Page 50 - Servo Motors and Industrial Control Theory -

42 2 Feedback Control Theory Continued

Fig. 2.24 An electronic C R 2
integrator

R 1
V 1 - V 0
OP-AMP
+

R

V (R+ 1 ) V (R · C· s +1 )
o := 2 · Cs o := 2 (2.32)
V R V R · C· s
i 1 i 1
If R is selected as zero then the OP-AMP becomes a pure integrator.
2
When a capacitor is attached to input side of an OP-AMP, it becomes a deriva-
tive and with the addition of a resistor in the input loop, the OP-AMP becomes a
derivative plus a lag network, which is often used to reduce the noise, and usually
amplified in the derivative action (Fig. 2.25).
To find the gain of an OP-AMP, the impedance of the feedback loop must be
divided with the input impedance. Doing this gives

V o := R 2 V o := (R · C· s ) (2.33)
2
V R + 1 V R · C· s +1
i 1 C·s i 1

When a capacitor is added to both input and output loop of the operational ampli-
fier, it becomes a lead-lag network (Fig. 2.26).

Fig. 2.25 An OP-AMP with R 2
derivative action
R 1
V 1
- V
OP-AMP 0
+

R