Section 4–3 / Pneumatic Systems 119
+–
e
a
b
(a) (b)
E(s) b X(s) Pc(s)
a+b
K
a
a+b
A
ks
X+x
Pc+pc
Ps
Figure 4–13
(a) Pneumatic proportional controller; (b) block diagram of the controller.
(a) (b)
(c)
e
a e
b
Ps
pc
X + x
Pc + pc
R
C
E(s) X(s) Pc(s)
K
x
t
t
t
a
a+b
A
ks
b
a+b
1
RCs+ 1
+
Figure 4–14
(a) Pneumatic
proportional-plus-
derivative controller;
(b) step change in e
and the corre-
sponding changes in
xandpcplotted
versust; (c) block
diagram of the
controller.
Consider the pneumatic controller shown in Figure 4–13(a). Considering small changes
in the variables, we can draw a block diagram of this controller as shown in Figure 4–13(b).
From the block diagram we see that the controller is of proportional type.
We shall now show that the addition of a restriction in the negative feedback path
will modify the proportional controller to a proportional-plus-derivative controller, or
a PD controller.
Consider the pneumatic controller shown in Figure 4–14(a). Assuming again small changes
in the actuating error, nozzle–flapper distance, and control pressure, we can summarize
the operation of this controller as follows: Let us first assume a small step change in e.
