Solution: 10.8.6.5 Wehave GH(s)= K (s+ 1)(s+2)(s+5) The Bode phase and magnitude plots are shown in Figure 1, The root locus 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 -50 0 Figure 1: Bode phase and magnitude plots of GH in Figure 2, and the polar plot of GH(I)inFigure 3. Weseefrom the root locus that we can achievealarge damping ratio over a wide range of gains. The polar lot shows that jGH(j!)j will decline rapidly once a magnitude of one is reached. Thus both phase margin and gain margin are prettygood indicators of system stabilityand performance. In this case gain margin mayhaveaslightadvantage, because we see that if weraisethe gain bya little under 20 dB wewillstill have30  of phase margin but very litte gain margin. So, a higher gains wewould proably relie on gain margin. -7 -6 -5 -4 -3 -2 -1 0 1 2 -4 -3 -2 -1 0 1 2 3 4 Real Axis Imag Axis Figure 2: Root locus -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Circle of radius 1 Figure 3: Polar plot of GH(I)