5.8.1.42 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(s +1)(s+21) : From the Table 1 wesee that there is a break-in near s = ;3:6anda break-out point near s = ;9:6. s -3.2 -3.4 -3.6 -4 -9.4 -9.6 -9.8 K 104.4 102.58 101.79 102 123.78 123.84 123.83 Table 1: Locating potential break-in and break-out points The pole/zero excess (pze) is 3 ;1=2, 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  =90  and270  : The asymptotes intersect at  i = P polesofGH ; P zeros of GH pze = (;1;21);(;2) 2 = ;10: The root locus, shown in Figure 2, is generated bytheMATLAB program: 1 K=linspace(0,25,1000);; gh = zpk([-2],[0 -1 -21],10) [R,K] = rlocus(gh,K);; plot(R,'k.') print -deps rl58142.eps -25 -20 -15 -10 -5 0 15 10 -5 0 5 10 15 Figure 2: Accurate root locus 2