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University of California, Santa Barbara
ECE 147b: Digital Control
Winter 2009
Homework 1.
Due 5.00pm Friday, 30th January, 2009 in the homework boxes on the 3rd ±oor of Harold
Frank Hall.
Problem 1.
Consider
x
(
t
) to be a 5 Hz triangle wave with
x
(0) = 1 and
x
(0
.
1) =

1. Find the lowest
sampling frequency,
f
s
, which ensures that at least 90% of the power in
x
(
k
) comes from frequencies which
are not aliased.
Problem 2.
Calculate the zeroorder hold equivalent of each of the following continuoustime systems.
Assume that the sampling time is
T
= 1 second.
a)
P
1
(
s
) =
s
s
+ 1
b)
P
2
(
s
) =
e

3
s
s
2
+
a
2
c)
P
3
(
s
) =
10
e

0
.
5
s
s
+ 5
Problem 3.
We are given a plant,
P
(
s
) =
2
s
+ 0
.
1
.
for which we would like to design a discretetime controller.
a) Design a continuoustime PI controller that achieves the following:
–
Gives zero steadystate error to a step.
–
Gives a rise time which is approximately 1/10th of the risetime of the openloop plant.
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This note was uploaded on 03/02/2009 for the course ECE 147b taught by Professor Staff during the Winter '08 term at UCSB.
 Winter '08
 Staff

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