99
A P P E N D I X A
Notation
Symbol Parameter Symbol Parameter
a
y
Lateral acceleration of vehicle
F
f
Lateral force of a front tire
d
Distance from the CG to front axle
F
r
Lateral force of a rear tire
F
y
Lateral tire force in tire y-axis (of
wheel plane)
F
L
Vertical load on left tires
F
z
Vertical force on tire
F
R
Vertical load on right tires
H
CG,s
COG height of sprung mass re-
spect to grand
h
Height of the roll center, measured
upward from the road
H
RC
Height of roll axis respect to grand
I
x
Roll moment of inertia of the
sprung mass, measured about the
roll axis
k
ϕ
Roll stiff ness of suspension
I
z
Yaw moment of inertia of the total
mass, measured about the z axis
M
RC
Roll moment, measured about roll
center
k
f
Cornering stiff ness coeffi cient of a
front tire
m
s
Sprung mass
k
r
Cornering stiff ness coeffi cient of a
rear tire
ϕ
Vehicle roll angle
L
Wheelbase of vehicle
ϕ
B
Road bank angle
m
Total mass of vehicle
δ
Steering wheel angle
r
Yaw rate of the sprung mass
a
Longitudinal distance to the front
axle
g
Gravitational acceleration
b
Longitudinal distance to the rear
axle
T
w
Track width of vehicle
C
f
Cornering stiff ness values for the
front tires
U
Forward speed of vehicle
C
r
Cornering stiff ness values for the
rear tires
v
Lateral speed of vehicle
100 A. NOTATION
ϕ
Roll rate of vehicle
c
s2
Equivalent damping coe cient of
the right suspension
ϕ
Roll acceleration of vehicle
z
s1
Vertical displacement of sprung
mass on the left
k
t1
Vertical sti ness of the left tires
z
s2
Vertical displacement of sprung
mass on the right
k
t2
Vertical sti ness of the right tires
β
f
Slip angle of the front tires
z
c
Vertical displacement of sprung
mass
β
r
Slip angle of the rear tires
z
u1
Vertical displacement of the left
unsprung mass
ϕ
s
Roll angle of the sprung mass
z
u2
Vertical displacement of the right
unsprung mass
ϕ
u
Roll angle of the unsprung mass
z
r1
Road input of the left tires
H
Height of center of mass, measures
upward from the road
z
r2
Road input of the right tires
F
zi
Vertical force of the other side tires
F
s1
Dynamic forces of the left suspen-
sion
θ
cr
Vehicle body critical title angle
F
s2
Dynamic forces of the right sus-
pension
μ
Coe cient of road adhesion
M
B
Anti-yaw torque
δ
d
Driver’s steering-wheel angle
k
s1
Vertical sti ness of the left suspen-
sion
τ
sw
Steering first-order time constant
k
s2
Vertical sti ness of the right sus-
pension
SR
Steering ratio
c
s1
Equivalent damping coe cient of
the left suspension
c
ϕ
Equivalent roll damping coe cient
of suspension
a
ylim
Desired lateral acceleration
r
d
Desired yaw rate
F
b2
Brake force of front-outer wheel
x(t)
State quantities of vehicle
F
b1
Brake force of front-inner wheel
K
e
Gain of yaw rate
C
b
Flow coe cient of solenoid valve
P
h
Prediction horizon
A
b
Area of ori ce throttle
C
h
Control horizon
K
b
Bulk modulus of the brake oil
Q
Output state coe cient
V
b
Volume of the wheel brake cylinder
R
Control weight coe cient
A. NOTATION 101
n
Index of solenoid valve
y(k)
Output state
p
w
Pressure of wheel brake cylinder
y
r
(k)
Output reference value
q
Average fl ow rate
∆U
Control increment
γ
Adiabatic index
A, B
Sate space equation matrix.
p
0
Initial pressure of the gas chamber
of accumulator
C
k
Coeffi cient matrix in the output
equation of state-space equation
V
0
Volume of the gas chamber of ac-
cumulator
t
s
Discrete sampling time
δ
u
Control quantity of front wheel
steering angle
ρ
Weight coeffi cient
δ
0
Accumulation of front wheel steer-
ing angle
ε
1
Relaxation factor
ϕ
d
Desired roll angle
M
ϕ
Roll moment induced by active
anti-roll bar
e
γ
Yaw rate error
y
d
Double integration of desired lat-
eral acceleration
τ
Time constant
y
d
Desired lateral displacement
y
Lateral displacement
u
c
Output of the sliding mode control
in consideration of roll rate
y
First integration of lateral acceler-
ation
u
d
Output of the sliding mode control
in consideration of lateral displace-
ment.
m
sf
Sprung mass of front axle
m
sr
Sprung mass of rear axle
m
uf
Unsprung mass of front axle
m
ur
Unsprung mass of rear axle
b
1
Longitudinal distance from the CG
to the middle axle
c
1
Longitudinal distance from the CG
to the rear axle
h
f
Height between the center of front
sprung mass and the roll center
h
r
Height between the center of rear
sprung mass and the roll center
h
uf
Height of the center of the front
unsprung mass, measured upward
from the road
h
ur
Height of the center of the rear
unsprung mass, measured upward
from the road
h
c
Height of the roll center, measured
upward from the road
h
cf
Height of the front roll center,
measured upward from the road
102 A. NOTATION
h
cr
Height of the rear roll center, mea-
sured upward from the road
I
Xf
Roll inertia of the front sprung
mass
I
Xr
Roll inertia of the front sprung
mass
φ
sf
Roll angle of the front sprung mass
φ
sr
Roll angle of the rear sprung mass
φ
uf
Roll angle of the front unsprung
mass
φ
ur
Roll angle of the rear unsprung
mass
F
Yr
Lateral force of the tires at the vir-
tual axle
M
r
Yaw moment caused by the virtual
rear axle
k
f
Equivalent roll stiff ness coeffi cient
of the front suspension
k
r
Equivalent roll stiff ness coeffi cient
of the rear suspension
k
uf
Equivalent roll stiff ness coeffi cient
of the front unsprung mass
k
uf
Equivalent roll stiff ness coeffi cient
of the rear unsprung mass
l
f
Equivalent roll damping coeffi cient
of the front suspension
l
r
Equivalent roll damping coeffi cient
of the rear suspension
k
b
Torsion stiff ness coeffi cient of vehi-
cle frame
β
m
Slip angle of the middle tires
k
m
Cornering stiff ness coeffi cient of a
middle tire
m
u
Unsprung mass
l
e
Equivalent wheelbase of the triaxle
bus
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