imtiazhussainfacultymuetedupk Contents Compensation Lead Compensation Lag Compensation LagLead Compensation Compensation Used to Improve the performance of stable or unstable systems Plant ID: 243853
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Slide1
1
Design & Compensation via Root Locus
imtiaz.hussain@faculty.muet.edu.pkSlide2
ContentsCompensationLead Compensation
Lag CompensationLag-Lead CompensationSlide3
Compensation Used to Improve the performance of stable or unstable systems.
Plant
G
(
S
)
Compensator
G
c
(
S
)
H
(
S
)
-Slide4
Lead Compensation Used to Improve the Transient behavior of the system.
Plant
G
(
S
)
Compensator
G
c
(
S
)
H
(
S
)
-Slide5
Lead CompensationConsider the Following Unity feedback system
k=4
p=[0 -2 ]z=[];usys=zpk(z,p,k)rlocus(usys)csys
=feedback(
usys,1
)
[
wn
b]=damp(
csys
)
sgrid
(
b,wn
)
axis
([-3
0
-3 3 ])
Lead Compensation contd…Slide6
Design Requirements It is desired to increase ω
n to 4 rad/sec without
changing damping ratio of closed loop poles. k=4p=[0 -2 ]z=[];usys=zpk(z,p,k)rlocus(usys
)
wn
=[2 4]; b=[0.5 0.5];
sgrid
(
b,wn
)
axis
([-5
0
-5 5 ])
Lead Compensation contd…Slide7
Lead Compensator (Follow the Class Work)
kc=4.68pc=-5.4zc=-2.9lc=zpk(zc,pc,kc)ltiview(lc)Lead Compensation contd…Slide8
Pzmap
of Lead Compensator
Lead Compensation contd…Slide9
Bode plot of Lead Compensator
Lead Compensation contd…Slide10
Root locus of Compensated & uncompensated Systems
b=0.5; wn=[2 4];
ku=4pu=[0 -2 ]zu=[ ];usys=zpk(zu,pu,ku)k=18.7p=[0 -2 -5.4]z=-2.9csys=zpk(z,p,k)rlocus(usys, ‘g’,csys,’b’)
Sgrid(b,wn)
Compensated Vs Uncompensated System
Lead Compensation contd…Slide11
Root locus of Compensated & uncompensated Systems
Compensated Vs Uncompensated SystemUncompensatedcompensatedLead Compensation contd…Slide12
Response of compensated & Uncompensated system
numu=4;
denu=[1 2 4];numc=[18.7 54.23];denc=[1 7.4 29.5 54.23];csys=tf(numc,denc);usys=tf(numu,denu);ltiview(usys, ‘g:’,csys,’b’)
Compensated Vs Uncompensated System
Lead Compensation contd…Slide13
Pzmap of Compensated & Uncompensated System
Compensated Vs Uncompensated System
UncompensatedcompensatedLead Compensation contd…Slide14
Step response of Compensated & Uncompensated System
Compensated Vs Uncompensated System
UncompensatedcompensatedLead Compensation contd…Slide15
Bode plot of Compensated & Uncompensated System
Compensated Vs Uncompensated System
UncompensatedcompensatedLead Compensation contd…Slide16
Steady State Error of Compensated & Uncompensated System
Compensated Vs Uncompensated System
According to final value theoremSteady state error is given byIn MATLAB
limit(f(x),x,0)
Returns the limit of a function
f(x)
as
x
0.
Lead Compensation contd…Slide17
Steady State Error of Compensated & Uncompensated System
Compensated Vs Uncompensated System
clearsyms snumu=4denu=s^2+2*sGu=numu/denunumc=18.7*s+54.23denc=s^3+7.4*s^2+10.8*sGc=numc/denc
kvu=limit(s*Gu,s,0)
kvc=limit(s*Gc,s,0)
essu=1/kvu
essc=1/kvc
Lead Compensation contd…Slide18
Exercise#1
Repeat the same tutorial using SISO Design tool.
Exercise#2Design another lead compensator for the same system and compare the results.Slide19
End of tutorialYou can download this tutorial from:
http://imtiazhussainkalwar.weebly.com/control-system-design-and-analysis.html