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EE 429
FINAL EXAM
29 APRIL 1996
Name:
ID#:
DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO
nnn
Problem
Weight
Score
1
25
2
25
3
25
4
25
Total
100
This test consists of four problems. Answer each problem on the exam itself; if you use additional
paper, repeat the identifying information above, and staple it to the rest of your exam when you
hand it in. The quality of your analysis and evaluation is as important as your answers. Your
reasoning must be precise and clear; your complete
English sentences should convey what you are
doing.
For your convenience, a zTransform table is provided on page 15 and a calibrated
scale is given on page 16.
1
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View Full DocumentProblem 1:
(25 points)
The sampleddata system shown in Fig. 1 consists of a proportional controller with gain
K
and a plant
with transfer function
G
(
z
). The sample period is
T
=0
.
1 sec. In Fig. 2 on page 4, the root locus of the
closedloop system is shown as
K
varies from zero to in±nity. The DC gain of the plant is 2.6.
±²
³´
±
±
±
±
²

+
∑
R
(
z
)
Y
(
z
)
G
(
z
)
K
Plant
Figure 1: Closedloop sampleddata system with proportional gain
K
.
Please answer parts (i) through (v) by directly using Fig. 2.
Do not solve this problem by fnding
G
(
z
)
From the rootlocus plot.
1. (5 points) Find the maximum gain
K
for which the closedloop system is BIBO stable.
2. (5 points) Compute the value of
K
that will result in a natural response which contains a term of the
form (0
.
1)
k
.
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