DATA REPRESENTATION
In the early days of computing, there were common
misconceptions about computers.
One misconception was that the computer was only a giant
adding
machine performing arithmetic operations. Computers
could do much more
than that, even in
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Classical design in the s-plane 119
5.3.2
The root locus method
This is a control system design technique developed by W.R. Evans (1948) that
determines the roots of the char
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Classical design in the frequency domain 155
(ii) Phase plot: This has three asymptotes
. A LF horizontal asymptote at 0
. A HF horizontal asymptote at 90
. A Mid-Frequency (
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Classical design in the s-plane 143
Demonstrate that
(i) the two breakaway points occur at
b1 0:623
b2 2:53
(ii) the imaginary axis crossover occurs when K 0:464
Solution
(a)
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Classical design in the frequency domain 179
in the s-plane to improve system performance. In a similar manner, it is possible
to design compensators (that are usually introd
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Classical design in the frequency domain 191
Case study
Example 6.7
A process plant has an open-loop transfer function
G(s)H (s)
30
(1 0:5s)(1 s)(1 10s)
(6:116)
As it stands
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State-space methods for control system design 251
where M is the controllability matrix,
P
a1 a2
T a2 a3
T
TF
WT F
TF
R an 1 1
1
0
equation (8.88)
Q
F F F an 1 1
FFF
1
0U
U
U
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State-space methods for control system design 239
Solution
State equation
P
QP
0
x1
R x2 S R 0
2
x3
QP Q P Q
1
0
x1
0
0
1 SR x2 S R 0 Su
6 3
1
x3
Output equation
P
y [4
Q
x1
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Digital control system design 203
f *(t )
1.0
0
T
2T
3T
4T
t
Fig. 7.7 z-Transform of a sampled unit step function.
Solution
From equations (7.6) and (7.7)
Z [1(t)]
I
1(kT )z
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Digital control system design 215
j
3s
8
Im
3s
8
s
8
3
4
s
8
4
r =1
s-plane
Re
z-plane
Fig. 7.18 Mapping constant ! from s to z-plane.
j
Im
x
8
x
9 22
x
5
x
6s
8
7
x
x
10
x
7