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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 6.5
+
+clc;
+clear; 
+s=poly(0,'s')
+//calculation of gain K
+//given for ramp input ess(steady state error ) is 1/15
+ess=1/15
+kv=1/ess
+// open loop transfer function G(s)=K/s*(s+1)
+//by definition of velocity error constant applying limit s=0 in G(s) 
+disp('the value of K is 15;')
+h=syslin('c',15/(s*(s+1)))
+bode(h)
+show_margins(h)
+xtitle("uncompensated system")
+//from the plot the phase margin of uncompensated system is 13
+//but the system requires phase margin of 45 so lead compensation required
+pm=45//choose PM of compensated system is 45 degree
+phim=37//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=5.6//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',(0.25*(1+0.36*s))/(1+0.09*s))
+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")