5.8.1.39 For the system of Figure 1 let For the system of Figure 1 G H C R + - Figure 1: Standard Closed Loop Con guration G(s)H(s)= K(s +2) s 2 (s +3)(s +10) : The pole/zero excess (pze) is 5;2=3,sothere will be three asympotes at  =60  ;;180  ;; and 300  : The asymptotes intersect at  i = P polesofGH ; P zeros of GH pze = (;1;20;40);(;2;3) 3 = ;18:67: The root locus, shown in Figure 2, is generated bytheMATLAB program: K=linspace(0,1000,1000);; gh = zpk([-2 -3],[0 0 -1 -30 -40],10) [R,K] = rlocus(gh,K) plot(R,'k.') print -deps rl58139.eps 1 -50 -40 -30 -20 -10 0 10 8 6 4 2 0 2 4 6 8 Figure 2: Accurate root locus 2