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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 6.2

+

+clc;

+clear; 

+s=poly(0,'s')

+//calculation of gain K

+kv=30//velocity error constant is 30sec^-1

+// open loop transfer function G(s)=K/s*(s+4)*(s+80)

+//by definition of velocity error constant applying limit s=0 in G(s) 

+disp('the value of K is 9600;')

+h=syslin('c',9600/(s*(s+4)*(s+80)))

+bode(h)

+show_margins(h) 

+xtitle("uncompensated system")

+//from the plot the phase margin of uncompensated system is 12

+//but the system requires phase margin of 33 so lag compensation required

+pm=38//choose PM of compensated system is 38 degree

+phigcn=38-180// phase of G(s) at new gain cross over frequency

+wgcn=4.7//the frequency corrosponding to  phase of -142 is 4.7 rad/sec

+agcn=16//db magnitude at wgcn

+//20log betaa=16

+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', (6.3*(1+2.13*s))/(1+13.419*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")

+

+