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+//Example 10.3
+//page 658
+//Control Systems: Principles and Design 
+//M Gopal, Second Edition, Tata McGraw-Hill
+//Chapter:Compensator design using Bode Plots
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+s=poly(0,"s")
+w=poly(0,'w')
+G=1/((s^2)*(0.2*s+1))
+Ka=10
+pm=35 //degrees
+K=Ka/horner((s^2)*G,0)
+G1=syslin('c',K*G)
+[gm,frg]=g_margin(G1)
+[pm0,frp]=p_margin(G1)
+//Finding extra phase lead required
+phi=pm-pm0+15
+//As phi is large, we use 2 lead compensators in cascade
+phi=phi/2
+alpha= (1-sind(phi))/(1+sind(phi))
+gain_uncomp=-20*log(1/(sqrt(alpha)))
+wc=4.7 //New gain crossover frequency
+z=wc*sqrt(alpha) //z=1/T
+p=wc/sqrt(alpha) //p=1/(alpha*T)
+Kc=K/alpha
+D=Kc*(((s+z)/(s+p))^2)
+disp(D,'Lead Compensator=')
+Gc=syslin('c',G1*D)
+f=figure()
+bode(G1)
+bode_asymp(G1)
+title('Bode plot of uncompensated system')
+a=gca();
+a.parent.background=8; 
+f=figure()
+bode(Gc)
+bode_asymp(Gc)
+title('Bode plot of compensated system')
+a=gca();
+a.parent.background=8; 
+