Solution: 10.8.6.2 Wehave GH(s)= K s(s +1)(s+5) The Bode phase and magnitude plots are shown in Figure 1 In this case both gain margin and 10 -2 10 -1 10 0 10 1 10 2 10 3 -80 -60 -40 -20 0 20 10 -2 10 -1 10 0 10 1 10 2 10 3 -250 -200 -150 -100 Figure 1: Bode phase and magnitude plots of GH phase margin are good indicators. The Bode magnitude plot was drawn for K =0:4. We see that wehave80  of phase margin and nearly 40 dB of gain margin. The root locus near the origin, shown in Figure 2 con rms this. Wecanachievegooddamping ratios for the proper choice of gain, if that gain is lowenough.Ifwehaveagood damping ratio then we are assured that both phase and gain margin will simultaneously be good. As weraise the gain of the system, both gain margin and phase margin decline together. So in this case they are of about equal value in assessing stability. -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -6 -4 -2 0 2 4 6 Figure 2: Root locus near the origin