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Compensators
Q
UESTION
17
For the closed–loop system in Figure 17 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 17
There are
m
= 2 finite open–loop zeros located at –5 and –8
There are
n
= 3 finite open–loop poles located at –12, –2 and –6
There are
n
= 3 branches and
n
–
m
= 1 branch goes to infinity
The Root Locus is on the real axis from –2 to –5, –6 to –8, and –12 to –∞
The closed–loop characteristic equation is
Substituting
s
=
jω
into the closed–loop characteristic equation and rearranging
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This note was uploaded on 02/01/2012 for the course MECH ENG 279 taught by Professor Landers during the Spring '11 term at Missouri S&T.
 Spring '11
 LANDERS

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