5.8.1.41 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 +1) s(s +5)(s + 6)(s+ 20) : The pole/zero excess (pze) is 4 ;1=3, and there is one nite zero at s = ;1. This means that one of the limbs of the root locus will terminate at the zero at s = ;1, and the other three limbs will terminate at zeros at in nity,located at the ends of the asymptotes at  =60  ;;180  ;; and 300  : The asymptotes intersect at  i = P polesofGH ; P zeros of GH pze = (;5;6;20);(;1) 3 = ;10 The root locus, shown in Figure 2, is generated bytheMATLAB program: K=linspace(0,1000,1000);; gh = zpk([-1],[0 -5 -6 -20],10) [R,K] = rlocus(gh,K);; plot(R,'k.') print -deps rl58141.eps 1 -35 -30 -25 -20 -15 -10 -5 0 5 -20 -15 -10 -5 0 5 10 15 20 Figure 2: Accurate root locus 2