EE 428
PROBLEM SET 9
DUE: 16 December 2007
Reading assignment: Ch 7, sections 7.1, 7.5, and 7.7.1 (we previously covered concepts in sections 7.2, 7.3, 7.4, and
7.6)
Laboratory sections meet during the week of December 10.
Problem 40:
(25 points)
Consider the closedloop system in Figure 1 where
G
p
(
s
)=
1
s
(10
s
+1)
.
Figure 1: Feedback control system using cascade compensation.
Design a
phaselead
compensator
G
c
(
s
) so that
•
the steadystate error due to a ramp input
r
(
t
t
1(
t
) is less than 1/11, and
•
the peak overshoot to unitstep input is less than 20%.
Your solution must contain the following elements:
1. An analysis showing how the controller parameters are chosen, including appropriate Bode plots.
2. A Bode magnitude and phase plot of the compensated openloop transfer function
G
c
(
s
)
G
p
(
s
). Indicate the
gaincrossover frequency and phase margin on the Bode plot.
3. A plot of the unitstep response of the closeloop system. Use MATLAB to determine the peak overshoot.
4. If the peak overshoot is not within speci±cation, a brief description of what parameter(s) of the design you
would change in the next iteration of the control design and the reason for doing so.
Problem 41:
(35 points)
The concept of state feedback is an important topic in control systems engineering. Consider an
n
th
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 Fall '07
 SCHIANO
 1g, closedloop transfer function

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