Solution: 10.8.6.4 Wehave GH(s)= K(s+5) s(s +0:5)(s+4)(s+10) 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 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 wecanachieveagood damping ratio only at lowgain. Only here will both phase margin and gain margin be simultaneously good indicators of stability. The polar lot shows that the system has a low phase margin at almost all frequencies. Thus phase margin is the better overall indicator of system stability and performance. -12 -10 -8 -6 -4 -2 0 2 4 -10 -8 -6 -4 -2 0 2 4 6 8 10 Real Axis Imag Axis Figure 2: Root locus Re(GH) Im(GH) Figure 3: Polar plot of GH(I)