Solution 5.8.1.36 G H C R + - Figure 1: Feedbackcon guration For the system shown above GH(s)= K(s+1) s 2 (s +3)(s+100) We don't expect break-in or break-out points, but wecheckanyway. The data are shown in Table 1. From Table 1 weseethat there are no break-in s -1.1 -1.2 -1.3 -1.4 -1.5 -1.6 -1.8 -2.2 -2.4 -2.8 K 2274 1280 945 773 664 460 477 315 241 85 Table 1: Gain along real axis or break-out points. There are four poles and one zero so there are three asymptotes. The asymptotes intersect the real axis at  i = ;3;100 + 1 3 = ;34: The root locus shown in Figure 2 was generated by the MATLAB dialogue: EDU>K=linspace(0,1000,1000);; EDU>gh=zpk([-1],[0 0 -3 -100],10) Zero/pole/gain: 10 (s+1) ----------------- 1 -120 -100 -80 -60 -40 -20 0 -10 -8 -6 -4 -2 0 2 4 6 8 10 Real Axis I mag A x i s Figure 2: MATLAB generated root locus s^2 (s+3) (s+100) EDU>rlocus(gh,K) EDU>print -deps rl58136.eps EDU> 2