This document presents information on lead compensators. It discusses: 1) What a lead compensator is and how it improves undesirable frequency responses in feedback control systems. 2) How to design phase-lead compensators using the Bode plot method in MATLAB. This includes coding to analyze the response of uncompensated and compensated systems. 3) How to analyze the step response and response to a unit ramp input of uncompensated and compensated systems. 4) Applications of lead-lag compensators in fields like robotics, satellite control, and laser frequency stabilization.

1. Presented by:
Guddu Ali
U.I.D: K10990
Mechanical
TOPIC
LEAD COMPENSATOR
Presented to
Mr. SOMESH
CHATURVEDI
Assistant professor of electrical department

2. CONTENTS:
1. Introduction
2. Compensator
3. Design of phase-lead compensators using bode plot method
4. Response of phase-lead compensators
5. Design uncompensated and compensated systems
6. Response of uncompensated and compensated systems
7. Step response of uncompensated and compensated
system
8. Uncompensated and compensated systems due to
unit ramp input and their response
9. Application

3. INTRODUCTION
Lead compensator:
 A lead compensator is a component in a control system that
improves an undesirable frequency response in a feedback and
control system. It is a fundamental building block in classical
control theory.
with |z| < |p|. That is, zero closer to origin than pole

4. COMPENSATOR
 Using root locus techniques, we have seen how the pole
positions of a closed loop can be adjusted by varying a
parameter
 What happens if we are unable to obtain that performance
that we want by doing this?
 Ask ourselves whether this is really the performance that
we want
 Ask whether we can change the system, say by buying
different components
 Seek to compensate for the undesirable aspects of the
process

5. DESIGNOFPHASE-LEADCOMPENSATORSUSING
BODEPLOTMETHOD
 MATLAB CODING:
clear all;
wm = 4.5; % gain-crossover frequency
alpha = 0.3; % phase-lead compensator parameter
T = 1/wm/sqrt(alpha); % phase-lead compensator time constant
K = 10; % DC compensator gain
% Phase-lead compensator C(s)
cnum = K*[T 1];
cden = [T*alpha 1];
% Open-loop sys G(s)
gnum = [1];
gden = [1 1 0];
% Unity-Gain Feedback Loop H(s)
hnum = [1];
hden = [1];
% Open-loop sys C(s)*G(s)
numo = conv(cnum,gnum);
deno = conv(cden,gden);
% Closed-loop sys
[gnumc,gdenc] = feedback(K*gnum,gden,hnum,hden,-1);
[numc,denc] = feedback(numo,deno,hnum,hden,-1);
bode(cnum,cden);

6. RESPONSE
Frequency (rad/sec)
Phase(deg);Magnitude(dB)
Bode Diagrams
20
25
30
10
-1
10
0
10
1
10
2
10
20
30
Bode plot of phase-lead compensator
 sC
.

7. DESIGN UNCOMPENSATEDAND
COMPENSATED SYSTEMS
sys1 = tf(K*gnum,gden);
sys2 = tf(numo,deno);
[mag1,ph1,w]=bode(K*gnum,gden,logspace(-1,2,500));
[mag2,ph2,w]=bode(numo,deno,logspace(-1,2,500));
subplot(211); semilogx(w,20*log10(mag1),'r',
w,20*log10(mag2),'b');
title('Bode Diagrams'); ylabel('Magnitude (dB)');
legend('uncompensated','compensated', -1);
subplot(212); semilogx(w,ph1,'r', w,ph2,'b');
ylabel('Phase (deg)'); xlabel('Frequency (rad/sec)');
legend('uncompensated','compensated', -1);
MATLAB CODING

8. RESPONSE
10
-1
10
0
10
1
10
2
-100
-50
0
50
Bode Diagrams
Magnitude(dB)
uncompensated
compensated
10
-1
10
0
10
1
10
2
-180
-160
-140
-120
-100
-80
Phase(deg)
Frequency (rad/sec)
uncompensated
compensated
Bode plots of uncompensated and compensated systems.

9. For step response of uncompensated
and compensated system
figure;
sys1c = tf(gnumc,gdenc);
sys2c = tf(numc,denc);
step(sys1c,sys2c);grid;
legend('uncompensated','compensated',-1);
MATLAB coding:
Time (sec.)
Amplitude
Step Response
0 2 4 6 8 10 12
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
uncompensated
compensated

10. CODING FOR UNCOMPENSATED AND
COMPENSATED SYSTEMS DUE TO UNIT RAMP
INPUT:
t=0:0.01:5;
y = t;
[y1,x1]=step(gnumc,conv(gdenc,[1 0]),t);
[y2,x2]=step(numc,conv(denc,[1 0]),t);
[y3,x3]=step(numc,denc,t);
[y4,x4]=step(gnumc,gdenc,t);
plot(t,y1,'r',t,y2,'b',t,y,'g');grid;
xlabel('Time (sec)');
title('Unit Ramp Input response');
legend('uncompensated', 'compensated', 'desired',-1);

11. RESPONSE
0 1 2 3 4 5
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Time (sec)
Unit Ramp Input response
uncompensated
compensated
desired

12. APPLICATION
Lead–lag compensators influence disciplines as varied
as robotics, satellite control and laser frequency
stabilization.
They are an important building block in analog
control systems but it can also be used in digital
control
Controllers are used to improve system parameters but
it is also be done by compensators as well.

13. THANK YOU