver Models
The driver of a passenger car is responsible not only for controlling the vehicle speed by
actuating the brake and accelerator pedals, but also for controlling the direction in which
the vehicle is travelling. Thus, the tasks of the driver are threefold: navigation, path
following, and vehicle stability [Wal05]. In order to travel between two points, a driver
must first choose a suitable route. Criteria such as route length and travelling time might
be used to select the desired route. Navigation systems can help a driver plan a route
between two points, but the ultimate decision about which route to select is still made by
the driver. The second task of a driver is to define the desired path for the vehicle within
the chosen route based on additional information that is gathered along the way, such as
traffic conditions, traffic signs, and unexpected obstacles. Despite technological
advancements in this area, the path-following task cannot be fully automated using
control systems such as path-following cameras or inductive highway striping. The final
task of a driver is to keep the vehicle on the desired path using the available actuators (the
steering wheel, brake pedal, and accelerator pedal). Moreover, the driver is responsible
for the stability of the vehicle while driving through the desired path. The stability control
systems available on the market are either designed to maintain the stability of the
vehicle, or at least to support the driver in accomplishing this task. Since the driver must
perform the three aforementioned tasks simultaneously, a stability control system not
only helps the driver maintain the stability of the vehicle, but also indirectly helps him
accomplish the route-planning and path-following tasks. In the ideal case, a stability
control system will allow the driver to devote all his attention to the other two tasks.
From a control systems perspective, the driver and vehicle can be modelled as a
control loop, where the driver acts as a controller that is responsible for the stability of the
plant, which is the vehicle (Figure 2-1). In such a control loop, some disturbances act on
the driver (such as the relative motion between the vehicle and the driver, driver
distractions, and line-of-sight obstructions), and others act on the vehicle (such as cross
wind, different coefficients of friction on the road, and road roughness). In terms of the
lateral dynamics, the actuating variable that must be corrected by the driver is the steering
wheel angle; in terms of the longitudinal dynamics, the actuating variables are the brake
and accelerator pedal positions. The control deviation that must be corrected by the driver
31
2
Test Maneuvers and Analytical Driver Models
in the lateral dynamics domain is the difference between the desired and actual paths,
while in the longitudinal dynamics domain, the deviation between the desired and actual
speeds must be corrected. Moreover, the driver-vehicle-environment control loop is
considered to be a dynamic closed-loop system, whose stability depends mostly on the
vehicle behaviour and the capabilities of the driver. In other words, the stability of this
control loop depends on the ability of the controller (the driver) to handle large errors, the
behaviour of the control system under fast control actions, and the stability of the system
under the influence of external disturbances.
Figure 2-1: Graphical representation of the driver-vehicle-environment control loop
In general, the dynamic characteristics of the vehicle must match the capabilities
of the driver. The quality of this match defines the vehicle handling and performance
characteristics. In this regard, a vehicle is considered to have a good handling
characteristic if the following arguments are true [Wal05]:
1. There must be a good correlation between the steering wheel variation and the lanechange behaviour of the vehicle. This property defines the transfer function behaviour
of the vehicle as the plant of the control loop.
2. The driver must receive reasonable information about the condition of the vehicle in
order to predict its behaviour. For instance, changes in the steering wheel feedback
32
2
Test Maneuvers and Analytical Driver Models
torque, the vehicle sideslip angle, as well as tire squeak before reaching the physical
limit of adhesion will all help the driver predict the behaviour of the vehicle and,
ultimately, react correctly.
3. The external disturbances acting on the vehicle should cause little or no change in the
course of the vehicle – that is, the vehicle should be inherently stable.
4. The vehicle must have a high lateral acceleration limit, which defines the lateral
stability reserve of the vehicle; the larger this limit, the more stable the vehicle will
be.
It is important to note that there are no standard legal regulations about the vehicle
handling and performance characteristics, and every car manufacturer is free to set its
own specifications in this area. Looking at the vehicle handling and performance from the
driver‟s perspective, it is a completely subjective evaluation that can change from one
driver to another. Therefore, it is very difficult to set a standard criterion for quantifying
the quality of these evaluations. In fact, there is no comprehensive, objective definition
for the dynamic characteristics associated with the driver-vehicle-environment control
loop, as adequate data on the precise control characteristics of the human element are still
not available [Bos07]. For this reason, in practice, the assessment of the vehicle is
performed by expert drivers who can subjectively evaluate the measured data gathered
through a series of standard test maneuvers.
2.1
Test maneuvers for evaluating vehicle handling and performance
Many test maneuvers have been developed for evaluating the quality of the handling and
performance characteristics of a vehicle. Many of these test maneuvers are based on ideal
driving conditions, and some of them are motivated by the examination methods typically
used for control systems, such as step-steer and swept-sine-steer maneuvers (Figure
2-2). An extensive overview of different test maneuvers and their detailed descriptions
can be found in the publications of Roenitz, Braess, and Zomotor [Roe77, Roe98].
The test maneuvers that describe the vehicle behaviour in terms of the drivervehicle-environment control loop are known as „closed-loop‟ test maneuvers. To evaluate
these maneuvers, the quality of the match between the dynamic behaviour of the vehicle
and the driver‟s capabilities must be considered. These test maneuvers require a
33
2
Test Maneuvers and Analytical Driver Models
professional driver who can make judgments on the handling qualities of the vehicle
based on the combination of diverse subjective impressions. In the simulation
environment, an appropriate driver model is used, which can simulate the required
behaviour of a specific driver (professional or average driver) in following a desired
predefined path, in place of a test driver. If, on the other hand, the actuation variables in a
test maneuver are defined to be pure functions of time, and the dynamic behaviour of the
vehicle has no influence on the driver‟s response, then the test maneuver is known as an
„open-loop‟ maneuver. In an open-loop test maneuver, the driver is replaced by a
specific, objectively quantifiable interference factor, and the handling data derived from
the maneuver provides objective information about the handling qualities of the vehicle.
Open-loop test maneuvers also provide insight into the stability of the vehicle and the
sensitivity of the vehicle to external disturbances.
Figure 2-2: Different test maneuvers for evaluating vehicle handling and performance characteristics
[Roe77] (Y = yes and N = no)
It can be concluded that each test maneuver provides some information about the
dynamic behaviour of the vehicle in one or several respects, such as vehicle handling,
stability, path following, and longitudinal dynamics. Therefore, a comprehensive
34
2
Test Maneuvers and Analytical Driver Models
evaluation of the dynamic characteristics of a vehicle is only possible by examining the
results obtained from several different test maneuvers.
2.1.1 Selection and evaluation of chosen test maneuvers
As mentioned above, many test maneuvers are used in industry, and can provide insight
into the dynamic behaviour of the vehicle under different conditions (Figure 2-2).
However, a comprehensive evaluation of the dynamic characteristics of a vehicle and the
effectiveness of different chassis control systems can only be achieved when the results
obtained from different test maneuvers are combined and evaluated as a whole.
Therefore, a number of different test maneuvers are used in this work to provide
important information about different aspects of the dynamic behaviour of the vehicle
and the effectiveness of each individual chassis control system, as well as the
effectiveness of integrated chassis control management strategies. These test maneuvers
are chosen such that all aspects of vehicle dynamics are addressed. In other words, the
chosen test maneuvers act to clarify the performance and effect of different chassis
control systems on the driver-vehicle-environment control loop, and quantify the
advantages of each control method. The chosen test maneuvers are described in the
following.
1) ISO double-lane-change Maneuver
The ISO double-lane-change is a closed-loop test maneuver that is used to evaluate the
lateral dynamics of a vehicle based on the subjective evaluations of professional drivers.
The specifications of the ISO double-lane-change maneuver are described in the ISO
3888 standard, and the test track design is illustrated in Figure 2-3. As described in
[Pai05, Bau99], the driver starts this maneuver at a particular speed and releases the
throttle. The driver then attempts to negotiate the course without striking the cones. The
test speed is progressively increased until either instability occurs or the course can no
longer be negotiated. Since a severe double-lane-change maneuver effectively
demonstrates the cornering capability of a vehicle when driving at the friction limit in
both directions, many car manufacturers and research institutions consider it to be a
suitable test maneuver for assessing electronic stability controllers.
35
2
Test Maneuvers and Analytical Driver Models
In this work, the desired vehicle trajectory in a double-lane-change maneuver is
defined as a function of forward displacement using two fifth-order splines that are
connected with a straight line segment in the middle [Bod06]:
0

 c x5 +
+ c 5x + c 6
 1
y  f ( x) = 
3.0425
5
c x +
+ c11x + c12
 7
0

if
x  18.5
if 18.5  x  42
if
42  x  43
(2.1)
if 43  x  65.5
if
x  65.5
where c1 to c12 denote parameters that are determined by enforcing boundary conditions
on the splines. This desired vehicle trajectory is, in fact, the predefined target trajectory to
which the driver model refers while driving through the test maneuver, and is indicated
by a dashed line in Figure 2-3. Note that the second lane-change is more aggressive than
the first one and, thus, asymmetric steering inputs are required to follow the desired path.
In addition, the road is considered to be flat and dry with a coefficient of friction of  = 1.
Figure 2-3: ISO 3888 double-lane-change maneuver test track design [Bau99]
Due to the importance of the double-lane-change maneuver, six different plots
will be used to evaluate the performance of the vehicle and its different chassis control
systems.
1. Actual and desired vehicle trajectories: This plot is used to determine whether the
actual vehicle trajectory matches well with the predefined desired trajectory, and
whether the driver is able to negotiate the course without striking the cones.
2. Actual and desired vehicle yaw rate and sideslip angle as functions of time: Based on
these two plots, the quality of the match between the actual reaction of the vehicle
and the reaction of the reference bicycle model is evaluated. In this regard, the
36
2
Test Maneuvers and Analytical Driver Models
maximum sideslip angle ( 
max
) and maximum yaw rate ( 
max
) of the vehicle must
be observed, both of which should be small.
3. Lateral acceleration of the vehicle as a function of time: This plot reveals whether the
vehicle reaches its physical limit when driving through the maneuver. The maximum
lateral acceleration ( a y
max
) is observed, and should be a large number. A large lateral
acceleration at a given steering wheel angle indicates that the traction potential on
each tire is widely used to hold the vehicle on its desired path or, in other words, the
vehicle is able to follow the driver‟s steering request even during emergency
maneuvers [Bei00].
4. Driver‟s steering wheel input as a function of time: The gradient of this plot indicates
the driver‟s effort during the maneuver and is an important factor when evaluating the
quality of the handling and agility of the vehicle. In addition, the maximum steering
wheel angle (  SW
max
) is observed, which should be small. A small maximum
steering wheel angle ensures that the driver is not exhausted or over-demanded when
driving through an emergency maneuver.
5. Vehicle yaw rate as a function of steering wheel angle: This plot is a Lissajous figure
that demonstrates the relationship between the input signal (the steering wheel angle)
and the output signal (the vehicle yaw rate) of the driver-vehicle-environment control
system. The resulting pattern in a Lissajous figure is a function of the ratio of the
input and output signal frequencies [Cun89]. In addition, the hysteresis of the
resulting pattern describes the phase shift between the input and output signals.
Hence, this plot is considered to be a handling performance plot, where a smaller
amount of hysteresis indicates a phase shift between the driver‟s steering wheel input
and the yaw rate response of the vehicle, and better agility and responsiveness of the
vehicle. The size of the hysteresis (  H ) serves as a quantitative measure for
comparing the performance of different chassis control systems.
6. Vehicle speed as a function of time: By observing the vehicle speed as a function of
time, the effect of each chassis control system on vehicle speed is evaluated. The
gradient of the speed plot indicates whether the activation of a chassis control system
would have a detrimental effect on the vehicle longitudinal speed. Note that such a
speed reduction is perceived by the driver as being annoying. Moreover, the speed
37
2
Test Maneuvers and Analytical Driver Models
lost by the vehicle at the end of the maneuver ( vlost  vstart  vend ) is determined, and
should be as small as possible.
Table 2-I summarizes the requirements for a desirable vehicle response during a doublelane-change maneuver.
Parameter

Requirement
small
max

ay
max
small
max
large
 SW
max
small
 H
vlost
small
small
Table 2-I: Criteria for desirable vehicle response during a double-lane-change maneuver
2) Step-steer response maneuver
A step-steer response is an open-loop test maneuver used to examine both transient and
steady-state vehicle behaviour. In this test, the vehicle is driven in a straight line at a
constant speed of 90 km/h, and a sudden limited steering wheel input is applied. The road
is considered to be flat and dry, with a coefficient of friction of  = 1. Note that the rate
of change of the steering wheel input is limited to 300o/s, which corresponds to a driver‟s
reaction time. Therefore, the step-steer is, in fact, a steep ramp input that is applied to the
steering wheel. The steering wheel angle is determined such that a lateral acceleration of
ay = 4 m/s2 is reached [Wal05]. The vehicle speed is kept constant by the speed
controller.
The criteria for evaluating test results from this maneuver are similar to those
described in the literature for a step response of a dynamic system. In this regard, a fast
response of the vehicle yaw rate and lateral acceleration, with a sufficient amount of
damping, is desirable. From a multitude of different performance measures that are
defined in the literature for evaluating the step response of a dynamic system [Bol95],
two measures are chosen to describe the performance of a step-steer response: rise time
and percentage overshoot. The rise time ( t ) is defined as the time required for the yaw
rate response to rise from zero to 90% of the steady-state value. Rise time is a measure of
how fast the vehicle responds to the steering input. The overshoot is the maximum
amount by which the response exceeds the steady-state value. The overshoot is often
written as a percentage of the steady-state value, which is then called percentage
overshoot (PO) and is calculated as follows:
38
2
PO 
Test Maneuvers and Analytical Driver Models
 max  ss
 100%
 ss
(2.2)
where  max is the maximum yaw rate and  ss is the steady-state value of the yaw rate.
Both of these performance measures, t and PO, must be small, which indicates a small
phase delay and a good damping behaviour of the vehicle.
In addition, the maximum sideslip angle ( 
max
) and the rise time of the lateral
acceleration response of the vehicle ( ta y ) are also observed, both of which should, again,
be small numbers. Table M-II summarizes the requirements for a desirable vehicle
response during a step-steer test maneuver.
Parameter
Requirement
t
PO 
 max  ss
 100%
 ss
small
small

max
small
ta y
small
Table 2-II: Criteria for desirable vehicle response during a step-steer maneuver
3) Brake-in-turn maneuver
The brake-in-turn test maneuver simultaneously considers both the lateral and
longitudinal dynamics of the vehicle. Brake-in-turn is one of the most critical maneuvers
encountered in everyday driving. The reaction of the vehicle to this maneuver reveals the
compromise between steerability, stability, and deceleration [ISO85].
In this work, the brake-in-turn maneuver is considered to be a closed-loop test
maneuver, and begins with the vehicle being driven at a constant speed of 75 km/h into a
curve with a radius of 60 m. Once the vehicle has reached a steady-state lateral
acceleration, the driver intends to slow the vehicle to 20 km/h with a deceleration rate of
6 m/s2. The path-following driver model attempts to keep the vehicle on the predefined
circular path, while the speed controller reduces the vehicle speed at the predefined
deceleration rate. The road is considered to be flat and dry with a coefficient of friction of
 = 1.
Four plots are used to evaluate the behaviour of the vehicle in a brake-in-turn
maneuver. First, the vehicle trajectory is plotted and the maximum lateral deviation of the
vehicle with respect to the desired path ( ymax ) is measured. The lateral deviation should
be as small as possible. Second, the driver‟s steering wheel input is plotted as a function
39
2
Test Maneuvers and Analytical Driver Models
of time. The gradient of this plot indicates the driver‟s effort to keep the vehicle on the
desired path or, in other words, how easily the driver can control the vehicle when
braking in a turn. The maximum steering wheel angle (  SW
max
) is observed, which is an
important indicator of driver effort. The final two plots illustrate the vehicle yaw rate and
sideslip angle as functions of time. Due to the weight transfer away from the rear axle,
the vehicle yaw rate and sideslip angle grow as the vehicle progresses toward larger
deceleration rates. Again, the maximum yaw rate ( 
max
) and sideslip angle ( 
max
) are
observed, and should remain small. Table 2-III summarizes the requirements for a
desirable vehicle response during a brake-in-turn maneuver.
Parameter
ymax
 SW
Requirement
small
small
max

max
small

max
small
Table 2-III: Criteria for desirable vehicle response during a brake-in-turn maneuver
4) Straight-line braking on a -split road
In order to better differentiate between the performance and effects of different chassis
control systems on vehicle behaviour, a straight-line braking maneuver on a -split road
is conducted [Roe98]. Braking on a -split road is a very critical test maneuver, since the
vehicle will experience severe instability if the driver does not react immediately to
correct the course of the vehicle. During this test, due to the asymmetric braking forces
generated on the left and right tires, the vehicle will be pushed to the side of the road that
has a higher coefficient of friction. In most cases, the asymmetric braking forces are high
enough to cause the vehicle to turn around its vertical axis, which is a very dangerous
situation. In general, a real instability of this nature is corrected by inexperienced drivers
through the application of an inappropriate single steering wheel input that, in most cases,
makes the situation even worse. An experienced driver, on the other hand, can avoid such
a dangerous situation by performing a sequence of corrections based on the vehicle
response, thereby regaining control of the vehicle. In this work, the straight-line braking
on a -split road is considered as an open-loop test maneuver, in which the vehicle is
driven at a constant speed of 80 km/h while the steering wheel is held fixed. The driver
then attempts to stop the vehicle in an emergency braking situation on a -split road,
40
2
Test Maneuvers and Analytical Driver Models
which has a black ice patch (ice= 0.1) on the left side and is dry (dry= 1.0) on the right
side. The road is considered to be flat and the length of the ice patch is 10 meters.
In order to evaluate the performance of the vehicle and its chassis control systems,
three plots are examined. First, the trajectory of the vehicle is analyzed to determine
whether the vehicle becomes unstable and leaves the predefined road. The maximum
lateral deviation of the vehicle with respect to the desired straight-line trajectory ( ymax )
is measured. This lateral deviation should be as small as possible. In addition, the braking
distance of the vehicle ( xbraking ) is measured, which indicates the efficiency of a stability
controller in emergency braking situations. The braking distance is the distance that the
vehicle travels after the start of the braking action, and should be kept as small as
possible. Next, the yaw rate and sideslip angle of the vehicle are plotted as functions of
time. The gradients of these two plots indicate whether the vehicle becomes unstable and
the extent to which the vehicle is sensitive to external disturbances. Moreover, the
maximum yaw rate ( 
max
) and sideslip angle ( 
max
) are measured from these plots. It
is desirable to have small values for these two factors. Note that, in cases where an active
steering system is used, it is also necessary to plot the steering angle of the vehicle as a
function of time so that the activity of the active steering system can be analyzed. Table
2-IV summarizes the requirements for a desirable vehicle response during a straight-line
braking maneuver on a -split road.
Parameter
ymax
xbraking
Requirement
small
small

max
small

max
small
Table 2-IV: Criteria for desirable vehicle response during a straight-line braking maneuver on a -split road
2.1.2 Comprehensive evaluation of chosen test maneuvers
As mentioned earlier, a comprehensive evaluation of the dynamic characteristics of a
vehicle and the effectiveness of different chassis control systems can only be obtained
when the results of different test maneuvers are combined and evaluated as a whole. Four
test maneuvers are used in this work to provide important information about different
aspects of the dynamic behaviour of the vehicle and the effectiveness of each chassis
control system. The results of these test maneuvers are evaluated with respect to four
main performance characteristics: handling, stability, path-following capability, and
41
2
Test Maneuvers and Analytical Driver Models
longitudinal dynamics. Such an approach makes it possible to evaluate the influence of
each chassis control system on the reaction of the vehicle to the steering wheel input
(handling), as well as the stability, path-following capability, and longitudinal dynamics
of the vehicle during a maneuver. In this regard, each parameter measured during a test
maneuver is assigned to one or more of the four main performance characteristics, as
illustrated in Figure 2-4. The improvements in the dynamic behaviour of the vehicle are
evaluated with respect to the uncontrolled vehicle, and the effectiveness of each chassis
control system is estimated using the following quantitative assessment:
3 = very useful, very effective
2 = useful, effective
1 = useful and effective to some extent
 = no influence, ineffective
Once the effectiveness of each candidate controller has been evaluated based on
the four aforementioned driving maneuvers and with respect to the four main
performance characteristics, a final comprehensive evaluation is performed in which the
mean value of all individual test results within a category is calculated. In this way, each
candidate controller can be compared to the others in terms of the four main performance
characteristics.
Figure 2-4: Important properties of the dynamic behaviour of the vehicle evaluated by each test maneuver
2.2
Modelling the behaviour of a driver
In order to evaluate the handling and performance of the vehicle in the design stage and
the effectiveness of different chassis control subsystems before implementing them in a
42
2
Test Maneuvers and Analytical Driver Models
real vehicle, the simulation of a large number of different maneuvers is necessary. As
discussed above, there is a significant difference between open-loop test maneuvers,
which are defined by chronological control inputs and are routinely used for the
subjective evaluation of handling performance, and closed-loop test maneuvers, which
primarily involve a path-following task. However, in order to realize these test maneuvers
in the simulation environment, not only is a mathematical vehicle model needed for every
test maneuver, but a driver model must also be designed to simulate the closed-loop test
maneuvers. The role of the driver model is to calculate the control inputs required to
successfully follow a predefined path. Such a driver model can be implemented as an
inverse dynamics problem [Dix96] or by a representation of a driver that can look ahead,
preview the path, and change the steering wheel angle accordingly [Guo93, Oez95].
There exist a variety of controllers suitable for modelling driver behaviour, some
of which are more complex than the others. Therefore, one should first choose the level
of modelling fidelity required to achieve the task at hand, based on the needs of the
simulation. In general, driver models fall into two main categories: optimum control
models and moment-by-moment feedback models [Blu04]. Optimum control models use
some form of penalty function as a measure to assess the quality of the control achieved.
These models use repeated simulations of a specific event and numerical optimization
methods to tune the parameters of the driver model such that the value of the defined
penalty function is minimized over the duration of the event of interest. Although
optimum control models are suitable for learned events, such as the circuit driving of race
cars, some care must be exercised with their use for evaluating the performance of regular
passenger cars. Since the average driver of a passenger vehicle is generally unskilled, the
application of modelling techniques in which repeated simulations are used to discover
the so-called „best‟ way of achieving a maneuver may not be an appropriate way of
simulating an emergency situation, where the driver has only one attempt to complete the
maneuver [Guo93, Mac96]. Moment-by-moment feedback models are a subset of the
optimum control models, with the difference being that the feedback parameters of the
controller are set once by the analyst and remain constant thereafter. Although these
models are less appropriate for predicting the driver behaviour for circuit racing, they add
clarity in understanding the vehicle behaviour and driver inputs when driving through a
test maneuver [Sha00]. Such driver models are also more appropriate for understanding
43
2
Test Maneuvers and Analytical Driver Models
the effects of different chassis control systems on both the vehicle and the driver when
driving through closed-loop test maneuvers.
2.2.1 Development of a path-following driver model
With these facts in mind, a moment-by-moment feedback driver model that is similar to
the model described in [Oez95] is developed in this work, but is enhanced with a more
sophisticated path previewing technique. The driver model described in [Oez95] uses a
single-preview-point steering control model, whose objective is to steer a ground vehicle
along a reference line located in the middle of the lane to be followed. In this regard, a
single arbitrary look-ahead point is defined along the local longitudinal axis of the
vehicle, and the distance between the look-ahead point and the reference path is defined
as the “look-ahead offset”. The required steer angle is then calculated as a function of the
look-ahead offset, vehicle longitudinal velocity, and various vehicle parameters. A linear
bicycle model is used, as illustrated in Figure 2-5, to obtain the following linear statespace equation [Oez95]:
 C f  C r
  m u
v  
CG
r   b  C  a  C
 
r
f

Iz  u

b  C r  a  C f 
 C f


mCG  u
   v    mCG
a 2  C f  b2  C r   r   a  C f



Iz  u
 Iz

u 


 



(2.3)
where u , v , and r are, respectively, the longitudinal, lateral, and yaw rate vectors of the
vehicle, and u  u , v  v , and r    r are the magnitudes of these vectors. In
addition, a and b are the distances of the front and rear axles to the vehicle center of
gravity, mCG is the vehicle mass, Iz is the yaw moment of inertia,  is the steering angle of
the front wheel, and Cf and Cr are the total cornering stiffnesses of the front and rear
tires, respectively. As illustrated in Figure 2-5, V indicates the velocity vector of the
vehicle‟s center of gravity, whose magnitude is V  V  u 2  v 2 . Note that the vehicle
coordinate axes are in accordance with the ISO 4130 and DIN 70000 standards, where the
Z direction points upwards, the X-axis is along the vehicle longitudinal axis and points
towards the front of the vehicle, and the Y-axis points left when viewing along the
positive X direction.
44
2
Test Maneuvers and Analytical Driver Models
Figure 2-5: Linear bicycle model used for developing the driver model
Figure 2-6 illustrates the vehicle motion along a desired circular path of radius R,
where the distance between the center of gravity of the vehicle and the look-ahead point
is defined as look-ahead distance (d), the distance between the look-ahead point and the
point on the curve closest to it is defined as look-ahead offset (o), and the distance
between the look-ahead point and the center of the curve is defined as h. By considering
the steady-state motion of the vehicle along the curve, where the vehicle perfectly tracks
the desired path, explicit expressions are obtained for the variables vss, rss, Vss, ss, oss, and
hss. All of these expressions are in terms of the vehicle longitudinal speed u, the radius of
curvature R, and the vehicle parameters. Note that the subscript „ss‟ indicates that the
values are calculated when the vehicle is in a steady-state condition, where v  r  0 , the
center of gravity of the vehicle perfectly tracks the desired curve, the velocity vector V is
tangent to the curve, and the longitudinal velocity u is held constant. At steady-state,
equation (2.3) becomes the following:
 C f  C r
  m u
CG

 b  C r  a  C f

Iz  u

b  C r  a  C f 
 C f


mCG  u
   vss    mCG
 
a 2  C f  b2  C r   rss   a  C f



Iz  u
 Iz

u 


   ss



(2.4)
From equation (2.4), the steady-state lateral velocity (vss) can be calculated as a function
of the steady-state yaw rate (rss) as follows [Oez95]:
vss  T  rss , where T  b 
a  mCG  u 2
C r  (a  b)
(2.5)
45
2
Test Maneuvers and Analytical Driver Models
Figure 2-6: Steady-state vehicle motion along a circular path of radius R
In general, the following statements can be made for a vehicle in steady-state circular
motion [Oez95]:
Vss  u 2  vss2
(2.6)
Vss  R  rss
(2.7)
One can now obtain new expressions for rss and ss from equations (2.4) to (2.7) that are
only in terms of the vehicle longitudinal speed u, the radius of curvature R, and vehicle
parameters [Oez95]:
rss 
 ss 
u
(2.8)
R2  T 2

mCG  u 2   a  C f  b  C r  
a  b 


(a  b)  C f  C r
R 2  T 2 

1
46
(2.9)
2
Test Maneuvers and Analytical Driver Models
According to equation (2.5), the largest value for T is always less than b, which is the
distance of the rear axle to the vehicle center of gravity. Since, in reality, a vehicle with
front steering system can never have a radius of curvature less than its wheelbase,
equations (2.8) and (2.9) will never encounter a singularity problem.
In order to calculate an appropriate expression for the steady-state look-ahead
offset oss, where oss  hss  R , an expression for hss is first defined as follows [Oez95]:
v


hss  d 2  R 2  2 R  d  cos     = d 2  R 2  2 R  d  ss
Vss
2

(2.10)
Using equations (2.5), (2.7), and (2.10), the final expressions for hss and oss are obtained
as follows [Oez95]:
hss  d 2  R 2  2  d  T
(2.11)
oss  d 2  R 2  2  d  T  R
(2.12)
Finally, from equations (2.9) and (2.12), the ratio between the desired steering input ss
and the look-ahead offset oss is calculated as follows [Oez95]:

mCG  u 2   a  C f  b  C r  
a  b 


(a  b)  C f  C r
R 2  T 2 

2
2
R  d  2  d T  R
1
 ss
oss

(2.13)
At this point, two important assumptions are made by the authors of [Oez95] in order to
simplify equation (2.13). First, using Taylor‟s expansion:
x,   , x  0: if
and assuming that

x
1 
x   x 
d  (d  2  T )
R

2 x
(2.14)
1 , equation (2.13) can be rewritten as follows
[Oez95]:

mCG  u 2   a  C f  b  C r  
2a  b 



(a  b)  C f  C r
 ss



2
oss
T
1  2  d  (d  2  T )
R
Next, by assuming that
T
R
1 and, thus,
(2.15)
1
simplified as follows [Oez95]:
47
T2
 1 , equation (2.15) can be further
R2
2
Test Maneuvers and Analytical Driver Models

mCG  u 2   a  C f  b  C r  
2a  b 



(a  b)  C f  C r

 o
 ss 
ss
d  (d  2  T )
(2.16)
Equation (2.16) indicates that the steering angle required to keep the vehicle on a circular
path when in steady-state motion is a function of the look-ahead offset oss, the vehicle
longitudinal velocity u, the look-ahead distance d, and various vehicle parameters. It is
important to notice that equation (2.16) is independent of the radius of curvature R, which
makes it attractive for use in a driver model that is suitable for every possible road
profile. Moreover, since equation (2.16) is a function of vehicle forward velocity, it
updates itself as the vehicle speed changes, as in a gain scheduling controller. The
stability of this steering controller has been proven analytically in [Oez95] using the
Routh-Hurwitz technique.
Many researchers believe that using a single preview point for describing a driver
model is unrealistic and, therefore, unsatisfactory [Guo93, Mac96, Sha00]. If the lookahead point is too far in front of the vehicle, it will be inappropriate to act on the preview
information at the time of its acquisition, and the information has been lost by the time it
is useful. On the other hand, if the look-ahead point is too close to the vehicle, it
necessarily causes very poor control, especially at higher speeds. Moreover, if the road
profile is complex, a single-preview-point model can result in a situation where its
information does not coincide with the current state of the vehicle, even with a proper
look-ahead distance (Figure 2-7-a). Realistically, one cannot imagine that a human driver
only uses the information from a single look-ahead point in order to make an appropriate
decision on how to adjust the steering wheel.
In order to solve this problem, the single-preview-point driver model described by
equation (2.16) is enhanced in this work by taking two additional steps. First, the lookahead distance is redefined to be a function of the vehicle longitudinal velocity and the
driver‟s reaction time, as described in the following:
dlook  ahead (t )  dconst  tdriver  u(t )
(2.17)
where dconst is a constant distance that the driver will look ahead, even at lower velocities,
tdriver is the reaction time of the driver, and u is the vehicle longitudinal velocity. Notably,
the constant distance that the driver looks ahead is chosen to be 4 meters and the reaction
time of the driver is 0.7 seconds. Equation (2.17) indicates that the faster the vehicle is
48
2
Test Maneuvers and Analytical Driver Models
driven, the longer the look-ahead distance will be, which corresponds well with the
reaction of a real driver. In the second step, five preview points are defined on the
“optical lever” of the driver, which is along the local longitudinal axis of the vehicle,
between the vehicle center of gravity and the look-ahead distance. The coordinates of the
preview points on the optical lever of the driver are calculated as follows [Sha00]:
 x pp ,i (t )  xCG (t )  Ki  d look  ahead (t )  cos( (t ))

 y pp ,i (t )  yCG (t )  Ki  d look  ahead (t )  sin( (t ))
(2.18)
where xpp,i(t) and ypp,i(t) are the coordinates of the ith preview point, and xCG(t) and yCG(t)
define the coordinates of the vehicle center of gravity at time t in the global reference
frame, respectively. Ki is the relative distance between the ith preview point and the
vehicle center of gravity on the optical lever, dlook-ahead(t) is the look-ahead distance
defined in equation (2.17), and (t) is the vehicle yaw angle at time t. The lateral offset of
each preview point from its corresponding point on the desired path is calculated as the
distance between the preview point and the desired path, measured along a line that is
perpendicular to the optical lever, as shown in Figure 2-7-b.
Figure 2-7: (a) Single-preview-point and (b) multiple-preview-point driver models
The new look-ahead offset is then defined as the weighted sum of all the lateral offsets:
ei (t )   yR,i (t )  y pp ,i (t )   cos  (t )    xR ,i (t )  x pp ,i (t )   sin  (t ) 
(2.19)
5
o(t )    Gi  ei (t ) 
(2.20)
i 1
where ei(t) is the lateral offset, xR,i(t) and yR,i(t) are the coordinates of the intersection
between the line perpendicular to the optical lever and the desired path, and Gi is the
control gain of the ith preview point. Note that the control gains of the driver model are
derived in an ad hoc fashion based on intuition, not on any formal optimization scheme.
The following control gains are chosen for the driver model: G1 = 3, G2 = 5, G3 = 4, G4 =
49
2
Test Maneuvers and Analytical Driver Models
1, and G5 = 0.5. The new driver model is described by combining equations (2.16) and
(2.20) as follows:

mCG  u 2 (t )   a  C f  b  C r  
2a  b 



5
(
a

b
)

C

C

f

r


 ss (t ) 

 Gi  ei (t ) 


a  mCG  u 2 (t )   i 1
d look  ahead (t )   d look  ahead (t )  2   b 

C r  ( a  b)  


