Solution: 10.8.6.1 Wehave GH(s)= K(s+5) s 2 (s+ 9)(s;+20) The Bode phase and magnitude plots are shown in Figure 1 It would appear that wehave plenty 10 -1 10 0 10 1 10 2 10 3 -140 -120 -100 -80 -60 -40 -20 0 20 10 -1 10 0 10 1 10 2 10 3 -280 -260 -240 -220 -200 -180 Figure 1: Bode phase and magnitude plots of GH of phase margin, but if looks at the Nyquist plot in Figure 2 we see that wenever haveany phase margin. The root locus near the origin, shown in Figure 3 con rms this. The maximum damping ratio of the dominantpolesisalmost zero. Thus phase margin is the better indicator because it tells us that the system has almost no stability. Im(GH) Re(GH) Figure 2: Bode phase and magnitude plots of GH -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 -8 -6 -4 -2 0 2 4 6 8 Figure 3: Root locys near the origin