Solution 5.8.1.35 G H C R + - Figure 1: Feedbackcon guration For the system shown above GH(s)= K(s+1) s 2 (s+3)(s+10) Tosketch the root locus, wecompile the data shown in Table 1,to de- termine if there are break-in or break-out points. From Table1weseethat s -2.9 -2.8 -2.7 -2.5 -2.3 -2 -1.8 -1.6 -1.4 -1.2 K 3.1 6.3 9.4 15.6 21.9 32 39.9 50.2 67.4 114 Table 1: Gain alonbg real axis there are no break-in 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;10 + 1 3 = ;4: 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 -15],10) Zero/pole/gain: 10 (s+1) ---------------- 1 -15 -10 -5 0 5 -20 -15 -10 -5 0 5 10 15 20 Real Axis Imag Axis Figure 2: MATLAB generated root locus s^2 (s+3) (s+15) EDU>rlocus(gh,K) EDU>print -deps rl58135.eps EDU> 2