MEEN 364
Homework Set 12
Fall 2004
November 22, 2004
1
Homework Set 12 – Due November 29, 2004 @ 5:00 PM
(1)
a)
Determine the Gain Margin (GM) and the Phase Margin (PM) of the following
transfer function, (do not use MATLAB):
()
100
4
Gs
ss
=
+
b)
For the transfer function given, determine the gain margin and phase margin using
MATLAB. Also determine whether the negativefeedback system with a unity controller
gain is stable or unstable. Justify your answer.
(2)
Consider the open loop transfer function
4
k
=
+
a)
Determine the gain
k
such that the
phase margin
of the ClosedLoop System with
Unity Negative Feedback and the above open loop transfer function is 30
°
.
(
Hint
: Consider only positive
k
)
b)
What is the gain margin in this case?
(
Note
: Do not use MATLAB. Show the details of your work for full credit)
(3)
For the lead compensator
1
1
Ts
Ds
Ts
α
+
=
+
,
where
1
<
.
a)
Show that the phase of the lead compensator is given by
11
tan (
) tan (
)
TT
φ
ωα
ω
−−
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 '08
 Staff
 Controls, 30°, 40°, 0.5 %, 25 sec

Click to edit the document details