1. Lecture 23 – Freq. Domain Compensator Design
5/18/2018
Lecture 23 – Freq. Domain Compensator Design
Review:
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2. 5/18/2018
Review (cont.)
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3. Lead Compensator Design in Freq. Domain
5/18/2018
Lead Compensator Design in Freq. Domain
What’s wrong with using Gc(s) = K to meet gain and phase margin specs?
Form of the Lead Compensator:
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4. Lead Compensator Design in Freq. Domain
5/18/2018
Lead Compensator Design in Freq. Domain
Let’s look at a Bode Plot of
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5. Lead Compensator Design in Freq. Domain
5/18/2018
Lead Compensator Design in Freq. Domain
Parameters which need to be designed:
Procedure:
Pick Kc(s) to meet ess specs
Lump Kc(s) in with G(s) and make Bode Plot of KcG(s)
Measure gain and phase margins
Choose m such that:
Find  where
Find frequency cgnew where
Solve for T
Go back
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6. Lead Compensation Example
G(s) = 4/(s+2)
Specs: ess|ramp = 1/40
gm > 10 dB
pm  50o
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7. Lead Compensation Example
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8. Lead Compensation Example
Matlab Code:
» num=40
num = 40
» den=poly([0 -2])
den =
» margin(num,den)
 m =
Inf
pm =
wcp =
NaN
wcg =
6.1685
» phim=
phim =
» sin(pi*phim/180)
ans =
0.6023
» alpha=(1-ans)/(1+ans)
alpha =
0.2482
» margin(1/sqrt(alpha)*num,den)
» wcgnew=8.8496
wcgnew =
8.8496
» T=1/(sqrt(alpha)*wcgnew)
T =
0.2268
» numc=num*[T 1]
numc =
» denc=conv(den,[alpha*T 1])
denc =
» margin(numc,denc)
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9. Lead Compensator Design in Freq. Domain
5/18/2018
Lead Compensator Design in Freq. Domain
Form of Lag Compensator:
How the heck can we insert a lag compensator and improve stability??????
Idea:
Parameters which need to be designed:
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10. Lag Compensator Design in Freq. Domain
5/18/2018
Lag Compensator Design in Freq. Domain
Parameters which need to be designed:
Procedure:
Pick Kc(s) to meet ess specs
Lump Kc(s) in with G(s) and make Bode Plot of KcG(s)
Measure gain and phase margins
Find frequency cgnew where
Set  where
Set 1/T
Go Back
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11. Lag Compensation Example
G(s) = 4/(s+2)
Specs: ess|ramp = 1/40
gm > 10 dB
pm  50o
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12. Lag Compensation Example
Matlab Code:
» num=40
num = 40
» den=poly([0 -2])
den =
» [gm,pm,wcp,wcg]=margin(mag,(phs-55),w)
gm =
0.0855
pm =
wcp =
1.4004
 wcg =
6.1684
» wcgnew=wcp
wcgnew =
» beta=1/gm
beta =
» T = 10/wcgnew
T =
7.1408
» numlag=num*[T 1]
numlag =
» denlag=conv(den,[beta*T 1])
denlag =
» margin(numlag,denlag)
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13. Lag Compensation Example
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14. Differences in the Lead and Lag Design
5/18/2018
Differences in the Lead and Lag Design
Classic 2nd Order System:
Relationship Between Bandwidth and Settling Time:
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