(2.21)
It is important to note that one can also add an orientation error, the error between the
desired and actual vehicle yaw angles, to equation (2.20) in order to make the steering
input of the driver model a function of position error as well as orientation error.
However, in this work, only position error is considered.
2.2.2 Development of a speed-control driver model
As mentioned earlier, one of the tasks of a driver model is to adjust the brake and
accelerator pedal positions such that the deviation between the desired and actual vehicle
speeds is minimized. In order to do this, a gain scheduling PID controller is developed as
the speed controller for the AUTO21EV. PID controllers are very popular and are widely
used in industry because of their simple structure and robust performance in a wide range
of operating conditions. The design of such controllers requires the specification of three
parameters: the proportional, integral, and derivative gains. The important problem of
tuning a PID controller involves finding appropriate settings for these three gains. The
conventional approach to defining the PID parameters is to study a mathematical model
of the dynamic system and attempt to derive a fixed set of gain parameters that are valid
in a wide range of operating conditions. One well-known example of such an approach is
the Ziegler-Nichols method [Zie42]. Such a method works well for processes or dynamic
systems that can be modelled using linear first- or second-order systems; however, most
real industrial processes or dynamic systems have characteristics such as higher-order
dynamics, dead-zones, or nonlinearity that make modelling them with simple linear
systems inaccurate. Therefore, in the last couple of decades, there have been some efforts
to find and improve tuning methods that can update the gain parameters of PID
controllers at any instant based on a structurally fixed parameter-evolving process model.
One of these tuning methods is adaptive control, which uses a control scheme that
is capable of modifying its behaviour in response to changes in the dynamic system.
There are three well-known adaptive control schemes: gain scheduling, model-reference
50
2
Test Maneuvers and Analytical Driver Models
adaptive control, and self-tuning regulators. The gain scheduling technique is based on
the adjustment of controller parameters in response to the operating conditions of a
dynamic system. This type of control system is particularly useful when the variations in
the dynamic system are predictable and when the control parameters need to be adjusted
quickly in response to these variations [Kar04]. Figure 2-8 shows a block diagram of the
gain scheduling speed controller developed in this work. As shown in the figure, the
difference between the driver‟s speed request and the actual vehicle speed is measured
and amplified by the PID controller at each time step; the PID controller then outputs the
required motor torque at each wheel accordingly. At this stage, it is assumed that the
torque calculated by the gain scheduling speed controller ( TDriver ,req ) is applied to each
wheel. In other words, the total amount of torque that is applied to the vehicle is equal to
the following:
Ttotal  4  TDriver , req
(2.22)
In this case, the required motor torque ( TDriver ,req ) is the input to the in-wheel motor
controller described in [Vog07]. However, it is important to note that the required motor
torque at each wheel may be modified by the advanced slip controller and/or the
advanced torque vectoring system, which will be discussed later, depending on the
traction potential of the tire or the vehicle driving dynamics.
The proportional ( K P ), integral ( K I ), and derivative ( K D ) gains of the gain
scheduling PID controller are all defined to be proportional to the vehicle forward speed,
as follows:
Figure 2-8: Block diagram of the gain scheduling speed controller
51
2
Test Maneuvers and Analytical Driver Models
K P  K P  uact
(2.23)
K I  K I  uact
(2.24)
K D  K D  uact
(2.25)
where KP = 70, KI = 0.05, and KD = 0.05 are constant gains and uact is the actual
longitudinal speed of the vehicle. Thus, the following equation describes the output of the
gain scheduling PID controller:
Treq (t )  K P  e  K I   e  dt  K D 
de
dt
(2.26)
where e  udes  uact is the difference between the desired (udes) and actual (uact) vehicle
speed. Since the proposed gain scheduling PID controller is part of a digital control
system, the derivative and integral parts of the controller are approximated as follows:
t

e  dt 
t  Ts
1
 e(t )  e(t  Ts )   Ts
2
(2.27)
de e(t )  e(t  Ts )

dt
Ts
(2.28)
where t is the current simulation time and Ts is the sampling time. It is important to notice
that the controller gain parameters, namely KP, KI, and KD, are tuned manually using a
trial-and-error approach such that a sufficiently fast response with no overshoot is
obtained over the entire speed range.
2.3
Evaluation of the path-following and speed-control driver models
The performance of the proposed path-following driver model, described in equation
(2.21), is evaluated using two test maneuvers. First, a severe ISO double-lane-change
maneuver with obstacle avoidance is used to evaluate the performance of the driver
model. As mentioned before, the ISO double-lane-change maneuver is a closed-loop test
maneuver typically used to adjust the dynamics of a vehicle based on the subjective
evaluations of professional drivers. In addition, the complexity of the course used in this
maneuver is a good example for demonstrating the performance of the path-following
driver model.
Figure 2-9 illustrates the concept behind the path-following driver model. At each
time step, the driver model looks ahead along the vehicle longitudinal axis and calculates
52
2
Test Maneuvers and Analytical Driver Models
the look-ahead offset as the weighted sum of five lateral offsets. As mentioned earlier,
each lateral offset is calculated as the distance between the preview point and the desired
path measured along a line that is perpendicular to the optical lever. Using equation
(2.21), the driver model changes the steering wheel angle based on the look-ahead offset,
the vehicle longitudinal speed, the look-ahead distance, and vehicle parameters.
Figure 2-9: Path-following driver model concept in a double-lane-change maneuver
Figure 2-10-a illustrates the vehicle trajectory when driving through the doublelane-change maneuver at 40 km/h. In this simulation, the full AUTO21EV vehicle model
developed in the ADAMS/View environment is used (Appendix A), which is equipped
with tires using the Pacejka 2002 [Pac02] tire model. The simulation time is 8 seconds
with a sample time of 1 millisecond. A fixed-step fourth-order Runge-Kutta solver is
used to integrate the dynamic equations of motion. As shown in the figure, the pathfollowing driver model is able to steer the vehicle through the desired path such that the
actual vehicle trajectory matches well with the desired one. Figure 2-10-b illustrates the
steering wheel input applied by the driver model, and Figure 2-10-c shows the vehicle
yaw rate with respect to the driver‟s steering wheel input. Note that the steering system
has a gear ratio of 1:18 (Appendix A). Figure 2-10-c demonstrates the handling
capabilities of the vehicle, as the closer this plot is to a straight narrow line, the more the
vehicle behaves like its reference bicycle model, which indicates better responsiveness of
the vehicle to the driver‟s steering input. Looking at the vehicle yaw rate and sideslip
angle shown in Figure 2-11, it is clear that the actual vehicle yaw rate is very close to the
desired yaw rate, which is calculated using the reference bicycle model (Chapter 4,
equation 4.12). Moreover, the vehicle sideslip angle is very small – less than 0.4 degrees
– which indicates a slight understeering behaviour of the vehicle.
53
2
Test Maneuvers and Analytical Driver Models
Figure 2-10: (a) Desired and actual vehicle trajectories, (b) driver‟s steering wheel input, and (c) vehicle
yaw rate with respect to the steering wheel angle when driving through a double-lane-change maneuver at
40 km/h using the path-following driver model
In order to investigate the behaviour of the driver model in the nonlinear operating
regime of the vehicle, the double-lane-change maneuver is repeated at a speed of 75
km/h. Figure 2-12-a illustrates the vehicle trajectory when driving through the doublelane-change maneuver. Due to the fact that the vehicle is operating at its physical limit,
the path-following driver model is unable to exactly match the actual vehicle trajectory
with the desired one; however, the driver model is able to keep the vehicle under control
throughout the entire maneuver, using counter-steering at some points. Figure 2-12-b
shows the driver‟s steering wheel input which, in comparison to that shown in Figure 210-b, is much larger. Figure 2-12-c illustrates the vehicle yaw rate with respect to the
driver‟s steering wheel input, which is considered to be a handling performance figure.
Comparing this plot with Figure 2-10-c, it is clear that the phase shift between the vehicle
yaw rate and the driver‟s steering wheel input is much larger when driving through the
double-lane-change maneuver at a high speed, which ultimately indicates that the vehicle
responsiveness has been reduced. Figure 2-13 illustrates the vehicle yaw rate and sideslip
angle for this maneuver, and confirms that the vehicle was operating within its physical
limits.
54
2
Test Maneuvers and Analytical Driver Models
Figure 2-11: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when driving through a
double-lane-change maneuver at 40 km/h using the path-following driver model
Figure 2-12: (a) Desired and actual vehicle trajectories, (b) driver‟s steering wheel input, and (c) vehicle
yaw rate with respect to the steering wheel angle when driving through a double-lane-change maneuver at
75 km/h using the path-following driver model
The second test maneuver that is used to evaluate the performance of the multiplepreview-point path-following driver model is a steady-state constant radius cornering
maneuver. Here, the AUTO21EV is driven through a circular path with a radius of 75
meters. The driver model attempts to keep the vehicle on the predefined path while the
vehicle speed is continuously increasing from an initial speed of 5 km/h to a maximum
speed of 90 km/h. As illustrated in Figure 2-14-a, the driver model is able to keep the
vehicle on the predefined circular path even at higher velocities. Figure 2-14-b shows the
steering wheel angle that the driver model applies to keep the vehicle on the circular path.
55
2
Test Maneuvers and Analytical Driver Models
As can be seen, the driver model continuously adjusts the steering wheel angle in order to
keep the vehicle on the desired path. As the vehicle speed is increased, the driver model
applies a larger steering wheel angle, thereby generating larger lateral forces on the front
axle in order to compensate for the larger centripetal acceleration. Figure 2-14-c
illustrates the desired and actual vehicle forward speeds as functions of time. This figure
confirms the performance of the gain scheduling PID speed controller, as the actual
vehicle speed precisely follows the driver‟s speed request.
Figure 2-13: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when driving through a
double-lane-change maneuver at 75 km/h using the path-following driver model
Figure 2-14: (a) Desired and actual vehicle trajectories, (b) required steering wheel angle applied by the
driver model, and (c) desired and actual vehicle longitudinal speeds when driving through the steady-state
constant radius maneuver using the path-following and speed-control driver models
56
2
Test Maneuvers and Analytical Driver Models
The steering wheel angle applied by the driver model as a function of vehicle
lateral acceleration is illustrated in Figure 2-15-a. It is apparent that the steering wheel
angle has a linear gradient up to a lateral acceleration of 4 m/s 2 and then progressively
increases as lateral acceleration grows. This plot very clearly indicates the understeering
characteristic of the AUTO21EV. In fact, the slope of the linear region of this curve is
equal to the understeering gradient of the vehicle calculated in the design stage [Bod06].
As illustrated in Figure 2-15-b, the gradient of the sideslip angle is approximately linear
for the majority of the lateral acceleration range, which indicates good vehicle handling.
The maximum sideslip angle of the vehicle is measured as 
max
 5.7 , which is
acceptable. Moreover, the maximum lateral acceleration is calculated to be 8.3 m/s2,
which is acceptable for a small vehicle like the AUTO21EV. This value indicates a good
usage of the adhesion potential on all tires in order to keep the vehicle on its desired path.
The steering ratio can be calculated as the ratio of the steering wheel angle at the
beginning of the circular path (  SW  25.8 ), where the lateral acceleration is small, and
the Ackermann angle (  A 
iS 
a  b 1.8

 1.375 ), as follows:
R
75
 SW 25.8

 18.8
 A 1.375
(2.29)
This ratio agrees well with the steering ratio of the AUTO21EV calculated in the design
stage [Bod06].
Figure 2-15: (a) Driver‟s steering wheel input and (b) vehicle sideslip angle as functions of vehicle lateral
acceleration when driving through the steady-state constant radius maneuver using the path-following and
speed-control driver models
57
2
Test Maneuvers and Analytical Driver Models
In order to further evaluate the performance of the gain scheduling PID speed
controller, the vehicle is accelerated and then braked in a stepwise speed-variation mode
while driving in a straight line. In this test, the driver first increases the vehicle speed
from 10 km/h to the maximum speed of 90 km/h in increments of 20 km/h. Next, the
driver reduces the vehicle speed back to 10 km/h, again in a stepwise manner. Figure 216 illustrates the driver‟s speed request and the actual vehicle speed response for this
maneuver. As can be seen, the actual vehicle velocity follows the driver‟s request very
well, without causing any overshoot or significant over-damped conditions. Note that the
torque of the in-wheel motors reduces as the vehicle drives faster as a result of the
undesirable induction voltage produced by the permanent magnets. Consequently, the
acceleration response at lower speeds is faster than that at higher speeds (Figure 2-16).
This effect is confirmed by Figure 2-17, which illustrates the motor torques during this
maneuver. Note that, at the beginning and end of the test maneuver, where the vehicle is
travelling at lower speeds, the maximum motor torque is available at each wheel; as the
vehicle speed increases, the maximum possible motor torque decreases. It is important to
notice that the slip controllers on the front axle have limited the motor torques at the
beginning of the maneuver in order to avoid tire spin-out, and the slip controllers at the
rear wheels have limited the motor torques at the end of the maneuver in order to avoid
tire lock-up [Jal10]. The development of the fuzzy slip controller is the subject of the next
chapter.
Figure 2-16: Stepwise speed request from the driver model and the actual speed of the vehicle
58
2
Test Maneuvers and Analytical Driver Models
Figure 2-17: Motor torques during the stepwise speed variation test when driving in a straight line
59
3
Advanced Fuzzy Slip Control System
In the last 30 years, advances in electronics have revolutionized many aspects of the
automobile industry. Areas like engine management and safety systems, such as anti-lock
braking systems (ABS), traction control systems (TCS), and electronic stability control
(ESC) systems, have received particular attention. These safety systems involve the use
of electronic control units to modulate the brake and accelerator pedal inputs provided by
the driver in order to control the slip of individual tires during emergency braking (ABS)
or accelerating (TCS), or to control the stability of the vehicle by braking individual
wheels (ESC) [Zan00, Alb96, Ack99].
ABS is by no means a new innovation, and its development and acceptance has
occurred over a number of decades. The first ABS system was developed by Dunlop
Maxaret in 1952, and was used on aircraft landing systems [Vel01]. In 1978, Robert
Bosch GmbH introduced the modern anti-lock braking system for passenger vehicles
[Mar02-a, Mar02-b]. By the 1990s, ABS was a common option on many vehicles, and is
now a standard feature, or at least an optional feature, on nearly all new vehicles. In 1971,
the Buick division of GM introduced MaxTrac as the first TCS, which was used to detect
rear wheel spin and modulate the engine power delivered to those wheels in order to
provide the most traction possible. Since then, more sophisticated TCS systems have
been developed by different companies, such as Cadillac and Robert Bosch GmbH, and
involve an engine management controller that cooperates with the brake system in order
to prevent the driven wheels from spinning out. A comprehensive overview of the
history, operation, and types of slip control systems can be found in [Bur93].
The primary task of a slip control system, such as ABS or TCS, is to influence the
longitudinal dynamics of a vehicle by preventing the tires from locking up when braking
or spinning out when accelerating, thereby enhancing the directional stability of the
vehicle. According to a study conducted by the Monash University Accident Research
Centre, ABS has reduced the risk of multiple vehicle crashes by 18% and the risk of runoff-road crashes by 35% [Bur04]. Another study conducted by the National Highway
Traffic Safety Administration (NHTSA) confirms that a statistically significant decrease
in multi-vehicle crashes and fatal pedestrian strikes is achievable using an ABS system
[Maz01]. As a result, the European Automobile Manufacturers Association has been
60
3
Advanced Fuzzy Slip Control System
committed to equipping all new vehicles with ABS since 2003 [Bur04]. Figures from the
United States suggested that about 95% of new vehicles were equipped with ABS in 2003
[Vel01].
3.1
Conventional slip control systems
Conventional slip control systems use the hydraulic brake system and/or the engine
management controller in order to control the tire slip ratio, thereby influencing the
longitudinal dynamics of the vehicle. Slip control systems are closed-loop control devices
that prevent tire lock-up and spin-out during braking and acceleration, respectively. In a
closed-loop control system, the measured response of a physical system is compared to a
desired response, and the difference between these two responses initiates actions that
will cause the actual response of the system to approach the desired response. Preventing
tire lock-up and spin-out helps maintain the stability and steerability of the vehicle.
An ABS system detects the onset of wheel lock-up due to a high braking force,
and then limits the braking pressure to prevent wheel lock-up. An ABS system is
considered a stand-alone system (it can be installed independently of other control
systems), and consists of a wheel speed sensor, a hydraulic modulator, and an electronic
control unit (ECU) for signal processing, control, and triggering the actuators in the
hydraulic modulator [Bos07]. The ECU recognizes wheel lock-up by detecting sharp
increases in wheel deceleration, and reduces the braking force in a closed-loop process
until the lock-up situation vanishes. The cyclic application and reduction of the braking
force ensures that the brakes operate at or near their most efficient operating point and the
vehicle maintains steering control. This cyclic application is also responsible for the
pulsation that a driver feels through the brake pedal when the system is activated. In
general, when a driver presses the brake pedal, the brake slip increases until the point of
maximum friction between the tire and the road surface is reached, which is the limit
between the stable and unstable regions. At this point, any increase in brake pressure will
reduce the friction between the tire and the road surface, and the wheel will tend towards
skidding. In a vehicle with a conventional braking system, as the wheels tend towards
lock-up, the lateral force potential of the tires that enables steering is greatly reduced, and
approaches zero when the wheels are fully locked. By preventing wheel lock-up,
however, the lateral force potential of the tires is maintained at a high level, allowing the
61
3
Advanced Fuzzy Slip Control System
driver to retain steering control during emergency braking. Therefore, the task of an ABS
system is to use the friction coefficient between the tires and the road surface in an
optimal fashion in order to minimize the braking distance while retaining steerability.
Tire slip can also be controlled in an acceleration mode using a combination of
the hydraulic brake system and the engine management controller to prevent tire spin-out.
This task is accomplished by a TCS system, which is a constructive add-on to an existing
ABS system and cannot be installed alone. In a TCS, the ECU recognizes wheel spin-out
by detecting sharp increases in wheel acceleration. The ECU then reduces the engine
torque through the engine management controller in a closed-loop process to reduce the
traction force on the driven wheels. If the ECU was unable to prevent a spin-out situation
using this first method of intervention, it operates the brakes in order to stop the wheel
from spinning out. The cyclic application and the cooperation between the engine
management controller and the brake system together ensure that the friction coefficient
between the tires on the driven wheels and the road surface is used in an optimal fashion,
maximizing the traction force while retaining stability and steerability. Note that the aim
of a TCS system is defined based on the vehicle configuration. In a front-wheel-drive
(FWD) vehicle, TCS aims to maximize the traction force while retaining steerability,
whereas in a rear-wheel-drive (RWD) vehicle, TCS intends to maintain vehicle stability
while maximizing the traction force.
3.2
Development of an advanced fuzzy slip control system
In Chapter 1, two different methods of adjusting the tire slip ratio in a slip control system
are explained. As explained earlier, the tire slip ratio can be controlled either by limiting
the maximum possible slip ratio to a fixed amount or by adjusting the tire slip ratio such
that the maximum possible traction force can be generated at all slip angles. On the other
hand, the adhesion coefficient versus tire slip ratio plot shown in Figure 3-1 suggests that
the maximum adhesion coefficient for different road conditions can be generated at a slip
ratio of about 15%. Although this limit closely corresponds to the position of the peak
adhesion coefficient for only a dry road, the descending slopes associated with other road
conditions are small up to this slip limit; thus a slip ratio of 15% can be considered to
represent the maximum traction at other road conditions as well. With this in mind, and
noting that higher vehicle stability is more advantageous than maximum traction when
62
3
Advanced Fuzzy Slip Control System
driving in a curve, the limited tire slip ratio method from Chapter 1 has been chosen for
the advanced fuzzy slip controller of the AUTO21EV.
Figure 3-1: Typical adhesion coefficient characteristics as a function of tire slip ratio for different road
conditions
The actual slip ratio of each tire is calculated as a positive number using the
following equations for brake and acceleration modes, respectively:
brake, i 
accel , i 
vw, xi - w,i rdyn ,i
if vw, xi  0, w,i  0, and w,i rdyn ,i  vw, xi
(3.1)
w,i rdyn ,i - vw, x 
if vw, x   0, w,i  0, and w,i rdyn ,i  vw, x 
w,i rdyn ,i
(3.2)
vw, xi
i
i
i
where i FL, FR, RL, RR , vw, xi is the speed of the wheel center along the wheel plane,
rdyn is the dynamic tire radius, and w is the angular velocity of the tire. It is important to
note that, although all of the variables mentioned above are accessible in a simulation
environment, they must be measured or estimated in real life. The dynamic tire radius,
which is also known as the effective tire radius, is the ratio of the linear velocity of the
wheel center in the longitudinal direction to the angular velocity of the wheel [Blu04].
Although the dynamic tire radius has to be estimated in real life, in this work for
simplicity, the calculated dynamic tire radius is deployed directly from the tire model at
each time step. Note that the static loaded tire radius, which is the loaded radius of a
stationary tire inflated to the normal recommended pressure, is also used in the literature,
but it is associated with high inaccuracy [Bei00, Kie05]. If the vehicle travels in a straight
line and the tires roll freely without skidding and without any torque applied to them, the
speed of the wheel center along the wheel plane is equivalent to the speed of the center of
63
3
Advanced Fuzzy Slip Control System
gravity of the vehicle. In the presence of simultaneous longitudinal and lateral wheel
slips, however, the wheel center speeds are estimated by transferring the vehicle velocity
( vCG ) to the wheel centers [Kie05].
Figure 3-2 illustrates a two-track model of the vehicle in the horizontal plane,
which can be used to calculate the wheel speeds. The vehicle velocity vCG and the
magnitudes of the longitudinal aCG , x and lateral aCG , y accelerations are calculated as
follows:
vCG  vCG, x  ex  vCG , y  ey
(3.3)
aCG, x  vCG , x  vCG , y 
(3.4)
aCG, y  vCG, y  vCG, x 
(3.5)
Figure 3-2: Planar two-track vehicle model
where ex and e y are unit vectors along the longitudinal and lateral axes of the vehicle,
respectively, vCG , x and vCG , y are the longitudinal and lateral speeds of the vehicle, and 
is the vehicle yaw rate. In real life, the longitudinal ( vCG , x ) and lateral ( vCG , y )
accelerations of the vehicle are measured with two accelerometers, which are positioned
at the center of mass of the vehicle along the longitudinal and lateral vehicle axes,
64
3
Advanced Fuzzy Slip Control System
respectively. The yaw rate  is measured using a gyroscope positioned at the center of
gravity of the vehicle, along its vertical axis. It is important to note that, in real life, the
vehicle velocity ( vCG ) must be estimated as well. Three common methods of estimating
the vehicle velocity are as follows [Kie05, Bos07]:

Transforming the measured wheel speeds to the center of gravity of the vehicle
and fusing the data from all rotational wheel speeds with the integrated
longitudinal acceleration signal,

Using a Kalman filter, and

Using a fuzzy estimator.
In this work, however, for the sake of accuracy and simplicity, the vehicle velocity is
obtained directly from the simulation environment and is not estimated.
The sideslip angle () of the vehicle, which is the angle between the direction of
motion of the vehicle and its longitudinal axis, cannot be measured directly using a
sensor. In this work, a neural network similar in structure to that proposed by Durali and
Bahramzadeh [Dur03] is used to estimate this angle. The neural network is constructed
using 3 layers and 5 hidden nodes, and is able to estimate the vehicle sideslip angle at the
current time step given the current steering wheel input, the current and two previous
lateral and longitudinal accelerations, and the two previous estimates of the sideslip angle
(Figure 3-3). This neural network is trained with data obtained by driving the vehicle
through several maneuvers at different speeds. As demonstrated by Figure 3-4, the
resulting neural network provides a reliable vehicle sideslip angle calculation when
driving through different maneuvers. Knowing the sideslip angle of the vehicle, the
longitudinal and lateral speeds of the vehicle are calculated as follows:
vCG , x  vCG  cos(  )
(3.6)
vCG , y  vCG  sin(  )
(3.7)
Looking at Figure 3-2, the wheel center velocities vw,i can be calculated as follows
[Kie05]:
t 

vw, FL   vCG , x   f  ex   vCG , y    a  e y
2

(3.8)
65
3
t

vw, FR   vCG , x    f
2

Advanced Fuzzy Slip Control System

 ex   vCG , y    a  e y

(3.9)
t 

vw, RL   vCG , x   r  ex   vCG , y   b  e y
2

(3.10)
t 

vw, RR   vCG , x    r  ex   vCG , y   b  e y
2

(3.11)
Note that all of these wheel center velocities are calculated with respect to the local
coordinate system of the vehicle.
Figure 3-3: Block diagram of neural network sideslip estimator proposed by Durali and Bahramzadeh
[Dur03]
Figure 3-4: Performance of the neural network sideslip angle estimator during a double-lane-change
maneuver
According to equations (3.1) and (3.2), the slip ratio of a tire is calculated along
the wheel plane. Since the rear wheels do not steer, their local coordinate systems are
66
3
Advanced Fuzzy Slip Control System
parallel to the vehicle coordinate system. Thus, the portion of the wheel center velocity
along the x-axis from equations (3.10) and (3.11) can be used directly to calculate the
wheel slip for the rear tires:
vw, xRL  vw, xRL  vCG , x  
tr
2
(3.12)
vw, xRR  vw, xRR  vCG , x   
tr
2
(3.13)
Note that vw, xRL and vw, xRR
indicate the wheel center velocities of the rear-left and rear
right tires with respect to the local coordinate systems of the wheels. The local coordinate
systems of the front wheels are rotated by the steering angle so equations (3.8) and
(3.9) must be transformed into the appropriate wheel coordinate systems. Looking at
Figure 3-5, the wheel center velocities of the front wheels can be calculated as follows:
t 

vw, xFL  vw, xFL  cos( )  vw, yFL  sin( )   vCG , x   f   cos( )   vCG , y    a   sin( ) (3.14)
2

t 

vw, xFR  vw, xFR  cos( )  vw, yFR  sin( )   vCG , x    f   cos( )   vCG , y    a   sin( ) (3.15)
2

Figure 3-5: (a) Translational and (b) rotational tire motion
One advantage of the AUTO21EV is that both ABS and TCS systems can be
realized through the available in-wheel motors without using the conventional brake
system or engine management controller. The torque response of an electric motor is
several milliseconds, which is 10 to 100 times faster than that of an internal combustion
67
3
Advanced Fuzzy Slip Control System
engine or even a hydraulic brake system [Hor04]. When coupled with the ability to
individually control the wheel slip at each corner of the vehicle, this platform has allowed
us to design a very advanced slip control system for the AUTO21EV using its in-wheel
motors. Figure 3-6 illustrates the block diagram that is used to calculate the actual slip
ratio of the front-left (FL) tire as an example.
Figure 3-6: Block diagram for calculating the actual slip ratio of the front-left tire
Fuzzy logic control systems are robust and flexible inference methods that are
well suited for tackling complicated nonlinear dynamic control problems. As such, they
are ideal candidates for controlling the highly nonlinear behaviour inherent in vehicle
dynamics. Fuzzy control systems can tolerate imprecise information and can describe
expert knowledge in vague linguistic terms, which suits the subjective nature of vehicle
dynamics and slip control systems [Kar04].
The rule base of the fuzzy slip controller was designed using the slip ratio error
e(λ) and the rate of change of the slip ratio error e(λ) as the inputs; the corrective motor
torque Tcorr is the output of the slip controller (see Table 3-I). The tire slip ratio error is
calculated by comparing the actual tire slip with the desired slip limit at every time step.
The rate of change of the slip ratio error is calculated by subtracting the previous slip
ratio error from the current one, and dividing the result by the sample time of the
controller.
68
3
Advanced Fuzzy Slip Control System
Variable
Definition
Input 1
e(λ) = λ lim - λ act
Input 2
e(λ) =
e(λ) k - e(λ) k-1
sample time
Tcorr
Output
Table 3-I: Definition of the input and output variables of the fuzzy slip controller
The controller inputs and output are normalized to simplify the definition of the
fuzzy sets. Four and seven fuzzy sets are used for the slip ratio error and the rate of
change of the slip ratio error, respectively, in order to provide enough rule coverage. Nine
fuzzy sets are used to describe the output of the fuzzy slip controller.
The fuzzy inference system processes the list of rules in the knowledge base using
the fuzzy inputs obtained from the previous time step of the simulation, and produces the
fuzzy output which, once defuzzified, is applied in the next time step. The Mamdani
fuzzy inference method is used, which is characterized by the following fuzzy rule
schema:
IF e  λ  is A AND e  λ  is B THEN Tcorr is C
(3.16)
where A, B, and C are fuzzy sets defined on the input and output domains. The control
rule base of the proposed fuzzy slip controller is developed based on expert knowledge
and extensive investigation. Figure 3-7 illustrates the control rule base and control surface
of the fuzzy slip controller. The linguistic terms that have been used in this table are listed
in Table 3-II. The shape and distribution of the membership functions used for the input
and output variables of the fuzzy slip controller are shown in Figure 3-8. Since only
positive membership functions have been used for e(λ) and the slip controller is only
activated when e(λ) is negative (i.e., when the actual slip ratio of a tire is greater than the
slip limit), the slip ratio error must be converted into a positive number before entering
the fuzzy slip controller. This procedure is shown in Figure 3-9, where the block diagram
of the entire slip control system is illustrated.
69
3
Advanced Fuzzy Slip Control System
Figure 3-7: Control rule base (left) and control surface (right) of the fuzzy slip control system
Acronym
Linguistic Variable
NVL
NL
NM
NS
ZE
PS
PM
PL
PVL
Negative Very Large
Negative Large
Negative Medium
Negative Small
Zero
Positive Small
Positive Medium
Positive Large
Positive Very Large
Table 3-II: Linguistic variables used in the fuzzy rules
Figure 3-8: Shape and distribution of membership functions for the input and output variables of the fuzzy
slip controller
70
3
Advanced Fuzzy Slip Control System
Figure 3-9: Block diagram of the advanced slip control system for the front-left tire
3.3
Evaluation of the advanced fuzzy slip control system
The performance of the fuzzy slip controller is tested using four different maneuvers.
First, the AUTO21EV is accelerated in a straight line from 5 km/h to its maximum speed
of 90 km/h. The acceleration starts at 0.5 seconds into the simulation and the vehicle
reaches its maximum speed after 5 seconds (Figure 3-10-a). As illustrated in Figure
3-10-b, a maximum acceleration of about 0.85g is achievable up to a speed of 28 km/h,
where the maximum motor torques are available.
Figure 3-10: (a) Vehicle speed and (b) vehicle longitudinal acceleration versus forward speed during the
straight-line acceleration maneuver
Figure 3-11 illustrates the slip ratio of each tire during the straight-line
acceleration maneuver. The plots shown in Figure 3-11 clearly indicate that the slip
controllers on the front wheels have limited the tire slips after the start of acceleration up
to about 1 second, where tire spin-out would have otherwise occurred due to the
availability of high motor torques and the dynamic weight shift to the rear axle.
Moreover, the slip controllers on the rear wheels are activated for a short period of time
(0.1 seconds) in order to generate the maximum possible traction force while preventing
71
3
Advanced Fuzzy Slip Control System
any tire spin-out. The activation of the slip controllers can also be verified by looking at
the motor torque histories in Figure 3-12. The required torque from the driver model
(TDriver,req) is modified by the slip controllers ( TSCi ,req ) such that, during a period of about
0.1 seconds after the start of the acceleration, the rate of change of each motor torque is
limited by its respective slip controller to prevent spin-out. The slip controllers on the
front wheels have continued limiting the motor torques up to about 1.3 seconds of the
simulation, at which point the maximum motor torques are automatically reduced due to
the induction voltages and magnetization losses that occur at higher motor speeds. On the
rear wheels, however, the actual torque of the motors is restricted by the maximum torque
limit, not by the slip controllers. Moreover, due to the shifting of weight to the rear axle
of the vehicle, the traction potentials of the rear tires have increased, thereby preventing
these tires from spinning out. Note that the oscillatory behaviour of the slip ratios of the
rear tires in the first second of the simulation is caused by the tire model and not the
controllers. Notice that the Pacejka 2002 tire model that is used in this work is not very
suitable for low speeds and ABS braking control applications (see Figure A-18 in the
Appendix). However, it was the best tire model that was available for this work.
Figure 3-11: Tire slip ratios during the straight-line acceleration maneuver
72
3
Advanced Fuzzy Slip Control System
Figure 3-12: Motor torques during the straight-line acceleration maneuver
The second maneuver used to evaluate the performance of the slip control design
is a straight-line braking test. In this test, the driver intends to stop the AUTO21EV from
a maximum speed of 80 km/h in an emergency braking situation. Figure 3-13-a indicates
that the braking distance is about 39.7 meters, which is a very impressive result
considering the regulations on braking systems for passenger vehicles in the European
Union (EU). As stated in the EU directives and regulations for braking systems, the
braking distance of passenger-type vehicles must be less than 50.7 meters for an initial
test speed of 80 km/h [Bos07]. It takes about 4 seconds to bring the vehicle to a final
speed of 5 km/h (Figure 3-13-b), during which time none of the tires lock up. Note that
the vehicle speed is only reduced to 5 km/h due to the instability of the Pacejka tire model
at low speeds. Figure 3-13-c indicates that a maximum deceleration of 0.82g is
achievable at speeds lower than 45 km/h. These results confirm that the proposed slip
controller is capable of replacing the conventional brake system in the AUTO21EV. In
other words, the in-wheel motors are capable of taking over the entire functionality of a
conventional brake system for the entire speed range. As a fail-safe back-up, however, a
redundant hand-brake system must be installed in the AUTO21EV.
73
3
Advanced Fuzzy Slip Control System
Figure 3-13: (a) Braking distance, (b) vehicle speed, and (c) vehicle longitudinal deceleration versus
forward speed during the straight-line braking test
As illustrated in Figure 3-14, the slip controllers are only activated on the rear
tires at about 1.4 seconds, where tire lock-up would have otherwise occurred due to the
dynamic weight shift to the front axle and higher available braking torques at lower
speeds. This control effort is also apparent in Figure 3-15, in which the motor torques at
the rear wheels are shown to be restricted to about 500 Nm, while the in-wheel motors on
the front axle are permitted to apply the maximum torque of 700 Nm. In addition, since
the slip controllers prevent any tire lock-up, there is no need to introduce an extra braking
force distribution technique, as is common in conventional brake systems. As mentioned
earlier, the rapid oscillations in the slip ratio plots that occur after the third second of the
simulation (when the vehicle speed is about 10 km/h) are caused by the tire model and
not the controllers.
The third test for the fuzzy slip controller is performed on a -split road, where
the road is dry on the right side and icy on the left side. In this test, the driver holds the
steering wheel fixed and accelerates the vehicle in a straight line from an initial speed of
10 km/h. The road is considered to be dry before x = 15 m and after x = 25 m. As shown
in Figure 3-16, a black ice patch is present on the left side of the road for
15 m < x < 25 m. Although the intention of the driver is to travel in a straight line, the car
is pushed to the left side of the road due to the asymmetrical traction forces on the left
and right sides of the vehicle. In order to keep the vehicle on the road, this side-pushing
effect must be corrected either through a counter-steering input from the driver or by an
74
3
Advanced Fuzzy Slip Control System
active stability control system. Note that the slip control system has done its job by
maximizing the available acceleration.
Figure 3-14: Tire slip ratios during the straight-line braking maneuver
Figure 3-15: Motor torques during the straight-line braking maneuver
Figure 3-16: Vehicle trajectory when accelerating on a -split road
75
3
Advanced Fuzzy Slip Control System
Figure 3-17 illustrates the tire slips of the vehicle during this acceleration
maneuver. The slip controllers have limited the tire slips on the front axle at the
beginning of the acceleration, where tire spin-out would have occurred due to the
available high motor torques and the dynamic weight shift to the rear axle. In addition,
the slip controllers on the left side of the vehicle are activated when the vehicle drives
over the black ice patch, thereby preventing tire spin-out while still generating the
maximum possible traction force on the ice patch. As shown in Figure 3-18, the motor
torques on the front wheels are limited by the slip controllers for about 0.6 seconds after
the start of the acceleration. When driving over the black ice patch, the motor torques on
the left side of the vehicle are reduced to about 40 Nm to avoid tire spin-out.
Figure 3-17: Tire slip ratios during the straight-line acceleration maneuver on a -split road
Figure 3-18: Motor torques during the straight-line acceleration maneuver on a -split road
76
3
Advanced Fuzzy Slip Control System
The final test for the fuzzy slip controller is braking on a -split road, which is a
very critical test since the vehicle will experience severe instability if the driver does not
react immediately to correct the course of the vehicle. In this test, the driver holds the
steering wheel fixed and attempts to stop the vehicle in an emergency braking situation
from 80 km/h on a road that has a black ice patch on the left side for 15 m < x < 25 m. As
illustrated in Figure 3-19, the vehicle is pushed to the right side of the road due to the
asymmetrical braking forces on the left and right sides of the vehicle. More important is
the fact that these asymmetrical braking forces are high enough to turn the vehicle around
its vertical axis. In order to avoid such a dangerous situation, a driver must correct the
course of the vehicle through a sequence of steering corrections based on the vehicle
response, which is a very difficult task for an average driver. Although the slip controller
has done its job to maximize the braking forces, further control is needed to maintain a
safe trajectory.
Figure 3-19: Vehicle trajectory when braking on a -split road
As shown in Figure 3-20, the slip controllers on the left side of the vehicle have
limited the tire slips when driving over the -split portion of the road, which occurs
between 0.7 and 1.2 seconds after the start of the simulation. The rear-right tire will also
begin experiencing a lock-up situation due to the shifting vehicle weight and a high
braking torque at around 1.1 seconds, which is prevented by the rear-right slip controller.
Furthermore, since the vehicle starts to turn around its vertical axis, large lateral forces
are generated on all tires, which simultaneously reduce the braking force potential on all
four tires. This yawing motion explains why the front-left, front-right, rear-left, and rearright slip controllers are becoming active at around 1.95, 1.4, 1.6, and 1.1 seconds,
respectively, to prevent tire lock-up. The activation of the slip controllers is also
confirmed by Figure 3-21, which illustrates the motor torques. Note that, due to the
77
3
Advanced Fuzzy Slip Control System
vehicle spin occurring in this test, only the meaningful range of data has been plotted in
Figures 3-20 and 3-21.
Figure 3-20: Tire slip ratios during the straight-line braking maneuver on a -split road
Figure 3-21: Motor torques during the straight-line braking maneuver on a -split road
3.4
Chapter summary
In this chapter, an advanced fuzzy slip controller is developed for the AUTO21EV that
combines the functionalities of an ABS, a TCS, and the brake system of the vehicle.
Since the developed fuzzy slip controller is able to control the slip ratio of all four tires in
all driving conditions, thereby realizing the most advanced All-Wheel-Drive system. The
developed fuzzy slip controller is based on a chassis platform that has four individual
78
3
Advanced Fuzzy Slip Control System
electric drives, the reaction time of this slip controller is much faster than that of any
other conventional slip control system based on a hydraulic brake system or internal
combustion engine. The performance and functionality of the developed fuzzy slip
control system have been evaluated using four test maneuvers.
79
4
Genetic Fuzzy Yaw Moment Controller
As mentioned in Chapter 1, most stability control systems generate a corrective yaw
moment around the vertical axis of the vehicle by affecting the linear or nonlinear
characteristics of the tire-road contact forces. A corrective yaw moment can be created
directly using the lateral force of the tires by manipulating the steering or camber angle of
the tires, such as in an active steering or active camber system, or using the longitudinal
force of the tires by manipulating the drive or brake torque of individual wheels, such as
in an electronic stability control (ESC) or torque vectoring control system. It is important
to notice that longitudinal and lateral tire forces can both be influenced indirectly by
manipulating the wheel load and defining the maximum possible transfer force, such as in
an active suspension or an active anti-roll bar system. Regardless of the means by which
forces are applied, generating a corrective yaw moment around the vertical axis of the
vehicle is the main objective of all these systems.
Having this in mind, a yaw moment controller is designed for the AUTO21EV
that acts as a high-level supervisory module, assigning tasks to the low-level controllers
and actuators. This hierarchical approach addresses the complexities of integrated chassis
control management and allows the low-level controllers and actuators, such as the torque
vectoring controllers and the in-wheel motors, to be designed simply as tracking
controllers that track the reference signals generated by the supervisory yaw moment
controller. In addition, since such a yaw moment controller represents an ideal controller,
in that the required corrective yaw moment can be generated directly without being
restricted by the performance and limitations of actuators, the performance of this yaw
moment controller can be used as a reference against which the performance of other
stability control systems can be compared.
In this chapter, a genetic fuzzy yaw moment controller (YMC) is developed for
the AUTO21EV, the objective of which is to calculate the corrective yaw moment
required to minimize the sideslip angle and yaw rate errors of the vehicle, comparing the
actual values from the vehicle to those obtained using a reference bicycle model. At this
stage, the calculated corrective yaw moment is applied to an imaginary torque driver that
is placed at the center of mass of the vehicle, acting about its vertical axis.
80
4
4.1
Genetic Fuzzy Yaw Moment Controller
Simplified vehicle model with in-wheel motors
A full vehicle model, such as the AUTO21EV model created in the ADAMS
environment (Appendix A), involves a large number of both equations and parameters,
which makes it difficult for a control engineer to investigate the effects of different
control strategies and discover the source of possible problems. In fact, from a vehicle
motion control perspective, it is more desirable to start with a simpler vehicle model and
increase the level of fidelity once the effectiveness of a control strategy has been
confirmed. In addition, numerical formulation techniques, such as those employed in the
ADAMS software, are very computationally expensive because these techniques generate
system matrices that are only valid for an instant of time and, thus, must be reformulated
at every time step of a simulation. Furthermore, the optimization of control parameters
using a genetic algorithm procedure involves many simulation runs, which can be a timeconsuming process, especially when the system model is complicated.
With this in mind, a fast simulation model was desired to allow for the testing of
different control strategies, and for applying a genetic algorithm procedure to the
development of the chassis control systems. Therefore, an alternative 14-degree-offreedom (DOF) vehicle model was developed using DynaFlexPro, a Maple package that
uses symbolic formulation procedures and linear graph theory to generate
computationally efficient simulation code [Sch04]. Symbolic formulation techniques
combine the system parameters and modelling variables to create sets of equations that
describe a dynamic system for all time. Therefore, such approaches are ideal for real-time
applications, such as hardware- and human-in-the-loop scenarios, which require a fast
computation time. In addition, the 14-DOF vehicle model used herein was recommended
by Sayers [Say96] for analyzing the handling and stability behaviour of vehicles, and has
been adopted by several commercial software packages such as CarSim [Sch08].
The AUTO21EV was modelled in the DynaFlexPro environment with
independent suspensions, four direct-drive in-wheel motors, and a steering system on the
front axle, as shown in Figure 4-1. Note that the in-wheel motors are integrated directly in
the vehicle model, combining the mechanical and electrical domains of this mechatronic
system together. The topology of the vehicle model was defined in block diagram form
using ModelBuilder, a graphical user interface companion for DynaFlexPro. The
generated DynaFlexPro model of the vehicle was later imported into the
81
4
Genetic Fuzzy Yaw Moment Controller
MATLAB/Simulink environment, and different chassis control systems and in-wheel
motor controllers were added to it. Note that DynaFlexPro has been superseded by the
Multibody package in MapleSim.
Figure 4-1: AUTO21EV vehicle model implemented in DynaFlexPro
The sprung mass of the vehicle is considered to be a single rigid body, which will
be referred to herein as the chassis. The position and orientation of the chassis, measured
with respect to a global reference frame, account for 6 DOF. The suspension system is
modelled using four lumped masses that are connected to the chassis via four prismatic
joints, each of which is associated with a linear spring and damper, representing the
suspension compliance. Together, these components add another 4 DOF to the vehicle
model. Note that these four lumped masses consist of those components of the suspension
and steering system that are considered to belong to the unsprung mass, including the
stator of the in-wheel motors. Each wheel consists of a tire, a rim, and the rotor of the inwheel motor, and is connected to its corresponding lumped mass with a revolute joint that
allows the wheel to spin around its rotation axis, thereby adding another 4 DOF to the
model. The steering system is modelled with two independent motion drivers on the front
axle, which facilitate the use of an Ackermann steering configuration using look-up
tables. Since the driver specifies the input to the steering system, these motion drivers do
not add any DOF to the model. The Pacejka 2002 tire model, which is the most
comprehensive version of the Magic Formula tire model [Pac02], is used in this vehicle
model. Pacejka 2002 is considered to be the state-of-the-art for modelling tire-road
82
4
Genetic Fuzzy Yaw Moment Controller
contact forces in vehicle dynamics applications and, thus, is recommended for all generic
vehicle handling and stability simulations, including steady-state cornering, double-lanechange, braking-in-turn, straight-line -split braking, and ABS braking maneuvers
[ADA02]. It is important to note that all the masses and moments of inertia of different
parts and subsystems of the vehicle and in-wheel motors, including the spring and
damper rates of the suspension system and the Ackermann steering behaviour, are taken
directly from the full vehicle model developed in ADAMS. Finally, a torque driver is
added at the center of mass of the vehicle around its vertical axis, which represents the
imaginary corrective yaw moment. As mentioned earlier, this torque driver represents
only the ideal case, where any required corrective yaw moment can be generated and acts
directly at the center of mass of the vehicle. Note that the required corrective yaw
moment must ultimately be generated by individual tire forces. More details about the
DynaFlexPro model of the AUTO21EV can be found in [Vog07].
4.2
Soft computing and hybrid techniques
As the complexity of an engineering problem increases, so does the need for more
advanced analytical control techniques. Many of the dynamic systems studied in recent
applications involve nonlinear, time-variant, and chaotic behaviour. While conventional
mathematical model-based control techniques can effectively address linear timeinvariant problems, their efficacy when applied to more complex nonlinear time-variant
problems is limited. The tools of soft computing have been shown to be highly effective
in situations where the performance of conventional techniques is poor [Kar04].
The term “soft computing” refers to a family of computational techniques, namely
fuzzy logic, evolutionary computation, and neural networks. These techniques have been
conceptualized and developed over the past forty years. Contrary to hard computational
techniques, which are characteristically rigid in structure, soft computing techniques have
the ability to operate in environments that are subject to uncertainty and imprecision. In
fact, in many applications, the precision offered by conventional techniques can
comfortably be sacrificed in order to arrive at more economical and intuitive solutions.
Each soft computing technique has its own set of strengths and weaknesses, some of
which are illustrated in Figure 4-2. While the tools of soft computing share some
common characteristics, these techniques are considered to be complementary, as
83
4
Genetic Fuzzy Yaw Moment Controller
desirable features lacking in one approach may be present in another. Although many
problems have been solved by using only one technique, many real-world problems
require the integration of two or more techniques in order to achieve the required speed
and accuracy for a given application. Therefore, by combining individual soft computing
techniques together, new and powerful hybrid techniques can be generated that exploit
the strengths of the constituent paradigms while reducing the effects of their weaknesses.
Figure 4-3 illustrates some of the possible hybrid techniques that can be obtained through
the fusion of two or more soft computing paradigms. Since building a genetic fuzzy YMC
is the main focus of this chapter, a brief overview of fuzzy logic and the genetic
algorithms is presented below.
Figure 4-2: Advantages and disadvantages of soft computing techniques
Fuzzy Logic: Since their initial development by Prof. L.A. Zadeh in the mid-1960s
[Kar04], the principles of fuzzy logic have been applied to a wide variety of applications.
In contrast to conventional Boolean or crisp methods, in which truth is represented by the
state 1 and falsity is represented by the state 0, fuzzy logic represents approximate
knowledge, and can be considered to be an extension of crisp two-state logic. Fuzzy logic
is based on fuzzy set theory in a manner that is similar to how crisp two-state logic is
based on crisp set theory. A fuzzy set is represented by a membership function. A
particular „element‟ value in the range of definition of the fuzzy set will have a grade of
membership, which gives the degree to which the particular element belongs to the set. In
this manner, it is possible for an element to belong to the set (to some degree) and,
84
4
Genetic Fuzzy Yaw Moment Controller
simultaneously, to not belong to the set (to a complementary degree), thereby allowing a
non-crisp, fuzzy membership [Kar04].
As the complexity of a system increases, the ability to develop precise analytical
models of the system diminishes until a threshold is reached, beyond which analytical
modelling simply becomes intractable. Under such circumstances, where precise modelbased decision-making is not practical, fuzzy knowledge-based decision-making is
particularly suitable. Fuzzy logic provides an approximate, yet practical, means of
representing knowledge about a system that is too complex or ill-defined and, therefore,
not easy to handle using precise mathematical means. At the same time, fuzzy logic
provides a means of making inferences using approximate knowledge, which can be used
to make decisions regarding the system and carry out appropriate actions. These features
allow fuzzy logic to effectively handle human-oriented knowledge.
Figure 4-3: Hybrid techniques possible through the combination of soft computing paradigms
Fuzzy inference systems represent knowledge in the simple and intuitive form of
„if-then‟ rules, and are able to approximate human reasoning capabilities given imprecise
information. As such, fuzzy systems tend to be more robust than traditional control
systems, and can be used to model and control complex nonlinear dynamic systems
without requiring a complex analytical model of the system. Although many applications
can be found in industry, fuzzy systems can only be used in situations where expert
85
4
Genetic Fuzzy Yaw Moment Controller
knowledge is available. However, as the complexity of a system increases, it becomes
more challenging to determine the correct set of fuzzy rules and the appropriate shape of
the membership functions. Unfortunately, fuzzy systems have no inherent learning or
adapting capabilities, so the fuzzy rules and membership functions must be designed and
tuned manually if a fuzzy system is implemented on its own.
Figure 4-4 illustrates the structure of a fuzzy rule-based system. As can be seen, a
fuzzy controller consists of four parts: fuzzification, the knowledge base, the inference
engine, and defuzzification. The inputs to the fuzzy controller are most often crisp
measurements obtained from some measuring equipment, so a preprocessor is necessary
for preparing the measurements before entering the controller. Some possible
preprocessing methods are as follows [Jan98]:

