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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 6.1
+
+clc;
+clear; 
+s=poly(0,'s')
+//calculation of gain K
+//for ramp input ess(steady state error ) is0.2
+ess=0.2
+kv=1/ess
+// open loop transfer function G(s)=K/s*(1+2*s)
+//by definition of velocity error constant applying limit s=0 in G(s) 
+disp('the value of K is 5;')
+h=syslin('c',5/(s*(1+2*s)))
+bode(h)
+show_margins(h)
+xtitle("uncompensated system")
+//from the plot the phase margin of uncompensated system is 18
+//but the system requires phase margin of 40 so lag compensation required
+pm=45//choose PM of compensated system is 45 degree
+phigcn=45-180// phase of G(s) at new gain cross over frequency
+wgcn=0.5//the frequency corrosponding to  phase of -135 is 0.5 rad/sec
+agcn=20//db magnitude at wgcn
+//20log betaa=20
+betaa=10^(agcn/20)
+disp(betaa,'the value for betaa is')
+zc=wgcn/10//zero of lag compensator
+t=10/wgcn 
+disp(t,'the value for t is')
+pc=1/(betaa*t)
+disp(pc,'pole of lag compensator is')
+//transfer function of lag compensation is (s+1/t)/(s+1/betaa*t))
+hc=syslin('c', (10*(1+20*s))/(1+200*s))
+disp(hc,'the transfer function of lag 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")
+
+