Modern Control Engineering

Section 6–8 / Lag-Lead Compensation 331

function for this compensator may be obtained as follows: The complex impedance Z 1

is given by

or

Similarly, complex impedance Z 2 is given by

Hence, we have

The sign inverter has the transfer function

Thus the transfer function of the compensator shown in Figure 6–53 is

(6–21)

Let us define

T 1 =AR 1 +R 3 BC 1 ,

T 1

g

=R 1 C 1 , T 2 =R 2 C 2 , bT 2 =AR 2 +R 4 BC 2

Eo(s)

Ei(s)

=

Eo(s)

E(s)

E(s)

Ei(s)

=

R 4 R 6

R 3 R 5

c

AR 1 +R 3 BC 1 s+ 1

R 1 C 1 s+ 1

dc

R 2 C 2 s+ 1

AR 2 +R 4 BC 2 s+ 1

d

Eo(s)

E(s)

=-

R 6

R 5

E(s)

Ei(s)

=-

Z 2

Z 1

=-

R 4

R 3

AR 1 +R 3 BC 1 s+ 1

R 1 C 1 s+ 1



R 2 C 2 s+ 1

AR 2 +R 4 BC 2 s+ 1

Z 2 =

AR 2 C 2 s+ 1 BR 4

AR 2 +R 4 BC 2 s+ 1

Z 1 =

AR 1 C 1 s+ 1 BR 3

AR 1 +R 3 BC 1 s+ 1

1

Z 1

=

1

R 1 +

1

C 1 s

+

1

R 3

• 
  

• –
  
  
  • 
    
  
  
  
  

C 1

C 2

R 1

R 5

Ei(s) E(s) Eo(s)

Lag–lead network Sign inverter

Z 1

Z 2

R 2

R 3

R 4 R^6

Figure 6–53
Lag–lead
compensator.