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+//control systems by Nagoor Kani A
+//Edition 3
+//Year of publication 2015
+//Scilab version 6.0.0
+//operating systems windows 10
+// Example 6.6
+
+clc;
+clear; 
+s=poly(0,'s')
+//calculation of gain K
+kv=50//given velocity error constant
+// open loop transfer function G(s)=K/s*(s+1)(s+5)
+//by definition of velocity error constant applying limit s=0 in G(s) 
+disp('the value of K is 250;')
+h=syslin('c',250/(s*(s+1)*(s+5)))
+bode(h)
+show_margins(h)
+xtitle("uncompensated system")
+//from the plot the phase margin of uncompensated system is -44
+//but the system requires phase margin of 20 so lead compensation required
+pm=20//choose PM of compensated system is 20 degree
+//since the lead angle required is greater than 60 we have to realise lead compensator as cascade of two compensators with each compensator providing half of required phase
+phim=69/2//maximum lead angle
+alpha=(1-sind(phim))/(1+sind(phim))
+disp(alpha,'the vale of alpha is')
+wmdb=-20*log(1/sqrt(alpha))////db magnitude
+wm=7.8//from the bode plot of uncompensated system the frequency wm corrosponding to db gain of -6db is 5.6rad/sec
+t=1/(wm*sqrt(alpha))
+disp(t,'the value of t is')
+//transfer function of lead compensator is (s+1/t)/(s+1/alpha*t)
+hc=syslin('c',(0.0784*(1+0.024*s)^2)/(1+0.067*s)^2)
+disp(hc,' transfer function of lead compensator is')
+//open loop transfer function of compensated system is h*hc
+hcmp=syslin('c',h*hc)
+disp(hcmp,'open loop transfer function of compensated system is ')
+figure()
+bode(hcmp)
+show_margins(hcmp)
+xtitle("compensated system")