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Fig. 14.3
Block diagram for the longitudinal dynamics of the controlled car
Fig. 14.4
Forces acting on the body
•
mg
: weight of the car.
•
θ
: road gradient.
•
l
f
,
l
r
: distance from the mass center to the front and rear axles.
•
h
: height of mass center.
The equation describing the balance of forces is Gillespie (
1992
):
m
x
¨
=
(
F
xf
+
F
xr
)
−
F
a
−
(
F
rf
+
F
rr
)
−
mg
sin
θ
(14.3)
Traction forces are given by:
F
x
=
μ
F
z
(14.4)
where
is the friction coefficient between the tyres and the road, which is explained
later. The load on each axle can be obtained from the balance of torques around
them. Neglecting the effect of wind, these loads have a static part depending on the
μ
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