ECE 147A FEEDBACK CONTROL SYSTEMS  THEORY AND DESIGN F09
Homework 4
Due Friday, October 23, 2009
Explain all answers!
Problem 1
Fact (which you will see explained later in the course): A third order polynomial
equation
s
3
+
as
2
+
bs
+
c
= 0
has roots with negative real part if and only if the coefficients
a
,
b
and
c
are all positive and
ab > c
.
For the third order plant
P
(
s
) =
50
(
s
+ 1)(
s
+ 5)(
s
+ 12)
consider using a PI controller with a zero at
s
=

1.
1. Find the range of nonnegative values for the gain of the controller so that the closedloop
system in unity negative feedback is stable.
2. Use the ‘bode’ command in matlab to plot the loop gain when the gain of the PI controller
is so that the closedloop is on the border of stability.
Comment on the slope of the
magnitude plot at the crossover frequency, and also the phase angle at the crossover
frequency.
3. Using the same Bode plot as in the previous plot, determine the crossover frequency when
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 '10
 VolkanRodoplu
 pi controller

Click to edit the document details