Information Technology Reference
In-Depth Information
2.1
Mechanical Transmission
The mechanical transmission consists of the engine which is coupled directly
on the driven wheel where the dynamics of the shaft are neglected. The train
dynamic contains the engine dynamics, the brake dynamics and the block which
calculates the present velocity of the train as a function of the friction force and
the angular momentum between the wheel-track system. The block produces the
values of the present torque on a driven wheel
T
w
, the angular velocity of the
wheel
ω
w
and the present velocity of the train
v
.
The angular momentum of the engine is modelled as a function of the drive
current (
I
) as the controlled variable, and the present angular velocity of the
engine (
ω
). The
i
s
and
w
s
are constants and the
t
n
and
ω
max
are parameters.
T
w
=
min
(
i
s
·
ω
+
t
n
·
I
,
w
s
·
ω
+
w
s
·
ω
max
·
I
)
(1)
The drive current is driven by a PI controller with the desired velocity and
the present velocity as input.
I
(
v
,
v
d
)=
P
d
·
(
v
d
−
v
)+
T
d
·
(
v
d
−
v
)
dt
(2)
To limit the maximum acceleration additional parts have been added. If the
current acceleration (
a
) exceeds the max acceleration (
max acc
) the difference
of them is multiplied by a scaling factor and then subtracted from the drive
current. Equation 2 can then be rewritten to:
P
d
·
(
v
d
−
v
)+
T
d
·
(
v
d
−
v
)
dt
:
a
≤
a
max
I
(
v
,
v
d
)=
(3)
P
d
·
(
v
d
−
v
)+
T
d
·
(
v
d
−
v
)
dt
−
(
a
−
a
max
)
·
a
limit
:
a
>
a
max
The dependency of the angular velocity
ω
and the toque is given by the
formula
ω
=
t
T
ω
−
R
w
·
(
F
e
+
F
b
)
dt
(4)
I
0
where
I
is the moment of inertia of the rotating mass of the engine and the driven
wheel,
F
e
is the resistance force of the environment,
R
w
denotes the radius of
the wheel and
F
b
describes the braking force. The present velocity is calculated
in the same way
v
=
t
F
t
−
F
e
−
F
b
dt
(5)
m
0
where
m
is the mass of the train and
F
t
the traction force induced from the
wheel into the track. The traction force is calculated by
F
t
=
T
w
R
w
·
μ
a
(6)
where
μ
a
denotes the adhesion coecient between wheel and track.
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