Quantization in connection with sampling or rounding to integers;

Normalization or scaling onto a particular standard range;

Filtering to remove noise;

Averaging to obtain long-term or short-term tendencies; and

Differentiation and integration, or their discrete equivalences.
Figure 4-4: Block diagram of a fuzzy control systems
The fuzzification block translates each piece of input data into degrees of
membership in one or several membership functions using tabulated data. Specifically,
the fuzzification block matches the input data with the conditions of the rules to
determine how well the condition of each rule matches that particular input. There is a
degree of membership for each linguistic term that applies to each input variable. The
knowledge base of the fuzzy controller consists of a data base (containing the definitions
86
4
Genetic Fuzzy Yaw Moment Controller
of the scaling factors and the membership functions of the fuzzy sets that, together,
specify the meaning of the linguistic terms) and a rule base (constituted by the collection
of fuzzy rules, specified in an „if-then‟ format). The inference engine is the driver
program of the knowledge base. Depending on the inputs and the data in the data base,
the inference engine operates on the knowledge in the knowledge base to solve problems
and arrive at conclusions. The defuzzification block converts the resulting fuzzy set to a
crisp number that can be sent to the controlled system as a control signal. There are
several defuzzification methods, including the center of gravity, bisector of area, mean of
maxima, and leftmost and rightmost maxima approaches [Kar04]. Finally, the
postprocessor scales the output to engineering units, in cases where the output has been
defined over a normalized range. The postprocessor often contains an output gain that can
be tuned.
Genetic Algorithms: Evolutionary or genetic algorithms (GAs) are general-purpose search
strategies that use principles inspired by biological evolution to solve optimization
problems. Evolutionary strategies are very robust and can be used in problem domains
where traditional optimization techniques fail. GAs are typically used in complex
problem spaces that are difficult to understand or predict, since they are effective at
exploring such spaces. The fundamental idea is to encode sets of system parameters in a
population of chromosomes, each of which represents a candidate solution to the
problem. The population of chromosomes is then evolved over time through competition
among its members and controlled variation [Kar04]. Genetic algorithms consist of three
operations: evaluation of the fitness of each individual chromosome, formation of a gene
pool through the selection of chromosomes from the preceding generation, and
recombination using the crossover and mutation operators.
A GA is initiated with a population of randomly generated chromosome, and
discovers fitter chromosomes by applying genetic operators that are modelled after the
genetic processes occurring in the nature. The population evolves by way of natural
selection. During successive iterations, or so-called „generations‟, the chromosomes in
the population are evaluated for their adaptation as solutions. On the basis of these
evaluations, a new population of chromosomes is formed using a selection mechanism
and specific genetic operators, such as crossover and mutation. It is important to note that
87
4
Genetic Fuzzy Yaw Moment Controller
a specific fitness function must be devised that describes the objective of the problem to
be solved. Given a particular chromosome (i.e., a candidate solution), the fitness function
returns a single numerical fitness value that is proportional to the utility or adaptation of
the solution represented by that chromosome.
Whereas traditional optimization techniques, such as hill-climbing algorithms,
search for global optima in a multi-dimensional space by iteratively refining a single
solution vector, genetic algorithms operate on an entire population of candidate solutions
in parallel. Therefore, GAs are less prone to becoming trapped by local optima. Local
optima are regions of the search space that hold good solutions relative to their
surrounding regions, but do not necessarily contain the best solutions in the entire
problem space, which are described as global optima. Parallelism is one of the main
strengths of GAs, since it helps to prevent premature convergence at local optima, and it
reduces the importance of carefully selecting the initial conditions. Note that the mutation
and crossover rates are among the most significant factors contributing to convergence
and, therefore, must be selected carefully [Gol89]. Although the stochastic search used by
genetic algorithms is exceptionally robust, its convergence is usually slower than that of
traditional techniques. Moreover, due to the stochastic nature of genetic algorithms and
the encoding of parameters into a finite number of genes, the solutions obtained by GAs
are only approximations; they will only find an exact global optimum by chance.
Genetic Fuzzy System: Fuzzy logic and genetic algorithms have both been applied to a
wide variety of problems. Still an active area of research, however, is the fusion of these
techniques into a hybrid system that exploits their strengths while reducing the effects of
their weaknesses. Two main hybrid approaches have been identified in this area: fuzzy
evolutionary algorithms and genetic fuzzy systems. A fuzzy evolutionary algorithm is an
evolutionary algorithm whose inherent parameters, such as its fitness function and
stopping criterion, are fuzzified. The resulting hybrid system is capable of tolerating
imprecision, which can reduce the computational resources required. Fuzzy inference
systems can be used to adapt the parameters of an evolutionary algorithm, such as its
mutation rate, crossover rate, and population size, or to adapt the genetic operators
themselves. In the first case, the inputs to the fuzzy system would be the current control
88
4
Genetic Fuzzy Yaw Moment Controller
parameters and performance measures, and the outputs would be the new control
parameters subsequently used by the genetic algorithm [Her96, Vog98].
In the 1990s, despite the previous success of fuzzy logic systems, their inability to
learn or adapt to their environment was found to severely limit their potential
applications; genetic fuzzy systems address this limitation. A genetic fuzzy system is
essentially a fuzzy system that is augmented by a learning process based on a genetic
algorithm. The most popular type of genetic fuzzy system is the genetic fuzzy rule-based
system, where an evolutionary algorithm is employed as a design method to learn or tune
different components of a fuzzy knowledge base. The structure of a genetic fuzzy system
is illustrated in Figure 4-5.
Figure 4-5: Block diagram of a genetic fuzzy control system
In order to use a genetic algorithm for optimizing a fuzzy knowledge base, the
rules or membership functions must first be represented as a set of tunable parameters. It
is also necessary to define an appropriate performance index, based on the optimization
criterion, with which to evaluate the proposed knowledge bases. Finally, the knowledge
base parameters must be transformed from the optimization space into a suitable genetic
representation [Cor04]. A genetic process can then be used to evaluate, select, and evolve
the genetically encoded candidate solutions. At this point, it is important to differentiate
between tuning and learning problems. Tuning is concerned with the optimization of an
existing fuzzy inference system having a predefined rule base. Learning, on the other
hand, constitutes an automated design method for determining fuzzy rule sets from
89
4
Genetic Fuzzy Yaw Moment Controller
scratch [Cor01]. In other words, learning processes do not require a predefined set of
rules. The objective in the case of tuning is to find the best possible set of parameters for
the data base of the fuzzy inference system. For instance, tuning can be applied to the
scaling functions that normalize the domain of the input and output variables. Linear
scaling functions can be parameterized by either a single scaling factor or by two
parameters; nonlinear scaling functions generally use three or four parameters [Cor01].
Tuning can also be applied to the fuzzy membership functions. In this case, each
chromosome encodes the parameterized membership functions associated with all the
rules in the rule base. The rule base of a fuzzy inference system can also be tuned using a
genetic algorithm, as described in [Yu02, Gur99].
4.3
Fuzzy yaw moment controller design
As mentioned earlier, fuzzy control systems are nonlinear control methods that can
handle complicated nonlinear dynamic control problems and, as such, they are ideally
suited for controlling the highly nonlinear behaviour inherent in vehicular dynamics. A
fuzzy controller is described in vague linguistic terms, which suits the subjective nature
of vehicle stability and handling, and allows one to encode expert knowledge directly in
the rule base of the fuzzy controller [Kar04]. In addition, the idea of using a fuzzy logic
controller as a high-level supervisory module that assigns tasks to low-level actuators and
controllers appears to be an ideal method of addressing the complexities of integrated
chassis control management. This approach allows the lower-level controllers to be
designed simply as tracking controllers that attempt to match the state of their respective
plants to the reference signals generated by the supervisory controller. In this work, a
fuzzy YMC is developed for the AUTO21EV that determines the corrective yaw moment
required to minimize the sideslip and yaw rate errors of the vehicle, comparing the actual
values to those obtained using a reference model, with the ultimate objective of following
the desired trajectory requested by the driver. The proposed controller requires two
vehicle states, the yaw rate and vehicle sideslip angle, to calculate the required corrective
yaw moment.
To date, yaw rate tracking algorithms have been used to improve the stability of a
vehicle when driving near the handling limit [Man07]. A recurring problem found
throughout the literature, however, is how to define the limits of handling and distinguish
90
4
Genetic Fuzzy Yaw Moment Controller
between emergency and normal driving situations. The studies of yaw rate stability are
dominated by the use of reference model feedback control, where the controller attempts
to match the nonlinear behaviour of the vehicle with that of a reference bicycle model. As
the vehicle approaches its performance limits, the actuation power required to reduce the
tracking error becomes large and may exceed the capability of any active chassis
subsystem. In general, information about the yaw rate alone is not always sufficient
because, for instance, a vehicle may be undergoing an acceptable yaw rate while skidding
sideways. Thus, many researchers claim that significantly more comprehensive control
can be achieved given vehicle sideslip angle information [Man07]. The vehicle sideslip
angle is defined as the angle between the longitudinal axis of the vehicle and the direction
in which it is travelling. Human drivers are particularly sensitive to the sideslip motion of
the vehicle, and tend to prefer small sideslip angles [Dix96]. This preference arises from
the sensation of instability at larger angles, which is perhaps rooted in the real potential
for the loss of control when the vehicle sideslip angle becomes too large. Thus, both
sideslip and yaw rate are extremely important factors influencing the driver‟s perception
of handling behaviour, especially when driving near the handling limit. As a result, the
quality of the driving experience depends strongly on the quality of the feedback signals
of these two states.
In order to calculate the desired yaw rate as the reference signal for the fuzzy yaw
moment controller, a bicycle model is used, which is illustrated in Figure 4-6. In this
model, the left and right tires on each axle are merged together, and the height of the
center of mass of the vehicle is set to zero. In addition, the longitudinal tire forces and the
variation of the vertical tire forces are not considered. The equations of motion of the
bicycle model are linearized such that only small slip angles are considered, where
sin( )   and cos( )  1 , and linear tire behaviour is assumed, where the lateral tire
stiffness (C) is a constant defining the linear relationship between the lateral force (Fy)
and the slip angle () of a tire as follows:
C 
Fy
(4.1)

Since the lateral inertial force acting on the center of mass of the vehicle is equal to the
centrifugal force resulting from driving in a curve with a radius of R and a rotational
speed of  (Figure 4-6), the following relationship can be assumed between the lateral
91
4
Genetic Fuzzy Yaw Moment Controller
acceleration of the vehicle (ay) and the speed (V), yaw rate ( ), and sideslip rate (  ) of
the vehicle [Wal05]:
mCG  a y  mCG 

V2
V
 mCG   (  R)  mCG  V    
R
R

(4.2)
where mCG is the total mass of the vehicle. Note that V  V ,    , and    are
the magnitudes of the velocity, yaw rate, and sideslip rate vectors of the vehicle,
respectively, and    is the magnitude of the rotational velocity of the vehicle.
Looking at Figure 4-6, the sideslip angle of the front (  F ) and rear (  R ) tires can be
estimated as follows:
F     
R   
a 
V
(4.3)
b 
V
(4.4)
where a and b are the distances of the front and rear axles from the vehicle center of mass
and  is the steering angle of the front wheel.
Figure 4-6: Linear bicycle model [Wal05]
92
4
Genetic Fuzzy Yaw Moment Controller
As a vehicle travels through a circular path in a steady-state motion, the speed (V), yaw
rate ( ), and sideslip angle () of the vehicle remain constant and, consequently, the
longitudinal acceleration, yaw acceleration, and rate of change of the sideslip angle of the
vehicle are zero ( ax  0,   0, and   0 ). Thus, in a steady-state circular motion, the
following statements can be assumed from equation (4.2):
a y  V 
(4.5)
1 

R V
(4.6)
Considering the sum of moments around the front and rear axles, the following equations
can be derived:
Fy , F  L  mCG  a y  b
(4.7)
Fy , R  L  mCG  a y  a
(4.8)
where Fy,F and Fy,R are the lateral forces of the front and rear axles, respectively, and
L  a  b is the wheelbase of the vehicle. Substituting equations (4.1), (4.3), and (4.4)
into equations (4.7) and (4.8), the following equations can be derived:
a  
b

C F     
  mCG  a y 
V 
L

(4.9)
b  
a

C R    
  mCG  a y 
V 
L

(4.10)
where C F and C R are the total lateral stiffnesses of the front and rear tires,
respectively. Calculating  from equation (4.9) and substituting it into equation (4.10),
the following relationship between the steering angle and the lateral acceleration of the
vehicle can be obtained:

L mCG

R
L
 b
a 


 ay
 C F C R 
(4.11)
Substituting equations (4.5) and (4.6) into equation (4.11), the relationship between the
vehicle yaw rate and the steering angle of the front wheel in a steady-state circular motion
can be calculated as follows:

V
m  b
a  2
L  CG 

V
L  C F C R 

(4.12)
93
4
Genetic Fuzzy Yaw Moment Controller
Equation (4.12) is widely used to describe the desired yaw rate of the vehicle as a
function of the steering angle by current stability controllers [Zan00]. In this work, a firstorder lag element is also added to equation (4.12) to account for the lag between the
steering input and the yaw rate response of the vehicle. Thus, the transfer function of the
desired yaw rate ( desired ( s) ) with respect to the steering angle ( ( s) ) is defined in the
linear s-domain as follows:
 desired ( s )

( s )
V ( s)
m
L  CG
L
 b
a  2


V ( s)
C
C
R 
 F
1
1  Ts
(4.13)
where the time constant of the lag element (T) is chosen to be 50 milliseconds. Note that
this time constant is chosen to keep the reaction time of the maximum desired yaw rate in
the range of 200 to 400 milliseconds, which is recommended for passenger cars [Wal05].
Furthermore, since the lateral acceleration of the vehicle is fundamentally limited by the
friction coefficient of the tire-road contacts, the desired yaw rate must also be limited by
a second value. Thus, from equation (4.2), the steady-state lateral acceleration of the
vehicle is expressed either as a function of the radius of curvature (R) or as a function of
the vehicle yaw rate ( ) as follows [Zan00]:
ay 
V2
 V 
R
(4.14)
At the same time, the maximum lateral acceleration of the vehicle is theoretically limited
by the friction coefficient of the tires:
a y  res g
(4.15)
where res is the resultant friction coefficient of the tires and g is the gravitational
acceleration. Combining equations (4.14) and (4.15), the desired yaw rate is limited as
follows [Zan00]:
 desired 
res g
(4.16)
V
Since estimation of the friction coefficient is not always possible, the measured
lateral acceleration can be used instead. This method is, in fact, used in the ESP system
developed by Robert Bosch GmbH [Zan00]. Finally, note that, in this work, the desired
sideslip angle is defined to be zero:
94
4
Genetic Fuzzy Yaw Moment Controller
desired  0
(4.17)
and the actual sideslip angle is estimated using the neural network described in Chapter 3.
Figure 4-7 illustrates the block diagram of the fuzzy YMC.
Figure 4-7: Block diagram of the fuzzy yaw moment controller
The rule base of the fuzzy controller was designed using the sideslip angle error
e(  ) , the yaw rate error e( ) , and the rate of change of the yaw rate error e( ) as the
inputs; the required corrective yaw moment M z is the output of the controller. Table 4-I
lists the definitions of the input and output variables. The input variables are preprocessed to the range [-1, 1] before entering the fuzzy controller. The output variable is
correspondingly post-processed to determine the required corrective yaw moment.
Whereas the scaling factors used for pre-processing the input variables are chosen based
on the actual vehicle states when driving through a severe maneuver, the scaling factor
used for post-processing the output variable is determined based on the actuation
potential of the in-wheel motors. In particular, the maximum allowable sideslip angle
error, yaw rate error, and rate of change of yaw rate error when driving through a severe
double-lane-change maneuver are assumed to be 10o, 35o/s, and 2000o/s2, respectively,
which correspond well with the limits found in the literature for normal passenger cars
[Kie05, Wal05]. Moreover, assuming that the maximum longitudinal tire force is about
3500 N by considering a nominal wheel load of 3800 N, the maximum possible yaw
moment that can be generated by the in-wheel motors is created by generating a couple
on the sides of the vehicle, applying negative torque to the wheels on one side and
positive torque to those on the other side. By doing so, and knowing that the track width
95
4
Genetic Fuzzy Yaw Moment Controller
of the AUTO21EV is 1.35 m, the maximum possible yaw moment is calculated as
follows:
M z ,max  3500 N  2  1.35 m  9450 Nm
(4.18)
Variable
Definition
Input 1
e(  )  desired  actual
Input 2
e( )   desired  actual
Input 3
e( ) 
Output
e( )k  e( )k 1
sample time
Mz
Table 4-I: Definition of the input and output variables of the fuzzy yaw moment controller
In order to provide enough rule coverage, five fuzzy sets are used for each of the
yaw rate and sideslip error variables, and three fuzzy sets are used for the rate of change
of the yaw rate error. Nine fuzzy sets are used to describe the output of the controller,
which ranges from a very large positive (counterclockwise) moment to a very large
negative (clockwise) moment. The fuzzy inference engine processes the list of rules in
the knowledge base using the fuzzy inputs obtained from the previous time step of the
simulation to create the fuzzy output for the current time step. A three-dimensional (3D)
rule base table is developed for the proposed fuzzy YMC, as shown in Figure 4-8; the
linguistic variables that have been used are listed in Table 4-II. These rules have been
developed based on expert knowledge and intensive investigation. In other words, based
on the possible sideslip angle error, the yaw rate error, and the rate of change of the yaw
rate error, the vehicle state at each driving conditions is analyzed and the required
corrective yaw moment at that specific condition is determined and translated into a
specific rule in the rule base table. The fuzzy controller uses the Mamdani fuzzy
inference method, which is characterized by the following fuzzy rule schema:
IF e(β) is A AND e(ψ) is B AND e(ψ) is C THEN Mz is D
(4.19)
where A, B, C, and D are fuzzy sets defined on the input and output domains. Given a
certain vehicle sideslip error, yaw rate error, and rate of change of the yaw rate error, the
3D fuzzy rule base can determine the direction and relative magnitude of the required
corrective yaw moment. The initial shape and distribution of the membership functions
used for the input and output variables of the fuzzy controller are illustrated in Figure 4-9.
96
4
Genetic Fuzzy Yaw Moment Controller
Figure 4-8: Three-dimensional rule base of the fuzzy YMC
Acronym
Linguistic Variable
NEG
NVL
NL
NM
Negative
Negative Very Large
Negative Large
Negative Medium
NS
ZE
PS
PM
PL
PVL
POS
Negative Small
Zero
Positive Small
Positive Medium
Positive Large
Positive Very Large
Positive
Table 4-II: Linguistic variables used in the fuzzy rules
Notice that, as is often the case, these fuzzy rules are formed using fuzzy variables
whose membership functions are of unknown shapes, sizes, and relative positions. Since
a fuzzy controller is unable to learn or adapt to its environment on its own, tuning the
fuzzy membership functions must be done manually, which is an inefficient and timeconsuming endeavour. Furthermore, looking at the corresponding control surfaces
between the input and output variables of the fuzzy YMC shown in Figure 4-10, it is clear
that the generated corrective yaw moment does not cover the entire output domain. In
other words, although the maximum possible yaw moment is defined to be 9450 Nm, as
97
4
Genetic Fuzzy Yaw Moment Controller
calculated in equation (4.18), according to the control surfaces in Figure 4-10, only 60%
of the maximum yaw moment is achievable using the initial fuzzy membership functions.
Figure 4-9: Initial shape and distribution of the membership functions for the input and output variables of
the fuzzy YMC
Figure 4-10: Control surfaces of the fuzzy YMC
4.4
Evaluation of the fuzzy yaw moment controller
In order to evaluate the performance of the fuzzy yaw moment controller, the
AUTO21EV is driven through an ISO double-lane-change maneuver using the pathfollowing driver model, whose characteristics are described in Chapter 2. An ISO doublelane-change maneuver is chosen because it can effectively demonstrate the cornering
capability of a vehicle when driving near its handling limit. T he AUTO21EV is driven
through the double-lane-change maneuver with an initial speed of 75 km/h, both with and
without using the fuzzy YMC. As can be seen in Figure 4-11, the driver model was not
98
4
Genetic Fuzzy Yaw Moment Controller
able to negotiate the maneuver without using the fuzzy YMC, and three of the cones were
struck along the way. In addition, a significant amount of effort was required, even
counter-steering at some points, in order to control the vehicle through the maneuver. In
comparison, the driver was able to negotiate the same maneuver much more easily and
smoothly when the fuzzy YMC was active.
Figure 4-11: Desired and actual vehicle trajectories when driving through the double-lane-change maneuver
with an initial speed of 75 km/h (a) using the driver model and (b) using the driver model with the fuzzy
YMC
Figure 4-12 illustrates the vehicle yaw rate and sideslip angle for this maneuver,
both of which are of a much smaller magnitude for the case when the fuzzy YMC is
active. Although the fuzzy YMC is not able to control the vehicle such that it performs
exactly like the desired reference bicycle model, it is able to reduce both the vehicle yaw
rate and sideslip angle considerably, thereby allowing the driver to complete the
maneuver with less effort. This performance is confirmed in Figure 4-13, which
illustrates the lateral acceleration of the vehicle, the driver‟s steering input, and the
vehicle forward speed as functions of time. The fact that the vehicle experiences a lateral
acceleration of about 8 m/s2 even when the fuzzy YMC is active confirms the severity of
the double-lane-change maneuver, as well as the fact that the adhesion potentials on all
tires are saturated widely in order to keep the vehicle on the desired path.
Looking at the plot of the driver‟s steering wheel angle (Figure 4-13-b), it is clear
that the driver requires less steering effort when the fuzzy YMC is active, which indicates
an easier and more comfortable drive. In addition, a reduction in the steering effort means
that the vehicle loses less speed when driving through the maneuver (Figure 4-13-c).
Figure 4-13-d, which illustrates the handling performance of the vehicle, clearly indicates
99
4
Genetic Fuzzy Yaw Moment Controller
that the vehicle handling and agility have been significantly improved by the fuzzy YMC,
as the hysteresis of the curve is considerably reduced. This plot indicates that the phase
shift between the input and output signal of the controlled system (the vehicle) is reduced
considerably. The generated corrective yaw moment is shown in Figure 4-14. Although
the fuzzy YMC is not able to eliminate the vehicle yaw rate and sideslip angle errors
during this severe double-lane-change maneuver (Figure 4-12), the maximum corrective
yaw moment that is generated by the controller is only about one-third of its limit
potential, as calculated in equation (4.18). This performance is due to the fact that the
initial fuzzy membership functions, with arbitrary shape, size, and relative distribution,
can only apply up to 60% of the maximum possible yaw moment.
Figure 4-12: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when driving through the
double-lane-change maneuver using the driver model, with and without the fuzzy YMC (FYMC)
4.5
Genetic tuning of the fuzzy yaw moment controller
The rule base developed for the fuzzy YMC was determined based on expert knowledge
and extensive investigation into the vehicle behaviour in different driving conditions.
However, due to the arbitrary shape, size, and relative positions of the fuzzy membership
functions, the performance of the resulting fuzzy YMC cannot be considered ideal. Since
a fuzzy controller is unable to learn or adapt to its environment on its own, and instead of
resorting to tuning the membership functions of the fuzzy controller manually, which is
an inefficient, arduous, and time-consuming task, a multi-criteria genetic algorithm is
used to tune the membership functions of the fuzzy YMC.
100
4
Genetic Fuzzy Yaw Moment Controller
Figure 4-13: (a) Lateral acceleration, (b) steering wheel angle, and (c) vehicle speed as functions of time;
and (d) vehicle yaw rate as a function of the steering wheel input when driving through the double-lanechange maneuver with and without the fuzzy YMC (FYMC)
Figure 4-14: Corrective yaw moment generated by the fuzzy YMC
The ISO double-lane-change maneuver with obstacle avoidance was used to
evaluate the effectiveness of each candidate controller in the genetic algorithm. As
101
4
Genetic Fuzzy Yaw Moment Controller
mentioned earlier, such a severe maneuver effectively demonstrates the cornering
capability of a vehicle when driving near its handling limit, which is why many car
manufacturers and research institutions consider it to be a suitable test maneuver for
assessing electronic stability controllers [Pai05]. The ISO double-lane-change maneuver
is typically performed as a closed-loop driving test, and is used to adjust the dynamics of
a vehicle based on the subjective evaluations of professional drivers. Due to the fact that
the membership functions of the fuzzy controller must be tuned in a general sense, not
based on a specific driver or driver model, the double-lane-change maneuver is
considered to be an open-loop test for the sake of the optimization procedure. In this
regard, the desired trajectory and the corresponding steering wheel input are determined
for a „neutral-steer‟ vehicle driving through the ISO double-lane-change test track at a
low speed. This fixed steering wheel input, expressed as a function of forward
displacement, is then considered to be the required steering input for driving through the
double-lane-change maneuver even at higher speeds. Any deviations from the desired
trajectory, yaw rate, or sideslip angle are considered to be stability errors that the fuzzy
YMC should correct. The task of the multi-criteria genetic algorithm is to find the ideal
shape and distribution for the membership functions of the fuzzy YMC such that the
vehicle trajectory, yaw rate, and sideslip angle errors are minimized.
Looking at equation (4.11), the required steering angle for a „neutral-steer‟ vehicle
can be calculated as a function of the wheelbase of the vehicle (L) and the radius of
curvature of the road (R) as follows:

L
R
(4.20)
The curvature of the road (, which is equal to the inverse of the radius of curvature, is
defined as the derivative of the tangential angle (  ) with respect to the arc length (s) as
follows [Cas96]:

1 d

R ds
(4.21)
where the arc length (s) can be calculated using Cartesian parametric equations x  x(t )
and y  y (t ) as follows (Figure 4-15):
s  x2  y 2
(4.22)
102
4
Genetic Fuzzy Yaw Moment Controller
Figure 4-15: Curvature of the road in a two-dimensional plane using Cartesian coordinate system
Substituting equation (4.22) into equation (4.21), the following equation can be derived:
d
1 d dt
 


R ds ds
dt
d
dt
2
x  y2
(4.23)
Looking at Figure 4-15, the tangential angle  can be calculated as follows:
dy
dy dt y
tan( ) 


dx dx x
dt
(4.24)
which can be differentiated to obtain an expression for  :
d
d xy  xy
d
tan( )  1  tan 2 ( ) 



2
dt
dt
x
dt
1 xy  xy xy  xy
 2
y2 x2
x  y2
1 2
x
(4.25)
Substituting equation (4.25) into equation (4.23), the following expression can be derived
for the curvature of the road:

xy  xy
x
2
y
2

3
(4.26)
2
For a two-dimensional curve written in the form y  f ( x ) , the equation of curvature
takes the following form:
103
4

Genetic Fuzzy Yaw Moment Controller
d2y
dx 2
  dy 
 1   
  dx 
2



3
(4.27)
2
Since the desired vehicle trajectory in a double-lane-change maneuver is defined as a
function of forward displacement using equation (2.1) in Chapter 2, the required steering
angle for a „neutral-steer‟ vehicle can be calculated by substituting equations (4.21) and
(4.27) into equation (4.20) as follows:
  L   L
d2y
dx 2
  dy 2 
 1    
  dx  
3
(4.28)
2
Figure 4-16 illustrates the fixed steering wheel angle calculated for this maneuver
using equation (4.28). Note that the amplitude and frequency associated with the first lane
change are larger, as the first lane change is slightly more aggressive than the second one.
Figure 4-17 illustrates the desired and actual vehicle trajectories, yaw rates, and sideslip
angles when driving through the double-lane-change maneuver with an initial speed of 25
km/h using the calculated fixed steering wheel input. This figure demonstrates that the
AUTO21EV is able to negotiate the maneuver with the calculated fixed steering wheel
input at a low speed.
Figure 4-16: Desired fixed steering wheel input for driving through the double-lane-change maneuver
104
4
Genetic Fuzzy Yaw Moment Controller
Figure 4-17: Desired and actual vehicle trajectories (top), and yaw rate and sideslip angle (bottom) when
driving through the double-lane-change maneuver with a fixed steering wheel input
The scaling function technique is chosen for the genetic tuning of the fuzzy
membership functions. Using scaling functions, the input and output variables are
mapped into the range over which the fuzzy sets are defined. From a control engineering
perspective, the scaling functions represent context information, while the membership
functions describe the relative semantics of the linguistic variables, independent from the
context. The scaling and membership functions together establish the absolute semantics
of the linguistic variables. The context information represented by scaling functions can
be related to the physical properties or dimensions of the controlled system, such as
restrictions imposed due to the limitations of the actuators, or can represent information
that affects the overall behaviour of the controlled system, such as conditioning the
desired behaviour of the controlled system and not its physical limits [Cor01]. From a
hierarchical point-of-view, modifying a rule consequence in the rule base of a fuzzy
system has only a small effect, in that it can only affect one entry of the rule matrix. On
the other hand, a single modified membership function has a somewhat greater effect, as
it affects an entire column or row of the rule matrix. Scaling an input or output variable
has a macroscopic impact, as it affects every rule in the rule base [Zhe92].
105
4
Genetic Fuzzy Yaw Moment Controller
Two types of scaling functions can be found in the literature, namely linear and
nonlinear scaling functions. Linear scaling uses a linear mapping, and is of the following
form [Cor01]:
f ( x)   x  
(4.29)
where x defines the original space and f(x) defines the scaled space. In addition,  is
responsible for enlarging or reducing the operating range, which can, in turn, decrease or
increase either the sensitivity of the controller with respect to an input variable, or the
corresponding gain of an output variable;  shifts the operating range and plays the role
of an offset to the corresponding variable (Figure 4-18). The main disadvantage of linear
scaling is the fixed relative distribution of the membership functions. Nonlinear scaling
can overcome this problem, as it modifies the relative distribution and changes the shape
of the membership functions. Although many different nonlinear scaling functions have
been proposed in the literature, only the family of scaling functions that produces the
widest range of fuzzy partitions with the smallest number of parameters is considered in
this work. A small number of parameters reduces the complexity of the search, while a
wide range of possible fuzzy partitions increases the approximation accuracy of the fuzzy
rule base system.
A common nonlinear scaling function used for a variable that is symmetric about
the origin is of the following form [Cor01]:
f ( x)  sign( x)  x

