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+//caption:root_locus
+//example 7.24.6
+//page 304
+clc;
+s=%s;
+syms K;
+clf();
+g=(K*(s+1)/(s^2+0.4*s+0.4));
+eq=(s^2+0.4*s+0.4)
+p=roots(eq)
+disp(p,"open loop poles are:");
+P=2;
+Z=1;
+k=0
+  A=((2*k+1)*180)/(P-Z);
+  disp(A,"asymptote are at angle:")
+  CH=(s^2+0.4*s+0.4)+K*(s+1)
+CH=sym('(s^2+0.4*s+0.4)+K*(s+1)');
+disp('=0',CH,"characterstics_eq,CH=")
+K=sym('-(s^2+0.4*s+0.4)/(s+1)')
+d=diff(K,s)
+e=s*(s+2)
+disp("break away point s=-2 as it lies on root locus")
+disp("since |G(s)*H(s)|=1")
+disp("which gives K=3.6")
+k=3.6
+g=(k*(s+1))/(s^2+0.4*s+0.4);
+G=syslin('c',g)
+evans(g,200)
+xgrid(1)
+v=[-20 1 -2 2]
+mtlb_axis(v);
+disp(" poles s=(-0.2+j0.6 and -0.2-j0.6)are equidistant from the zero s=-1, hence rootlocus plot is arc of the circle with centre s=-1 and radius 1.")