Solution 5.8.1.34 G H C R + - Figure 1: Nonunityfeedbackcon guration For the system shown above GH(s)= K(s+3) s(s +2)(s+15) : To drawtheroot locus wemakeuseofthe data in Table 1, whichindicates there is no break-in or break-out points between s = ;15 ands = ;3. s ;14 ;13 ;12 ;11 ;10 ;8 ;6 ;4 K 15.3 28.6 40 49.5 57.1 67.2 72 88 Table 1: Gains along the real axis The root locus on the real axis is between the poles at s =0ands = ;1, and to the left of the pole at s = ;15. The pole/sero excess is two, so there will be asymptotes at 90  and 270  .The asymptotes intersect the negative real axis at  i = ;2;15 + 3 2 = ;7: The root locus is shown in Figure 2 1 Re(s) j Im(s) -2 -3 -15 -7 Figure 2: Completed rootlocus 2