420 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response MethodDetermination of Static Velocity Error Constants. Consider the unity-feedback
control system shown in Figure 7–16. Figure 7–18 shows an example of the log-magnitude
plot of a type 1 system. The intersection of the initial –20-dBdecade segment (or its
extension) with the line v=1has the magnitude 20 log Kv. This may be seen as follows:
In a type 1 system
Thus,
The intersection of the initial –20-dBdecade segment (or its extension) with the 0-dB
line has a frequency numerically equal to Kv. To see this, define the frequency at this
intersection to be v 1 ; then
or
As an example, consider the type 1 system with unity feedback whose open-loop
transfer function is
If we define the corner frequency to be v 2 and the frequency at the intersection of the
–40-dBdecade segment (or its extension) with 0-dB line to be v 3 , then
v 2 =
F
J
, v^23 =
K
J
G(s)=
K
s(Js+F)
Kv=v 1
2
Kv
jv 1
(^2) = 1
20 log 2
Kv
jv
2
v= 1= 20 logKv
G(jv)=
Kv
jv
, for v 1
dB0- 20 dB/decade
- 40 dB/decade
v in log scale20 log Kvv 2 v 3 v 1v = 1Figure 7–18
Log-magnitude curve
of a type 1 system.Openmirrors.com