Modern Control Engineering

Section 7–2 / Bode Diagrams 421

dB

0

• 20 dB/decade


• 40 dB/decade


• 60 dB/decade

v in log scale

20 log Ka

v = 1

va = Ka

Figure 7–19
Log-magnitude curve
of a type 2 system.

Since

it follows that

or

On the Bode diagram,

Thus, the v 3 point is just midway between the v 2 andv 1 points. The damping ratio zof

the system is then

Determination of Static Acceleration Error Constants. Consider the unity-

feedback control system shown in Figure 7–16. Figure 7–19 shows an example of the

log-magnitude plot of a type 2 system. The intersection of the initial –40-dBdecade

segment (or its extension) with the v=1line has the magnitude of 20 log Ka. Since at

low frequencies

it follows that

20 log 2

Ka

(jv)^2

2

v= 1

= 20 logKa

G(jv)=

Ka

(jv)^2

, for v 1

z=

F

21 KJ

=

v 2

2 v 3

logv 1 - logv 3 =logv 3 - logv 2

v 1

v 3

=

v 3

v 2

v 1 v 2 =v^23

v 1 =Kv=

K

F