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 conrms 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