(4.30)
where  is responsible for increasing ( > 1) or decreasing ( < 1) the relative
sensitivity in the region around the origin, and has the opposite effect at the boundaries of
the operating range. With a fixed set of normalized membership functions in which
partitions are composed of regularly distributed isosceles triangles, a wide range of fuzzy
partitions can be generated if an appropriate nonlinear scaling function is employed
(Figure 4-18). As a result, the possible configurations of fuzzy partitions range from those
with lower granularity for middle values of the variable to lower granularity for extreme
values, including homogeneous granularity. Since the input and output variables of the
fuzzy YMC are using a fixed set of normalized membership functions that are distributed
symmetrically around the origin (Figure 4-9), four nonlinear scaling functions (one for
each variable), similar to the one described in equation (4.30), are used to tune the fuzzy
YMC. This method guarantees that the adjacency constraint is satisfied, which ensures
106
4
Genetic Fuzzy Yaw Moment Controller
that the sum of all membership functions is equal to unity for every point in the domain;
the final tuned membership functions are distributed symmetrically around the origin, and
the genetic search examines a wide range of fuzzy partitions. At the same time, due to the
fact that each of these nonlinear scaling functions uses only one parameter to affect the
overall distribution and shape of the membership functions, encoding these parameters
results in short chromosomes and, consequently, relatively fast computation times.
Altogether, four scaling parameters are used for the input and output variables of the
fuzzy YMC, and are concatenated to generate a chromosome for the genetic tuning
process.
The genetic algorithm is particularly well suited for solving the multi-criteria
optimization problem of tuning the input and output variables of the fuzzy YMC. The
objective of the tuning process is to minimize the mean square error (MSE) of the vehicle
trajectory, yaw rate, and sideslip angle, which are calculated as follows:
Figure 4-18: The effects of linear and nonlinear scaling functions on a fixed set of normalized membership
functions
2
MSETrajectory
1 N
=   ydesired (x k ) - yactual (x k )
N k=1
107
(4.31)
4
Genetic Fuzzy Yaw Moment Controller
2
MSE Yaw Rate
1 N
=   ψdesired (k) - ψactual (k)
N k=1
(4.32)
2
MSESideslip
1 N
=
βdesired (k) - βactual (k)
N k=1
(4.33)
where N is the number of sample points, ydesired (x k ) and yactual (x k ) are the desired and
actual lateral positions of the vehicle for a given forward position xk, ψdesired (k) and
ψactual (k) are the desired and actual vehicle yaw rates, and βdesired (k) and βactual (k) are the
desired and actual vehicle sideslip angles at a given time step k, respectively. Since the
objective of the multi-criteria genetic algorithm is to minimize these three errors, the
fitness function associated with each chromosome is defined as the weighted sum of the
inverses of the resulting vehicle trajectory, yaw rate, and sideslip angle mean square
errors, as follows:
Fitness Function =
w1
w2
w3
+
+
MSETrajectory MSE Yaw Rate MSESideslip
(4.34)
where w1, w2, and w3 are the weighting factors. The genetic algorithm was run for 50
generations, each of which had a population size of 500 chromosomes, a crossover rate of
95%, and a mutation rate of 15%. In addition, an elite selection rate of 2% was employed
to ensure that the fittest chromosomes were retained unaltered from one generation to the
next. Using the elite selection technique justifies the relatively high mutation rate and
guarantees the thorough exploration of the search space without losing the fittest
members of each generation. Convergence is assumed if the fittest chromosome survives
for 10 consecutive generations, or 50 generations have elapsed. Figure 4-19 illustrates the
maximum fitness function value for each generation and the convergence of the final
results.
Figure 4-20 illustrates the entire optimization procedure. The optimization starts
with a random set of chromosomes comprising the initial population, each of which
encodes the parameters of the nonlinear scaling functions for the input and output
variables of the fuzzy YMC. Next, the chromosomes are decoded into their
corresponding scaling parameters, and the scaling functions are applied to the input and
output variables of candidate fuzzy controllers. Subsequently, the AUTO21EV is driven
through the double-lane-change maneuver using each of the tuned fuzzy YMCs. At the
end of each simulation, the mean square error of the vehicle trajectory, yaw rate, and
108
4
Genetic Fuzzy Yaw Moment Controller
sideslip angle are calculated, and the corresponding fitness function is evaluated. These
steps are repeated for each chromosome in the current population.
Figure 4-19: Maximum fitness function value for each generation of the multi-criteria genetic algorithm
Figure 4-20: Block diagram of the multi-criteria genetic algorithm used for tuning the fuzzy YMC
Reproduction is the first genetic operation that is applied to the population. Each
chromosome is duplicated with a probability that is proportional to its fitness using the
Roulette wheel strategy; the fitter the chromosome, the more likely it is to be represented
in the next generation. Following reproduction, crossover proceeds by randomly mating
the members of the newly reproduced chromosomes. Each pair of mating chromosomes
undergoes crossover as follows:
109
4
Genetic Fuzzy Yaw Moment Controller
1. An integer position k along the chromosome is randomly selected between 1 and
L-1, where L is the length of the chromosome.
2. Two new chromosomes are created by swapping all genes of the mated
chromosomes between positions k+1 and L.
Although reproduction and crossover provide the majority of the processing
power of genetic algorithms, they can occasionally lose some potentially useful genetic
material. Whereas reproduction and crossover serve to explore variants of promising
existing solutions while eliminating bad ones, mutation serves an essential role by
introducing and reintroducing new genetic material, which can lead to even better
solutions by exploring new areas of the search space [Kar04]. Mutation is performed by
randomly altering the value of a gene in an individual chromosome. Once the genetic
operations have been applied to the members of the population, a new generation of
chromosomes will have been created, which will generally have better fitness values
compared to their ancestors. This optimization procedure is continued until either
convergence is achieved or the maximum number of generations is reached.
Figure 4-21 illustrates the resulting tuned membership functions for the input and
output variables, and provides some insight into the relative importance of each error
measure on the stability of the vehicle. As can be seen, the scaling functions have
adjusted the shape, size, and relative distribution of the membership functions of the
fuzzy YMC considerably. The new arrangement of the membership functions associated
with the yaw rate error indicates that any amount of yaw rate error is highly undesirable.
The scaling functions have forced the membership functions of the sideslip error and the
rate of change of the yaw rate error to have a higher density for extreme values, whereas
a high density is preferred in the middle of the yaw rate error domain. Furthermore, the
membership functions associated with the corrective yaw moment have been
redistributed to have higher density for extreme values. Comparing Figure 4-22, which
illustrates the control surfaces of the tuned fuzzy YMC, to Figure 4-10, it is clear that the
scaling functions have adjusted the membership functions of the fuzzy YMC such that the
tuned control surfaces extend to the limits of the output domain and cover the entire
control space.
110
4
Genetic Fuzzy Yaw Moment Controller
Figure 4-21: Shape and distribution of the genetically-tuned membership functions for the input and output
variables of the fuzzy YMC
Figure 4-22: Control surfaces of the genetically-tuned fuzzy YMC
4.6
Evaluation of the genetic fuzzy yaw moment controller
In order to evaluate the performance of the genetic fuzzy YMC, the AUTO21EV is
driven through a series of test maneuvers, which are described in Chapter 2.
4.6.1
ISO double-lane-change maneuver
The performance of the genetic fuzzy YMC is first compared to that of the untuned fuzzy
YMC as the vehicle is driven through the double-lane-change maneuver with an initial
speed of 75 km/h, using the path-following driver model. Figure 4-23 illustrates the
vehicle trajectory and demonstrates that the driver is able to negotiate the maneuver more
111
4
Genetic Fuzzy Yaw Moment Controller
easily and smoothly when the genetic fuzzy YMC is active, as compared to the case
where no stability controller is used (Figure 4-11-a).
Figure 4-23: Desired and actual vehicle trajectories when driving through the double-lane-change maneuver
with an initial speed of 75 km/h using the driver model and the genetic fuzzy YMC
Figure 4-24 illustrates the vehicle yaw rate and sideslip angle for this maneuver.
Comparing this figure with Figure 4-12, it is clear that the genetically tuned fuzzy YMC
is able to control the vehicle so that it performs more like the desired reference model
than it did before undergoing the tuning process.
Figure 4-24: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when driving through the
double-lane-change maneuver using the driver model, with and without the genetic fuzzy YMC (GFYMC)
Figure 4-25 illustrates the lateral acceleration of the vehicle, the driver‟s steering
input, and the vehicle forward speed as functions of time. As can be seen, the vehicle
experiences a more harmonic lateral acceleration than it did when no stability controller
was active. The maximum lateral acceleration is about 8.4 m/s2, which indicates that the
traction potentials on all tires are widely used to keep the vehicle on its desired path.
Comparing the required steering wheel angles shown in Figure 4-25-b, it is clear that the
driver requires the least steering effort when the genetic fuzzy YMC is active. As a result,
112
4
Genetic Fuzzy Yaw Moment Controller
the vehicle loses even less speed with the genetic fuzzy YMC than it did with the untuned
version of the controller. Figure 4-25-d illustrates the handling performance of the
vehicle, and clearly indicates that the vehicle handling and agility have been significantly
improved by the genetic fuzzy YMC. The hysteresis of this plot suggests an almost linear
relationship between the steering wheel input and the vehicle yaw rate, which
characterizes a vehicle with superior responsiveness. Note that, for clarity, the handling
performance plot of the vehicle when no stability controller is active is not shown. The
required corrective yaw moment shown in Figure 4-26 indicates that the genetic fuzzy
YMC is able to generate larger corrective yaw moments than the untuned fuzzy YMC
when the vehicle is driven through the same maneuver. Note that the generated corrective
yaw moment is now large enough to eliminate the yaw rate error completely and
minimize the sideslip angle error of the vehicle (Figure 4-24).
Figure 4-25: (a) Lateral acceleration, (b) steering wheel angle, and (c) vehicle speed as functions of time;
and (d) vehicle yaw rate as a function of the steering wheel input when driving through the double-lanechange maneuver without a controller, with the fuzzy YMC (FYMC), and with the genetic fuzzy YMC
(GFYMC)
113
4
Genetic Fuzzy Yaw Moment Controller
Figure 4-26: Comparison of the corrective yaw moment generated by the fuzzy and genetic fuzzy YMCs
Table 4-III summarizes the vehicle response during the double-lane-change
maneuver when the genetic fuzzy YMC is active. Since the genetic fuzzy YMC
demonstrates better performance in all aforementioned aspects than the untuned fuzzy
YMC, only the genetic fuzzy YMC will be considered in the reminder of the evaluation
process. Comparing different parameters of the vehicle response during the double-lanechange maneuver using the driver model with and without the genetic fuzzy YMC (Table
4-III), it can be seen that the genetic fuzzy YMC is very effective at improving all the
decisive parameters that describe the handling, stability, and longitudinal dynamics of the
vehicle (Figure 2-4). In particular, the genetic fuzzy YMC has reduced 
 SW
max
, and  H significantly, and has increased a y
max
max
, 
max
,
slightly, which together
indicate that the vehicle handling has been improved considerably by the genetic fuzzy
YMC. The reduction of 
max
and 
max
implies, at the same time, that the stability of
the vehicle has improved significantly. In addition, the fact that the vehicle loses less
speed when the genetic fuzzy YMC is active indicates that the controller is very effective
at improving the longitudinal dynamics of the vehicle.
Parameter

AUTO21EV
26.3o
115.4o/s
8.2 m/s2
GFYMC
6.20o
31.2o/s
8.4 m/s2
max

max
ay
max
 H
vlost
545o
163.8o/s
20.5 m/s
108o
21o/s
13.2 m/s
 SW
max
Table 4-III: Vehicle response during the double-lane-change maneuver using the driver model with and
without the genetic fuzzy YMC (GFYMC)
114
4
Genetic Fuzzy Yaw Moment Controller
4.6.2 Step-steer response maneuver
In order to evaluate the performance of the vehicle using the genetic fuzzy YMC in a
step-steer response maneuver, the vehicle yaw rate, sideslip angle, and lateral
acceleration response as functions of time are observed. Figure 4-27 illustrates the
steering wheel step input and the lateral acceleration response of the vehicle. As can be
seen, the vehicle reaches a lateral acceleration of about 4 m/s2 with a steering wheel input
of 18o when no stability controller is activated. The rise time of the lateral acceleration
response for the AUTO21EV model is about 0.66 seconds. This rise time is reduced to
0.51 seconds when the genetic fuzzy YMC is active, indicating an improvement in the
responsiveness of the vehicle.
Figure 4-27: (a) Required steering wheel input and (b) lateral acceleration of the vehicle when driving
through the step-steer maneuver
Figure 4-28 shows the yaw rate and sideslip angle of the vehicle with and without
the genetic fuzzy YMC. Looking at the rise times of the yaw rate response with and
without the controller, it is confirmed that the genetic fuzzy YMC improves the
responsiveness of the vehicle considerably. Note that, due to the sharp steering input, the
lateral forces on the front tires build up faster than those at the rear axle. Therefore, the
vehicle experiences a positive sideslip angle for a short period of time (Figure 4-28),
which diminishes and becomes negative once the lateral forces on the rear tires build up
and get to the level that can create equilibrium around the center of mass of the vehicle.
The short delay in the lateral acceleration plot, which occurs soon after the step input
when driving through the maneuver without using a stability control system, is due to this
phenomenon (Figure 4-27); however, the delay is suppressed when the genetic fuzzy
YMC is active.
115
4
Genetic Fuzzy Yaw Moment Controller
Figure 4-28: Yaw rate (top) and sideslip angle (bottom) of the vehicle when driving through the step-steer
maneuver with and without the genetic fuzzy YMC (GFYMC)
Table 4-IV summarizes the vehicle response during the step-steer test maneuver.
Comparing parameters of the vehicle response during the step-steer maneuver with and
without the genetic fuzzy YMC, it can be recognized that the genetic fuzzy YMC is very
effective at improving all the decisive parameters that describe the handling
characteristics of the vehicle (Figure 2-4).
Parameter
t
PO 
 max  ss
 100%
 ss

max
ta y
AUTO21EV
0.34 s
1.30%
1.43o
0.66 s
GFYMC
0.15 s
0.00%
1.38o
0.51 s
Table 4-IV: Vehicle response during the step-steer maneuver using a fixed step-steer input with and
without the genetic fuzzy YMC (GFYMC)
4.6.3 Brake-in-turn maneuver
Figure 4-29 illustrates the trajectory of the vehicle relative to the desired path during a
brake-in-turn maneuver. As can be seen, the vehicle becomes unstable and leaves the
predefined road when the YMC is not active; however, the driver is able to keep the
vehicle on the predefined circular path while severely braking when using the genetic
fuzzy YMC, and the lateral deviation of the vehicle from the desired path remains very
small throughout the maneuver. Looking at the driver‟s steering wheel input as a function
116
4
Genetic Fuzzy Yaw Moment Controller
of time, shown in Figure 4-30-a, it is clear that the driver model is not able to control the
vehicle when the YMC is inactive even when very large steering wheel angles are
applied. However, the driver model is able to control the vehicle when the genetic fuzzy
YMC is active by applying a maximum steering wheel angle of only 45 o. In addition, the
gradient of this plot indicates that it requires very little effort for the driver to control the
vehicle when braking in a turn. Figure 4-30-b illustrates the lateral acceleration of the
vehicle and confirms the stability of the vehicle when the genetic fuzzy YMC is active,
even though it is being driven near its handling limit. Such a large lateral acceleration
(7.7 m/s2) during a severe braking maneuver indicates that the traction potentials on all
tires are widely used to hold the vehicle on its desired path.
Figure 4-29: Desired and actual vehicle trajectories when braking in a turn using (a) the driver model only,
and (b) using the driver model with the genetic fuzzy YMC (GFYMC)
Figure 4-31 compares the vehicle yaw rate and sideslip angle when driving
through the brake-in-turn maneuver with and without the genetic fuzzy YMC. As can be
seen, the vehicle behaves almost like the desired reference bicycle model when the
genetic fuzzy YMC is active, and the driver is able to control the vehicle while braking in
the curve. This figure also confirms the stability of the vehicle, as the yaw rate and
sideslip angle both approach zero as the vehicle progresses toward larger deceleration
rates. Figure 4-32 shows the vehicle speed as a function of time and the vehicle
longitudinal acceleration as a function of vehicle speed. This figure confirms the
performance of the speed controller and the severity of the braking component of this
maneuver.
117
4
Genetic Fuzzy Yaw Moment Controller
Figure 4-30: (a) Required steering wheel input and (b) lateral acceleration of the vehicle when braking in a
turn with and without the genetic fuzzy YMC (GFYMC)
Figure 4-31: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when braking in a turn
using the driver model with and without the genetic fuzzy YMC (GFYMC)
Figure 4-32: (a) Vehicle speed as a function of time and (b) longitudinal acceleration as a function of
vehicle speed when braking in a turn using the driver model with and without the genetic fuzzy YMC
118
4
Genetic Fuzzy Yaw Moment Controller
Table 4-V summarizes the vehicle response during the brake-in-turn maneuver.
Comparing parameters of the vehicle response during the brake-in-turn maneuver using
the driver model with and without the genetic fuzzy YMC, it can be seen that the genetic
fuzzy YMC is very effective at improving all the decisive parameters that describe the
handling, stability, and path-following capability of the vehicle (Figure 2-4). In particular,
the genetic fuzzy YMC has reduced 
max
, 
max
, and  SW
max
significantly, which
indicates that this controller is very effective at enhancing the vehicle handling during
this maneuver. In addition, a reduction of 
max
and 
max
simultaneously indicates that
the genetic fuzzy YMC is very effective at improving the vehicle stability. Finally, the
fact that the maximum lateral deviation of the vehicle from the desired path remains very
small confirms that the genetic fuzzy YMC is enhancing the path-following capability of
the vehicle.
Parameter

max

max
ymax
 SW
max
AUTO21EV
126.5o/s
50.1o
3.67 m
700o
GFYMC
22.60o/s
4.36o
0.18 m
46.4o
Table 4-V: Vehicle response during the brake-in-turn maneuver using the driver model with and without
the genetic fuzzy YMC (GFYMC)
4.6.4 Straight-line braking on a -split road
Braking on a -split road is a critical test maneuver, and can be used to confirm the
performance and sensitivity of a vehicle and its stability control systems when subjected
to external disturbances. During this test, due to the asymmetric braking forces generated
on the left and right tires, the vehicle will be pushed to the side of the road that has a
higher coefficient of friction. Figure 4-33 shows the vehicle trajectory for this maneuver
and compares it to the case when the YMC is inactive. This comparison confirms that the
genetic fuzzy YMC is able to correct the side-pushing effect of the vehicle while braking
on a -split road, thereby preventing a dangerous instability situation. It is important to
note that the braking distance of the vehicle is 44.5 meters when the genetic fuzzy YMC
is active, which is an acceptable braking distance for this vehicle. Looking at the vehicle
yaw rate and sideslip angle illustrated in Figure 4-34, it is clear that the genetic fuzzy
YMC is able to limit and, later, diminish the yaw rate and sideslip angle of the vehicle
while driving over the black ice patch. Figure 4-35 illustrates the required corrective yaw
119
4
Genetic Fuzzy Yaw Moment Controller
moment that is applied by the genetic fuzzy YMC to compensate for the side-pushing
effect.
Figure 4-33: Desired and actual vehicle trajectories when braking on a -split road holding the steering
wheel fixed with and without the genetic fuzzy YMC (GFYMC)
Figure 4-34: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when braking on a split road holding the steering wheel fixed with and without the genetic fuzzy YMC (GFYMC)
Table 4-VI summarizes the vehicle response during the straight-line braking
maneuver performed on a -split road. Comparing parameters of the vehicle response
while braking on a -split road, it can be seen that the genetic fuzzy YMC is very
effective at improving all the decisive parameters that describe the stability, pathfollowing capability, and braking performance of the vehicle. In particular, the genetic
fuzzy YMC is able to reduce 
max
and 
max
significantly, which indicates that the
stability of the vehicle is greatly enhanced. Moreover, the braking distance of the vehicle
has been reduced considerably when the genetic fuzzy YMC is active, indicating an
120
4
Genetic Fuzzy Yaw Moment Controller
improvement in the longitudinal dynamics of the vehicle. The maximum lateral deviation
of the vehicle is also reduced significantly, and the vehicle remains on the predefined
road throughout the maneuver when the genetic fuzzy YMC is active.
Figure 4-35: (a) Corrective yaw moment required to counteract the side-pushing effect of the vehicle and
(b) vehicle speed while braking on a -split road holding the steering wheel fixed and using the genetic
fuzzy YMC
Parameter

AUTO21EV
24.2o
GFYMC
0.40o
max

xbraking
ymax
63.4o/s
48.4 m
15.9 m
1.85o/s
44.5 m
0.46 m
max
Table 4-VI: Vehicle response during the straight-line braking on a -split road maneuver holding the
steering wheel fixed with and without the genetic fuzzy YMC (GFYMC)
4.7
Chapter summary
In this chapter, a simple vehicle model is developed to allow for the testing of different
control strategies, and for applying a genetic tuning algorithm to the development of the
fuzzy yaw moment controller. The genetic tuning procedure is applied to the developed
fuzzy YMC to improve its performance. A variety of maneuvers are simulated to
demonstrate the effectiveness of the genetic fuzzy YMC. Table 4-VII provides a
subjective evaluation of the effectiveness of the genetic fuzzy YMC based on different
test maneuvers. In the next chapter, the issue of realistically generating the required
corrective yaw moment using an advanced torque vectoring controller is addressed.
121
4
Genetic Fuzzy Yaw Moment Controller
Table 4-VII: Subjective evaluation of the effectiveness of the genetic fuzzy YMC based on different test
maneuvers (3 = very effective, 2 = effective, 1 = effective to some extent, 0 = ineffective)
122
5
Advanced Torque Vectoring Controller
As mentioned previously, the AUTO21EV model with four direct-drive in-wheel motors
is an exciting platform on which to apply advanced motion control techniques, such as
advanced slip control and torque vectoring systems, since the motor torque and speed can
be generated and controlled quickly, precisely, and independently at each wheel. An
advanced slip control system is developed and tested in Chapter 3. In addition, a highlevel genetic fuzzy yaw moment controller is developed in Chapter 4, the objective of
which is to determine the corrective yaw moment required to minimize the vehicle yaw
rate and sideslip errors. This genetically-tuned fuzzy yaw moment controller acts as a
high-level supervisory module that assigns tasks to the lower-level controllers and
actuators. In this section, an advanced torque vectoring controller is developed for the
AUTO21EV that distributes the task of generating the calculated corrective yaw moment
to the in-wheel motors. The developed advanced torque vectoring controller consists of
left-to-right and front-to-rear torque vectoring components, which work together to
distribute the calculated corrective yaw moment in an integrated approach.
5.1
Control method for left-to-right torque vectoring distribution
In this section, an advanced torque vectoring system is developed based on the previously
developed genetic fuzzy yaw moment controller. The objective here is to distribute the
calculated corrective yaw moment to the individual in-wheel motors in order to stabilize
the vehicle driving dynamics. Assuming that Mz is the total required corrective yaw
moment that is calculated by the genetic fuzzy yaw moment controller, the tire forces on
each axle must be adjusted such that each axle generates a portion of the total corrective
yaw moment, as follows:
M z  M z , front  M z , rear   f  M z  r  M z
where Mz,
front
and Mz,
rear
(5.1)
are the portions of the required corrective yaw moment that
must be generated at the front and rear axles, respectively. In other words, f and r are
the percentages of the total required corrective yaw moment Mz that must be generated at
the front and rear axles, such that  f  r  100% . The relationship between f and r
defines the front-to-rear torque vectoring distribution and will be discussed later.
123
5
Advanced Torque Vectoring Controller
Generating a couple (equal and opposite traction forces) on each axle is the best
strategy for creating the required corrective yaw moment for two reasons: first, all tires
participate in generating the required corrective yaw moment; secondly, the desired
vehicle velocity will not be influenced by the activities of the torque vectoring system as
they would in an ESP system, provided the forces on the sides of each axle can be
generated without being restricted by the traction potential of the tires or the performance
of the in-wheel motors. In addition, since all of the tires are involved in generating the
corrective yaw moment, and since each tire can be accelerated or braked independently,
this strategy has a better efficiency than conventional torque vectoring and ESP systems,
in which only specific tires are involved to generate the corrective yaw moment. Figure
5-1 illustrates the proposed torque vectoring strategy, where a couple is generated on
each axle. The generated yaw moment on each axle is calculated as follows:
M z , front  Fx , FR 
tf
2
Fx , FR  Fx , FL  Fx , F
 Fx , FL 
tf 
M z , front

2   M z , front  Fx , F  t f  Fx , F 
tf


tr
t 
 Fx , RL  r 
M z , rear
2
2   M z , rear  Fx , R  tr  Fx , R 
tr

 Fx , R

M z , rear  Fx , RR 
Fx , RR  Fx , RL
(5.2)
(5.3)
where Fx,FR, Fx,FL, Fx,RR, and Fx,RL are the longitudinal tire forces of the front-right,
front-left, rear-right, and rear-left wheels, respectively; tf and tr are the front and rear
wheel tracks of the vehicle.
Figure 5-1: Advanced torque vectoring strategy using couple generation on each axle (the dash-dotted
ellipse surrounding each tire indicates the adhesion potential of that tire; the solid ellipse indicates the
actual friction ellipse)
124
5
Advanced Torque Vectoring Controller
In order to calculate the required motor torques, a torque balance is formed for
each wheel. Figure 5-2 illustrates the model of a single wheel, where Iyy,w denotes the
moment of inertia of the wheel about its spin axis, Tm denotes the motor torque, rdyn is the
tire dynamic radius, w is the angular velocity of the tire, Fz is the tire vertical force, and
Fx is the tire longitudinal force. Note that the tire rolling resistance and the aerodynamic
drag of the vehicle are neglected in this model for simplicity. By specifying the equation
of motion of the wheel, the traction force at the tire-road contact patch can be estimated
as follows:
Tm  Fx  rdyn  I yy , w  w  Fx 
1
 Tm  I yy , w  w 
rdyn
(5.4)
Figure 5-2: Torque balance at the tire-road contact patch
Substituting the traction force Fx from equation (5.4) into equations (5.2) and (5.3), the
required motor torque at each wheel can be calculated as follows:
Tm,i 
rdyn ,i
Tm,i 
rdyn ,i
tf
tr
 M z , front  I yy , w  w,i where i FR, FL
(5.5)
 M z , rear  I yy , w  w,i where i RR, RL
(5.6)
Note that when the required corrective yaw moment is positive, the wheels on the right
side of the vehicle must be driven and the wheels on the left side must be braked; when
the required corrective yaw moment is negative, the wheels on the right side of the
vehicle must be braked and those on the left side must be driven.
125
5
5.2
Advanced Torque Vectoring Controller
Calculation of tire adhesion potential
In order to prevent the tires from spinning out or locking up during the couple generation,
the maximum possible traction force of each tire is estimated at each time step of the
simulation and is used to limit the traction forces of the tires. In addition, the adhesion
potential of each tire is calculated and used to define the extent to which the tire forces
have been saturated. Estimating the adhesion potential requires information about the
horizontal and vertical forces acting on the tire, as well as the friction coefficient between
the tire and the road, the estimation of which is presented below.
The longitudinal and lateral tire forces are estimated using the well-known
“Magic Tire Formula” [Pac02, Pac97]. This model is a semi-empirical set of curve fits
that takes into account the coupling between the longitudinal and lateral tire forces
through combined-slip characteristics, a limited tire adhesion potential, the variation in
cornering stiffness with tire load, and the influence of the tire-road friction coefficient.
The combined-slip horizontal tire forces are estimated using the following equations
[Pac02]:



 cos C  arctan  B    E   B    arctan  B      
Fx ,i  Fxo,i  cos C  arctan B    E   B    arctan  B    
(5.7)
Fy ,i  Fyo,i
(5.8)
where i FL, FR, RL, RR . Note that these forces are calculated with respect to the
wheel coordinate system. Fxo,i and Fyo,i represent the pure-slip tire forces in the
longitudinal and lateral directions, respectively, and are calculated as follows [Pac02]:



 D  sin C  arctan  B    E   B    arctan  B      
Fxo,i  D  sin C  arctan B    E   B    arctan  B    
Fyo,i
(5.9)
(5.10)
In this tire model, the interdependence between the longitudinal and lateral tire forces is
considered, where peak factors D, shape factors C, stiffness factors B, and curvature
factors E are different for equations (5.7) to (5.10), and for the longitudinal and lateral
directions [Pac02]. All the parameters required by this model are taken from the Pacejka
2002 tire data obtained for a 175/55 R15 tire. In addition, the slip ratio of each tire is
calculated using equations (3.1) and (3.2) in Chapter 3, and the sideslip angle of each tire
is approximated using a bicycle model, as indicated below [Wal05]:
126
5
F     
R   
Advanced Torque Vectoring Controller
a 
vx
(5.11)
b 
vx
(5.12)
where  is the steering angle,  is the sideslip angle of the vehicle, a and b are the
distances of the front and rear axles from the vehicle center of gravity, vx is the vehicle
forward speed, and  is the vehicle yaw rate.
Approximating the longitudinal and lateral tire forces using equations (5.7) and
(5.8), the tire adhesion potential utilization  can be estimated using the following
elliptic relation:
2
 F   F 
i   xi    yi 


 Fxi ,max   Fyi ,max 
2
, 0  i  1 and i FL, FR, RL, RR 
(5.13)
where Fxi,max and Fyi,max represent the maximum possible forces in the longitudinal and
lateral directions, respectively. With the nominal tire load Fz0 and the tire-road friction
coefficients i, the maximum longitudinal and lateral tire forces can be approximated as
follows [Pac97]:

F  Fz 0 
Fxi ,max  i  Fzi  k x ,i   1  lx  zi

Fz 0 

(5.14)

F  Fz 0 
Fyi ,max  i  Fzi  k y ,i   1  l y  zi

Fz 0 

(5.15)
where kx,i and ky,i depend on the actual tire camber angle, and parameters lx and ly, which
define the degressive behaviour of the tire horizontal forces [Pac02], are set to 1. It is
important to note that, due to the absence of the suspension kinematics in the
DynaFlexPro model of the AUTO21EV (Figure 4-1), the camber angles are set to zero
and do not vary during the simulation. For the sake of simplicity, the camber angles in the
ADAMS model of the AUTO21EV are also assumed to be zero and constant throughout
the simulation.
The actual vertical force applied to each tire (Fzi) is approximated by neglecting
the coupling between the vehicle roll and pitch, and disregarding the suspension
dynamics. To this end, two half-car models are used one for the longitudinal direction
and one for the lateral direction. Figure 5-3-a illustrates a half-car model in the
127
5
Advanced Torque Vectoring Controller
longitudinal direction, where ax indicates the longitudinal acceleration of the vehicle. The
inertial force due to the longitudinal acceleration at the vehicle center of gravity (CG)
causes a weight shift to the rear axle, which simultaneously reduces the front axle load
and increases the rear axle load. Constructing the torque balance at the rear axle contact
point yields the following expression for the front axle load (Fz,F) [Kie05]:
M
y
Fz , F 
 0   a  b   Fz , F  mCG  g  b  mCG  a x  hCG  0 
(5.16)
b
h
mCG  g  CG mCG  a x
ab
ab
where a and b are the distances of the front and rear axles from the vehicle center of
gravity, mCG is the total mass of the vehicle, hCG is the height of the vehicle center of
gravity, and g is the gravitational acceleration constant. a x is the longitudinal
acceleration of the vehicle, and can be measured using an accelerometer. Subtracting the
front axle load (Fz,F) from the total vehicle weight, the rear axle load (Fz,R) is calculated
as follows:
F
z
 0  F z , F F z , R mCG  g  0  Fz , R 
a
h
mCG  g  CG mCG  a x
ab
ab
(5.17)
Figure 5-3: (a) Longitudinal weight shift during acceleration and (b) lateral weight shift during cornering
During cornering, the lateral acceleration causes a weight shift to one side of each
axle, whose distribution between the front and rear axles depends on the axle loads. The
two axles are considered to be decoupled from each other, and a half-car model is used to
calculate the lateral weight shift on each axle. For instance, Figure 5-3-b illustrates the
128
5
Advanced Torque Vectoring Controller
half-car model for the front axle, where the virtual mass of the front axle mF is
calculated as follows:
mF 
Fz , F
g

Fz , FL  Fz , FR
(5.18)
g
Considering the torque balance equation at the point of contact between the ground and
the front-left tire, the lateral weight shift at the front-right tire is calculated as follows:
M
x
 0  Fz , FR  t f  mF  a y  hCG  mF  g 
tf
2
0 
tf 
mF 

 a y  hCG  
tf 
2
Fz , FR
(5.19)
Substituting into equation (5.19) the virtual mass of the front axle ( mF ) from equation
(5.18) and the front axle load (Fz,F) from equation (5.16), the front-right dynamic wheel
load can be calculated as follows:
h
 b
 1 h a 
Fz , FR  mCG  
g  CG a x     CG y 
a  b   2
t f  g 
ab
(5.20)
By analogy, the dynamic loads of the other three wheels can be computed as follows:
h
 b
 1 h a 
Fz , FL  mCG  
g  CG a x     CG y 
a  b   2 t f  g 
ab
(5.21)
h
 a
 1 h a 
Fz , RR  mCG  
g  CG a x     CG y 
a  b  2
tr  g 
ab
(5.22)
h
 a
 1 h a 
Fz , RL  mCG  
g  CG a x     CG y 
a  b  2
tr  g 
ab
(5.23)
Note that the performance and accuracy of this method have been proven in [Kie05] by
comparing data measured during a severe cornering maneuver with the wheel loads
approximated by equations (5.20) to (5.23). Finally, substituting the traction force (Fx)
from equation (5.4) into equation (5.14), the maximum motor torque at each wheel can be
calculated as follows:
1
rdyn ,i

F  Fz 0 
 Tm ,imax  I yy ,wi  wi  i  Fzi  k x ,i   1  l x  zi

Fz 0 

Tm ,imax



F  Fz 0 
 rdyn ,i  i  Fzi  k x ,i   1  l x  zi
  I yy ,wi  wi
Fz 0 

129
(5.24)
5
Advanced Torque Vectoring Controller
As can be seen, the maximum motor torque in equation (5.24) is a function of the tireroad friction coefficient (). This indicates that in the future a friction coefficient
estimator must be implemented to the ATVC, such that the maximum possible motor
torque can be calculated correctly on all road conditions. Equation (5.24) is used by the
torque vectoring controller to limit the motor torque at each wheel when generating a
couple.
In summary, by comparing equations (5.5) and (5.6) with equation (5.24), the
motor torque at each wheel is limited as follows:
 r
 


F  Fz 0 
Tm,i  min  dyn ,i  M z , front  I yy ,w  w,i  ,  rdyn ,i  i  Fzi  k x ,i   1  lx  zi
 I yy ,wi  wi 



