Contents
0.1 List of Symbols . . . . iii
1 Introduction 1 1.1 Electronic Control Systems History . . . . 2
2 Vehicle Model 5 2.1 Vehicle Model . . . . 5
2.1.1 Vehicle equations . . . . 6
2.1.2 Vertical Load . . . . 7
2.1.3 On Demand Drive . . . . 8
2.2 Tyre Model . . . . 12
2.2.1 Reference Frame . . . . 12
2.2.2 Slip Quantities . . . . 13
2.2.3 Semi-Empirical Model . . . . 14
3 Simulink Model 17 3.1 Simulink Model . . . . 17
3.1.1 Vehicle Subsystem . . . . 17
3.1.2 Tyre Subsystem . . . . 19
3.1.3 Engine Model . . . . 23
3.1.4 Haldex Coupling Model . . . . 24
4 Active Yaw Control 26 4.1 ESP . . . . 26
4.1.1 ESP Working Principles . . . . 26
4.1.2 ESP Simulink Model . . . . 27
4.1.3 “Reference Yaw Rate” Value . . . . 27
4.1.4 “Lateral Acceleration” Difference . . . . 32
4.1.5 ESP Strategy . . . . 33
5 Redistribution of Torque 37 5.1 Drive Torque Control . . . . 39
5.1.1 Controller . . . . 39 i
6 Rear-Wheel Drive Car simulations 41
6.1 High Speed A . . . . 41
6.2 High Speed B . . . . 55
6.3 External Disturbance . . . . 57
6.4 Avoidance Manoeuvre . . . . 60
7 Front-Wheel Drive Car Simulations 63 7.1 High Speed . . . . 63
7.2 External Disturbance . . . . 65
7.3 Avoidance Manoeuvre A . . . . 68
7.4 Avoidance Manoeuvre B . . . . 69
8 Conclusions 72 A Rear-Wheel Drive Car Simulations II 74 A.1 External Disturbance (Understeer, 195/65-R15) . . . . 74
A.2 External Disturbance (195/65-R15) . . . . 77
A.3 High Speed (205/55-R15) . . . . 81
A.4 External Disturbance (205/55-R15) . . . . 86
A.5 Avoidance Manoeuvre (205/55-R15) . . . . 91
B Front-Wheel Drive Car Simulations II 95 B.1 External Disturbance (Oversteer, 195/65-R15) . . . . 95
B.2 High Speed (205/55-R15) . . . . 99
B.3 Avoidance Manoeuvre (205/55-R15) . . . 102
C Simulink Model Parameters 107 C.1 M-File . . . 108
C.2 Controllers . . . 110
C.2.1 Rear-Wheel Drive Vehicle . . . 110
C.2.2 Front-Wheel Drive Vehicle . . . 110
ii
0.1 List of Symbols
Symbol Name Unit
————- ——————————————————————————– ———–
a Distance center of gravity - front axle m
a1 Magic Formula coefficient, Dy N−1
a2 Magic Formula coefficient, Dy -
a3 Magic Formula coefficient, BCDy N
a4 Magic Formula coefficient, BCDy N
a6 Magic Formula coefficient, Ey N−1
a7 Magic Formula coefficient, Ey -
B Stiffness factor, Magic Formula -
b Distance center of gravity - rear axle m
b1 Magic Formula coefficient, Dx N−1
b2 Magic Formula coefficient, Dx -
b3 Magic Formula coefficient, BCDx N−1
b4 Magic Formula coefficient, BCDx -
b5 Magic Formula coefficient, BCDx N−1
b6 Magic Formula coefficient, Ex N−2
b7 Magic Formula coefficient, Ex N−1
b8 Magic Formula coefficient, Ex -
C Shape factor, Magic Formula -
Ci Cornering stiffness, front and rear axle N/rad
Cx Drag coefficient, car -
D Peak factor, Magic Formula N
d Roll center height, front and rear axle m
d1 Roll axis height under the center of gravity m
E Curvature Factor, Magic Formula -
e Distance external lateral force m
FL Lateral external force N
Fx(nm) Longitudinal force, tyre N
Fx0(nm) Longitudinal force in pure longitudinal slip conditions, tyre N
Fy(nm) Side force, tyre N
Fy0(nm) Side force in pure side slip conditions, tyre N
Fz Vertical load N
Hnm Distance between the wheel slip axis and the street m
h Center of gravity height m
J Moment of inertia around z axis, car kg m2
Jω(n,m) Moment of inertia around spin axis, wheel kg m2
k Longitudinal slip -
kφ Rolling stiffness, car N/rad
iii
Symbol Name Unit
————- ——————————————————————————— ———–
kφi Rolling stiffness, front and rear axle N/rad
L Relaxation length m
l Wheelbase m
Mcl Drive torque provided by the central coupling Nm
Men Drive torque provided by the engine Nm
Mnm Drive torque applied to the wheel Nm
Mb,nm Brake torque Nm
m Mass, car kg
N Total yaw moment Nm
R Corner radius m
Rest Estimated corner radius m
Rref Reference corner radius m
r Yaw rate, car rad/s
rref Reference yaw rate rad/s
re Rolling radius in free rolling conditions, tyre m
Tf0 Maximum drive torque transferrable Nm
by means of the “Haldex” coupling
t Track m
u Longitudinal speed, car m/s
u Estimated longitudinal speed m/s
VG Center of gravity speed, car m/s
Vx X-direction speed, tyre m/s
v Lateral speed, car m/s
X Total longitudinal force N
Y Total lateral force N
δ Steer angle rad
µx Longitudinal friction coefficient -
µy Side friction coefficient -
αnm Slip angle, tyre rad
β Slip angle, car rad
σ Total theoretical slip -
σx Theoretical longitudinal slip -
σy Theoretical side slip -
τd Transmission ratio, differential -
φ Roll angle rad
ω Rotational speed, wheel rad/s
ω0 Rotational speed in free rolling conditions, wheel rad/s ωr,f Rotational speed of the front and the rear drive shaft rad/s
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