HW/CE# 5
Due Thursday, Nov 5, 2009
(Where applicable, use the “more exact” table on page 2 of the ref sheets to answer the
following.)
1.
Suppose
)
10
(
100
)
(
s
s
s
G
is the openloop gain in a unity feedback system.
a)
What is the phase margin PM and crossover frequency
ω
c
for the system?
b)
Sketch the Nyquist plot for the system for
ω
> 0 in the vicinity of the 1 point.
c)
Suppose we consider the effects of delay in the feedback path such that
sec
041
.
0
where
)
(
o
st
t
e
s
H
o
Note that this will not change
ω
c
.
What is the new phase margin for the system?
d)
Make a rough sketch for the Nyquist plot for the system with delay added.
This need
not be detailed but should show generally what will happen in the vicinity of the 1 point
and zero point on the plot.
e) Estimate Mp, t
r
, and t
s
for the system with delay.
Note that although
ω
c
did not
change,
ω
n
will change in that the phase margin
( and ζ ) changed.
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.
 Fall '08
 Friedrich
 Phase margin

Click to edit the document details