Compensators
Q
UESTION
18
For the closed–loop system in Figure 18 with
and , complete the following:
a.
Sketch the Root Locus Diagram. Qualitatively describe the closed–loop system stability
and transient characteristics for 0 <
K
< ∞.
b.
For
K
= 5 and
r
(
t
) = 5, calculate the steady–state error.
c.
For
K
= 5 and
r
(
t
) = 5, simulate the closed–loop system and plot
y
(
t
),
e
(
t
), and
u
(
t
).
d.
Graphically determine the percent overshoot and 2% settling time.
Turn in your Matlab code.
G(s)
KG
C
(s)
U(s)
R(s)
+

Y(s)
E(s)
Figure 18
There are
m
= 3 finite open–loop zeros located at –5 and
There are
n
= 3 finite open–loop poles located at 0, –2, and –6
There are
n
= 3 branches and
n
–
m
= 0 branches go to infinity
The Root Locus is on the real axis from 0 to –2 and –5 to –6
The closed–loop characteristic equation is
Substituting
s
=
jω
into the closed–loop characteristic equation and rearranging
Setting the real and imaginary parts equal to zero and solving simultaneously, 680
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 Spring '11
 LANDERS
 Complex number, real axis, Root Locus Diagram, closed–loop characteristic equation

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