Modern Control Engineering

The solid curves in Figure 7–96 show the magnitude curve and phase-angle curve for the compen-

sated system. Note that the bandwidth is approximately equal to the gain crossover frequency. The

lead compensator causes the gain crossover frequency to increase from 6.3 to 9 radsec. The in-

crease in this frequency means an increase in bandwidth. This implies an increase in the speed of

response. The phase and gain margins are seen to be approximately 50° and ±qdB, respectively.

The compensated system shown in Figure 7–97 therefore meets both the steady-state and the

relative-stability requirements.

Note that for type 1 systems, such as the system just considered, the value of the static veloc-

ity error constant Kvis merely the value of the frequency corresponding to the intersection of

the extension of the initial –20-dBdecade slope line and the 0-dB line, as shown in Figure 7–96.

Note also that we have changed the slope of the magnitude curve near the gain crossover frequency

from–40dBdecade to –20dBdecade.

Section 7–11 / Lead Compensation 499

40

20

0

• 20


• 40

0 °

• 90 °


• 180 °

Gc

10

Kv

50 °

1246

v in rad/sec

10 20 40 60 100

Gc

10

GcG

GcG

• 6 dB

G 1 = 10 G

G 1 = 10 G

dB

Figure 7–96
Bode diagram for the
compensated system.

4

s(s+ 2)

41.7(s+ 4.41)

s+ 18.4

+

• Figure 7–97
  Compensated
  system.