EEL 4657 : LINEAR CONTROL SYSTEMS

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EEL 4657 LINEAR CONTROL SYSTEMS
LECTURE 33
INSTRUCTOR Dr. LATCHMAN UNIVERSITY OF FLORIDA
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Bode Plot Review

• 1. G(s) 1s?1
• G(jw) 1jw?1

? G(?) G(?)
0 1 0dB 0 1/
?1 1.414 3dB 45 ?
1??1 20log(??11) 90
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Bode Plot Review
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Bode Plot Review

• 2. G(s) 1/1 s?2

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Bode Plot Review
3. G(s) 1s ?1 /1 s?2
G(?)
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Bode Plot Review
3. G(s) ?2n / s2 - 2jz?n ?2n
1/(1- (?/?n)2 2jz (?/?n))
G(?)
?--gt
- 90
- 180
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Lead Design in the ?-domain
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Lead Design in the ?-domain

• 18dB Phase Margin from Gain Compensation
• k 99 system
• Need 60 Phase Margin. Design G(s) to add
• 60-18 42
• Add 5 degree margin of error, 425 47

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Lead Design in the ?-domain

• G(s)(1??s)/(1?s), ?gt1
• maxG(j?) occurs at ? ?m1/(?)1/2T
• G(j?) (?)1/2
• G(j?) ?m (47)
• sin(?m) (? - 1)/ (? 1)
• We want to add 46 degrees of PM at ? ?c
• sin(46) (? - 1)/ (? 1), gt ? 6.366

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Lead Design in the ?-domain

• To find ?m, the new cross over frequency,
• gt ?m 11.13
• But we know that ?m 1/ /(?)1/2T
• gt T 0.0356

G(s)99(10.22663s)/(10.0356s)