Fz 0 

 t f

 
(5.25)
where i FL, FR and
 r


 
F  Fz 0 
Tm,i  min  dyn ,i  M z ,rear  I yy ,w  w,i  ,  rdyn ,i  i  Fzi  k x ,i  1  lx  zi
  I yy ,wi  wi 
Fz 0 
 
 tr


(5.26)
where i RL, RR . As indicated in equation (5.1), Mz, front and Mz, rear are the portions of
the required corrective yaw moment that must be generated at the front and rear axles,
respectively. The relationship between these two moments defines the front-to-rear torque
vectoring distribution, and will be defined in the next section.
5.3
Control method for front-to-rear torque vectoring distribution
As mentioned earlier, if a middle differential were used to distribute the driving torque
between the front and rear axles, the fixed torque distribution could be established on the
basis of the axle-load ratio, the design philosophy of the vehicle, or the desired handling
characteristics of the vehicle. In the case of an active differential, however, this fixed
ratio is adjusted according to the traction conditions or driving dynamics of the vehicle
[Rei02]. Since no mechanical linkage exists between the wheels of the AUTO21EV, the
front-to-rear torque distribution ratio must be set virtually and adjusted based on the
vehicle driving dynamics or traction conditions. In normal driving conditions, a fixed
50:50 ratio has been chosen to split the required corrective yaw moment evenly between
the front and rear axles. However, this ratio will be adjusted by a yaw rate feedback
controller at high maneuvering speeds and in emergency situations in which the vehicle is
operating near its handing limits. This approach uses the yaw rate error calculated for the
130
5
Advanced Torque Vectoring Controller
genetic fuzzy YMC (Table 4-I) and sets the front-to-rear distribution ratios, namely f
and r, such that the deviation between the desired and actual yaw rate of the vehicle is
minimized. This objective is accomplished by a PD controller as follows:
 f   f , fixed  K P  e    K D 
d
e  
dt
(5.27)
r  100%   f
(5.28)
where f, fixed is the predefined fixed ratio of 50%, and KP and KD are the proportional and
derivative feedback gains of the PD controller, respectively. Note that the controller gains
are chosen manually using a trial-and-error approach. The performance and stability of
this controller have been examined through numerous driving maneuvers in the
simulation environment. Since the proposed PD controller is part of a digital control
system, the derivative part of the controller is approximated as follows:
d
e( )k  e( )k 1
e( ) 
dt
sample time
(5.29)
where e( )k and e( )k 1 are the current and previous values of the yaw rate error,
respectively.
5.4
Evaluation of the advanced torque vectoring controller
In order to evaluate the performance of the advanced torque vectoring controller (ATVC),
the AUTO21EV is driven through a series of test maneuvers, as described in Chapter 2.
5.4.1 ISO double-lane-change maneuver
The performance of the ATVC is first evaluated by driving the AUTO21EV through the
double-lane-change maneuver with an initial speed of 75 km/h and using the pathfollowing driver model. Figure 5-4 illustrates the vehicle trajectory and demonstrates that
the driver is able to negotiate the maneuver when the ATVC is active.
Figure 5-4: Desired and actual vehicle trajectories when driving through the double-lane-change maneuver
with an initial speed of 75 km/h using the path-following driver model and the ATVC
131
5
Advanced Torque Vectoring Controller
Figure 5-5 illustrates the vehicle yaw rate and sideslip angle during this maneuver.
As can be seen, the ATVC is not able to exactly match the actual vehicle yaw rate with
the desired yaw rate calculated using the reference bicycle model. In addition, due to the
actuation of the in-wheel motors, there are some oscillations in the actual vehicle yaw
rate that might be perceived by the driver as being annoying. However, the sideslip angle
of the vehicle is very close to that obtained when the genetic fuzzy YMC is active (see
Figure 4-24).
Figure 5-5: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when driving through the
double-lane-change maneuver using the driver model with and without the ATVC
Figure 5-6-a illustrates the vehicle lateral acceleration as a function of time. As
can be seen, the results using the ATVC are very similar to those observed using the
genetic fuzzy YMC except at the handling limits, where the activation of the in-wheel
motors causes some oscillations in the lateral acceleration of the vehicle. As mentioned
before, this type of oscillation might be perceived by the driver as being annoying, and
should be avoided. Looking at Figure 5-6-b, it is confirmed that, except during the second
lane-change, the driver requires about the same amount of steering wheel input as is the
case when the genetic fuzzy YMC is active. Figure 5-6-c illustrates the vehicle speed
during the double-lane-change maneuver, and confirms the advantage of the couple
generation by the ATVC. Specifically, due to the couple generation at the front and rear
axles, the speed reduction during this maneuver is much smoother and more linear than
the case where no stability controller is active. As such, the vehicle loses almost the same
amount of speed as is the case when the genetic fuzzy YMC is active. Figure 5-6-d
illustrates the handling performance of the vehicle and indicates that the hysteresis of this
132
5
Advanced Torque Vectoring Controller
plot is twice as large as that of the analogous plot for the genetic fuzzy YMC. In other
words, although the responsiveness and agility of the vehicle are considerably improved
compared to the case where no stability controller is active, they are not as good as the
case when the genetic fuzzy YMC is used to generate the corrective yaw moment.
Figure 5-6: (a) Lateral acceleration, (b) steering wheel angle, and (c) vehicle speed as functions of time;
and (d) vehicle yaw rate as a function of the steering wheel input when driving through the double-lanechange maneuver without a controller, with the genetic fuzzy YMC (GFYMC), and with the ATVC
Figure 5-7 illustrates the torque of each in-wheel motor during the double-lanechange maneuver. It is very important to notice that, at each wheel, the requested motor
torque from the torque vectoring controller can be restricted by the maximum possible
motor torque, which is calculated by equation (5.24), the slip controller that prevents the
tires from locking up or spinning out, or by the power limitation of the in-wheel motor.
As mentioned earlier, the performance of the in-wheel motors decreases the faster the
motors rotate due to the inductive voltage losses. Looking at the motor torque plots, it can
be seen that, although the ATVC has always requested couple forces on the sides of both
axles, the requested motor torques could not always be generated due to one of the
aforementioned limitations. For instance, between 1.2 and 1.45 seconds of the simulation,
133
5
Advanced Torque Vectoring Controller
the actual motor torques generated at the front wheels and the rear-right wheel are less
than the requested torques because, at a speed of 72 km/h, the motors are not powerful
enough to generate the requested torques. At the rear-left tire, however, the requested
motor torque is restricted by the maximum allowable torque. Another interesting region
to observe is between 2.45 and 3.1 seconds of the simulation, during which time the
transition between the minimum and maximum lateral accelerations occurs (Figure
5-6-b). As can be seen, the left-to-right torque vectoring controller has first ordered the
left wheels to brake and the right wheels to accelerate in order to correct an oversteering
situation, where the actual yaw rate is larger than the desired one (Figure 5-5). At 2.73
seconds of the simulation, however, as the transition from a negative lateral acceleration
to a positive one occurs and the yaw rate error becomes zero, the left-to-right torque
vectoring controller changes its request by ordering the left wheels to accelerate and the
right wheels to brake, which is again done to correct an oversteering situation.
Figure 5-7: Requested and actual motor torque at each wheel when driving through the double-lane-change
maneuver using the driver model with the ATVC
Looking at the activation plot of the front-to-rear torque vectoring controller in
Figure 5-8, it can be confirmed that the actions of the left-to-rear torque vectoring
controller have been supported by the front-to-rear torque vectoring controller. In
particular, the front-to-rear torque vectoring controller has requested the front motors to
generate up to 72% of the total required corrective yaw moment between 2.45 and 2.73
seconds and, later, it changes its request by asking for more torque from the rear motors
134
5
Advanced Torque Vectoring Controller
between 2.73 and 3.1 seconds of the simulation. Note that generating more torque at the
front motors rather than the rear ones reduces the lateral force potential at the front axle
and increases that at the rear axle. The asymmetric lateral force potentials on the front
and rear axles is used to generate the required corrective yaw moment. The effect of the
front-to-rear torque vectoring controller can also be seen in Figure 5-7. For instance,
between 2.45 and 2.73 seconds, the front-to-rear torque vectoring controller has requested
the front-left motor to generate up to 900 Nm of braking torque and the front-right motor
to generate up to 900 Nm of driving torque while, at the same time, the controller has
requested up to 350 Nm of braking and driving torques from the rear-left and rear-right
motors, respectively. Note that, although the controller has requested the front motors to
generate large motor torques, the motors are not powerful enough to generate the
requested torques when the vehicle is travelling at a speed of 66 km/h. The effects seen in
Figure 5-7 can also be confirmed by looking at the tire traction potentials and tire slip
ratios shown in Figures 5-9 and 5-10, respectively. For instance, the maximum traction
potential of the rear-left tire has been exceeded once at 1.2 seconds and then between
3.37 and 3.56 seconds of the simulation (Figure 5-9). Looking at Figures 5-7 and 5-10, it
can be confirmed that the requested motor torque on the rear-left wheel is first restricted
by the maximum torque limiter (at 1.2 seconds) and then by the slip controller (between
3.37 and 3.56 seconds) in order to prevent tire spin-out. This observation suggests that the
excess of the traction potential of the rear-left tire is due to the fact that the lateral force
of the tire has exceeded its limit.
Figure 5-8: Front-to-rear torque vectoring ratios when driving through the double-lane-change maneuver
using the driver model with the ATVC
135
5
Advanced Torque Vectoring Controller
Figure 5-9: Traction potential of each tire when driving through the double-lane-change maneuver using
the driver model with the ATVC
Figure 5-10: Tire slip ratios when driving through the double-lane-change maneuver using the driver
model with the ATVC
Table 5-I summarizes the vehicle response during the double-lane-change
maneuver using the driver model when the advanced torque vectoring controller is active,
and compares it to the results obtained when no stability controller is active and when the
genetic fuzzy YMC is active. Comparing different parameters of the vehicle response
during the double-lane-change maneuver, it can be seen that, although the ATVC has
136
5
Advanced Torque Vectoring Controller
improved all the decisive parameters that describe the handling, stability, and longitudinal
dynamics of the vehicle, it cannot be considered as effective as the genetic fuzzy YMC,
which represents the ideal case but is not directly realizable. With respect to the handling
of the vehicle, the ATVC has reduced 
max
and 
max
by about the same amount as the
genetic fuzzy YMC. The maximum lateral acceleration of the vehicle, a y
max
, has
increased the same amount as it did when the genetic fuzzy YMC was active; however,
when the ATVC is active, the driver requires a larger maximum steering wheel angle to
negotiate the maneuver. In addition, the hysteresis of the performance plot (  H ) is
about 1.7 times larger than it is when the genetic fuzzy YMC is active. Altogether, the
ATVC is considered to be an effective controller for improving the handling
characteristics of the vehicle. Since the ATVC has reduced 
max
and 
max
by about the
same amount as the genetic fuzzy YMC, it is considered to be as effective at improving
the stability of the vehicle. The speed lost during the maneuver is about the same as that
observed when the genetic fuzzy YMC is used and, therefore, the ATVC is also
considered to be a very effective controller for improving the longitudinal dynamics of
the vehicle.
Parameter

max

max
ay
max
 SW
max
 H
vlost
AUTO21EV
26.3o
115.4o/s
8.2m/s2
545o
163.8o/s
20.5m/s
GFYMC
6.2o
31.2o/s
8.4m/s2
108o
21o/s
13.2m/s
ATVC
6.1o
36.4o/s
8.4m/s2
140o
35.5o/s
13.5m/s
Table 5-I: Vehicle response during the double-lane-change maneuver using the driver model without a
controller, with the genetic fuzzy YMC (GFYMC), and with the ATVC
5.4.2 Step-steer response maneuver
In order to evaluate the performance of the vehicle using the ATVC in a step-steer
response maneuver, the vehicle yaw rate, sideslip angle, and lateral acceleration as
functions of time are observed. Figure 5-11 illustrates the steering wheel input and the
lateral acceleration of the vehicle. As can be seen, the lateral acceleration when using the
ATVC is similar to that obtained when using the genetic fuzzy YMC; however, due to the
actuation of the in-wheel motors, some small oscillations can be observed in the lateral
acceleration plot. The rise time of the lateral acceleration response is about 0.47 seconds
when using the ATVC. Figure 5-12 shows the yaw rate and sideslip angle of the vehicle
137
5
Advanced Torque Vectoring Controller
during this maneuver. A severe oscillation can be observed in the yaw rate response when
using the ATVC, which would be perceived by the driver as being annoying, and should
be avoided. Therefore, in practice, the ATVC should only be activated when the yaw rate
error exceeds a particular threshold and should not be used to correct small yaw rate
errors. Although the rise time of the yaw rate response is similar to that obtained when
using the genetic fuzzy YMC, an overshoot is clearly visible when using the ATVC. The
sideslip angle of the vehicle is slightly less than that observed when using the genetic
fuzzy YMC but, again, some oscillations can be seen in the response.
Figure 5-11: (a) Required steering wheel input and (b) lateral acceleration of the vehicle when driving
through the step-steer maneuver using the ATVC
Figure 5-12: Yaw rate (top) and sideslip angle (bottom) of the vehicle when driving through the step-steer
maneuver using the ATVC
138
5
Advanced Torque Vectoring Controller
Table 5-II summarizes the vehicle response during the step-steer test maneuver.
Comparing different parameters of the vehicle response with and without the ATVC, it
can be recognized that the ATVC is effective at improving all the decisive performance
parameters of the vehicle which, for this maneuver, describe the vehicle handling
characteristics. However, two problems must be addressed: the severe oscillation in the
yaw rate response of the vehicle and the overshooting effect of the yaw rate response.
PO 
 max  ss
 100%
 ss

ta y
Parameter
t
AUTO21EV
0.34s
1.30%
1.43o
0.66s
GFYMC
0.15s
0.00%
1.38o
0.51s
ATVC
0.15s
16.1%
1.36o
0.47s
max
Table 5-II: Vehicle response during the step-steer maneuver using the driver model without a controller,
with the genetic fuzzy YMC (GFYMC), and with the ATVC
5.4.3 Brake-in-turn maneuver
Figure 5-13-a illustrates the trajectory of the uncontrolled vehicle relative to the desired
path during a brake-in-turn maneuver and compares it to the case when the ATVC is
active (Figure 5-13-b). As can be seen, the vehicle becomes unstable and leaves the
predefined road when no stability controller is active. However, the driver model is able
to keep the vehicle very close to the predefined circular path while severely braking when
the ATVC is active, and the lateral deviation of the vehicle from the desired path remains
very small throughout the maneuver. Looking at the driver‟s steering wheel input as a
function of time, shown in Figure 5-14-a, it is clear that the driver model is able to control
the vehicle when the ATVC is active by applying a maximum steering wheel angle of
only 48o. In addition, the gradient of this plot indicates that it is very easy for the driver to
control the vehicle when braking in a turn. Figure 5-14-b illustrates the lateral
acceleration of the vehicle and confirms that the vehicle remains stable when the ATVC
is active, even though it is being driven near its handling limit. As can be seen, the lateral
acceleration of the vehicle when using the ATVC is very similar to that obtained when
the genetic fuzzy YMC is active, but contains some oscillations at higher lateral
accelerations.
139
5
Advanced Torque Vectoring Controller
Figure 5-13: Desired and actual vehicle trajectories when braking in a turn using (a) the driver model only
and (b) the driver model with the advanced torque vectoring controller (ATVC)
Figure 5-14: (a) Required steering wheel input and (b) lateral acceleration of the vehicle when braking in a
turn using the driver model without a controller, with the genetic fuzzy YMC (GFYMC), and with the
ATVC
Figure 5-15 illustrates the vehicle yaw rate and sideslip angle when driving
through the brake-in-turn maneuver using the genetic fuzzy YMC and the ATVC. Note
that, for clarity, the yaw rate and sideslip angle of the vehicle are not shown for the case
where no stability controller is active. As can be seen, the vehicle yaw rate follows the
desired reference model, but it is superimposed with oscillations. In addition, for a short
time after the braking starts (between the fourth and fifth seconds of the simulation), the
ATVC is not able to minimize the yaw rate error. However, the driver is still able to
control the vehicle while braking in the curve. This figure also confirms the stability of
the vehicle, since the yaw rate and sideslip angle both approach zero as the vehicle
progresses towards larger deceleration rates. Figure 5-16 shows the vehicle speed as a
function of time and the vehicle longitudinal acceleration as a function of vehicle speed.
140
5
Advanced Torque Vectoring Controller
These plots confirm the performance of the speed controller as well as the severity of the
braking component of this maneuver.
Table 5-III summarizes the vehicle response during the brake-in-turn maneuver
using the driver model. Comparing different parameters of the response when this
maneuver is performed without a controller, with the genetic fuzzy YMC, and with the
ATVC, it can be seen that the ATVC is as effective as the genetic fuzzy YMC at
improving all the decisive parameters that describe the handling, stability, and pathfollowing capability of the vehicle during a brake-in-turn maneuver. In particular, the
ATVC has reduced 
max
, 
max
, and  SW
max
significantly, which indicates that this
controller is very effective at enhancing the handling capabilities of the vehicle. It is
important to notice that, due to the severe oscillations in the yaw rate response of the
vehicle (Figure 5-15), the driver would perceive the activation of the ATVC as being
disruptive. A reduction of 
max
and 
max
by the ATVC indicates that it is also very
effective at improving the stability of the vehicle. Since the maximum lateral deviation of
the vehicle from the desired path remains very small throughout the maneuver, the ATVC
is also very effective at enhancing the path-following capability of the vehicle.
Figure 5-15: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when braking in a turn
using the driver model without a controller, with the genetic fuzzy YMC (GFYMC), and with the ATVC
141
5
Advanced Torque Vectoring Controller
Figure 5-16: (a) Vehicle speed as a function of time using the driver model with the ATVC and (b)
longitudinal acceleration as a function of vehicle speed when braking in a turn using the driver model
without a controller, with the genetic fuzzy YMC (GFYMC), and with the ATVC
Parameter

max

max
ymax
 SW
max
AUTO21EV
126.5o/s
50.1o
3.67m
700o
GFYMC
22.60o/s
4.36o
0.18m
46.4o
ATVC
24.00o/s
4.40o
0.18m
48.0o
Table 5-III: Vehicle response during the brake-in-turn maneuver using the driver model without a
controller, with the genetic fuzzy YMC (GFYMC), and with the ATVC
5.4.4 Straight-line braking on a -split road
As mentioned before, braking on a -split road can be used to confirm the performance
and sensitivity of a vehicle and its stability control systems when subjected to external
disturbances. Figure 5-17 shows the vehicle trajectory for this maneuver when no
stability controller is active and compares it to the case when the ATVC is active. This
comparison confirms that the ATVC is able to reduce the side-pushing effect of the
vehicle while braking on a -split road, but the vehicle still leaves the predefined road,
which is considered to be a dangerous situation. The braking distance of the vehicle is
reduced to about 47.3 meters when the ATVC is active. Looking at Figure 5-18, it is clear
that the ATVC is able to limit and, later, diminish the yaw rate and sideslip angle of the
vehicle while driving over the black ice patch, but does not prevent the vehicle from
leaving the predefined road.
142
5
Advanced Torque Vectoring Controller
Figure 5-17: Desired and actual vehicle trajectories when braking on a -split road holding the steering
wheel fixed with and without the ATVC
Figure 5-18: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when braking on a split road holding the steering wheel fixed with and without the ATVC
Figure 5-19 illustrates the tire slip ratios while braking on a -split road and
indicates that the slip controllers on the left wheels have limited the motor torques
between 0.7 and 1.15 seconds of the simulation in order to prevent the tires from locking
up while, at the same time, ensuring the maximum possible braking force is being applied
when braking on the black ice patch. Later in the simulation, due to the weight shift to the
front axle, the slip controllers on the rear axle have limited the motor torques to prevent
tire lock-up at higher deceleration rates. Looking at Figure 5-20, which illustrates the
motor torques for all four wheels, it is apparent that the slip controllers on the left wheels
have limited the braking torques to 20 Nm (between 0.7 and 1.15 seconds) in order to
prevent tire lock-up when braking on the black ice patch. As mentioned earlier, as a result
of the asymmetric braking forces generated on the left and right wheels, the vehicle is
143
5
Advanced Torque Vectoring Controller
pushed to the right side of the road. In order to prevent this side-pushing effect, the leftto-right torque vectoring controller has requested larger braking forces on the left wheels,
which are restricted by the slip controllers, and has reduced the braking forces on the
right wheels.
Figure 5-19: Tire slip ratios when braking on a -split road holding the steering wheel fixed and using the
ATVC
Figure 5-20: Requested and actual motor torque at each wheel when braking on a -split road holding the
steering wheel fixed and using the ATVC
144
5
Advanced Torque Vectoring Controller
Figure 5-21 illustrates the torque distribution requested by the front-to-rear torque
vectoring controller. As can be seen, the front-to-rear torque vectoring controller has
requested the front motors to generate up to 60% of the required corrective yaw moment
in order to correct the undesirable side-pushing effect when driving over the black ice
patch. Requesting more torque from the front motors reduces the lateral force potential of
the front axle and increases that of the rear axle. The asymmetric lateral force potentials
on the front and rear axles helps to generate the required corrective yaw moment.
Figure 5-21: Front-to-rear torque vectoring activation when braking on a -split road holding the steering
wheel fixed and using the ATVC
Table 5-IV summarizes the vehicle response during the straight-line braking on a
-split road maneuver when using the ATVC. Comparing different parameters of the
vehicle response during this maneuver, it can be seen that the effectiveness of the ATVC
at improving the stability, path-following capability, and braking performance of the
vehicle is limited. Although the ATVC has reduced the 
max
and 
max
values in
comparison to those obtained when no stability controller was active and has avoided
instability, its intervention was not large enough to prevent the vehicle from leaving the
predefined road. Moreover, when the ATVC is active, the braking distance of the vehicle
is longer than that observed when the genetic fuzzy YMC is active. Finally, the ATVC
could not keep the vehicle on the predefined road, which indicates that the ATVC cannot
be considered an effective controller for enhancing the path-following capability of the
vehicle when braking on a -split road.
145
5
Parameter

Advanced Torque Vectoring Controller
max

max
xbraking
ymax
AUTO21EV
24.2o
63.4o/s
48.4m
15.9m
GFYMC
0.40o
1.85o/s
44.5m
0.46m
ATVC
1.70o
9.70o/s
47.3m
2.70m
Table 5-IV: Vehicle response during the straight-line braking on a -split road maneuver holding the
steering wheel fixed without a controller, with the genetic fuzzy YMC (GFYMC), and with the ATVC
5.5
Chapter summary
In this chapter, an advanced torque vectoring controller is developed based on the
previously developed genetic fuzzy yaw moment controller. The objective of the
advanced torque vectoring controller is to distribute the calculated corrective yaw
moment to the individual in-wheel motors in order to stabilize the vehicle driving
dynamics. A novel algorithm is developed for the left-to-right torque vectoring on each
axle, and a PD controller is introduced for the front-to-rear torque vectoring distribution
action. A variety of maneuvers are simulated to demonstrate the performance and
effectiveness of the ATVC. Table 5-V provides a subjective evaluation of the
effectiveness of the ATVC based on different test maneuvers. In the next chapter, a
genetic fuzzy active steering controller is developed, which is considered to be an
alternative stability controller to the ATVC presented in this section.
Table 5-V: Subjective evaluation of the effectiveness of the ATVC based on different test maneuvers (3 =
very effective, 2 = effective, 1 = effective to some extent, 0 = ineffective)
146
6
Genetic Fuzzy Active Steering Controller
Active steering fills the gap between conventional steering systems and steer-by-wire
technology. Although an active steering system provides the capability of applying
driver-independent steering intervention, the mechanical linkage between the steering
wheel and the rack-and-pinion system remains in place, acting as a fail-safe mechanism.
An active steering system facilitates two major functions: a variable steering ratio, and
maintaining vehicle stability and maneuverability during emergency maneuvers or when
driving conditions call for a change in the steering response. In this chapter, however, we
shall limit our focus to the vehicle stabilization capability of an active steering system.
As mentioned earlier in Chapter 1, it is advantageous to employ steering
intervention rather than braking intervention to generate a corrective yaw moment when
controlling a vehicle on slippery surfaces, where the limits of adhesion are easily reached.
In general, steering intervention has a faster response than braking individual wheels, as
is done by an ESP system, since the later requires a certain period of time to build up
hydraulic brake pressure. Furthermore, modifying the reaction of the vehicle using
steering intervention is a more continuous process and, therefore, is not noticeable or, at
least, is not perceived as being annoying [Koe04]. In addition, active steering is highly
effective when driving on a -split road, and is able to correct the side-pushing effect that
occurs due to the different traction forces on the two sides of the vehicle. However, the
range of effectiveness of an active steering system is severely restricted by the actuator
range limit. For instance, the active steering system designed by BMW is only able to
manipulate the steering angle of the front wheels by up to 3° [Koe04], which is
equivalent to a driver steering wheel input of about 54°, when assuming a steering ratio
of 1:18.
A complete steering system has been developed for the AUTO21EV in the
ADAMS/View environment [Bod06], where the kinematics and dynamics of the steering
system have been analyzed. This steering system has a 55% Ackermann behaviour in
order to provide smaller turning radii and a higher lateral force capacity on the front tires
when turning at higher speeds. The nonlinear characteristics of the steering system have
been implemented in the DynaFlexPro model of the AUTO21EV (Figure 4-1) using lookup tables and independent motion drivers for the front-left and front-right wheels. A
147
6
Genetic Fuzzy Active Steering Controller
genetic fuzzy active steering controller is developed based on this steering system, which
can generate the required corrective yaw moment by manipulating the steering angle of
the front tires, augmenting the steering input provided by the driver.
6.1
Fuzzy active steering controller design
Almost every active steering system available on the market today is based on the
classical PID control system [Koe04, Yih05, Mam02, Kno99, Ack98, Rei04]. In general,
tuning the gains of such a PID controller requires extensive and rigorous field tests that
are conducted by vehicle experts in a car manufacturing company. In this work, however,
a novel fuzzy active steering controller (ASC) and a reliable method by which its
membership functions can be tuned in an optimized way are developed, which may make
most of the expensive field testing unnecessary.
As mentioned in Chapter 4, fuzzy control systems are well suited for tackling the
highly nonlinear behaviour inherent in vehicle dynamics. In addition, the rule base of the
fuzzy ASC can be described in vague linguistic terms using expert knowledge, which
suits the subjective nature of vehicle stability and handling. Although many researchers
argue that more comprehensive control can be achieved by simultaneously considering
the vehicle yaw rate and sideslip angle [Man07], an active steering system is not expected
to be of significant help when driving a vehicle near its handling limit due to the limited
range of effectiveness caused by actuator restrictions. In other words, in cases where a
high sideslip angle is likely, an active steering system would not be considered the
primary control system for stabilizing the vehicle; rather, it is a complementary system
that can help to stabilize the vehicle in collaboration with other active chassis subsystems
[Gor03, And06]. With this in mind, the inputs to the fuzzy ASC are defined to be the yaw
rate error e( ) and the rate of change of the yaw rate error e( ) , and the output of the
controller is the corrective steering angle that will augment the driver‟s steering input in
order to stabilize the vehicle. The desired yaw rate to which the controller attempts to
match the nonlinear behaviour of the vehicle is calculated using the linear bicycle model
that is introduced in Chapter 4. Figure 6-1 illustrates the block diagram of the fuzzy ASC.
Table 6-I lists the definitions of the input and output variables of the fuzzy ASC.
The input variables are pre-processed to the range [-1, 1] before entering the fuzzy
controller, and the output variable of the controller is post-processed to determine the
148
6
Genetic Fuzzy Active Steering Controller
required corrective steering angle. Note that the fuzzy ASC uses the same input variables
and corresponding scaling factors that were defined for the genetic fuzzy yaw moment
controller in Chapter 4; thus, it is unnecessary to calculate them again. The scaling
functions for the yaw rate error and the rate of change of the yaw rate error are, again,
assumed to be 35o/s and 2000o/s2, respectively. Note that the scaling factor used for postprocessing the output variable of the fuzzy ASC is determined based on the active
steering actuator range limit. In order for the simulation to be as realistic as possible, the
actuator range limit of the active steering controller developed by BMW is adopted,
which only allows a steering angle manipulation of up to 3° [Koe04].
Figure 6-1: Block diagram of the fuzzy active steering controller
Variable
Definition
Input 1
e( )   desired  actual
Input 2
e( ) 
e( )k  e( )k 1
sample time
 corr
Output
Table 6-I: Definition of the input and output variables of the fuzzy active steering controller
In order to provide enough rule coverage, five fuzzy sets are used for the yaw rate error
and the rate of change of the yaw rate error; nine fuzzy sets are used to describe the
output of the controller, which is the required corrective steering angle. A Mamdani fuzzy
inference system processes the input variables through the list of rules in the knowledge
base and calculates the output based on the following fuzzy rule schema:
IF e(ψ) is A AND e(ψ) is B THEN  corr is C
149
(6.1)
6
Genetic Fuzzy Active Steering Controller
where A, B, and C are fuzzy sets defined on the input and output domains. The initial
shape and distribution of the membership functions used for the input and output
variables of the fuzzy ASC are illustrated in Figure 6-2.
Figure 6-2: Initial shape and distribution of the membership functions for the input and output variables of
the fuzzy ASC
A two-dimensional (2D) rule base table is developed for the fuzzy ASC, whose
rules are determined based on expert knowledge and extensive investigation into the
dynamic behaviour of the vehicle in different driving conditions. Figure 6-3 illustrates the
2D fuzzy rule base and the corresponding control surface of the fuzzy ASC using the
initial untuned fuzzy membership functions. The linguistic terms that have been used in
the rule base table are defined in Table 4-II. Note that these fuzzy rules are formed using
fuzzy variables whose membership functions are of unknown shapes, sizes, and relative
positions. As a result, the generated corrective steering angle of the fuzzy ASC can only
cover up to 75% of the output domain, as is evident from the control surface shown in
Figure 6-3.
Figure 6-3: Rule base (left) and control surface (right) of the proposed fuzzy active steering controller
150
6
6.2
Genetic Fuzzy Active Steering Controller
Evaluation of the fuzzy active steering controller
The performance of the fuzzy ASC is evaluated by driving the AUTO21EV through the
ISO double-lane-change maneuver using the path-following driver model, whose
characteristics are described in Chapter 2. Since the effective range of the fuzzy ASC is
limited, the initial speed for this maneuver is chosen to be 60 km/h. Figure 6-4 illustrates
the desired and actual vehicle trajectories when driving through the double-lane-change
maneuver using the path-following driver model with and without the fuzzy ASC. The
driver model is able to negotiate the maneuver even without using the fuzzy ASC.
Figure 6-4: Desired and actual vehicle trajectories when driving through the double-lane-change maneuver
with an initial speed of 60 km/h (a) using the driver model and (b) using the driver model with the fuzzy
ASC
The performance of the fuzzy ASC becomes clear when looking at the vehicle
yaw rate and sideslip angle for this maneuver, which are shown in Figure 6-5. Although
the fuzzy ASC is not able to control the vehicle such that it performs exactly like the
desired reference model, it is able to reduce the magnitudes of both the maximum yaw
rate and the maximum sideslip angle of the vehicle. The performance of the fuzzy ASC is
confirmed in Figure 6-6, which illustrates the lateral acceleration of the vehicle, the
driver‟s steering wheel input, and the vehicle forward speed as functions of time. The
vehicle experiences a lateral acceleration of about 7 m/s2, which indicates that the vehicle
is undergoing a severe maneuver. Looking at Figure 6-6-b, which illustrates the driver‟s
steering wheel input and the equivalent corrective steering wheel input that the fuzzy
ASC has added to the driver‟s steering request, it is clear that the driver requires less
steering effort when the fuzzy ASC is active. Note that the generated corrective steering
angle is not large enough to eliminate the yaw rate error of the vehicle entirely (Figure 6151
6
Genetic Fuzzy Active Steering Controller
5). A reduction in the final steering angle also means that the vehicle loses less speed
when driving through this maneuver (Figure 6-6-c). The handling performance of the
vehicle is illustrated in Figure 6-6-d, which clearly indicates that the vehicle handling is
improved by the fuzzy ASC, as the hysteresis of the plot has been reduced.
Figure 6-5: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when driving through the
double-lane-change maneuver using the driver model with and without the fuzzy ASC (FASC)
Figure 6-6: (a) Lateral acceleration, (b) steering wheel angle, and (c) vehicle speed as functions of time;
and (d) vehicle yaw rate as a function of the steering wheel input when driving through the double-lanechange maneuver with and without the fuzzy ASC (FASC)
152
6
6.3
Genetic Fuzzy Active Steering Controller
Genetic tuning of the fuzzy active steering controller
As mentioned above, due to the arbitrary shape, size, and distribution of the fuzzy
membership functions, the performance of the resulting fuzzy ASC cannot be considered
optimal. Since the fuzzy ASC is unable to learn or adapt to its environment on its own,
and instead of resorting to the tedious task of tuning the membership functions manually,
a multi-criteria genetic algorithm is used to adjust the membership functions and achieve
better controller performance. A procedure similar to that used for tuning the membership
functions of the input and output variables of the fuzzy YMC, described in Chapter 4, is
used for genetically tuning the membership functions of the fuzzy ASC. The ISO doublelane-change maneuver with obstacle avoidance is used to evaluate the effectiveness of
each candidate controller in the genetic algorithm. Once again, due to the fact that the
membership functions of the fuzzy ASC must be tuned in a general sense, not based on a
specific driver or driver model, the double-lane-change maneuver is treated as an openloop test, in which a predefined fixed steering input is used to drive the AUTO21EV
through the maneuver. Details about the fixed steering input can be found in Chapter 4.
Using this fixed steering input, any deviations from the desired vehicle trajectory, yaw
rate, and sideslip angle are considered to be stability errors that the fuzzy ASC should
correct. The goal of the multi-criteria genetic algorithm is to identify the ideal shape, size,
and distribution of the membership functions so as to minimize the vehicle trajectory,
yaw rate, and sideslip angle errors.
The scaling function technique is chosen for the genetic tuning of the fuzzy
membership functions. Since the input and output variables of the fuzzy ASC are initially
described using a set of normalized membership functions that are distributed
symmetrically around the origin (Figure 6-2), three nonlinear scaling functions, similar to
that described in equation (4.12) of Chapter 4, are again used to tune the membership
functions of the input and output variables. Since each of these nonlinear scaling
functions uses only one parameter to affect the overall distribution and shape of the
membership functions, only three scaling parameters are required, which are
concatenated to form a chromosome for the genetic tuning process. This method of
tuning also guarantees that the adjacency constraint is satisfied, which ensures that the
sum of all membership functions is equal to unity for every point in the domain, the final
153
6
Genetic Fuzzy Active Steering Controller
tuned membership functions are distributed symmetrically around the origin, and the
genetic search examines a wide range of fuzzy partitions.
The objective of the multi-criteria genetic algorithm is to tune the input and output
variables of the fuzzy ASC such that the mean square errors (MSE) of the vehicle
trajectory, yaw rate, and sideslip angle are minimized when driving through the doublelane-change maneuver. These mean square errors are calculated as follows:
2
MSETrajectory
1 N
=   ydesired (x k ) - yactual (x k )
N k=1
MSE Yaw Rate
1 N
=   ψdesired (k) - ψactual (k)
N k=1
(6.2)
2
(6.3)
2
MSESideslip
1 N
=  βdesired (k) - βactual (k)
N k=1
(6.4)
where N is the number of sample points, ydesired (x k ) and yactual (x k ) are the desired and
actual lateral positions of the vehicle for a given forward position xk, ψdesired (k) and
ψactual (k) are the desired and actual vehicle yaw rates, and βdesired (k) and βactual (k) are the
desired and actual vehicle sideslip angles at a given time step k, respectively. Since the
objective of the multi-criteria genetic algorithm is to minimize these three errors, the
fitness function associated with each chromosome is defined as the weighted sum of the
inverses of the resulting vehicle trajectory, yaw rate, and sideslip angle mean square
errors as follows:
Fitness Function =
w1
w2
w3
+
+
MSETrajectory MSE Yaw Rate MSESideslip
(6.5)
where w1, w2, and w3 are the weighting factors. The genetic algorithm was run for 50
generations, each of which had a population size of 200 chromosomes, a crossover rate of
95%, and a mutation rate of 15%. In addition, an elite selection rate of 2% was employed
to ensure that the fittest chromosomes were retained unaltered from one generation to the
next. Using the elite selection technique justifies the relatively high mutation rate, which
facilitates the thorough exploration of the search space without losing the fittest members
of each generation. Convergence is assumed if the fittest chromosome in a given
generation survives for 10 consecutive generations, or after 50 generations have elapsed.
154
6
Genetic Fuzzy Active Steering Controller
Figure 6-7 illustrates the maximum fitness function value for each generation, and the
convergence of the final results.
Figure 6-7: Maximum fitness function value for each generation of the multi-criteria genetic algorithm
Comparing Figure 6-8, which illustrates the control surface of the tuned fuzzy
ASC, with Figure 6-3, it is clear that the scaling functions have adjusted the membership
functions of the output variable of the fuzzy controller such that the control surface
reaches the limits of the output domain, thereby covering the entire control space. Figure
6-9 illustrates the resulting tuned membership functions for the input and output variables
of the genetic fuzzy ASC. As can be seen, the scaling functions have adjusted the shape,
size, and distribution of the membership functions of the fuzzy ASC considerably (see
Figure 6-2). The new distribution of the membership functions associated with the yaw
rate error indicates that the controller does not tolerate small yaw rate errors. The tuning
process has had the opposite effect on the membership functions for the rate of change of
the yaw rate error, essentially reducing the relative severity of having small errors
associated with this performance metric.
Figure 6-8: Control surface of the genetically-tuned fuzzy ASC
155
6
Genetic Fuzzy Active Steering Controller
Figure 6-9: Shape and distribution of the genetically-tuned membership functions for the input and output
variables of the fuzzy ASC
6.4
Evaluation of the genetic fuzzy active steering controller
In order to evaluate the performance of the genetic fuzzy ASC, the AUTO21EV is driven
through a series of test maneuvers, which are described in Chapter 2.
6.4.1 ISO double-lane-change maneuver
The performance of the genetic fuzzy ASC is first compared to that of the untuned fuzzy
ASC as the vehicle is driven through the double-lane-change maneuver with an initial
speed of 60 km/h using the path-following driver model. Figure 6-10 illustrates the
vehicle trajectory and demonstrates that the driver model is able to negotiate the
maneuver when the genetic fuzzy ASC is active. Figure 6-11 illustrates the vehicle yaw
rate and sideslip angle for this maneuver. Comparing this figure with Figure 6-5, it is
clear that the genetically-tuned fuzzy ASC is better able to control the vehicle yaw rate
such that it tracks that of the reference bicycle model. The sideslip angle of the vehicle is
also less than it was prior to the tuning process.
Figure 6-10: Desired and actual vehicle trajectories when driving through the double-lane-change maneuver
with an initial speed of 60 km/h using the driver model and the genetic fuzzy ASC
156
6
Genetic Fuzzy Active Steering Controller
Figure 6-11: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when driving through the
double-lane-change maneuver with an initial speed of 60 km/h using the driver model, with and without the
genetic fuzzy ASC (GFASC)
Figure 6-12 illustrates the lateral acceleration of the vehicle, the driver‟s steering
input, and the vehicle forward speed as functions of time. As can be seen, the vehicle
experiences less lateral acceleration than it did when either no stability controller or the
fuzzy ASC was active. This result can be attributed to the fact that the vehicle is more
stable when the genetic fuzzy ASC is active, so less steering effort is required to
negotiate the maneuver. Comparing the steering wheel angles applied by the driver, as
shown in Figure 6-12-b, it is clear that the driver requires the least steering effort when
the genetic fuzzy ASC is active. In addition, note that the generated corrective steering
angle is much larger than that observed when using the untuned fuzzy ASC. As a result of
using less total steering angle, the vehicle loses even less speed with the genetic fuzzy
ASC than it did with the untuned controller. Figure 6-12-d illustrates the handling
performance of the vehicle, and clearly indicates that the vehicle handling and agility
have been significantly improved by the genetic fuzzy ASC. The hysteresis of the
performance plot is the least when the genetic fuzzy ASC is active, which characterizes a
vehicle with superior responsiveness.
Since the genetic fuzzy ASC demonstrates better performance in all
aforementioned aspects when compared to the untuned fuzzy ASC, only the genetic fuzzy
ASC will be considered in the reminder of the evaluation process. Moreover, since the
performance of the genetic fuzzy ASC must be compared to that of the other stability
157
6
Genetic Fuzzy Active Steering Controller
controllers (namely, the genetic fuzzy YMC and the advanced torque vectoring
controller) using the same test maneuvers, the double-lane-change maneuver is repeated
using an initial speed of 75 km/h.
Figure 6-12: (a) Lateral acceleration, (b) steering wheel angle, and (c) vehicle speed as functions of time;
and (d) vehicle yaw rate as a function of the steering wheel input when driving through the double-lanechange maneuver with an initial speed of 60 km/h without a controller, with the fuzzy ASC (FASC), and
with the genetic fuzzy ASC (GFASC)
Figure 6-13 illustrates the vehicle trajectory when driving through the doublelane-change maneuver with an initial speed of 75 km/h when using the genetic fuzzy
ASC. As can be seen, at higher speeds, the genetic fuzzy ASC is not powerful enough to
help the driver negotiate the maneuver without hitting the cones. This performance is
confirmed by looking at the vehicle yaw rate and sideslip angle shown in Figure 6-14.
Due to the actuator range limit of the active steering system, the genetic fuzzy ASC is not
able to control the behaviour of the vehicle such that it performs like the desired reference
bicycle model when driving through this maneuver. Nevertheless, the genetic fuzzy ASC
is able to reduce the maximum vehicle yaw rate and sideslip angle by more than half
when compared to the case when no stability controller is active.
158
6
Genetic Fuzzy Active Steering Controller
Figure 6-13: Desired and actual vehicle trajectories when driving through the double-lane-change maneuver
with an initial speed of 75 km/h using the driver model and the genetic fuzzy ASC
Figure 6-14: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when driving through the
double-lane-change maneuver with an initial speed of 75 km/h using the driver model, with and without the
genetic fuzzy ASC (GFASC)
Figure 6-15 illustrates the lateral acceleration of the vehicle, the driver‟s steering
input, and the vehicle forward speed as functions of time. As can be seen, the maximum
lateral acceleration that the vehicle experiences is about 8.4 m/s2, which indicates the
severity of this maneuver. Comparing the required steering wheel angles shown in Figure
6-15-b, it is clear that the driver requires more steering effort when the genetic fuzzy
ASC is used than when either the genetic fuzzy YMC or the ATVC is used. Although the
fuzzy ASC augmentes the driver‟s steering input, its intervention is not sufficient to
eliminate the vehicle yaw rate and sideslip errors completely and, thus, is unable to fully
stabilize the vehicle. Since the driver requires more steering effort when the genetic fuzzy
ASC is active than when the other stability controllers are active, the vehicle loses more
speed in this case (Figure 6-15-c). The handling performance curve of the vehicle,
illustrated in Figure 6-15-d, clearly indicates that the genetic fuzzy ASC is not as
effective at improving the vehicle handling and agility as are the other stability
controllers.
159
6
Genetic Fuzzy Active Steering Controller
Figure 6-15: (a) Lateral acceleration, (b) steering wheel angle, and (c) vehicle speed as functions of time;
and (d) vehicle yaw rate as a function of the steering wheel input when driving through the double-lanechange maneuver with an initial speed of 75 km/h without a controller, with the genetic fuzzy YMC
(GFYMC), with the ATVC, and with the genetic fuzzy ASC (GFASC)
Table 6-II summarizes the vehicle response during the double-lane-change
maneuver when the driver model is used with the genetic fuzzy ASC, and compares it to
the performance observed when the driver model is used with no stability controller, with
the genetic fuzzy YMC, and with the ATVC. Comparing different parameters of the
vehicle response during this maneuver, it can be seen that the genetic fuzzy ASC has
improved all the decisive parameters that describe the handling, stability, and longitudinal
dynamics of the vehicle when compared to the case in which no stability controller is
active; however, it is not as effective as the genetic fuzzy YMC or the ATVC. With
respect to the handling characteristic of the vehicle, 
max
, 
max
, and  SW
max
are about
twice as large when the genetic fuzzy ASC is active than they are when the genetic fuzzy
YMC is active. In addition, the hysteresis of the performance plot (  H ) is about four
times larger than that observed when the genetic fuzzy YMC is active. Note that the
160
6
Genetic Fuzzy Active Steering Controller
driver was not able to negotiate the maneuver at a high speed without hitting the cones.
Therefore, the genetic fuzzy ASC is considered to be a controller that can improve the
handling characteristics of the vehicle to some extent, but it is not considered to be as
effective as the genetic fuzzy YMC or the ATVC. The genetic fuzzy ASC is considered
to be an effective stability controller because it has reduced 
max
and 
max
by more
than half when compared to the case where no stability controller is used. The genetic
fuzzy ASC is also considered to be an effective controller for improving the longitudinal
dynamics of the vehicle.
Parameter

