Solution 5.8.1.33 G H C R + - Figure 1: Feedbackcon guration For the system shown above GH(s)= K(s+2) (s+1+j)(s+1;j)(s+20)(s+40) Tosketch the root locus, wecompile the data shown in Table 1, which determine if there are break-in or break-out points. From Table 1 wesee s -19 -17 -13 -10 -8.5 -8 -7.5 -4.5 -4 -3.5 -3 K 401 1182 2491 3075 3191 3200 3194 2916 2880 2911 3145 Table 1: Gain alonbg real axis that ther is a break-out pointnears = ;8. That means there must be a break-in pointtothe rightofs = ;8. There are four poles and one zero so wehave three asymptotes at 60  ,140  and 300  . The asymptotes intersect the negativerealaxis at s = ;1;1;20;40+ 2 3 = ;20: The completed root locus is shown in Figure 2. The root locus shown in Figure 3 was generated by the MATLAB dialogue: EDU>K = linspace(0,2000,200);; EDU>gh = zpk([-2],[0 -1 -20 -40],10) 1 X XX X Re(s) Im(s) -1 -2-20-40 Figure 2: Sketchofrootlocus 2 -50 -40 -30 -20 -10 0 10 -25 -20 -15 -10 -5 0 5 10 15 20 25 Real Axis I mag A x i s Figure 3: MATLAB generated root locus Zero/pole/gain: 10 (s+2) --------------------- s(s+1) (s+20) (s+40) EDU>rlocus(gh) EDU>print -deps rl58133.eps EDU> 3