Compensators
Q
UESTION
1
For the closed–loop system in Figure 1 with
(
29
1
=
s
G
C
and
(
29
2
5
4
5
G s
s
s
=
+
+
, complete the
following:
a.
Sketch the Root Locus Diagram. Qualitatively describe the closed–loop system stability
and transient characteristics for 0 <
K
< ∞.
b.
Calculate
K
such that the steady–state error for a unit step input is 0.15.
c.
For the value of
K
calculated in part b, simulate the closed–loop system for
r
(
t
) = 1 and
plot
y
(
t
),
e
(
t
), and
u
(
t
).
d.
For the value of
K
calculated in part b, calculate the closed–loop pole locations. For each
complex conjugate pair, determine its natural frequency and damping ratio. For each real
pole, determine its time constant.
Turn in your Matlab code.
G(s)
KG
C
(s)
U(s)
R(s)
+

Y(s)
E(s)
Figure 1
There are
m
= 0 finite open–loop zeros
There are
n
= 2 finite open–loop poles located at
2
j

±
There are
n
= 2 branches and
n
–
m
= 2 branches go to infinity
The Root Locus is not on the real axis
The asymptote real–axis intercept is
[
]
[
]
2
2
0
2
a
j
j
n
m
σ

+



=
= 

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 Spring '11
 LANDERS
 Complex number, 2%, 5k, ζ, 2 rad, 5.416 j

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