max

max
ay
max
 SW
max
 H
vlost
AUTO21EV
26.3o
115.4o/s
8.2m/s2
545o
163.8o/s
20.5m/s
GFYMC
6.2o
31.2o/s
8.4m/s2
108o
21o/s
13.2m/s
ATVC
6.1o
36.4o/s
8.4m/s2
140o
35.5o/s
13.5m/s
GFASC
13.6o
60.1o/s
8.4m/s2
211o
79.5o/s
14.6m/s
Table 6-II: Vehicle response during the double-lane-change maneuver using the driver model without a
controller, with the genetic fuzzy YMC (GFYMC), with the ATVC, and with the genetic fuzzy ASC
(GFASC)
6.4.2 Step-steer response maneuver
In order to evaluate the performance of the vehicle using the genetic fuzzy ASC in a stepsteer response maneuver, the vehicle yaw rate, sideslip angle, and lateral acceleration as
functions of time are observed. Figure 6-16-a illustrates the fixed step-steer input and the
equivalent corrective steering input generated by the genetic fuzzy ASC. As can be seen,
the genetic fuzzy ASC has applied a large steering correction at the beginning of the stepsteer input in order to match the behaviour of the vehicle to that of the desired bicycle
model. Due to the augmented steering input, the vehicle experiences a lateral acceleration
of 4.3 m/s2, which is larger than that obtained when using the other stability control
systems and when no stability controller is active (Figure 6-16-b). The rise time of the
lateral acceleration response is about 0.53 seconds when the genetic fuzzy ASC is active,
which indicates an improvement in the responsiveness of the vehicle when compared to
the case where no stability controller is active. Figure 6-17 illustrates the vehicle yaw rate
and sideslip angle when the genetic fuzzy ASC is active, and compares the response to
that obtained when no stability controller is active, when the genetic fuzzy YMC is
active, and when the ATVC is used. As can be seen, the vehicle experiences the largest
161
6
Genetic Fuzzy Active Steering Controller
sideslip angle when the genetic fuzzy ASC is active, which is due to the fact that the
genetic fuzzy ASC applies a larger steering angle than is applied in the other cases.
Figure 6-16: (a) Required steering wheel input and (b) lateral acceleration of the vehicle when driving
through the step-steer maneuver using the genetic fuzzy ASC (GFASC)
Figure 6-17: Yaw rate (top) and sideslip angle (bottom) of the vehicle when driving through the step-steer
maneuver using the genetic fuzzy ASC (GFASC)
Table 6-III summarizes the vehicle response during the step-steer test maneuver.
Comparing different parameters of the vehicle response during this maneuver when it is
performed with and without the genetic fuzzy ASC, this controller can be considered very
effective at improving all the decisive parameters of the vehicle that describe its handling
characteristics.
162
6
Genetic Fuzzy Active Steering Controller
PO 
 max  ss
 100%
 ss

ta y
Parameter
t
AUTO21EV
0.34s
1.30%
1.43o
0.66s
GFYMC
0.15s
0.00%
1.38o
0.51s
ATVC
0.15s
16.1%
1.36o
0.47s
GFASC
0.15s
2.20%
1.53o
0.53s
max
Table 6-III: Vehicle response during the step-steer maneuver using the driver model without a controller,
with the genetic fuzzy YMC (GFYMC), with the ATVC, and with the genetic fuzzy ASC (GFASC)
6.4.3 Brake-in-turn maneuver
Figure 6-18 illustrates the vehicle trajectory relative to the desired circular path during a
brake-in-turn maneuver using the driver model with and without the genetic fuzzy ASC.
As can be seen, the driver model is not able to control the vehicle during this maneuver
when no stability controller is active. However, the driver model is able to keep the
vehicle on the predefined circular path while severely braking when the genetic fuzzy
ASC is active, and the lateral deviation of the vehicle from the desired path remains
negligible throughout the maneuver.
Figure 6-18: Desired and actual vehicle trajectories when braking in a turn using (a) the driver model only
and (b) the driver model with the genetic fuzzy ASC
Figure 6-19-a illustrates the driver‟s steering wheel input as a function of time,
and indicates that the driver model is able to control the vehicle very smoothly and with
little steering effort when the genetic fuzzy ASC is active. This figure also shows the
activity of the active steering controller as it augments the driver‟s steering wheel input at
each time step. Figure 6-19-b illustrates the lateral acceleration of the vehicle and
163
6
Genetic Fuzzy Active Steering Controller
confirms that the vehicle remains stable when the genetic fuzzy ASC is active. Note that,
for clarity, the driver‟s steering input and the lateral acceleration of the vehicle when no
stability controller is active have not been illustrated in Figure 6-19.
Figure 6-19: (a) Required steering wheel input and (b) lateral acceleration of the vehicle when braking in a
turn using the driver model with the genetic fuzzy YMC (GFYMC), with the ATVC, and with the genetic
fuzzy ASC (GFASC)
Figure 6-20 compares the vehicle yaw rate and sideslip angle when driving
through the brake-in-turn maneuver using the driver model with the genetic fuzzy YMC,
with the ATVC, and with the genetic fuzzy ASC. Again, for clarity, the yaw rate and
sideslip angle of the vehicle when no stability controller is active are not illustrated.
When the genetic fuzzy ASC is active, the vehicle behaves almost like the desired
reference model until the braking begins. After the start of braking, the genetic fuzzy
ASC attempts to minimize the yaw rate error by augmenting the driver‟s steering input
(Figure 6-19-a). As can be seen in Figure 6-20, the genetic fuzzy ASC is more effective
at minimizing the yaw rate error of the vehicle than the ATVC, and it does not cause the
severe oscillations that the ATVC causes. Figure 6-20 also confirms that the genetic
fuzzy ASC is able to stabilize the vehicle when braking in a turn, since the yaw rate and
sideslip angle both approach zero as the vehicle progresses toward larger deceleration
rates. Figure 6-21-a illustrates the vehicle speed as a function of time and confirms the
performance of the speed controller. Figure 6-21-b illustrates the vehicle longitudinal
acceleration as a function of vehicle speed, and confirms the severity of the braking
action in this maneuver.
164
6
Genetic Fuzzy Active Steering Controller
Figure 6-20: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when braking in a turn
using the driver model with the genetic fuzzy YMC (GFYMC), with the ATVC, and with the genetic fuzzy
ASC (GFASC)
Figure 6-21: (a) Vehicle speed as a function of time when braking in a turn using the driver model with the
genetic fuzzy ASC, and (b) longitudinal acceleration as a function of vehicle speed when braking in a turn
using the driver model without a controller, with the genetic fuzzy YMC (GFYMC), with the ATVC, and
with the genetic fuzzy ASC (GFASC)
Table 6-IV summarizes the vehicle response during the brake-in-turn maneuver
when the genetic fuzzy ASC is active, and compares it with the performance observed
when no stability controller is used, when the genetic fuzzy YMC is used, and when the
ATVC is used. Comparing different parameters of the vehicle response during this
maneuver, it can be seen that the genetic fuzzy ASC is very effective at improving all the
decisive parameters that describe the handling, stability, and path-following capabilities
of the vehicle. The genetic fuzzy ASC is able to reduce 
max
, 
max
, and  SW
max
significantly, which indicates that this controller is very effective at enhancing the vehicle
handling during this maneuver. Simultaneously, a reduction of 
165
max
and 
max
by the
6
Genetic Fuzzy Active Steering Controller
genetic fuzzy ASC indicates that it is also very effective at improving the vehicle
stability. Finally, the fact that the maximum lateral deviation of the vehicle from the
desired path remains very small throughout the maneuver confirms that the genetic fuzzy
ASC enhances the path-following capability of the vehicle as well.
Parameter

max

max
ymax
 SW
max
AUTO21EV
126.5o/s
50.1o
3.67m
700o
GFYMC
22.60o/s
4.36o
0.18m
46.4o
ATVC
24.00o/s
4.40o
0.18m
48.0o
GFASC
22.45o/s
4.25o
0.16m
45.7o
Table 6-IV: Vehicle response during the brake-in-turn maneuver using the driver model without a
controller, with the genetic fuzzy YMC (GFYMC), with the ATVC, and with the genetic fuzzy ASC
(GFASC)
6.4.4 Straight-line braking on a -split road
As the final test, the AUTO21EV is driven on a -split road and the driver model
attempts to stop the vehicle in an emergency braking situation. Figure 6-22 illustrates the
vehicle trajectory for this maneuver when no stability controller is active and compares it
to the case when the genetic fuzzy ASC is active. As can be seen, the genetic fuzzy ASC
is able to correct the side-pushing effect of the vehicle while braking on a -split road,
and prevents the vehicle from leaving the predefined road. The braking distance of the
vehicle is about 45.7 meters. Looking at Figure 6-23, it is clear that the genetic fuzzy
ASC is able to limit and, later, diminish the yaw rate and sideslip angle of the vehicle
while driving over the black ice patch, which indicates that the vehicle remains stable
during this maneuver. Note that, for clarity, the yaw rate and sideslip angle of the vehicle
observed when no controller is active are not illustrated here.
Figure 6-22: Desired and actual vehicle trajectories when braking on a -split road while holding the
steering wheel fixed, with and without the genetic fuzzy ASC (GFASC)
166
6
Genetic Fuzzy Active Steering Controller
Figure 6-23: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when braking on a split road while holding the steering wheel fixed and using the genetic fuzzy ASC (GFASC)
Figure 6-24 illustrates the fixed steering wheel input and the equivalent corrective
steering wheel angle that is generated by the genetic fuzzy ASC to counteract the sidepushing effect of the vehicle. As can be seen, the active steering controller has applied up
to 54o of equivalent steering wheel angle in order to correct the side-pushing effect of the
vehicle. Figure 6-25 illustrates the tire slip ratios while braking on the -split road, and
indicates that the slip controllers on the left wheels have limited the motor torques
between 0.7 and 1.15 seconds of the simulation in order to prevent tire lock-up while
ensuring the maximum possible braking force is applied when braking on the black ice
patch. Later in the simulation, due to the weight shift to the front axle, the slip controllers
on the rear axle have limited the motor torques to prevent tire lock-up at higher
deceleration rates. The activation of the slip controllers is confirmed in Figure 6-26,
which illustrates the motor torques for all four wheels.
Table 6-V summarizes the vehicle response during the straight-line braking on a
-split road maneuver when holding the steering wheel fixed and using the genetic fuzzy
ASC. Comparing different parameters of the vehicle response during this maneuver, it
can be seen that the genetic fuzzy ASC is very effective at improving all the decisive
parameters that describe the stability, path-following capability, and braking performance
of the vehicle. In particular, the genetic fuzzy ASC has reduced the 
max
and 
max
values significantly, which indicates an enhancement in the stability of the vehicle.
167
6
Genetic Fuzzy Active Steering Controller
Moreover, the braking distance of the vehicle has been reduced considerably by the
genetic fuzzy ASC, indicating an improvement in the longitudinal dynamics of the
vehicle. The genetic fuzzy ASC also reduces the maximum lateral deviation of the
vehicle such that the vehicle remains on the predefined road throughout the maneuver.
Figure 6-24: Equivalent corrective steering wheel input applied by the genetic fuzzy ASC (GFASC),
augmenting the fixed steering input of the driver in order to correct the side-pushing effect of the vehicle
when braking on a -split road
Figure 6-25: Tire slip ratios when braking on a -split road while holding the steering wheel fixed and
using the genetic fuzzy ASC (GFASC)
168
6
Genetic Fuzzy Active Steering Controller
Figure 6-26: Requested and actual motor torque at each wheel when braking on a -split road while holding
the steering wheel fixed and using the genetic fuzzy ASC (GFASC)
Parameter

max

max
xbraking
ymax
AUTO21EV
24.2o
63.4o/s
48.4m
15.9m
GFYMC
0.40o
1.85o/s
44.5m
0.46m
ATVC
1.7o
9.70o/s
47.3m
2.70m
GFASC
1.6o
2.50 o/s
45.7m
0.36m
Table 6-V: Vehicle response during the straight-line braking on a -split road maneuver without a
controller, with the genetic fuzzy YMC (GFYMC), with the ATVC, and with the genetic fuzzy ASC
(GFASC)
6.5
Chapter summary
In this chapter, the simplified 14-DOF vehicle model introduced in Chapter 4 is used to
develop an active steering controller. Use of this simplified vehicle model facilitates the
testing of different control strategies and the application of a genetic algorithm procedure
to the development of the fuzzy active steering controller. A genetic tuning procedure is
applied to the developed fuzzy ASC to improve its performance. A variety of maneuvers
are simulated to demonstrate the performance and effectiveness of the genetic fuzzy
ASC. Table 6-VI provides a subjective evaluation of the effectiveness of the genetic
fuzzy ASC based on different test maneuvers.
169
6
Genetic Fuzzy Active Steering Controller
Table 6-VI: Subjective evaluation of the effectiveness of the genetic fuzzy ASC based on different test
maneuvers (3 = very effective, 2 = effective, 1 = effective to some extent, 0 = ineffective)
170
7
Integration of the Advanced Torque Vectoring and
Genetic Fuzzy Active Steering Controller
As mentioned earlier in Chapter 1, the optimum driving dynamics can only be achieved
when the tire forces on all wheels in all three coordinate directions are monitored and
controlled precisely. This advanced level of control is only possible when the vehicle is
equipped with various active chassis control systems that are networked together in an
integrated fashion. Taking advantage of the strengths of each active chassis subsystem,
the ideal traction and stability performance of the vehicle can be obtained by activating
the subsystem or subsystems that will be most effective given the required and actual
behaviour of the vehicle. In the previous chapters, the performance and effectiveness of
each stability control system, namely the advanced torque vectoring controller (ATVC)
and the genetic fuzzy active steering controller (GFASC), were studied and evaluated
individually. In this chapter, we investigate whether the integration of these stability
control systems enhances the performance of the vehicle in terms of handling, stability,
path-following, and longitudinal dynamics. An integrated approach is introduced that
distributes the required control effort between the in-wheel motors and the active steering
system.
7.1
Integration of chassis control systems using an activation function
As mentioned in Chapter 6, superimposing the steering input provided by the driver with
a correction generated by the GFASC is considered to be a continuous process, and is not
perceived by the driver as being annoying. It is also advantageous to employ steering
intervention rather than braking or driving individual wheels when controlling the vehicle
on slippery surfaces, since steering intervention requires less frictional force between the
tire and the road to generate a corrective yaw moment. However, the GFASC is not of
significant help when the vehicle is driven near its handling limits due to its limited range
of effectiveness (caused by actuator restrictions). In Chapter 5, on the other hand, it has
been confirmed that the ATVC is very effective at improving the vehicle stability and
handling, even when driving the vehicle near its handling limits. It has also been
observed, however, that the activation of the in-wheel motors to generate a corrective
171
7 Integration of the Advanced Torque Vectoring and Genetic Fuzzy Active Steering
yaw moment can cause some oscillations in the vehicle states, which might be perceived
by the driver as being disruptive and annoying.
Figure 7-1 compares the performance and effectiveness of the genetic fuzzy yaw
moment controller (GFYMC), ATVC, and GFASC based on different test maneuvers,
which are listed in Tables 4-VII, 5-V, and 6-VI, respectively. Recall that the GFYMC is
considered to be the ideal stability controller against which the performance and
effectiveness of all other controllers are compared. As can be seen, neither the ATVC nor
the GFASC can match the performance and effectiveness of the GFYMC in all four
categories. Moreover, although the ATVC demonstrates better performance in the
stability category when compared to the GFASC, the performance and effectiveness of
the GFASC is superior in the other three categories (namely, vehicle handling, pathfollowing, and longitudinal dynamics). Therefore, it makes sense to integrate these two
controllers such that their individual strengths can be exploited, the effects of their
weaknesses can be reduced, and the overlapping of their functionalities can be avoided.
Handling
Path-following Capability
3
3
2.5
2.5
2
2
1.5
1.5
1
1
0.5
0.5
0
0
GFYMC
ATVC
GFYMC
GFASC
Stability
ATVC
GFASC
Longitudinal Dynamics
3
3
2.5
2.5
2
2
1.5
1.5
1
1
0.5
0.5
0
0
GFYMC
ATVC
GFYMC
GFASC
ATVC
GFASC
Figure 7-1: Subjective evaluation of the performance and effectiveness of the GFYMC, ATVC, and
GFASC based on different test maneuvers (3 = very effective, 2 = effective, 1 = effective to some extent, 0
= ineffective)
In this work, the integration of the ATVC and GFASC is realized by using the
activation function illustrated in Figure 7-2. This activation function is a standard
Gaussian curve generated using the following exponential function:
172
7 Integration of the Advanced Torque Vectoring and Genetic Fuzzy Active Steering


  
corr
corrmax
exp 

2

2
 ATVC  corr   


100%



2

  100% ,  corr  3


,  corr  3
(7.1)
where  ATVC  corr  is the ATVC activation function, which is defined as a function of the
corrective steering angle (  corr );  corrmax is the actuator range limit of the active steering
controller, which is set at 3o; and  is the standard deviation, which is set at 0.7 in order
to form the bell curve shown in Figure 7-2. Note that the shape of this activation function
is designed such that the contribution of the ATVC is introduced gradually rather than
abruptly. In other words, depending on the driving conditions and the difference between
the desired and actual behaviour of the vehicle, the GFASC first attempts to stabilize the
vehicle without receiving any support from the ATVC. As the required corrective
steering angle increases, the activation function gradually activates the ATVC to support
the GFASC in its effort to stabilize the vehicle. If the required corrective steering angle is
larger than 3o, thus exceeding the actuator range limit of the active steering controller, the
activation function fully activates the ATVC such that both controllers are fully deployed
to help stabilize the vehicle.
Figure 7-2: Activation function used for the integration of the ATVC and GFASC
173
7 Integration of the Advanced Torque Vectoring and Genetic Fuzzy Active Steering
7.2
Evaluation of the integrated control of the advanced torque
vectoring and genetic fuzzy active steering
In order to evaluate the performance and effectiveness of the integrated control of the
ATVC and GFASC, the AUTO21EV is driven through a series of test maneuvers, as
described in Chapter 2.
7.2.1 ISO double-lane-change maneuver
The performance of the integrated control system consisting of the ATVC and the
GFASC is first evaluated by driving the AUTO21EV through the double-lane-change
maneuver with an initial speed of 75 km/h and using the path-following driver model.
Figure 7-3 illustrates the vehicle trajectory and demonstrates that the driver is able to
negotiate the maneuver without hitting the cones when the integrated control strategy is
used. Note that the path-following driver model is not able to negotiate this maneuver at
higher speeds without hitting the cones when only the GFASC is active (see Figure 4-11).
Figure 7-3: Desired and actual vehicle trajectories when driving through the double-lane-change maneuver
with an initial speed of 75 km/h using the path-following driver model and the integrated control of the
ATVC and GFASC
Figure 7-4 illustrates the vehicle yaw rate and sideslip angle during this maneuver.
In contrast to the individual performance of the ATVC and GFASC (Figures 5-6 and 615), the integrated control scheme using both the ATVC and GFASC is able to match the
actual vehicle yaw rate with the desired yaw rate that is calculated using the reference
bicycle model. Note that the oscillations in the actual vehicle yaw rate that were observed
when the ATVC was used on its own are not present when the integrated control
approach is used. In addition, the maximum yaw rate and sideslip angle of the vehicle are
almost the same as those obtained when the GFYMC was active (Figure 7-25). Figure
7-5-a illustrates the vehicle lateral acceleration as a function of time. As can be seen, the
lateral acceleration when using the integrated control approach is, in some regions,
174
7 Integration of the Advanced Torque Vectoring and Genetic Fuzzy Active Steering
similar to that observed when using the GFASC and, in other regions, is similar to that
observed when using the ATVC. At the handling limits, oscillations can be seen in the
lateral acceleration of the vehicle, which are caused by the activation of the in-wheel
motors, but they are mostly damped out. Figure 7-5-b confirms that, except during the
second lane-change, the driver requires about the same amount of steering wheel input as
is the case when only the ATVC is used. Figure 7-5-c illustrates the vehicle speed during
the double-lane-change maneuver, and confirms that the vehicle loses the least amount of
speed when the integrated control approach is used. This lack of deceleration can be
attributed to the fact that only relatively small steering angles are needed to negotiate the
maneuver (Figure 7-5-b) and the fact that the couples generated at the front and rear axles
do not slow the vehicle down. As a result, the speed reduction during this maneuver when
using the integrated control approach is even less than that observed when the GFYMC is
active. Figure 7-5-d illustrates the handling performance of the vehicle and indicates that
the hysteresis of this plot is less than that of the analogous plots for the GFASC and the
ATVC. In other words, the responsiveness and agility of the vehicle are considerably
improved compared to the cases where only individual controllers (namely, the GFASC
and the ATVC) are active. However, the responsiveness and agility of the vehicle are not
as good as they are when the GFYMC is used to generate the required corrective yaw
moment.
Figure 7-4: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when driving through the
double-lane-change maneuver with an initial speed of 75 km/h using the driver model and the integrated
control of the ATVC and the GFASC
175
7 Integration of the Advanced Torque Vectoring and Genetic Fuzzy Active Steering
Figure 7-5: (a) Lateral acceleration, (b) steering wheel angle, and (c) vehicle speed as functions of time;
and (d) vehicle yaw rate as a function of the steering wheel input when driving through the double-lanechange maneuver with the GFYMC, the ATVC, the GFASC, and the integrated control of the ATVC and
GFASC
Figure 7-6 illustrates the torque of each in-wheel motor during the double-lanechange maneuver. Comparing this figure to Figure 5-7, it is clear that the use of the
ATVC is reduced to a minimum by the activation function. In other words, the ATVC is
only activated when the GFASC is unable to stabilize the vehicle on its own, which
generally only happens when the vehicle is driven near its handling limits. Looking at the
motor torque plots, it can be seen that the GFASC is able to stabilize the vehicle most of
the time, and the ATVC is only activated at three time periods. For instance, between 2.4
and 2.65 seconds of the simulation, during which time the vehicle experiences the
maximum lateral acceleration of 8.5 m/s2 (Figure 7-5-a), the left-to-right torque vectoring
controller has ordered the left wheels to brake and the right wheels to accelerate, thereby
generating a positive corrective yaw moment to compensate for an oversteering situation,
where the actual yaw rate is larger than the desired one (Figure 7-4). Looking at the
torque vectoring ratios shown in Figure 7-7, it can be confirmed that the front-to-rear
176
7 Integration of the Advanced Torque Vectoring and Genetic Fuzzy Active Steering
Figure 7-6: Requested and actual motor torque at each wheel when driving through the double-lane-change
maneuver using the driver model with the integrated control of the ATVC and GFASC
Figure 7-7: Front-to-rear torque vectoring ratios when driving through the double-lane-change maneuver
using the driver model with the integrated control of the ATVC and GFASC
torque vectoring controller supports both the GFASC and the left-to-right torque
vectoring controller in a coordinated effort to stabilize the vehicle. For instance, between
2.4 and 2.65 seconds, the front-to-rear torque vectoring controller has requested that the
front motors generate up to 61% of the total required corrective yaw moment. Note that
generating more torque with the front motors and less with the rear ones reduces the
lateral force potential at the front axle and increases that at the rear axle, and vice versa.
The asymmetric lateral force potentials on the front and rear axles help to generate the
177
7 Integration of the Advanced Torque Vectoring and Genetic Fuzzy Active Steering
required corrective yaw moment. The activation of the front-to-rear torque vectoring
controller can also be confirmed in Figure 7-6. For instance, between 2.4 and 2.65
seconds, the front-to-rear torque vectoring controller has requested the front-left motor to
generate up to 770 Nm of braking torque and the front-right motor to generate up to 770
Nm of driving torque while, at the same time, the controller has requested up to 510 Nm
of braking and driving torques from the rear-left and rear-right motors, respectively. Note
that, although the controller has requested large motor torques from the front motors, the
motors are not powerful enough to generate the requested torques at a speed of 68 km/h.
The effects seen in Figure 7-6 can also be confirmed by looking at the tire traction
potentials and tire slip ratios shown in Figures 7-8 and 7-9, respectively. For instance, the
maximum traction potential of the rear-left tire is only exceeded once, at 3.35 seconds
(Figure 7-8). Looking at Figures 7-6 and 7-9, it can be confirmed that the requested motor
torque at the rear-left wheel is restricted by the slip controller during this time period in
order to prevent tire spin-out. Thus, the plot of the traction potential of the rear-left tire
exceeds 1 due to the fact that the lateral force of the tire has exceeded its limit. The same
explanation is valid for the rear-right tire when its traction potential is exceeded at 2.45
seconds.
Figure 7-8: Traction potential of each tire when driving through the double-lane-change maneuver using the
driver model with the integrated control of the ATVC and GFASC
Table 7-I summarizes the vehicle response during the double-lane-change
maneuver when the driver model is used with the integrated control of the ATVC and
178
7 Integration of the Advanced Torque Vectoring and Genetic Fuzzy Active Steering
GFASC. The vehicle response is compared to the cases where the driver model is used
with no stability controller, with the GFYMC, with the ATVC, and with the GFASC.
Comparing different parameters of the vehicle response during the double-lane-change
maneuver, it can be seen that the performance of the integrated controller – in all the
decisive parameters that describe the handling, stability, and longitudinal dynamics of the
vehicle – is better than that of either of the individual controllers (namely, the ATVC and
the GFASC). Moreover, with respect to the handling of the vehicle, the integrated control
approach has reduced 
max
and 
max
by about the same amount as the GFYMC. The
maximum lateral acceleration of the vehicle ( a y
max
) is also about the same as it is when
the GFYMC is active; however, when the integrated control system is active, the driver
requires a larger maximum steering wheel angle to negotiate the maneuver. In addition,
the hysteresis of the performance plot (  H ) is about 1.4 times larger than that observed
when the GFYMC is active. However, the speed lost during the maneuver is less than that
lost when the GFYMC is active. Altogether, the integrated control approach is considered
to be very effective at improving the handling and stability characteristics of the vehicle.
Since the least amount of speed is lost during the maneuver when the integrated control
approach is used, it is considered to be the most effective controller for improving the
longitudinal dynamics of the vehicle.
Figure 7-9: Tire slip ratios when driving through the double-lane-change maneuver using the driver model
with the integrated control of the ATVC and GFASC
179
7 Integration of the Advanced Torque Vectoring and Genetic Fuzzy Active Steering
Parameter

max

ay
max
max
 SW
max
 H
vlost
AUTO21EV
26.3o
115.4o/s
8.2m/s2
545o
163.8o/s
20.5m/s
GFYMC
6.2o
31.2o/s
8.4m/s2
108o
21.0o/s
13.2m/s
ATVC
6.1o
36.4o/s
8.4m/s2
140o
35.5o/s
13.5m/s
GFASC
13.6o
60.1o/s
8.4m/s2
211o
79.5o/s
14.6m/s
ATVC+GFASC
7.5o
31.5o/s
8.5m/s2
136o
30.2 o/s
10.3m/s
Table 7-I: Vehicle response during the double-lane-change maneuver using the driver model without a
controller, with the GFYMC, with the ATVC, with the GFASC, and with the integrated control of the
ATVC and GFASC
7.2.2 Step-steer response maneuver
In order to evaluate the performance of the vehicle using the integrated control of the
ATVC and GFASC in a step-steer response maneuver, the vehicle yaw rate, sideslip
angle, and lateral acceleration as functions of time are observed. Figure 7-10-a illustrates
the fixed step-steer input and the equivalent corrective steering input generated by the
GFASC. As can be seen, the intervention of the GFASC is almost the same as that
observed when the GFASC is used on its own (Figure 6-16-a). In other words, the
GFASC is able to match the behaviour of the vehicle to that of the desired bicycle model
without requiring a significant amount of support from the ATVC. As a result, the vehicle
experiences a lateral acceleration of 4.3 m/s2, which is similar to that obtained when the
GFASC is used on its own (Figure 7-10-b).
Figure 7-10: (a) Required steering wheel input and (b) lateral acceleration of the vehicle when driving
through the step-steer maneuver using the integrated control of the ATVC and GFASC
Figure 7-11 illustrates the vehicle yaw rate and sideslip angle when the integrated
control of the ATVC and GFASC is used, and compares the response to that obtained
180
7 Integration of the Advanced Torque Vectoring and Genetic Fuzzy Active Steering
when no stability controller is used, and when the GFYMC, ATVC, and GFASC are
used. As can be seen, the yaw rate and sideslip angle of the vehicle are similar to the
results obtained when the GFASC is active. Table 7-II summarizes the vehicle response
during the step-steer test maneuver. By comparing different parameters of the vehicle
response during this maneuver when it is performed with and without the integrated
control of the ATVC and GFASC, we can conclude that the integrated control approach
is very effective at improving all the decisive parameters of the vehicle that describe its
handling characteristics.
Figure 7-11: Yaw rate (top) and sideslip angle (bottom) of the vehicle when driving through the step-steer
maneuver using the integrated control of the ATVC and GFASC
PO 
 max  ss
 100%
 ss

ta y
Parameter
t
AUTO21EV
0.34s
1.30%
1.43o
0.66s
GFYMC
0.15s
0.00%
1.38o
0.51s
ATVC
0.15s
16.1%
1.36o
0.47s
GFASC
0.15s
2.20%
1.53o
0.53s
ATVC+GFASC
0.15s
2.20%
1.53o
0.53s
max
Table 7-II: Vehicle response during the step-steer maneuver using the driver model without a controller,
with the GFYMC, with the ATVC, with the GFASC, and with the integrated control of the ATVC and
GFASC
7.2.3 Brake-in-turn maneuver
Figure 7-12 illustrates the vehicle trajectory relative to the desired circular path during a
brake-in-turn maneuver, using the driver model with and without the integrated control of
181
7 Integration of the Advanced Torque Vectoring and Genetic Fuzzy Active Steering
Figure 7-12: Desired and actual vehicle trajectories when braking in a turn using (a) the driver model only
and (b) the driver model with the integrated control of the ATVC and GFASC
the ATVC and GFASC. As can be seen, the driver model is able to keep the vehicle on
the predefined circular path while severely braking when the integrated controller is
active, and the lateral deviation of the vehicle from the desired path remains negligible
throughout the maneuver. Figure 7-13-a illustrates the driver‟s steering wheel input as a
function of time, and indicates that the driver model is able to control the vehicle very
smoothly and with little steering effort when the integrated controller is used. This figure
also shows the activity of the active steering controller when using the integrated control
approach as it superimposes a corrective signal atop the driver‟s steering wheel input at
each time step. Comparing this figure to Figure 6-19-a, it can be confirmed that the
integrated control approach requires a smaller corrective steering angle than the GFASC,
which can be attributed to the fact that the ATVC also helps to stabilize the vehicle.
Figure 7-13-b illustrates the lateral acceleration of the vehicle and confirms that the
vehicle remains stable when the integrated control approach is used. This figure also
confirms that the vehicle does not experience any high oscillations at higher lateral
accelerations, as is the case when the ATVC is used on its own. Note that, for clarity, the
driver‟s steering input and the lateral acceleration of the vehicle when no stability
controller is active are not illustrated in Figure 7-13.
Figure 7-14 compares the vehicle yaw rate and sideslip angle when driving
through the brake-in-turn maneuver using the driver model with the GFYMC, the ATVC,
the GFASC, and the integrated control of the ATVC and GFASC. Note that, for clarity,
the yaw rate and sideslip angle of the vehicle when no stability controller is active are not
illustrated. When the integrated control approach is used, the vehicle behaves almost like
182
7 Integration of the Advanced Torque Vectoring and Genetic Fuzzy Active Steering
the desired reference model until the braking action begins, using primarily the GFASC
because the required corrective steering angle remains below 1o. However, once the
braking begins, both the GFASC and the ATVC contribute to minimizing the yaw rate
error. As can be seen in Figure 7-13-a, the GFASC superimposes the driver‟s steering
input with a steering angle of up to 2.7o at 4.3 seconds of the simulation, which is
equivalent to a steering wheel angle of about 48o, assuming a steering ratio of 1:18. In
other words, the activation function engages the ATVC up to 90% of its full potential at
4.3 seconds in order to support the GFASC as it attempts to stabilize the vehicle.
Figure 7-13: (a) Required steering wheel input and (b) lateral acceleration of the vehicle when braking in a
turn using the driver model with the GFYMC, the ATVC, the GFASC, and the integrated control of the
ATVC and GFASC
Figure 7-14: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when braking in a turn
using the driver model with the GFYMC, the ATVC, the GFASC, and the integrated control of the ATVC
and GFASC
Figure 7-15 illustrates the torque of each in-wheel motor during this maneuver.
Until the braking begins, the speed-control driver model requests up to 63 Nm of drive
183
7 Integration of the Advanced Torque Vectoring and Genetic Fuzzy Active Steering
torque from all four motors to keep the vehicle speed constant. When the braking begins,
the ATVC increases the braking torque request on the right wheels and reduces that on
the left wheels; however, at a speed of 70 km/h, the motors are not powerful enough to
provide the motor torques requested by the ATVC. Braking the vehicle in a curve causes
a weight shift to the front and, in this case, right side of the vehicle that considerably
reduces the traction potential of the left tires. Therefore, the slip controllers limit the
braking torque of the front-left wheel between 4 and 4.1 seconds, and that of the rear-left
wheel between 4.1 and 5.3 seconds, in order to avoid wheel lock-up. The slip controller
for the rear-right wheel limits its braking torque between 5.5 and 5.9 seconds in order to
avoid a lock-up situation caused by the high available braking torque and the weight shift
to the front axle. The activation of the slip controllers can be confirmed in Figure 7-16,
which illustrates the slip ratio of each tire. Figure 7-17 shows the traction potential at
each tire and clearly indicates that the traction potentials of the left tires have exceeded
their limits. In other words, although the slip controllers have limited the braking torques
on the left wheels, the high lateral acceleration of the vehicle has caused the resultant tire
forces on the left wheels to exceed their traction potentials. Figure 7-18 illustrates the
front-to-rear torque vectoring ratios and indicates that this controller also supports the
driver in stabilizing the vehicle while braking in a turn, requesting more braking torque
from the rear wheels than the front wheels, thereby reducing the lateral force potential at
the rear axle and increasing that at the front axle. Figure 7-19-a illustrates the vehicle
speed as a function of time and confirms the performance of the speed controller. Figure
7-19-b illustrates the vehicle longitudinal acceleration as a function of vehicle speed, and
confirms the severity of the braking action in this maneuver.
Table 7-III summarizes the vehicle response during the brake-in-turn maneuver
when the integrated control approach is used, and compares it with the performance
observed when no stability controller is used, and when the GFYMC, ATVC, and
GFASC are used. Comparing different parameters of the vehicle response during this
maneuver, it can be seen that the integrated control approach is very effective at
improving all the decisive parameters that describe the handling, stability, and pathfollowing capabilities of the vehicle. The integrated control of the ATVC and GFASC is
able to reduce 
max
, 
max
, and  SW
max
significantly in comparison to those obtained
when no stability controller is used, which indicates that the integrated control approach
184
7 Integration of the Advanced Torque Vectoring and Genetic Fuzzy Active Steering
is very effective at enhancing the vehicle handling during this maneuver. Simultaneously,
a reduction of 
max
and 
max
indicates that the integrated control approach is also very
effective at improving the vehicle stability. Finally, the fact that the maximum lateral
deviation of the vehicle from the desired path remains very small throughout the
maneuver confirms that the integrated control approach enhances the path-following
capability of the vehicle as well.
Figure 7-15: Requested and actual motor torque at each wheel when braking in a turn using the driver
model with the integrated control of the ATVC and GFASC
Figure 7-16: Tire slip ratios when braking in a turn using the driver model with the integrated control of the
ATVC and GFASC
185
7 Integration of the Advanced Torque Vectoring and Genetic Fuzzy Active Steering
Figure 7-17: Traction potential of each tire when braking in a turn using the driver model with the
integrated control of the ATVC and GFASC
Figure 7-18: Front-to-rear torque vectoring ratios when braking in a turn using the driver model with the
integrated control of the ATVC and GFASC
Figure 7-19: (a) Vehicle speed as a function of time when braking in a turn using the driver model with the
integrated control of the ATVC and GFASC, and (b) longitudinal acceleration as a function of vehicle
speed when braking in a turn using the driver model with the GFYMC, the ATVC, the GFASC, and the
integrated control of the ATVC and GFASC
186
7 Integration of the Advanced Torque Vectoring and Genetic Fuzzy Active Steering
Parameter

