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+//caption:root_locus_and_value_of_K

+//example 12.49

+//page 576

+s=%s;

+syms K;

+GH=(K*(s+4))/(s+2)^2

+disp("the characterstics eq. is determined as:")

+CH=(s+2)^2+(K*(s+4))

+CH=sym('((s+2)^2)+K*(s+4)');

+disp('=0',CH,"characterstics_eq,CH=")

+K=sym('((s+2)^2/(s+4))')

+d=diff(K,s)

+e=(s+2)*(s+6)

+r1=roots(e)

+disp(r1,"roots=")

+disp("-2 and -6 is break away point")

+g=(s+4)/((s+2)^2)

+G=syslin('c',g)

+clf();

+evans(g,10)

+xgrid(2)

+disp("for wd=2rad/sec,the point on root locus is s=-4+j2")

+disp("the value of K at s=-4+j2 is 4")

+K=4

+k=4

+g=k*(s+4)/((s+2)^2)

+cl=g/(1+g)

+disp(cl,"C(s)/R(s)=")
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