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s=%s;
s=poly(0,'s');
t=[0:0.05:10];
syms Kv;
g=(Kv/(s*(0.5*s+1)));
// given Kv=20
Kv=20;
g=(20/(s*(0.5*s+1)));
G=syslin('c',g)
fmin=0.01;
fmax=100;
subplot(2,2,1)
bode(G)
subplot(2,2,2),
plot2d(t,csim('step',t,G))
//bode(G,fmin,fmax)
//show_margins(G)
xtitle("uncompensated system")
[gm,freqGM]=g_margin(G)
[pm,freqPM]=p_margin(G)
disp(gm,"gain_margin=")
disp((freqGM*2*%pi),"gain margin freq=");
disp(pm,"phase margin=")
disp((freqPM*2*%pi),"phase margin freq=");
printf("since P.M is less than desired value so we need phase lead network")
disp("selecting zero of lead compensting network at w=3.9rad/sec and pole at w=24.37rad/sec and applying gain to account attenuation factor.")
gc=(1+0.26*s)/(1+0.04*s)
Gc=syslin('c',gc)
disp(Gc,"transfer function of lead compensator=");
G1=G*Gc
disp(G1,"overall transfer function=");
fmin=0.01;
fmax=100;
subplot(2,2,3)
bode(G1)
subplot(2,2,4),
plot2d(t,csim('step',t,G1))
//bode(G1,fmin,fmax);
//show_margins(G1)
xtitle("compensated system")
[gm,freqGM]=g_margin(G1);
[pm,freqPM]=p_margin(G1);
disp(pm,"phase margin of compensated system=")
disp((freqPM*2*%pi),"gain cross over frequency=")
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