max

max
ymax
 SW
max
AUTO21EV
126.5o/s
50.1o
3.67m
700o
GFYMC
22.60o/s
4.36o
0.18m
46.4o
ATVC
24.00o/s
4.40o
0.18m
48.0o
GFASC
22.45o/s
4.25o
0.16m
45.7o
ATVC+GFASC
22.45o/s
4.45o
0.17m
46.1o
Table 7-III: Vehicle response during the brake-in-turn maneuver using the driver model without a
controller, with the GFYMC, with the ATVC, with the GFASC, and with the integrated control of the
ATVC and GFASC
7.2.4 Straight-line braking on a -split road
As a final test, the AUTO21EV is driven on a -split road and the driver model attempts
to stop the vehicle in an emergency braking situation. Figure 7-20 illustrates the vehicle
trajectory for this maneuver when no stability controller is active and compares it to the
case when the integrated control of the ATVC and GFASC is used. As can be seen, the
integrated control approach is able to correct the side-pushing effect of the vehicle while
braking on a -split road, and prevents the vehicle from leaving the predefined road. The
braking distance of the vehicle remains the same as it was when the GFASC was used
alone. Looking at Figure 7-21, it is clear that the integrated control approach is able to
limit and, later, diminish the yaw rate and sideslip angle of the vehicle while driving over
the black ice patch, which indicates that the vehicle remains stable during this maneuver.
Note that the yaw rate and sideslip angle of the vehicle when no controller is active have
been omitted from Figure 7-21 for clarity.
Figure 7-20: Desired and actual vehicle trajectories when braking on a -split road while holding the
steering wheel fixed, with and without using the integrated control of the ATVC and GFASC
187
7 Integration of the Advanced Torque Vectoring and Genetic Fuzzy Active Steering
Figure 7-21: Desired and actual vehicle yaw rate (top) and sideslip angle (bottom) when braking on a split road while holding the steering wheel fixed, using the integrated control of the ATVC and GFASC
Figure 7-22 illustrates the fixed steering wheel input and the equivalent corrective
steering wheel angle required to counteract the side-pushing effect of the vehicle, which
is generated by the GFASC. As can be seen, the active steering controller has applied up
to 3o of corrective steering angle, which is equivalent to 54o of steering wheel angle, in
order to correct the side-pushing effect of the vehicle. Thus, the activation function has
engaged the ATVC up to 100% of its full potential in order to support the driver in
stabilizing the vehicle. This level of activation can be confirmed by looking at Figure 723, which illustrates the motor torques for all four wheels. As can be seen, between 0.7
and 0.9 seconds of the simulation, the left-to-right torque vectoring controller has
requested more braking torque from the left motors than the right motors in order to
counteract the side-pushing effect of the vehicle. Note that the left motors are not able to
generate the high braking torques requested by the ATVC due to their performance limits
at high speeds, but the braking torques on the right motors are adjusted accordingly. The
opposite situation occurs at 1.15 seconds, when a corrective steering angle of up to -3o is
generated by the GFASC. In this case, the ATVC requests more braking torque from the
right motors than the left ones which are, once again, unable to meet the demands of the
ATVC.
188
7 Integration of the Advanced Torque Vectoring and Genetic Fuzzy Active Steering
Figure 7-22: Equivalent corrective steering wheel input applied by the GFASC when using the integrated
control of the ATVC and GFASC, augmenting the fixed steering input in order to correct the side-pushing
effect of the vehicle when braking on a -split road
Comparing Figures 7-23 and 5-20, it can be confirmed that, when using the
integrated control approach, the ATVC only becomes activated when the GFASC reaches
its actuator range limits. Looking at Figure 7-23, it is also apparent that the slip
controllers on the left wheels have limited the braking torques to 20 Nm (between 0.7 and
1.15 seconds) in order to prevent wheel lock-up while, at the same time, ensuring the
maximum possible braking force is being applied when braking on the black ice patch.
The activation of the slip controllers is confirmed in Figure 7-24, which illustrates the tire
slip ratios while braking on the -split road. Note that, later in the simulation, due to the
weight shift to the front axle, the motor torques at the rear axle are limited by the
maximum possible motor torques (calculated by equation (5.24) in Chapter 5) to prevent
wheel lock-up at higher deceleration rates. This observation is confirmed in Figure 7-25,
which illustrates the traction potential for each tire. As can be seen, the traction potentials
of the rear tires are restricted and do not exceed their limits. Figure 7-26 illustrates the
torque distribution applied by the front-to-rear torque vectoring controller. As can be
seen, this controller has requested that the front motors generate up to 52.5% of the
required corrective yaw moment in order to correct the undesirable side-pushing effect
when driving over the black ice patch. Requesting more torque from the front motors
reduces the lateral force potential on the front axle and increases that on the rear axle. The
asymmetric lateral force potentials on the front and rear axles also help to generate the
required corrective yaw moment around the vertical axis of the vehicle.
189
7 Integration of the Advanced Torque Vectoring and Genetic Fuzzy Active Steering
Figure 7-23: Requested and actual motor torque at each wheel when braking on a -split road while holding
the steering wheel fixed, using the integrated control of the ATVC and GFASC
Figure 7-24: Tire slip ratios when braking on a -split road while holding the steering wheel fixed, using
the integrated control of the ATVC and GFASC
Table 7-IV summarizes the vehicle response during the straight-line braking on a
-split road maneuver when holding the steering wheel fixed and using the integrated
control of the ATVC and GFASC. Comparing different parameters of the vehicle
response during this maneuver, it can be seen that the integrated control approach is very
effective at improving all the decisive parameters that describe the stability, path190
7 Integration of the Advanced Torque Vectoring and Genetic Fuzzy Active Steering
following, and braking performance of the vehicle. In particular, the integrated control
approach has reduced the 
max
and 
max
values significantly, which indicates an
enhancement in the stability of the vehicle. The braking distance of the vehicle has also
been reduced considerably by the integrated control approach, indicating an improvement
in the longitudinal dynamics of the vehicle. The integrated control approach reduces the
maximum lateral deviation of the vehicle as well, and prevents the vehicle from leaving
the predefined road throughout the maneuver.
Figure 7-25: Traction potential of each tire when braking on a -split road while holding the steering wheel
fixed, using the integrated control of the ATVC and GFASC
Figure 7-26: Front-to-rear torque vectoring ratios when braking on a -split road while holding the steering
wheel fixed, using the integrated control of the ATVC and GFASC
191
7 Integration of the Advanced Torque Vectoring and Genetic Fuzzy Active Steering
Parameter

max

max
xbraking
ymax
AUTO21EV
24.2o
63.4o/s
48.4m
15.9m
GFYMC
0.40o
1.85o/s
44.5m
0.46m
ATVC
1.70o
9.70o/s
47.3m
2.70m
GFASC
1.60o
2.50o/s
45.7m
0.36m
ATVC+GFASC
1.45o
2.35o/s
45.6m
0.27m
Table 7-IV: Vehicle response during the straight-line braking on a -split road maneuver while holding the
steering wheel fixed without a controller, with the GFYMC, with the ATVC, with the GFASC, and with the
integrated control of the ATVC and GFASC
7.3.
Chapter summary
In this chapter, an activation function is introduced that integrates the control efforts of
the ATVC and the GFASC. A variety of test maneuvers are simulated to demonstrate the
performance and effectiveness of this integrated control approach. Table 7-V provides a
subjective evaluation of the effectiveness of the integrated control of the ATVC and
GFASC based on different test maneuvers.
Table 7-V: Subjective evaluation of the effectiveness of the integrated control of the ATVC and GFASC
based on different test maneuvers (3 = very effective, 2 = effective, 1 = effective to some extent, 0 =
ineffective)
Figure 7-27 compares the performance and effectiveness of the GFYMC, ATVC,
GFASC, and the integrated control of the ATVC and GFASC based on different test
maneuvers (as listed in Tables 4-VII, 5-V, 6-VI, and 7-V, respectively). Note that the
GFYMC is considered to be the ideal stability controller against which the performance
and effectiveness of all other controllers are compared. As can be seen, the performance
and effectiveness of the integrated control approach exceeds that of the individual control
192
7 Integration of the Advanced Torque Vectoring and Genetic Fuzzy Active Steering
systems in all four categories. In addition, the integrated control of the ATVC and
GFASC demonstrates the same performance as the GFYMC in the stability and
longitudinal dynamics categories. Although the performance of the integrated control
approach in the handling category cannot match that of the GFYMC, the integrated
controller demonstrates better performance in the path-following category.
Handling
Path-following Capability
3
3
2.5
2.5
2
2
1.5
1.5
1
1
0.5
0.5
0
0
GFYMC
ATVC
GFASC
GFYMC
ATVC+GFASC
Stability
ATVC
GFASC
ATVC+GFASC
Longitudinal Dynamics
3
3
2.5
2.5
2
2
1.5
1.5
1
1
0.5
0.5
0
0
GFYMC
ATVC
GFASC
GFYMC
ATVC+GFASC
ATVC
GFASC
ATVC+GFASC
Figure 7-27: Subjective evaluation of the performance and effectiveness of the GFYMC, ATVC, GFASC,
and integrated control of the ATVC and GFASC based on different test maneuvers (3 = very effective, 2 =
effective, 1 = effective to some extent, 0 = ineffective)
193
8
Conclusions and Future Work
The vision for the future automotive chassis is to interconnect the lateral, longitudinal,
and vertical dynamics by controlling the driving, braking, steering, and damping actions
of each wheel separately. Drive-by-wire technology is currently being used in concept
vehicles for the electronic control and actuation of braking, steering, suspension, and
drive systems. These technologies attract strong interest from the automotive industry
but, for the most part, are not yet commercially available.
The chassis control systems developed today are distinguished by the way the
individual subsystems work in order to provide vehicle stability and control. Since the
influences of individual subsystems are interconnected and coupled through the tire-road
characteristics, each individual subsystem often influences two of the three vehicle
dynamics domains (namely, the longitudinal, lateral, or vertical dynamics). Therefore, by
installing more than one chassis control system into a vehicle, it must be ensured that the
systems function together properly and do not interfere with each other. This level of
cooperation requires that the individual chassis control systems are integrated and
networked together using a high-level supervisory control system that can monitor and
coordinate the behaviour of the individual subsystems, assigning appropriate tasks to
each of them depending on the driving maneuver and road conditions. Ultimately, the
optimum driving dynamics can only be achieved when the tire forces on all wheels and in
all three directions can be influenced and controlled precisely. Only in this way can the
highest level of active safety, ride quality, and driving pleasure be achieved in every
possible driving situation, up to the limits of adhesion.
Recently, mostly due to global warming concerns and high oil prices, electric
vehicles have attracted a great deal of interest as an elegant solution to environmental and
energy problems. In fact, we are likely to see more changes in automotive powertrains in
the next five years than we have seen in the last 100 years. Many car companies have
already revealed their plans to bring plug-in hybrid and battery electric vehicles to the
commercial market in the next five years [Adc10]. In addition to the fact that electric
vehicles have no tailpipe emissions and are more efficient than internal combustion
engine vehicles, they represent an exciting platform on which to apply advanced motion
194
8
Conclusions and Future Work
control techniques, since the torque of an electric motor can be generated and controlled
quickly and precisely in an efficient way.
The prime focus of this thesis is to develop effective control strategies to improve
driving dynamics and safety based on the philosophy of individually monitoring and
controlling the tire forces on each wheel. In this regard, an electric vehicle with four
direct-drive in-wheel motors and an active steering system is designed and modelled in
the ADAMS/View environment. This platform represents a two-passenger electric allwheel-drive urban vehicle (AUTO21EV) that has a similar configuration to the
commercially-available Smart fortwo. The front and rear suspension systems of the
AUTO21EV are designed, analyzed, and tuned to have a high amount of flexibility in
their kinematic layouts, providing self-steering behaviour, Ackermann steering, anti-squat
mechanism, and maintaining the maximum lateral force potential on the tires when
cornering. The dynamic characteristics of the suspension systems are also analyzed and
optimized to minimize the effects of the large sprung mass and the vibrations and
dynamic loads that are transmitted to the chassis and suspension components. The full
kinematic model of the AUTO21EV is later transformed into a dynamic model in
ADAMS/View by equipping the vehicle with Pacejka tire models and introducing a road
model. The results of these analyses are presented in Appendix A.
In Chapter 2, a number of different open-loop and closed-loop test maneuvers are
identified that can provide important information about different aspects of the dynamic
behaviour of the vehicle and the performance and effectiveness of individual chassis
control systems. These test maneuvers are chosen such that all aspects of the vehicle
dynamics are addressed. In addition, a comprehensive evaluation method is presented that
combines the results of different test maneuvers and evaluates them as a whole to identify
the advantages of each control method. Since closed-loop test maneuvers are used in this
work, two driver models are developed and implemented in the simulation environment
for providing the driver inputs required to successfully negotiate the maneuvers. In this
regard, a multiple-preview-point path-following driver model is developed that can look
ahead and adjust the steering wheel angle based on the lateral offset between predefined
preview points on the optical lever of the driver and the desired path. Moreover, a gain
scheduling PID controller is developed for the speed-control driver model, which can
adjust the speed of the vehicle to that requested by the driver by controlling the torques of
195
8
Conclusions and Future Work
the in-wheel motors. The performance and effectiveness of the driver models are
evaluated and confirmed using some standard test maneuvers. It has been confirmed that
both the path-following and speed-control driver models are able to negotiate complex
test maneuvers, such as the ISO double-lane-change maneuver and brake-in-turn
maneuver, very well.
In Chapter 3, an advanced fuzzy slip controller is developed for the AUTO21EV
that combines the functionalities of an ABS, a TCS, and the brake system of the vehicle.
This slip controller is designed based on the idea of limiting the maximum possible tire
slip ratio to a fixed, predefined amount in order to generate the maximum possible
braking or traction force while decelerating or accelerating, respectively, on different
road conditions. The performance and functionalities of the developed fuzzy slip control
system are evaluated using several standard test maneuvers. It has been confirmed that
the fuzzy slip controller is able to fulfill the functionalities of the ABS and conventional
hydraulic brake systems by outperforming the regulations on braking systems for
passenger vehicles. It has been also confirmed that the fuzzy slip controller is able to
maximize the traction potential of each tire when accelerating.
In Chapter 4, a 14-degree-of-freedom vehicle model is developed to allow for the
testing of different control strategies, and for applying a genetic tuning algorithm to the
development of the fuzzy yaw moment controller. Based on this simplified vehicle
model, a fuzzy yaw moment controller is developed for the AUTO21EV that determines
the corrective yaw moment required to minimize the sideslip and yaw rate errors of the
vehicle, comparing the actual values to those obtained using a reference model, with the
ultimate objective of following the desired trajectory requested by the driver. The fuzzy
yaw moment controller is designed as a high-level supervisory module that assigns tasks
to low-level actuators and controllers, employing an integrated chassis control
management philosophy. However, at this stage of development, the calculated corrective
yaw moment is applied directly to a torque driver that is positioned at the center of mass
and around the vertical axis of the vehicle. Although this torque driver symbolizes an
unrealistic control system, the fuzzy yaw moment controller represents the ideal stability
control system, in which any corrective yaw moment can be generated without being
restricted by the actuator range limits or performance. In addition, a novel hybrid geneticfuzzy tuning technique is developed to optimize the shape and distribution of the
196
8
Conclusions and Future Work
membership functions of the fuzzy controller. By combining a multi-criteria genetic
algorithm with the fuzzy yaw moment controller, a more powerful genetic fuzzy yaw
moment controller is produced that provides better performance. The effectiveness and
performance of the genetic fuzzy yaw moment controller is evaluated using a variety of
test maneuvers. In particular, it has been confirmed through several maneuvers that the
genetic fuzzy yaw moment improves the handling, stability, path-following, and
longitudinal dynamics of the vehicle considerably in comparison to those obtained when
no stability controller is active.
Chapter 5 describes the development of an advanced low-level torque vectoring
controller that receives tasks from the previously developed high-level genetic fuzzy yaw
moment controller. The objective of the advanced torque vectoring controller is to
generate the required corrective yaw moment through the torque intervention of the
individual in-wheel motors to stabilize the vehicle during normal and emergency driving
maneuvers. A novel algorithm is developed for the left-to-right torque vectoring control
on each axle, and a PD controller is introduced for the front-to-rear torque vectoring
distribution action. Again, the effectiveness and performance of the advanced torque
vectoring controller is evaluated using several test maneuvers. It has been confirmed that,
although the advanced torque vectoring controller has improved all the decisive
parameters that describe the handling, stability, path-following, and longitudinal
dynamics of the vehicle in comparison to the results obtained when no stability controller
is active, it cannot be considered as effective as the genetic fuzzy yaw moment controller,
which represents the ideal case but is not directly realizable. In addition, it has been
observed that the actuation of the in-wheel motors when stabilizing the vehicle near its
handling limits would cause severe oscillation in the yaw rate response, which would be
perceived by the driver as being disruptive and annoying. Therefore, in practice, the
advanced torque vectoring controller should not be used for correcting small yaw rate
errors.
In Chapter 6, a novel fuzzy active steering controller is developed, and a reliable
method to tune its membership functions in an optimized way is presented, which can
make it unnecessary to perform much of the expensive field testing that would otherwise
be used to tune a stability control system. Fuzzy logic is chosen for the active steering
controller because it represents a robust and flexible inference method that is well suited
197
8
Conclusions and Future Work
for tackling the highly nonlinear behaviour inherent in vehicle dynamics. The rule base of
the fuzzy active steering controller is described in vague linguistic terms using expert
knowledge, which suits the nonlinear behaviour of vehicle dynamics. A novel multicriteria genetic algorithm, which is similar to the one introduced in Chapter 4, is
presented to optimize the distribution of the fuzzy membership functions of the input and
output variables in order to improve the performance of the fuzzy active steering
controller. Again, the performance and effectiveness of the genetic fuzzy active steering
controller are evaluated using several test maneuvers. It has been confirmed that the
genetic fuzzy active steering controller can improve all the decisive parameters that
describe the handling, stability, path-following, and longitudinal dynamics of the vehicle
when compared to the case in which no stability controller is active; however, it is not as
effective as the genetic fuzzy yaw moment controller. In addition, it has been confirmed
that the performance and effectiveness of the genetic fuzzy active steering controller is
superior in the vehicle handling, path-following, and longitudinal dynamics when
compared to the results obtained using the advanced torque vectoring controller.
However, due to the actuator rage limits of the genetic fuzzy active steering controller,
the advanced torque vectoring controller demonstrates better performance in the stability
category.
Chapter 7 addresses the integration of the developed advanced torque vectoring
controller and genetic fuzzy active steering controller. Comparing the performance and
effectiveness of the individual control systems, it has been found that the intervention of
the genetic fuzzy active steering controller is considered to be a continuous process, and
is not perceived by the driver as being annoying. It is also advantageous to employ
steering intervention rather than braking or driving individual wheels when controlling
the vehicle on slippery surfaces, since steering intervention requires less frictional force
between the tire and the road to generate a corrective yaw moment. However, the genetic
fuzzy active steering controller suffers from its limited range of effectiveness (caused by
actuator restrictions). The advanced torque vectoring controller, on the other hand, is
found to be very effective at improving the vehicle stability and handling, even when the
vehicle is driven near its handling limits. However, it has also been observed that the
actuation of the in-wheel motors to generate a corrective yaw moment can cause some
oscillations in the vehicle states, which might be perceived by the driver as being
198
8
Conclusions and Future Work
disruptive. To overcome the shortcomings of each of these control systems, a novel
activation function is introduced that takes advantage of the strengths of each chassis
control system and distributes the required control effort between the in-wheel motors
and the active steering system based on the difference between the desired and actual
behaviour of the vehicle. The performance and effectiveness of the integrated approach
are evaluated using several maneuvers. It is confirmed that the integrated control
approach has superior performance over the individual control systems in all chosen test
maneuvers. The integrated control of the advanced torque vectoring and genetic fuzzy
active steering controller has demonstrated the same performance as the genetic fuzzy
yaw moment controller in the stability and longitudinal dynamics categories. Moreover,
although the performance of the integrated control approach in the handling category
cannot match that of the genetic fuzzy yaw moment controller, the integrated controller
demonstrates better performance in the path-following category.
Although all of the control strategies developed in this work have demonstrated a
good performance and effectiveness at increasing the vehicle stability, handling, pathfollowing, and longitudinal dynamics, further effort has been invested into discovering an
optimal method of generating the required corrective yaw moment using the available
actuators and controllers. In this regard, a more elegant approach can be found in the
aerospace and marine vessel industries, which deal with over-actuated systems, and is
called the „control allocation‟ technique [Hae03, Dur93, And07, Ore06]. In this method,
the control effort is determined in two separate steps: in the first step, conventional
control laws are used to determine the total control effort that must be produced; in the
second step, a control allocator is used to map the total control demand onto individual
actuator settings, taking into account various actuator constraints. Therefore, a logical
future extension of this work should involve the use of an optimization-based control
allocation method that can allocate the required corrective yaw moment generated by the
genetic fuzzy yaw moment controller between the in-wheel motors and the active steering
controller in an optimal way. It would be very interesting to compare the performance
and effectiveness of the control allocation method with the results obtained using the
integrated control approach developed in this work. In this way, the effectiveness of each
control system can be compared against an optimization based control allocation method
199
8
Conclusions and Future Work
and better conclusions can be made about the operation and effectiveness of the
developed controllers in this work.
It is also very important to examine the robustness of the developed control
systems against internal and external disturbances. This should be done both in the
simulation environment and, later, through various field testing of a physical prototype of
the AUTO21EV. In this regard, a parameter sensitivity analysis should be performed to
understand the most important model parameters and the sensitivity of the different
control systems with respect to these parameters. Note that the sensitivity of the control
systems against the various parameters of the Magic Tire Formula should contain the
major part of this analysis. Moreover, the sensitivity of the control systems to different
sampling times has to be analyzed.
As mentioned earlier, there is also an immediate need for a friction coefficient
estimator, since the bicycle model and the maximum torque estimator of the advanced
torque vectoring controller require knowledge of the current friction coefficient between
the tire and the road in order to adequately adapt to various road conditions.
Although the performance of the advanced fuzzy slip controller and the genetic
fuzzy active steering controller have been confirmed in a driving simulator set up, the
performance of the advanced torque vectoring controller and the integrated control
approach of the genetic fuzzy active steering controller and the advanced torque
vectoring controller have to be confirmed in the driving simulator environment as well.
Ultimately, the performance and effectiveness of all of the developed control systems
have to be examined, analyzed, and confirmed on a physical prototype of the
AUTO21EV using a human driver. In this regard, the human driver can subjectively
evaluate the effectiveness of each candidate controller in real driving conditions and
compare his evaluations with those performed using a driver model in this work.
200
References
[Ack98] Ackermann, J.: “Active steering for better safety, handling, and comfort”,
Conference on Advances in Vehicle Control and Safety, Amiens, France, 1998.
[Ack99] Ackermann, J., Odenthal, D., and Bünte, T.: “Advantages of active steering for
vehicle dynamics control”, 32nd International Symposium on Automotive Technology
and Automation, Vienna, pp. 263-270, 1999.
[ADA02] ADAMS/Tire manual: “Using ADAMS/Tire”, Mechanical Dynamics, Part Nr.
120TIRG-01, 2002.
[Adc10] Adcock, I., Bailey, S., and Simanaitis, D.: “Propulsion Prognostications: Who‟s
coming out with what – and when?”, Road & Track magazine, Vol. 61, No. 7, March
2010.
[Aga03] Aga, M. and Okada, A.: “Analysis of Vehicle Stability Control (VSC)‟s
effectiveness from accident data”, Paper Number 541, Proceedings of the 18th
International Technical Conference on the Enhanced Safety of Vehicle, National
Highway Traffic Safety Administration, Washington DC, 2003.
[Aks06] Akshay, S.: Special ADAMS/Car Training for Universities, MSC Software,
2006.
[Alb96] Alberti, V. and Babbel, E.: “Improved driving stability by active braking of the
individual wheels”, Proceedings of the International Symposium on Advanced Vehicle
Control, Aachen, pp. 717-732, 1996.
[And06] Andreasson, J., Knobel, C., and Bünte, T.: “On road vehicle motion control –
striving towards synergy”, Proceedings of the 8th International Symposium on Advanced
Vehicle Control, AVEC060209, Taiwan, 2006.
[And07] Andreasson, J.: On Generic Road Vehicle Motion Modelling and Control, Ph.D.
Dissertation, Royal Institute of Technology, Stockholm, Sweden, 2007.
[ATZ06] ATZ magazine: “Automobiltechnische Zeitschrift”, ISSN 0001-2785-10810,
May, 2006.
[Bau99] Bauer, H. et al.: Driving-safety Systems, Society of Automotive Engineers and
Robert Bosch GmbH, 2nd edition, Warrendale, 1999.
[Bei00] Beiker, S.: Improving the Vehicle Dynamics Behaviour through Integrated
Control Systems, (“Verbesserungsmoeglichkeiten des Fahrverhaltens von Pkw durch
201
References
zusammenwirkende Regelsysteme”), Ph.D. Dissertation, Technical University of
Braunschweig, Germany, 2000.
[Bix95] Bixel, R., Heydinger, G.J., Durisek, N. J., and Guenther, D.A.: “Developments in
vehicle center of gravity and inertial parameter estimation and measurement”, SAE
World Congress, 950356, 1995.
[Blu04] Blundell, M. and Harty, D.: The Multibody Systems Approach to Vehicle
Dynamics, Society of Automotive Engineers, 2004.
[Bod06] Bode, K.H.: Preliminary Suspension Design and Stability Control Strategies for
an Electric Vehicle with Four Independently Driven In-Wheel Motors, Project Thesis,
University of Waterloo, 2006.
[Bol95] Bolton, W.: Mechatronics – Electronic Control Systems in Mechanical
Engineering, Longman Scientific and Technical, 1995.
[Bos07] Bosch Automotive Handbook, 7th edition, Robert Bosch GmbH, Plochingen,
2007.
[Bow93] Bowman, J.E. and Law, E.H.: “A feasibility study of an automotive slip control
braking system”, SAE World Congress, 930762, Detroit, 1993.
[Bra94] Brandt, B.: Build Your Own Electric Car, TAB Books, 1994.
[Bur04] Burton, D., Delaney, A., Newstead, S., Logan, D., and Fildes, B.: “Effectiveness
of ABS and vehicle stability control systems”, Royal Automobile Club of Victoria
(RACV) Ltd., Report Number 04/01, April 2004.
[Bur93] Burckhardt, M.: Chassis and Suspension Design: Slip Control Systems
(Fahrwerktechnik: Radschlupfregelsysteme), Vogelverlag, Wuerzburg, 1993.
[Cas96] Casey, J.: Exploring Curvature, Friedrich Vieweg and Sohn Verlag, Wiesbaden,
Germany, 1996.
[Cor01] Cordon, O., Herrera, F., Hoffmann, F., and Magdalena, L.: Genetic Fuzzy
Systems: Evolutionary Tuning and Learning of Fuzzy Knowledge Bases (Advances in
Fuzzy Systems - Applications and Theory), 19, World Scientific Publishing, 2001.
[Cor04] Cordon, O., Gomide, F., Hoffmann, F., and Magdalena, L.: “Ten years of genetic
fuzzy systems: current framework and new trends”, Fuzzy Sets and Systems, 141, pp.
5-31, 2004.
[Cun89] Cundy, H. and Rollett, A.: “Lissajous figures”, Section 5.5.3 in Mathematical
Models, 3rd edition, Tarquin Publication, Stradbroke, England, pp. 242-244, 1989.
202
References
[Dan04] Dang, J.: Preliminary Results Analyzing Effectiveness of Electronic Stability
Control (ESC) Systems, DOT HS 809 790, 2004.
[Dix96] Dixon, J.C.: Tires, Suspension, and Handling, Society of Automotive Engineers,
2nd edition, 1996.
[Don95] Donges, E.: “Supporting drivers by chassis control systems”, in Smart Vehicles,
J.P. Pauwelussen, H.B. Pacejka (eds.), pp. 276-296, Delft, 1995.
[Dur03] Durali, M. and Bahramzadeh, Y.: “Vehicle stability improvement using fuzzy
controller and neural-network slip angle observer”, SAE World Congress, 2003-01-2883,
Detroit, 2003.
[Dur93] Durham, W.C.: “Constrained control allocation”, Journal of Guidance, Control,
and Dynamics, 16(4), pp. 717-725, 1993.
[Elb04] Elbers, C., Ersoy, M., and Fecht, N.: Automotive Chassis Technology –
Fundamentals, concepts, processes and trends, ZF Lemfoerder Fahrwerktechnik, printed
by the Verlag Moderne Inductrie, 2004.
[Far04] Farmer, C.: “Effect of electronic stability control on automobile crash risk”,
Traffic Injury Prevention, 5, pp. 317-325, 2004.
[FMV07] FMVSS No. 126, Electronic Stability Control Systems; Controls and Displays,
Docket No. NHTSA–200727662, 2007.
[Gil92] Gillespie, T.D.: Fundamentals of Vehicle Dynamics, Society of Automotive
Engineers, 1992.
[Gol89] Goldenberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine
Learning, Addison-Wesley, 1989.
[Gor03] Gordon, T.: “Integrated control methodology for road vehicles”, Vehicle System
Dynamics, 40(1-3), pp. 157-190, 2003.
[Gre06] Green, P. and Woodrooffe, J.: The Effect of Electronic Stability Control on
Motor Vehicle Crash Prevention, UMTRI200612, Transportation Research Institute,
University of Michigan, 2006.
[Gri98] Gribben, C.: Debunking the Myth of EVs and Smokestacks, Electric Vehicle
Association of Greater Washington, D.C., 1998.
[Guo82] Guo, K.H.: “A statistical analysis of vehicle vibration and dynamic loads, and
selection of suspension design parameters”, Technical Report UM-MEAM-82-15, Dep.
of Mech. Eng., University of Michigan, Ann Arbor, 1982.
203
References
[Guo93] Guo, K. and Guan, H.: “Modeling of driver/vehicle directional control system”,
Vehicle System Dynamics, 22(3-4), pp. 141-184, 1993.
[Gur99] Gurocak, H.B.: “A genetic-algorithm-based method for tuning fuzzy logic
controllers”, Fuzzy Sets and Systems, 108(1), pp. 39-47, 1999.
[Hae03] Haerkegrad, O.: Backstepping and Control Allocation with Applications to
Flight Control, Ph.D. Thesis, University of Linkoping, 2003.
[Ham03] Hammett R.C. and Babcock, P.S.: “Achieving 10-9 dependability with drive-bywire systems” SAE World Congress, 2003-01-1290, Detroit, 2003.
[Han94] Hanselman, D.C.: Brushless Permanent Magnet Motor Design, McGraw-Hill,
New York, 1994.
[Her96] Herrera, F. and Lozano, M.: “Adaptation of genetic algorithm parameters based
on fuzzy logic controllers”, in Genetic Algorithms and Soft Computing, F. Herrera and
J.L. Verdegay (eds.), Physica-Verlag, pp. 95-125, 1996.
[Hor04] Hori, Y.: “Future vehicle driven by electricity and control – research on four
wheel motored UOT Electric March II”, IEEE Transactions on Industrial Electronics,
51(5), pp. 954-962, 2004.
[Hro81] Hrovat, D. and Hubbard, M.: “Optimum vehicle suspensions minimizing RMS
rattle space, sprung-mass acceleration and jerk”, Journal of Dynamic Systems
Measurement and Control, ASME, 103(3), pp. 228-236, 1981.
[Ise02] Isermann, R., Schwarz, R., and Stölzl, S.: “Fault-tolerant drive-by-wire systems”,
IEEE Control Systems Magazine, 2002.
[ISO82] ISO 4138: Passenger cars – Steady-state Circular Test Procedure, 1982.
[ISO85] ISO 7975: Passenger cars – Braking in a Turn: Open-loop Test Procedure, 1985.
[Jal04] Jalali, K.: The Concept and Development of an Optimized Actuator for the Clutch
of a Transfer Case, Diploma Thesis, RWTH Aachen, 2004.
[Jal05] Jalali, K.: “Design, Optimization, and Kinematics Analysis of a Front DoubleWishbone Suspension Using ADAMS/View”, ME752 course project report, University
of Waterloo, 2005.
[Jal07] Jalali, K., Lambert, S., and McPhee, J.: “Optimization of a vehicle suspension
using a genetic algorithm method”, 21st Canadian Congress of Applied Mechanics,
CANCAM, 2007.
204
References
[Jal10] Jalali, K., Uchida, T., Lambert, S., and McPhee, J.: “Development of an advanced
slip controller and an active steering system for an electric vehicle with in-wheel motors
using soft computing techniques”, awaiting publication, 2010.
[Jan98] Jantzen, J.: “Design of fuzzy controllers”, Technical University of Denmark,
Department of Automation, Tech. Report Number 98-E 864 (design), 19 August, 1998.
[JB04] JB: “Drive-by-Wire Pininfarina Autosicura  White Paper”, Pi Technology, UK,
2004.
[Jur06] Jurgen, R.K.: Electronic Braking, Traction, and Stability Control, Volume 2, SAE
International, 2006.
[Kar04] Karray, F.O. and de Silva, C.: Soft Computing and Intelligent Systems Design,
Pearson Education Limited, 2004.
[Kie05] Kiencke, U. and Nielsen, L.: Automotive Control Systems for Engine, Driveline,
and Vehicle, 2nd edition, Springer, 2005.
[Kno99] Knoop, M., Leimbach, K.D., and Schroeder, W.: “Increased driving comfort and
safety by electric active steering”, Active Safety TOPTEC, Wien, September, 1999.
[Koe04] Koehn, P. and Echrich, M.: “Active steering – The BMW approach towards
modern steering technology”, SAE World Congress, 2004-01-1105, Detroit, 2004.
[Koe06] Koehn, P., Eckrich, M., Smakman, H., and Schaffert, A.: “Integrated chassis
management: Introduction into BMW‟s approach to ICM”, SAE World Congress, 200601-1219, Detroit, 2006.
[Lib05] Liebemann, E.K., Meder, K., Schuh, J., and Nenninger, G.: “Safety and
performance enhancement: The Bosch Electronic Stability Control (ESP)”, Paper
Number 05-0471, International Technical Conference of the Enhanced Safety of Vehicles
(ESV), Washington, DC, 2005.
[Lie05] Lie A., Tingvall, C., Krafft, M., and Kullgren, A.: “The effectiveness of ESC
(Electronic Stability Control) in reducing real life crashes and injuries”, Paper Number
050135, Proceedings of the 19th International Technical Conference on the Enhanced
Safety of Vehicle, National Highway Traffic Safety Administration, Washington DC,
2005.
[Mac96] MacAdam, C.C. and Johnson, G.F.: “Application of elementary neural networks
and preview sensors for representing driver steering control behavior”, Vehicle System
Dynamics, 25(1), pp. 3-30, 1996.
205
References
[Mam02] Mammar, S. and König, D.: “Vehicle handling improvement by active
steering”, Vehicle System Dynamics, 38(3), pp. 211-242, 2002.
[Man07] Manning, W.J. and Crolla, D.A.: “A review of yaw rate and sideslip controllers
for passenger vehicles”, Transactions of the Institute of Measurement and Control, 29(2),
pp. 117-135, 2007.
[Mar02-a] Marshek, K., Cuderman II, J., and Johnson, M.: “Performance of anti-lock
braking system equipped passenger vehicles - Part I: Braking as a function of brake pedal
application force”, SAE World Congress, 2002-01-0304, Detroit, 2002.
[Mar02-b] Marshek, K., Cuderman II, J., and Johnson, M.: “Performance of anti-lock
braking system equipped passenger vehicles - Part II: Braking as a function of initial
vehicle speed in braking maneuver”, SAE World Congress, 2002-01-0307, Detroit, 2002.
[Maz01] Mazzae, E.N., Garrott, W.R., Barickman, F., Ranney, T.A., and Snyder, A.:
“NHTSA light vehicle anti-lock brake system research program-Task 7.1: Examination of
ABS-related behavioral adaptation - License plate study”, DOT HS 809 430, November
2001.
[McP05] McPhee, J.: Unified Modeling Theories for the Dynamics of Multidisciplinary
Multibody Systems, in Advances in Computational Multibody Systems, J. Ambrosio
(ed.), Springer-Verlag, pp. 129-158, 2005
[Mil02] Milliken W.F. and Milliken, D.L.: Chassis Design: Principles and Analysis 
Based on Unpublished Technical Notes by Maurice Olley, Society of Automotive
Engineers, 2002.
[Mil95] Milliken, W.F. and Milliken, D.L.: Race Car Vehicle Dynamics, Society of
Automotive Engineers, Warrendale, 1995.
[Mit82] Mitschke, M.: Dynamic der Kraftfahrzeuge, Band A, Springer Verlag, 1982.
[MMG10]
L-3
Communications
Magnet-Motor
GmbH,
Starnberg,
Germany,
http://www.magnet-motor.de, 2010.
[Oez95] Oezguener, O., Uenyelioglu, K.A., and Hatipoglu, C.: “An analytical study of
vehicle steering control”, Proceedings of the 4th IEEE Conference on Control
Applications, pp. 125-130, 1995.
[Ore06] Orend, R.: Integrierte Fahrdynamikregelung mit Einzelradaktorik – Ein Konzept
zur Darstellung des fahrdynamischen Optimums, Ph.D. Dissertation, University of
Erlangen-Nuernberg, Erlangen, 2006.
206
References
[Pac02] Pacejka, H.B.: Tire and Vehicle Dynamics, SAE International, Warrendale,
2002.
[Pac97] Pacejka, H.B. and Besselink, I.J.M.: “Magic formula tire model with transient
properties”, Vehicle System Dynamics, 27 (Suppl.), pp. 234-249, 1997.
[Pai05] Paine, M.: “Electronic stability control: Review of research and regulations”,
Vehicle Design and Research Pty Limited, Report Number G248, June, 2005.
[Pel05] Pelchen, C., Zdych, R., Baasch, D., and Kubalczyk, R.: “Improvement of vehicle
agility and safety by means of wheel torque based driving dynamics”, 14th Aachen
Colloquium, Automobile and Engine Technology, 2005.
[Pen96] Peng, H. and Hu, J.S.: “Traction/braking force distribution for optimal
longitudinal motion during curve following”, Vehicle System Dynamics, 26, pp. 301-320,
1996.
[Pet05] Petersen, W.: “Development of a tool for rapid design and analysis of trailing and
semi-trailing arm suspensions”, Project Thesis, University of Waterloo, 2005.
[Pil89] Pillay, P. and Krishnan, R.: “Modeling, simulation, and analysis of permanent
magnet motor drives, Part I: The permanent-magnet synchronous motor drive”, IEEE
Transactions on Industry Applications, 25(2), pp. 265-273, 1989.
[Rah85] Rahman, M.A. and Slemon, G.R.: “Promising applications of neodymium boron
iron magnets in electrical machines”, IEEE Transactions on Magnetics, MAG-21(5), pp.
1712-1716, 1985.
[Rei02] Reimpell, J., Stoll, H., and Betzler, W.: The Automotive Chassis: Engineering
Principles, Society of Automotive Engineering, 2nd edition, 2002.
[Rei04] Reinelt, W., Klier, W., Reimann, G., Schuster, W., and Grossheim, R.: “Active
front steering (Part 2): safety and functionality”, SAE World Congress, 2004-01-1101,
Detroit, 2004.
[Rey03] Reynolds, B. and Wheals, J.: “Torque vectoring driveline: Design, simulations,
capabilities and control”, 12th Aachen Colloquium, Automobile and Engine Technology,
pp. 1497-1523, 2003.
[Rie05] Rieger, G., Scheef, J., Becker, H., Stanzel, M., and Zobel, R.: “Active safety
systems change accident environment of vehicles significantly – A challenge for vehicle
design”, Paper Number 050052, Proceedings of the 19th International Technical
207
References
Conference on the Enhanced Safety of Vehicle, National Highway Traffic Safety
Administration, Washington DC, 2005.
[Rie99] Rieth, P.: “Electronic driver assistance” (in German), in VDA-Technischer
Kongress, pp. 119-136, Frankfurt, 1999.
[Roe77] Roenitz, R., Braess, H.H., and Zomotor, A.: “Methods and criterions for
evaluation of the behaviour of the passenger vehicle – Part I”, (“Verfahren und Kriterien
zur Bewertung des Fahrverhaltens von Personenkraftwagen  Stand und Problematik,
Teil 1”), ATZ Automobiltechnische Zeitschrift, 1/77 and 3/77, pp. 29-38 and 39-46,
1977.
[Roe98] Roenitz, R., Braess, H.H., and Zomotor, A.: “Methods and criterions for
evaluation of the behaviour of the passenger vehicle – Part II”, (“Verfahren und Kriterien
zur Bewertung des Fahrverhaltens von Personenkraftwagen – Ein Rueckblick auf die
letzten 20 Jahre, Teil 2”), ATZ Automobiltechnische Zeitschrift, 99/100, pp. 780-786,
1998.
[San05] Sanna, L.: “Driving the solution: The plug-in hybrid vehicle”, EPRI Journal,
2005.
[Say96] Sayers, M.W. and Han, D.: “A generic multibody vehicle model for simulating
handling and braking”, Vehicle System Dynamics, 25(Suppl.), pp. 599-613, 1996.
[Sch04] Schmitke, C.: Modelling Multibody Multi-domain Systems using Subsystems
and Linear Graph Theory, Ph.D. Thesis, University of Waterloo, 2004.
[Sch08] Schmitke, C., Morency, K., and McPhee, J.: “Using graph theory and symbolic
computing to generate efficient models for multi-body vehicle dynamics”, Journal of
Multibody Dynamics, 222(K4), pp. 339-352, 2008.
[Sem06] Semmler, S.J., Reith, P.E., and Linkenbach, S.J.: “Global chassis control – The
networked chassis”, SAE World Congress, 2006-01-1954, Detroit, 2006.
[Sha00] Sharp, R.S., Casanova, D., and Symonds, P.: “A mathematical model for driver
steering control, with design, tuning and performance results”, Vehicle System
Dynamics, 33, pp. 289-326, 2000.
[Sma10] Smart Canada, fortwo coupé specifications, http://www.thesmart.ca, 2010.
[Ter97] Terashima, M., Ashikaga, T., Mizuno, T., Natori, K., Fujiwara, N., and Yada,
M.: “Novel motors and controller for high-performance electric vehicle with four
in-wheel motors”, IEEE transactions on industry electronics, 44(1), February, 1997.
208
References
[TM410] TM4 Inc., Quebec, Canada, http://www.tm4.com/home.aspx, 2010.
[Vel01] Veloso, F. and Fixson, F.: “Make-buy decisions in the auto industry: New
perspectives on the role of the supplier as an innovator”, Technological Forecasting and
Social Change, 67, pp. 239-257, 2001.
[Vog07] Vogt, H.: Real Time Dynamics Simulation of an Electric Vehicle with In-Wheel
Motors, Project Thesis, University of Waterloo, 2007.
[Vog09] Vogt, H., Schmitke, C., Jalali, K., and McPhee, J.: “Unified modelling and realtime simulation of an electric vehicle”, International Journal of Vehicle Autonomous
Systems, 6(3-4), pp. 288-307, 2009.
[Vog98] Voget, S. and Kolonko, M.: “Multidimensional optimization with a fuzzy
genetic algorithm”, Journal of Heuristics, 4(3), pp. 221-244, 1998.
[Wal05] Wallentowitz, H.: Vertical and Lateral Dynamics of Passenger Vehicles,
Automotive Technology II, (“Vertical- und Querdynamik von Kraftfahrzeugen,
Voerlesungsumdruck Fahrzeugtechnik II”), course notes, Institute of Automotive
Engineering, Aachen University of Technology, Germany, 2005.
[Wal06] Wallentowitz, H. and Reif, K.: Handbuch Kraftfahrzeugelektronik: Grundlagen,
Komponenten, Systeme, Anwendungen, ATZ/MTZ-Fachbuch, Friedr. Vieweg & Sohn
Verlag, 2006.
[Whe02] Wheals, J.C.: “Torque vectoring center differential for AWD: Design and
integration”, Innovative Fahrzeug-Getriebe Symposium, IIR Deutschland GmbH, 2002.
[Whe05] Wheals, J.C., Baker, H., Ramsey, K., and Turner, W.: “Torque vectoring
driveline: SUV-based demonstrator and practical actuation technologies”, SAE World
Congress, 2005-01-0553, Detroit, 2005.
[Wun05] Wunschelmeier, U. and Huchtkoetter, H.: “Traction and stability enhancement
using active limited-slip differentials”, 14th Aachen Colloquium, Automobile and Engine
Technology, 2005.
[Yam91] Yamamoto, M.: “Active control strategy for improved handling and stability”,
SAE World Congress, 911902, pp. 1638-1648, Detroit, 1991.
[Yih05] Yih, P.: Steer-by-Wire: Implications for Vehicle Handling and Safety, Ph.D.
Dissertation, Department of Mechanical Engineering, Stanford University, January 2005.
209
References
[Yu02] Yu, Y., Zeng, B., Zhong, G., and Peng, H.: “A real-time method to tune rule base
of fuzzy control system”, Proceedings of the 2002 IEEE International Conference on
Fuzzy Systems, pp. 425-430, 2002.
[Zan00] van Zanten, A.T.: “Bosch ESP systems: 5 years of experience”, SAE World
Congress, 2000-01-1633, Detroit, 2000.
[Zhe92] Zheng, L.: “A practical guide to tune of proportional and integral (PI) like fuzzy
controllers”, IEEE International Conference on Fuzzy Systems, pp. 633-640, 1992.
[Zie42] Ziegler, J.G. and Nichols, N.B.: “Optimum setting for automatic controllers”,
Transactions of the ASME, 65, pp. 756-765, 1942.
210
Appendices
A
Design and Modelling of the AUTO21EV
Many controller designs have been proposed for the control of individual vehicles. The
combination and coordination of these active systems, however, has not been fully
addressed, even though some of them have similar or complementary objectives. Since
the translational and rotational degrees-of-freedom of a vehicle are coupled, one chassis
control system may adversely affect the operation of other systems. As such, it is evident
that the appropriate integration of chassis control systems could be used to improve
vehicle stability, safety, and comfort simultaneously. Hence, the integration of various
control systems has the potential to optimize the dynamic behaviour of the vehicle
independently of the driving maneuver by controlling the allocation of the horizontal and
vertical forces at each individual wheel.
The objective of this research is to develop effective control strategies to improve
vehicle dynamics, based on the philosophy of individually monitoring and controlling the
tire-road forces on each wheel. In this regard, a full vehicle with four in-wheel motors
and an active steering system has been modelled in the ADAMS/View environment in
order to investigate advanced vehicle stability and traction control strategies. This
platform represents a two-passenger electric all-wheel-drive urban vehicle (AUTO21EV)
that has a similar configuration to the commercially-available Smart fortwo (Figure A-1).
An electric vehicle with four direct-drive in-wheel motors is the most exciting platform
on which to apply advanced motion control techniques, since the motor torque and speed
can be generated and controlled quickly and precisely. In fact, the torque response of an
electric motor is on the order of a few milliseconds and, therefore, responds 10 to 100
times faster than the internal combustion engines and hydraulic braking systems in use
today [Hor04]. The use of small but powerful direct-drive in-wheel motors allows for the
implementation of the most advanced torque vectoring system possible, in which any
desired torque distribution between the four wheels can be realized. Such a platform also
represents the most advanced all-wheel-drive (AWD) system, generating the optimal
amount of traction by controlling the slip ratio of each tire. In addition, steer-by-wire
211
A Design and Modelling of the AUTO21EV
technology on the front axle facilitates the inclusion of an active steering system, which
helps maintain vehicle stability by electronically augmenting the driver‟s steering input.
Figure A-1: AUTO21EV concept car (left) and the commercially-available Smart fortwo [Sma10] (right)
A.1
Preliminary vehicle design
As a first step in the design of the AUTO21EV, the vehicle dynamics in the longitudinal,
lateral, and vertical directions are examined.
A.1.1 Longitudinal dynamics
The initial design stage involves a comprehensive acceleration analysis to determine the
power and traction force demands of the vehicle. Various sizes of electric in-wheel
motors are considered, and the vehicle performance is assessed to ensure that the vehicle
is able to bend safely with ordinary city traffic and drive up a regulated maximum slope.
Figure A-2 illustrates the acceleration performance of the selected direct-drive in-wheel
motors. Here, Fresist_0% to Fresist_30% indicate the total stationary resistive forces as a
function of vehicle speed on different upward slopes, and Ftraction_total indicates the total
available traction force as a function of speed. The available traction effort results in a
fairly high acceleration potential even at higher speeds. For example, an acceleration
potential of about 5 m/s2 at the vehicle‟s maximum speed of 90 km/h allows the vehicle
to maneuver easily in urban traffic. In addition, due to the high motor torques available,
the vehicle experiences its maximum acceleration of about 8.3 m/s2 at zero speed when
driving on a dry flat road. Note that, due to the high acceleration rate at low speeds and,
consequently, a weight transfer to the rear axle, the front tires will spin out if their
respective motor torques are not controlled by a slip controller.
The traction effort and power characteristics of the vehicle are used to size an
appropriate electric motor for the AUTO21EV. Although the in-wheel motors currently
212
A Design and Modelling of the AUTO21EV
on the market are generally designed as direct-drive permanent magnet synchronous
machines (PMSM), in this stage of the design process, permanent magnet direct current
(PMDC) motors are used in order to simplify the modelling process. Direct-drive electric
motors use no gear reduction between the motor and the drive shaft, thereby reducing the
weight and size of the system, but they require the speed-torque characteristics of the
motor to directly meet the requirements of the vehicle. These machines are characterized
by containing permanent magnets in their rotor, usually rare-earth magnets to increase the
power density, where the rotor can be attached to the rim of the tire. Furthermore, these
motors are brushless and, therefore, are very robust and reliable. PMSMs have the
advantage that the magnetization loss in the field of the motors can be eliminated, which
not only improves the efficiency, but also prevents overheating of the tires by the outer
rotor [Ter97]. Figure A-3 illustrates the run-up characteristics of the chosen PMDC
motor, where the motor voltage, torque, and power are shown as functions of motor
speed.
Figure A-2: AUTO21EV longitudinal traction effort characteristics
Figure A-3: Direct-drive PMDC in-wheel motor run-up characteristics
213
A Design and Modelling of the AUTO21EV
Table A-I illustrates the specifications of the chosen PMDC motor. Based on
these characteristics, the vehicle power system characteristics are defined, as illustrated in
Figure A-4. Here, Prequired_0% to Prequired_30% illustrate the power required to overcome the
stationary resistive forces on different road gradients as a function of vehicle speed, and
Pavailable indicates the total available power as a function of speed. It is confirmed that the
chosen drivetrain is powerful enough to offer sufficient acceleration potential throughout
the entire speed range, and enables the vehicle to drive up the maximum slope of 30
percent gradient. Note that the power characteristics curve of the vehicle must be greater
than the maximum power required to drive up the maximum slope of 30 percent gradient.
Specification
Value
Unit
Peak Power
40
kW
Peak Torque
700
Nm
Maximum Speed
1650
rpm
Maximum Voltage
350
V
Maximum Current
311
A
Total Mass
30
kg
Rotor Mass
11.2
kg
Internal Resistance
0.768

