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Digital Control Theory

ELE4 DCT

Digital Control Theory
Assignment 2
This assignment
is due by 2:00pm, Monday
1
9
October
2015
.
You must show all working clearly and neatly.
Late submissions will not be assessed.
(Total: 25
marks)
Question 1
.
For the
sampled
data system in
Figure 1
, express the output C(z)
as a
function of the input and the transfer functions shown
.
(5
marks)
H
(
s
)
G
(
s
)
R
(
s
)
C
(
s
)
T
E
2
(
s
)
E
1
(
s
)
T
Figure
1
Question 2
.
A discrete
time system is described by the signal
flow graph in
Figure
2
.
The state variables are
labeled
as
)
(
1
k
x
and
)
(
2
k
x
in Figure 1
.
(a)
Write th
e
state
space
equation
of the system
.
(
5
marks)
(b)
D
erive the pulse transfer function
)
(
)
(
z
U
z
Y
of the system in Figure 1
.
(5 marks)
u(k)
0.4
0.8
y(k)
1
2
1
1
z
1
z
1
x
1
(k)
x
2
(k)
Figure
2
Question 3
.
A discrete
time system is given by
)
(
0
1
)
(
0
1
0
5
.
0
)
1
(
k
u
k
k
















x
x
)
(
]
5
.
0
5
.
0
[
)
(
k
k
y
x

(a)
Design a full
state feedback controller of the form
)
(
)
(
k
k
u
Kx


to place the
two closed
loop poles at
,
5
.
0
1

z
8
.
0
2

z
.
(5 marks)
(b)
With the full
state feedback controller designed in (a), write the closed
loop
state equation
.
(5 marks)
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Category: Sample Questions