5.8.1.43 G H + R CΣ Figure 1: Standard Closed Loop Con guration For the system of Figure 1 G(s)H(s)= K(s +2) s 2 (s +25)(s+50) : From the Table 1 wesee that there is a break-in near s = ;5:1anda break-out point near s = ;8. s -5.6 -5.4 -5.1 -5 -6 -7 -8 -9 K 7503 7497 7496.8 7500 7524 7585 7616 7591 Table 1: Locating potential break-in and break-out points The pole/zero excess (pze) is 4 ;1=3, and there is one nite zero at s = ;2. This means that one of the limbs of the root locus will terminate at the zero at s = ;2, and the other three limbs will terminate at zeros at in nity,located at the ends of the asymptotes at  =60  ;;=180  ;;and300  : The asymptotes intersect at  i = P polesofGH ; P zeros of GH pze = (;25;50);(;2) 3 = ;24:33: The root locus, shown in Figure 2, is generated bytheMATLAB program: 1 K=linspace(0,1000,1000);; gh = zpk([-2],[0 0-25-50],10) [R,K] = rlocus(gh,K);; plot(R,'k.') print -deps rl58143.eps -60 -50 -40 -30 -20 -10 0 8 6 4 2 0 2 4 6 8 Figure 2: Accurate root locus 2