1. 5. Root-LocusKuo-91 (p.428) Example 5.1 )s(R Locations of the roots on the complex plane (s plane) Poles : D 1 (s)=0 Zeros: N 1 (s)=0 Number of branches (D 1 (s) is 5 th degree) n1=[1,3];a1=conv([1,5,0],[1,6]); a2=[1,2,2];p=roots(a2) d1=conv(a1,a2) rlocus(n1,d1) Symmetric about real axis Denominator of H(s)

2. Intersect of asymptotes: From Routh tabulation (Example 3.1) k=35; a=polyadd(d1,k*n1);p=roots(a) Break out (or in) points: n1d=[1];d1d=[5,4*13,3*54,2*82,60]; a=polyadd(conv(n1d,d1),-conv(d1d,n1));roots(a)

3. ksi=0.6;wn=2;sg=-ksi*wn;w=wn*sqrt(1-ksi^2); hold on;plot([0,sg],[0,w]);hold off;rlocfind(n1,d1) rlocfind command is used in order to determine the controller gain K, which gives the desired damping ratio for the system.