Motor Constant
1.95
mH
Current Restriction Factor
3.25
-
Table A-I: PMDC motor characteristics
Figure A-4: AUTO21EV power requirements
214
A Design and Modelling of the AUTO21EV
The brakes of the AUTO21EV are designed to ensure that the rear brakes do not
lock before those on the front axle, which would result in vehicle instability. The
relationship between the front and rear braking force distribution is illustrated in Figure
A-5, where each axis describes the braking force at each axle relative to the total weight
of the vehicle. The ideal braking force ratio represents the optimal braking force ratio on
the front and rear axles for every possible adhesion situation and, thus, every possible
braking condition. The optimal braking force distribution depends on various parameters,
such as the vehicle‟s center of gravity, speed, and payload. In order to ensure that the
front wheels consistently lock earlier than the rear wheels, the constant braking ratio must
remain below the ideal braking ratio for all adhesion coefficients. Based on legislative
braking guidelines, a constant braking ratio is only allowed to exceed the ideal braking
distribution curve after an adhesion coefficient of 0.8 has been reached [Wal05].
Figure A-5: Ideal braking force distribution and a braking force limiter technique for different CG heights
It is the job of the proportioning valve to adjust the braking force balance and
achieve a close approximation to the ideal distribution, as illustrated by the parabolic
curves in Figure A-5. These curves represent the ideal braking force distributions for
vehicles with center of gravity heights of 0.4 m and 0.5 m. This figure confirms that the
lower the location of the vehicle‟s center of mass, the lower the braking ratio required. If
no braking force proportioning valve is installed, then the distribution of the braking
force forms a straight line whose slope is the ratio of the braking force at the front and
rear axles. The point at which the front wheels lock is found at the intersection of the base
215
A Design and Modelling of the AUTO21EV
distribution and the lines representing the respective coefficients of friction (the dotted
lines with slope -1 in Figure A-5). However, a braking force limit proportioning valve is
usually installed to actuate after the braking distribution line reaches the ideal braking
force distribution, so that the rear axle braking force does not increase further.
An extensive braking system analysis is performed to examine different vehicle
center of mass locations and braking ratios. Based on these calculations, the vehicle‟s
center of gravity position is chosen to be located at 0.4 m above the ground and at
0.82 m behind the front axle for the curb weight plus driver. Moreover, a constant base
braking ratio of 75 percent to the front axle and 25 percent to the rear axle is selected,
which stops the vehicle from its top speed of 90 km/h in about 3 seconds, requiring a
braking distance of 36 m.
A.1.2 Lateral dynamics
A bicycle model is used to investigate the effects of front and rear tire cornering
stiffnesses, center of gravity location, mass, and moment of inertia of the vehicle on the
steering performance, yaw damping rate, and yaw natural frequency of the vehicle. The
usefulness of a bicycle model is limited to lateral accelerations less than 0.4g, where the
vehicle and tire behaviour can be considered to be linear [Wal05]. The results of an
analysis of the bicycle model for a vehicle with the same tires on the front and rear is
illustrated in Figure A-6.
Figure A-6: Self-steering characteristics of the bicycle model when the position of the vehicle center of
gravity varies and the tire lateral stiffnesses are the same on both axles
If the vehicle center of gravity position is closer to the front axle, traction is first
lost at the front wheels and, consequently, an increasing steering angle is required at
higher speeds in order to keep the vehicle on the desired path, as compared to a neutral216
A Design and Modelling of the AUTO21EV
steered vehicle. In addition, an understeered vehicle possesses a characteristic speed at
which the vehicle is most „responsive‟, reacting quickly and accurately to any steering
inputs with no overshoot or delay. The AUTO21EV center of gravity is located at 0.82 m
behind the front axle and 0.98 m from the rear axle and, therefore, it has an understeered
characteristic with a characteristic speed of 105 km/h. Note that most available passenger
cars on the market are designed as understeered vehicles with characteristic speeds
between 65 and 100 km/h, which is the speed range in which vehicles are driven most
often and, thus, require the best responsiveness [Wal05]. Transient skid-pad testing is
used to describe the behaviour of the vehicle. The transient behaviour of a vehicle can be
analyzed by writing the equations of motion of the linearized bicycle model as functions
of sideslip angle (Figure A-6).
The yaw natural frequency and yaw damping rate of the vehicle can be calculated
by comparing the coefficients of the resulting homogeneous differential equation with a
spring-damper system. Figure A-7 illustrates the range of yaw damping rates and natural
frequencies for available passenger cars. Normal passenger cars (mid-performance
vehicles) have an average yaw damping rate of approximately 0.8 and a yaw natural
frequency between 2 and 4 Hz. These values correspond to typical speed ranges between
60 and 100 km/h [Wal05]. The yaw damping rate and natural frequency of the
AUTO21EV are illustrated in Figure A-8. As can be seen, the high steering
responsiveness of the AUTO21EV is set to be between the speed ranges of 60 and 90
km/h, reflecting the predominant driving situation for an urban vehicle. Comparing the
AUTO21EV transient behaviour with Figure A-7, it can be confirmed that the yaw
damping rate and natural frequency of the AUTO21EV are defined to be in the typical
range of normal passenger cars, with a tendency towards sports cars.
Figure A-7: Typical range of yaw damping rate and natural frequency for available passenger cars [Wal05]
217
A Design and Modelling of the AUTO21EV
Figure A-8: Yaw natural frequency (top) and damping rate (bottom) of the AUTO21EV as functions of
forward speed
A.1.3 Vertical dynamics
The spring and damper rates of the AUTO21EV suspension system are estimated by
considering a quarter-car model, and are further refined using a formal optimization
procedure. The suspension system spring rates are designed to provide a frequency for
the sprung mass that lies within the comfort range for the human body, which is
considered to be between 1 and 4 Hz [Rei02]. The rear suspension is designed for a target
sprung mass frequency of 1 Hz. The front suspension is designed to have a 30 percent
lower ride rate than the rear suspension, based on Olley‟s recommendation for a
comfortable ride [Gil92].
The design of a vehicle suspension is generally a compromise between competing
design requirements, aiming to simultaneously provide a comfortable ride as well as safe
handling performance. There are multiple excitation sources for vehicle ride vibrations,
but these can generally be divided into two classes: road roughness and on-board sources
[Wal05]. For an electric vehicle, on-board sources are restricted to tires, rims, and the
rotating parts of the electric motors, as there is no powertrain. These excitations are
considered to be insignificant in the following analysis, which considers only road
roughness as the excitation source. The suspension parameters are selected based on an
optimization of the half-car model shown in Figure A-9. The ride performance of the
218
A Design and Modelling of the AUTO21EV
vehicle is described by the root mean square (RMS) of the chassis vertical acceleration
(which is based on the evaluation of the transfer function of the chassis acceleration with
respect to the road excitation) and the Laplace transform of the temporal power spectral
density (PSD) of the road surface profile [Guo82, Hro81]. The optimization problem is
limited by four design constraints. The first design constraint requires that the vehicle
holds to the ground by minimizing the fluctuation of the adhesion force between the tire
and road. In other words, the probability of the tire leaving the ground must remain below
some acceptable limit. The second design constraint is defined based on the allowable
roll angle of the vehicle. Assuming that no anti-roll bar is included in the suspension, the
suspension stiffness is directly limited by the allowable roll angle. An empirical value for
the acceptable roll angle for a normal passenger car is used: less than about 3o for a lateral
acceleration of 0.5g [Wal05]. The third constraint limits the maximum suspension
dynamic displacement to avoid hitting the bump stops. The fourth and final constraint
concerns the life of the tire: the smaller the tire stiffness, the larger its deflection and the
shorter its life. The tire static deflection should be less than 8 to 13 percent of the profile
height of the tire [Jal07].
Figure A-9: Half-car suspension model when assuming an equal static mass distribution on the front and
rear axles [Jal07]
A genetic algorithm (GA) optimization tool is developed to calculate the optimal
suspension and tire parameters based on the above considerations. Figure A-10 illustrates
the results of the GA tool for the AUTO21EV when it is driven with an initial speed of 36
219
A Design and Modelling of the AUTO21EV
km/h on a rough road. The suspension stiffness and damping rates are determined by
setting the stiffness of the tires to the same values as those used on the Smart fortwo:
130.5 kg/cm. The optimal suspension stiffness and damping rate are calculated to be 51.7
kg/cm and 5.7 kg/cm/s, respectively. The resulting probability of the tire leaving the
ground is equal to 0.13 percent, and the RMS of the vertical chassis acceleration is
0.355g. Both values are reasonable for passenger cars.
Vehicle Suspension Vibration Optimization
Design Parameters:
Coefficient of Road Irregularity A = 1.0
Vehicle Velocity v = 10.0 [m/s]
Sprung Mass M = 0.9072 [kg/cm/s2]
Unsprung Mass m = 0.1883 [kg/cm/s2]
Dynamic Load Coefficient b0 = 0.13
Optimization Results:
Suspension Stiffness C = 103.3 [kg/cm]
Tire Stiffness Ck = 260.1 [kg/cm]
Damping Force Coefficient k = 11.34 [kg/cm/s]
Figure A-10: Optimization results for the AUTO21EV suspension system
A.2
Detailed suspension design
Double-wishbone suspension configurations are selected for the front and rear axles of
the AUTO21EV. Specific suspension characteristics (Figure A-11), such as toe-in angle,
camber angle, caster angle, and track width changes during vertical wheel travel, are
chosen to optimize the cornering behaviour. The suspensions are designed to provide
desirable self-steering characteristics for the vehicle, such as camber thrust, roll steer, and
lateral load transfer. Other considerations include mechanisms to reduce body pitch angle
during acceleration and braking, and roll motion during cornering. By designing a passive
suspension with ideal characteristics, the stability control systems do not need to correct
for faulty suspension system behaviour, and can focus on improving the driving dynamics
of the vehicle. Extensive analyses are performed on various suspension configurations by
German exchange students directly supervised by the author. Detailed analyses are
220
A Design and Modelling of the AUTO21EV
performed on trailing arm and semi-trailing arm [Pet05], double-wishbone [Jal05], and
multi-link [Bod06] suspension systems.
Figure A-11: Sign convention for camber, caster, and toe angle on a double-wishbone suspension [Jal05]
Since the parameters of an independent suspension system are interrelated, virtual
prototyping software (ADAMS/View) is used to model the suspension systems. The
double-wishbone suspensions of the front and rear axles are illustrated in Figure A-12.
The following steps are performed during the design process of the suspension system on
each axle:
1) Redistribution of forces: The kingpin inclination, kingpin offset, caster angle, and
caster trail are adjusted to fall in the ranges found on commercial vehicles in order to
reduce the amount of force acting on the steering axis and tie rods (Figure A-13). The
front and rear suspensions are designed to have a kingpin inclination of  = 15.5o and a
negative kingpin offset of r = -21.7 mm at static ride height. The front double-wishbone
suspension has a caster angle of  = 7.5o and a positive caster trail of r,k = 18.4 mm,
whereas the rear suspension is designed to have zero caster angle and zero caster trail in
the design position.
2) Modification of the control arms to define a desirable roll axis: The determination of
the roll center height on each axle is done at static ride height by changing the control
arm slopes in the front view. The target values are chosen based on Olley‟s
recommendations [Mil02], where a desirable roll center height of less than 127 mm is
recommended for the front axle and a roll center height below 410 mm is recommended
for the rear axle. A higher roll center height at the rear axle provides a roll understeering
221
A Design and Modelling of the AUTO21EV
effect. The final vehicle model has a front roll center height of 89.4 mm and a rear roll
center height of 94.7 mm in the static design position.
Figure A-12: Front and rear suspension systems of the AUTO21EV
3) Incorporation of anti-pitch characteristics: By inclining the suspension control arms
towards one another on both axles, the body pitch motion can be reduced during
acceleration and braking. The inclined angles cause part of the additional vertical force
created by the dynamic weight shift during braking or acceleration to reduce spring
deformation [Bod06]. Three rules are considered to determine the desired positions of the
front and rear suspension pitch poles, Of and Or (Figure A-14-a). First, to provide the
driver with some feedback during acceleration and braking, the complete elimination of
the pitch motion is avoided [Gil92]. A pitch angle reduction of 60% was chosen,
compared to a vehicle without an anti-pitch mechanism. Figure A-14-b illustrates the
effect of the anti-pitch mechanism during acceleration and braking for the AUTO21EV.
Secondly, the resultant force due to the control arms should be located as close to the
center of gravity as possible. Finally, for independent wheel suspensions, it is important
for the pitch poles to be higher than the wheel center of the driven axle [Rei02].
4) Design of an appropriate steering geometry: An electric-motor-driven rack-and-pinion
principle has been chosen for the steering system. The location, length, and angle of the
tie rods on the front axle and suspension links on the rear axle are analyzed and set to
values that provide the best handling properties, including a roll understeering effect,
reduced wheel fight and rolling resistance, and minimal toe angle change during bump
travel. The vertical position of the inner hard-points of the tie rods and links are defined
based on Olley‟s recommendations for an „ideal‟ steering geometry [Mil02], using a
222
A Design and Modelling of the AUTO21EV
graphical method introduced by Reimpell [Rei02]. Figure A-15 illustrates the roll
understeering behaviour of the vehicle when driving in a turn. At the front axle, the outer
bump-travelling wheel experiences a toe-out situation and the inner rebounding wheel
experiences a toe-in situation. At the rear axle, the opposite phenomenon occurs to realize
roll understeering at high speeds.
Kingpin inclination &
Kingpin offset (front suspension)
Caster angle &
Caster trail (front suspension)
rear
view
side
view
front
Figure A-13: Illustration of kingpin inclination (), kingpin offset (r), caster angle (), and caster trail (r,k)
in front suspension of the AUTO21EV
Figure A-14: (a) Pitch poles of the front and rear axles, and (b) AUTO21EV body pitch motion for
accelerating and braking with and without the anti-pitch mechanism
223
A Design and Modelling of the AUTO21EV
Figure A-15: Roll understeering behaviour through toe angle changes on the front and rear suspensions
when driving in a curve
In the next step, the steering rack position in the horizontal direction is determined
based on the Ackermann differential steering angle , which describes the difference
between the inside i and outside o,A steering angles (Figure A-16-a). Perfect Ackermann
steering describes the situation in which the front tires have the same instantaneous center
of rotation in a turn. In practice, however, a smaller differential steering angle is used
because the tires must not come into contact with the wheel arch or other components of
the front axle [Rei02]. On the other hand, the smallest possible turning circle for the
vehicle can only be achieved if the steer angle of the outside wheel is as large as possible.
In order to avoid impairing the cornering behaviour of the vehicle while simultaneously
increasing the lateral force capacity of the front outside tire and decreasing the cornering
radius, the steering angle on the outside wheel is designed to be larger than that
calculated by Ackermann. In this regard, a reduction to 55% Ackermann is chosen as the
target for the preliminary design, which is close to the setup of the BMW 3-Series
[Rei02]. Figure A-16-b illustrates the influence of the steering rack location on the
differential steering angle.
224
A Design and Modelling of the AUTO21EV
Figure A-16: (a) Differential steering angle ( i - o,A > 0) according to Ackermann, and (b) influence
of steering rack position on differential steering angle
5) Adjustment of suspension kinematics: Since negative camber angles on the tires of an
axle increase the lateral force potential on that axle, it is important to provide the tires
with negative camber angles during all driving maneuvers [Wal05]. Therefore,
suspensions are designed to have a negative camber angle at the static ride height.
Furthermore, the kinematics of the front and rear suspensions are designed such that the
outer wheels are pushed into more negative camber and the inner wheels are pushed into
positive camber when cornering. In this way, the suspension system not only counteracts
the effects of body roll on tire camber, but also increases the lateral force potential of the
more heavily-loaded outside tires. Finally, the wheel track change is reduced by changing
the upper control arm length.
A.3
Dynamic model of the AUTO21EV
In order to simulate test maneuvers to investigate different control strategies, full
kinematic and dynamic models of the AUTO21EV are developed in ADAMS/View
(Figure A-17). ADAMS is a comprehensive multi-body dynamic simulation package that
225
A Design and Modelling of the AUTO21EV
is used in this project. The extension of the kinematic model into a dynamic model
requires the development and adoption of appropriate tire and road models in
ADAMS/View. These data are used by subroutines to calculate the forces and moments
that tires exert on a vehicle as a result of the interaction between the tires and the road
surface. ADAMS/Tire can be employed to model tires for either vehicle handling or
vehicle durability analyses. Handling analyses are advantageous for studying vehicle
dynamic responses to steering, braking, and throttle inputs, whereas durability analyses
are suitable for generating road load histories as well as stress and fatigue studies
requiring component forces and accelerations. Figure A-18 illustrates the different tire
models available in ADAMS and the typical applications for each tire model.
Figure A-17: (a) Kinematic and (b) dynamic models of the AUTO21EV
Based on this information, a Pacejka 2002 tire model is chosen for this project.
The Pacejka 2002 tire model is the most recommended model for handling and real-time
control studies [Pac02]. The yaw, roll, and pitch moments of inertia of the vehicle are
estimated based on the vehicle weight and center of gravity height, as well as geometric
measurements, including the track width, roof height, wheelbase, and overall vehicle
length. The accuracy of this estimation procedure has been confirmed by experimental
results obtained from the Inertial Parameter Measurement Device located at the Vehicle
Research and Test Center in East Liberty, Ohio [Bix95]. The moments of inertia of other
vehicle parts, such as the suspension and steering system components, are calculated
using the ADAMS software, based on the component shape and constituent material. The
moments of inertia of the in-wheel motors, tires, and rims are determined by hand
226
A Design and Modelling of the AUTO21EV
calculation [Vog07]. To fine-tune the understeering characteristic of the vehicle, an antiroll bar is added to the front axle of the vehicle prior to running the simulations. The
stiffness of the anti-roll bar is chosen to be 1.1 Nm/deg, which provides an understeering
effect and a maximum roll angle of 3o for the vehicle.
Figure A-18: Typical applications for ADAMS tire models [Aks06]
A.4
Permanent magnet synchronous in-wheel motor
As mentioned earlier, the in-wheel motors currently on the market are generally designed
as direct-drive permanent magnet synchronous machines (PMSM). Use of PMSMs
implies that no gear reduction exists between the motor and the drive shaft of the wheel,
which can reduce the weight and size of the system, but also requires that the speedtorque characteristics of the motor meet the performance requirements of the vehicle.
These motors generally contain rare-earth permanent magnets in the rotor, which provide
a high power density and employ electric commutation through the use of inverters,
allowing the design of a robust and reliable brushless, variable-speed PMSM motor with
a high power-to-weight ratio [Han94]. PMSMs are designed upside-down, which means
that the rotor is the rotating external part (which can also be attached to the rim) and the
stator is attached to the wheel shaft. This strategy is primarily used to reduce the moment
of inertia of the rotating parts, thereby reducing the amount of energy required to stop or
227
A Design and Modelling of the AUTO21EV
accelerate the wheels. In addition, PMSMs have the ability to increase performance and
efficiency by eliminating the magnetization losses in the field of the motors. The fluxweakening characteristic of the PMSM not only improves the efficiency of the motors,
but also prevents overheating of the tires by the rotor. Figure A-19 illustrates two possible
examples for PMSM in-wheel motors that are offered by L-3 Communications MagnetMotor GmbH and TM4.
Figure A-19: PMSM in-wheel motor offered by L-3 Communications Magnet-Motor GmbH [MMG10]
(left) and TM4 Inc. [TM410] (right)
Details on the modelling, simulation, and analysis of inverter-fed PMSM-type
motors can be found in the literature (e.g., [Rah85, Ter97, Pil89]). The PMSM motors
used in this model are assumed to consist of a cage-less surface permanent magnet rotor
and a stator with three-phase windings and a sinusoidal back electromotive force. A
balanced sinusoidal three-phase current is enforced in the stator to achieve synchronous
operation and a smooth torque profile [Rah85]. Although these characteristics are usually
achieved using an inverter by establishing pulse-width modulation (PWM) control, the
switching effects have been neglected here for simplicity; it is assumed that the PWM
works like an ideal three-phase variable voltage source. Moreover, saturation, eddy
currents, hysteresis losses, and field current dynamics have also been neglected.
228
A Design and Modelling of the AUTO21EV
The number of pole pairs in a PMSM determines the amount of rotor rotation per
complete sine wave in the stator. If the number of pole pairs (P) is known, the following
equation can be used to relate the (electric) stator angle  s and the (mechanical) rotor
angle  r :
s  P  r
(A.1)
or
s  P  r
(A.2)
for angular velocities. A common approach for modelling a PMSM is to use the d,q-axis
model. This approach uses the Park transformation to reduce a three-phase system to an
equivalent two-phase system [Han94]. The inductances in the two-phase system remain
constant since the reference frame is assumed to rotate. The Park transformation of
voltages from a three-phase system (a-b-c) to a two-phase system (d-q-0) is as follows:
 vq 
cos( s ) cos( s  2 / 3) cos( s  2 / 3)   va 
2
 v    sin( ) sin(  2 / 3) sin(  2 / 3)    v 
s
s
s
 d 3
  b
1/ 2
1/ 2
 v0 
 1 / 2
  vc 
(A.3)
where v0 is equal to zero in a balanced three-phase system. The Park transformation can
also be used to relate the current in a three-phase system (ia, ib, ic) to that in the equivalent
two-phase system (iq, id). The governing equations of the latter then take the following
form:
vq  Rs  iq  Lq 
diq
vd  Rs  id  Ld 
did
 s  Ld  id
dt
dt
 s  Ld  id  s  B
(A.4)
(A.5)
where Rs is the phase resistance, B is the magnetic flux linkage, and Lq and Ld are the qand d-axis phase inductances, respectively. These four parameters, together with the
number of pole pairs (P), must be specified for the motor. Although the phase resistances
of the two- and three-phase systems are identical, the q- and d-axis phase inductances
could be different and are not identical to the phase inductance of the original system
(Ls). In the case of surface permanent magnets, however, the following relationship can
be assumed:
Lq  Ld 
3
Ls
2
(A.6)
229
A Design and Modelling of the AUTO21EV
The magnetic flux linkage represents the effect of the permanent magnets, and can
be determined by measuring the no-load line-to-line voltage of the motor while it is
externally driven at a constant speed. The motor torque of a PMSM can be determined
using the Park transform as follows:
TM 
3
P   B  iq  ( Ld  Lq )  iq  id 
2 
(A.7)
For the special case of surface permanent magnets, this equation simplifies to the
following:
TM 
3
P  B  iq
2
(A.8)
Equation (A.8) defines the coupling between the electrical and mechanical domains. In
order to calculate the applied torque, equations (A.4) and (A.5) must both be solved.
After substituting equations (A.2) and (A.6) into equations (A.4) and (A.5), and rewriting
in state-space form, the following equations can be derived:
diq
dt

1 
3

vq  Rs  iq  P  r   Ls  id  B  

Lq 
2

did
1

dt Ld
3


 vd  Rs  id  P  r  Ls  iq 
2


(A.9)
(A.10)
Finally, the original phase voltages (va, vb, vc) must be transformed into the two-phase
voltages (vd, vq) using equation (A.3), which relies on the vehicle model by means of
equation (A.1). In summary, five parameters and two state variables are identified for the
motor model. The three-phase voltages are the inputs to the motor model and the motor
torque is the output; the mechanical angle and angular velocity, which are state variables
in the vehicle model, are treated as external parameters. Further details about the motor
model and motor controller units used in this work can be found in [Vog07, Vog09]. In
order to address the multidisciplinary nature of the whole system, it is desirable to obtain
one model rather than separate mechanical and electrical models [McP05]. This multidomain approach has been accomplished through the use of linear graph theory. A
component template for the PMSM-type motor was developed [Sch04] and added to the
existing vehicle model [Vog07]. Table A-II lists the specifications of the PMSM in-wheel
motors used in this work.
230
A Design and Modelling of the AUTO21EV
Specification
Value
Unit
Peak Power
40
kW
Peak Torque
700
Nm
Maximum Speed
3200
rpm
Maximum Voltage
350
V
Maximum Current
311
A
Total Mass
30
kg
Rotor Mass
11.2
kg
Magnetic Flux (B)
0.5
V/rad/s
Phase Inductance (Ls)
4
mH
Phase Resistance (Rs)
0.5

Number of Pole Pairs (P)
12
–
Table A-II: PMSM in-wheel motor characteristics
231
Was this manual useful for you? yes no
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Download PDF

advertisement