ME 131 Vehicle Dynamics Homework 4
Due Tuesday, March 16th, 2010
1
Cruise Control Design and Simulation
1.1
Upper Level Controller Design
We would like to simulate the engine dynamics of our vehicle for testing and analysis. For designing purposes
it has been suggested that we use a firstorder filter model for our vehicle:
τ
d
dt
¨
x
+ ¨
x
= ¨
x
des
(1)
Let’s choose a PI control law of the form: ¨
x
des
=

k
p
(
v

v
des
)

k
i
R
(
v

v
des
)
dt
(a) Find the ordinary differential equation relating
v
des
to
v
. Show that if
v
des
=
constant
then
v
ss
=
v
des
.
By assuming the solution to be
v
(
t
) =
e
λt
and setting
v
des
= ˙
v
des
= 0, find the characteristic equation.
It is often easier in control system design to work in the Laplace domain. In this domain the plant model
and the PI controller may be represented as:
P
(
s
) =
v
¨
x
des
=
1
s
(
τs
+ 1)
(2)
C
(
s
) =
k
p
+
k
i
s
(3)
The closedloop system representing the transfer function from
v
to
v
des
can be found by the formula:
T
(
s
) =
P
(
s
)
C
(
s
)
1 +
P
(
s
)
C
(
s
)
(4)
(b) Show that by setting
s
=
λ
the denominator of the closedloop transfer function is the characteristic
equation found above.
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 Spring '09
 vdes, PI control law, mades

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