Solution 5.8.6.2 Im(s) Re(s) XX X -1 -2 -40 s s + 40 s + 2 s s + 1 Figure 1: Angles from Complex poles and zeros The loop transfer function is GH(s)= K(s+2) s(s+ 1)(s+40) Figure 1 shows howwewould calculate the gain in the vicinityofs = ;3:5 whichisthe approximate location of the break-in point. Thus, K = jsjjs+1jjs+40j js+2j : The MATLAB program z=2;; p1 =0;; p2 = 1;; p3 =40;; s=linspace(-3,-6,100);; K=(abs(s + p1).*abs(s + p2).*abs(s+p3))./abs(s+z);; plot(s,K) print -deps 5862b.eps generates the plot shown in Figure 2, which shows the break-in pointisjust to the left of s = ;3:5 rightaboutwhereweexpected it to be. 1 -6 -5.5 -5 -4.5 -4 -3.5 -3 210 215 220 225 230 235 240 245 250 255 Figure 2: K versus s along real axis 2