Design Project 1 for EE4580
As in the distributed notes, the linearized model for inverted pendulum consists of two
transfer functions. We aim to design
G
yu
(
s
)and
G
θu
(
s
) such that the dominant dynamics for
the closedloop system have damping ratio 0.83, and natural frequency 1.83. Moreover the
steadystate error for the position of the cart is zero. The design can proceed as follows:
1. We consider ﬁrst design of
G
(
s
)=
num
(
s
)
den
g
(
s
)
=
K
gy
s
+
z
y
s
+
p
g
G
θu
(
s
num
θu
(
s
)
den
g
(
s
)
=
K
gθ
s
+
z
θ
s
+
p
g
such that the transient performance is satisﬁed. Iterative design method can be employed
using both 0
o
and 180
o
root locus methods.
2. We then modify the compensators into the form
G
(
s
num
(
s
)
den
g
(
s
)
=
K
(
s
+
z
y
)(
s
+
z
²
)
s
(
s
+
p
g
)
G
θu
(
s
num
θu
(
s
)
den
g
(
s
)
=
K
s
+
z
θ
s
+
p
g
with
z
²
>
0 a very small number. Note that other parameters need be adjusted approri
ately in order to satisfy the transient performance reqirements.
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 Fall '10
 GU
 Root Locus, Root Locus Methods, iterative design method, transient performance

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