16.06 Principles of Automatic Control
Recitation 6
Bode Diagrams
10ps ` 5q
ps ` 0.1qps ` 20q
First, re-write in Bode form:
10 ¨ 5ps{5 ` 1q
25ps{5 ` 1q
“
0.1p10s ` 1q20ps{20 ` 1q p10s ` 1qps{20 ` 1q
α “ 0, K “ 25.
LFA:
slope “ α “ 0
M “ 25 at ω “ 1
HFA:
slope “ ´pn ´ mq “ ´1
Break Points: pole at 0.1, 20, zero at 5.
(At poles, slope decreases by one, at zeros, slope increases by 1)
1
Magnitude
40
20
0
−20
−40
10
−2
10
0
10
2
ω
Phase (deg)
0
−50
−100
−150
10
−2
0
10
Frequency, ω (rad/sec)
10
2
ω
Break points are the same for phase.
Start at 0˝ because α “ 0˝ . At poles phase drops 90˝ , at zeros it increases by 90˝ . For the
phase plot though, we use construction lines to help us draw plot better.
2
100
10
1
0.1
0.01
0.001
0.01
0
0.1
1
10
5
-90
3
100
20
1000
100
10
1
0.1
0.01
0.001
0.01
0
0.1
1
10
5
-90
4
100
20
1000
100
10
1
0.1
0.01
1
0.001
0.01
0
0.1
1
10
5
-90
5
100
2
0
20
1000
100
10
1
0.1
0.01
0.001
0.01
0
0.1
1
10
5
-90
6
100
20
1000
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16.06 Principles of Automatic Control
Fall 2012
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