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Simon Fraser University
School of Engineering Science
ENSC 483  Modern Control Systems
Spring 2007–Assignment 7
1. Consider the inverted pendulum mounted on a motor driven cart as shown in the Figure 1.
This is a model of the attitude control of a space booster on takeoﬀ, where the objective of the
attitude control problem is to keep the space booster in a vertical position. Applying Newton’s
second law and making some simplifying assumptions (e.g. that the rod is massless, pendulum
mass is concentrated at the end, sin
θ
≈
θ,
cos
θ
≈
1, and
θ
˙
θ
2
≈
0) we get the following state
space representation of the system:
˙
x
=
0
1 0 0
M
+
m
Ml
g
0 0 0
0
0 0 1

m
M
g
0 0 0
x
+
0

1
Ml
0
1
M
u,
x
=
θ
˙
θ
x
˙
x
y
=
ˆ
1 0 0 0
0 0 1 0
!
x
Figure 1: Inverted pendulum on a cart
(a) Assuming that
M
= 2
kg,m
= 0
.
1
kg
and
l
= 0
.
5
m
, investigate if this system is com
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 Spring '07
 MehrdadSaif

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