Solution: 10.8.6.3
Wehave
GH(s)=
K
s
2
(s+10)
The Bode phase and magnitude plots are shown in Figure 1 In this case both gain margin and phase
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
margin can both be good indicators. The root locus plot, shown in Figure 2, conrms this. We
can achivegood damping ratios for the proper choice of gain, meaning that wewillsimultaneously
havegood phase margin and good gain margin. As we increase the gain both phase margin and
gain margin decline, so wewould hvetosaythat in this case both are of equal value in assessing
stability.This is the usual case, and one reason whywecanrelie so heavily on phase margin in
our designs in chapter 11.
-10 -8 -6 -4 -2 0 2 4
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
Real Axis
Imag Axis
Figure 2: Root locus