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Lecture 23 – Freq. Domain Compensator Design
5/18/2018 Lecture 23 – Freq. Domain Compensator Design Review: EE571 EE571
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5/18/2018 Review (cont.) EE571 EE571
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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: EE571 EE571
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Lead Compensator Design in Freq. Domain
5/18/2018 Lead Compensator Design in Freq. Domain Let’s look at a Bode Plot of EE571 EE571
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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 EE571 EE571
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Lead Compensation Example
G(s) = 4/(s+2) Specs: ess|ramp = 1/40 gm > 10 dB pm 50o EE571 EE571
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Lead Compensation Example
EE571 EE571
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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) EE571 EE571
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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: EE571 EE571
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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 EE571 EE571
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Lag Compensation Example
G(s) = 4/(s+2) Specs: ess|ramp = 1/40 gm > 10 dB pm 50o EE571 EE571
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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) EE571 EE571
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Lag Compensation Example
EE571 EE571
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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: EE571 EE571
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