Appendix C
Simulink Model Parameters
C.1
M-File
——————————————————— ————————————————————– g = 9.81 gravity acceleration
m = 1000 vehicle mass
J = 1680 vehicle inertia, zz
a = 1.2 distance center of gravity-front axle b = 1.4 distance center of gravity-rear axle
l = a + b wheelbase
t = 1.3 track
H1 = 0.25 spin axis height front tyres H2 = 0.25 spin axis height rear tyres
ro = 1.3 air density
Cx = 0.35 drag coefficient
S = 1.8 vehicle frontal section
Jw1 = 1 front wheel inertia moment (spin axis) Jw2 = 1 rear wheel inertia moment (spin axis) re1 = 0.3 front wheel rolling radius in
free rolling conditions re2 = 0.3 rear wheel rolling radius in
free rolling conditions
F Z10 = m ∗ g ∗ b/(l ∗ 2) front wheel static vertical load F Z20 = m ∗ g ∗ a/(l ∗ 2) rear wheel static vertical load kf i1 = 50000 front axle rolling stiffness kf i2 = 50000 rear axle rolling stiffness kf i = kf i1 + kf i2 total rolling stiffness
d1 = 0.35 roll center height of the front axle d2 = 0.35 roll center height of the rear axle
d = (b ∗ d1 + a ∗ d2)/l roll axis height under the center of gravity h = 0.5 center of gravity height
lt1 = 1/t ∗ (b/l ∗ d1 + kfi1/kfi ∗ (h − d)) front axle load transfer coefficient (sub-model) lt2 = 1/t ∗ (a/l ∗ d2 + kfi2/kfi ∗ (h − d))108rear axle load transfer coefficient (sub-model)
a01 = ∗ ∗ ∗ Magic Formula coefficients
(vehicle; 1 front tyre, 2 rear tyre)
a02 = ∗ ∗ ∗ a11 = ∗ ∗ ∗ a12 = ∗ ∗ ∗ a21 = ∗ ∗ ∗ a22 = ∗ ∗ ∗ a31 = ∗ ∗ ∗ a32 = ∗ ∗ ∗ a41 = ∗ ∗ ∗ a42 = ∗ ∗ ∗ a61 = ∗ ∗ ∗ b41 = ∗ ∗ ∗ b42 = ∗ ∗ ∗ b51 = ∗ ∗ ∗ b52 = ∗ ∗ ∗ b61 = ∗ ∗ ∗ b62 = ∗ ∗ ∗ b71 = ∗ ∗ ∗ b72 = ∗ ∗ ∗ b81 = ∗ ∗ ∗ b82 = ∗ ∗ ∗ b91 = ∗ ∗ ∗ b92 = ∗ ∗ ∗ b101 = ∗ ∗ ∗ b102 = ∗ ∗ ∗
rl1 = 0.1 front tyre relaxation length rl2 = 0.1 rear tyre relaxation length taug = 1 gear transmission ratio
taud = 1/2 differential transmission ratio
u0 = 35 initial speed
D20 = (a12∗ F Z20/1000 + a22) ∗ F Z20/1000 Magic Formula coefficients (sub-model)
C20 = a02
B20 = (a32∗ sin(2 ∗ atan(F Z20/(a42∗ 1000))))∗
/((C20 ∗ D20) ∗ 1000) ∗ 180/pi
D10 = (a11∗ F Z10/1000 + a21) ∗ F Z10/1000
C10 = a01
B10 = (a31∗ sin(2 ∗ atan(F Z10/(a41∗ 1000))))∗
/((C10 ∗ D10) ∗ 1000) ∗ 180/pi
F lat = 2000 Lateral Force
e = 0.3 Lateral force distance from the center of gravity
—————————————————————– ————————————————— 109
C.2
Controllers
C.2.1
Rear-Wheel Drive Vehicle
• PIAL = 75s+40 s • PIYR = 2500s+40 s
C.2.2
Front-Wheel Drive Vehicle
• PIAL = 75s+40 s • PIYR = 500s+40 s 110
