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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 6.9
+
+clc;
+clear; 
+s=poly(0,'s')
+//calculation of gain K
+kv=80//given velocity error constant
+// open loop transfer function G(s)=K/s*(s+3)(s+6)
+//by definition of velocity error constant applying limit s=0 in G(s) 
+disp('the value of K is 1440;')
+h=syslin('c',1440/(s*(s+3)*(s+6)))
+bode(h)
+show_margins(h)
+xtitle("uncompensated system")
+//from the plot the phase margin of uncompensated system is -46
+pm=40//choose PM of compensated system is 40 degree
+phigcn=40-180// phase of G(s) at new gain cross over frequency
+wgcn=1.8//the frequency corrosponding to  phase of -140 is 1.8 rad/sec
+wgcl=4//choose gain cross over frequency of lag compensator as 4rad/sec
+agcl=23//db magnitude at egcl is 23db
+//agcl=20log*betaa
+betaa=10^(agcl/20)
+disp(betaa,'the value of betaa is')
+zc1=wgcl/10//zero of lag compensator
+t1=10/wgcl 
+disp(t1,'the value of t1 is ')
+pc1=1/(betaa*t1)
+disp(pc1,'pole of lag compensator is')
+//transfer function of lag section is (betaa*1+st1)/(1+s*betaa*t1)
+hc1=syslin('c',(14*(1+2.5*s))/(1+35*s))
+disp(hc1,'transfer function of lag section')
+alpha=1/betaa
+disp(alpha,'the value of alpha is')
+wmdb=-20*log(1/sqrt(alpha))////db magnitude
+wm=17//from the bode plot of uncompensated system the frequency wm corrosponding to db gain of -12db is 17rad/sec
+t2=1/(wm*sqrt(alpha))
+//transfer function of lead section is (alpha*1+st2)/(1+s*alpha*t2)
+hc2=syslin('c',(0.07*(1+0.22*s))/(1+0.0154*s))
+disp(hc2,'transfer function of lead section')
+hc3=syslin('c',hc1*hc2)
+disp(hc3,'the tansfer function of lag lead compensation system is')
+//open loop transfer function of compensated system is h*hc3
+hcmp=syslin('c',h*hc3)
+disp(hcmp,'the overll transfer function of compensated system')
+figure()
+bode(hcmp)
+show_margins(hcmp)
+xtitle("compensated system")
+