Page 23 - Servo Motors and Industrial Control Theory -

1.10 Frequency Response 15

Fig. 1.12 Reduction of a
negative feedback control X(s) G Y(s)
system to a single block
1+HG

Fig. 1.13 Reduction of a
positive feedback to a single X(s) G Y(s)
block. G is the forward path 1-GH
transfer function and H is
the feedback path transfer
function

Fig. 1.14 Frequency 20
response (amplitude ratio
(db)) of a second order f (ω)
system g (ω) 0
h (ω)
–20
fl (ω)
–40
0.1 1 10 100
ω

1
M =
ω 2 4ζω 2
2
2
(1− ) +
ω 2 ω 2
n n
 ω 
 2ζ ω 
ϕ =− tan  n 
−
1
2
 ω 
2 
  1− ω 
n
The frequency response and phase angle for various ξ are shown in Figs. 1.14 and
1.15.
For ς 7 = 0.1, ς = 0.5, ς = 1, ς = 2,
it can be seen that the amplitude ratio response has two asymptudes: one straight
line at low frequency (0 db line) and one straight line at 40 db/decade at high fre-