ECE 147A FEEDBACK CONTROL SYSTEMS  THEORY AND DESIGN F09
Homework 6
Due Friday, November 13th, 2009
Explain all answers!
Problem 1
(
Inspired by Problem 2 of the midterm.
) Consider the plant given in Problem 2 of the
midterm, i.e.,
P
(
s
) =
6(
s
2
+ 4
s
+ 5)
(
s
+ 1)(
s
+ 2)(
s
+ 3)
and the closedloop system arising from the unity negative feedback conFguration using a controller
C
(
s
), setting the reference signal to the constant
r
(
t
) = 4 and the input disturbance as
d
(
t
) =
3 cos(2
t
).
1. Simulate the closedloop system using the controller you proposed on the midterm. (The grader
won’t know what you proposed on the midterm, but there is no shame in being honest here.
The point is to learn from mistakes.)
Does the plant output converge asymptotically to the
reference signal? Why or why not?
2. Simulate the closedloop system using the controller proposed in the solution to the midterm.
Does the plant output converge asymptotically to the reference signal?
Explain why this is
the case by explicitly forming the transfer function from reference to tracking error and the
transfer function from disturbance to plant output and observing where on the
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 Spring '10
 VolkanRodoplu
 Root Locus

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