Modern Control Engineering

Section 7–13 / Lag–Lead Compensation 511

7–13 Lag–Lead Compensation

We shall first examine the frequency-response characteristics of the lag–lead compen-

sator. Then we present the lag–lead compensation technique based on the frequency-

response approach.

Characteristic of Lag–Lead Compensator. Consider the lag–lead compensator

given by

(7–27)

whereg>1andb>1.The term

produces the effect of the lead network, and the term

produces the effect of the lag network.

s+

1

T 2

s+

1

bT 2

=ba

T 2 s+ 1

bT 2 s+ 1

b (b 7 1)

s+

1

T 1

s+

g

T 1

=

1

g

°

T 1 s+ 1

T 1

g

s+ 1

¢ (g 7 1)

Gc(s)=Kc±

s+

1

T 1

s+

g

T 1

≤±

s+

1

T 2

s+

1

bT 2

≤

dB

40

30

20

10

0

• 10


• 20


• 90 °


• 180 °


• 270 °
  0.7 1 2 4 6 8 10 20

Large gain

Small

gain

v in rad/sec

f 0 f^0

Figure 7–108
Bode diagram of a
conditionally stable
system.