This preview shows pages 1–2. Sign up to view the full content.
Compensators
Q
UESTION
15
For the closed–loop system in Figure 15 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 15
There are
m
= 2 finite open–loop zeros located at –5 and –1
There are
n
= 3 finite open–loop poles located at –0.1, –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 –0.1 to –1, –2 to –5, and –6 to –∞
The closed–loop characteristic equation is
Substituting
s
=
jω
into the closed–loop characteristic equation and rearranging
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '11
 LANDERS

Click to edit the document details