Modern Control Engineering

Section 4–3 / Pneumatic Systems 113

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Orifice

Actuating error signal

Flapper

Nozzle

Pneumatic relay

(a)

(b) (c)

Ps

e

a

b

F

Pb+pb

X+x

Z+z

Y+y

Pc+pc

Error signal Error signal

Feedback

signal

E(s) X(s) Pc(s)

Y(s)

(e)

b

a+b

a

a+b

A

ks

E(s)

(f)

Pc(s)

K Kp

b

a+b

e

ee

yy

x

aa

bba+aby

–=

(d)

displacement of bellows equal to the displacement of the diaphragm equal to the

nozzle back pressure equal to and the control pressure equal to When an actuating

error exists, the nozzle–flapper distance, the displacement of the bellows, the displacement

of the diaphragm, the nozzle back pressure, and the control pressure deviate from their re-

spective equilibrium values. Let these deviations be x, y, z, pb, and pc, respectively. (The pos-

itive direction for each displacement variable is indicated by an arrowhead in the diagram.)

P

–

P c.

–

b^ ,

Z

–

Y ,

–

,

Figure 4–8
(a) Schematic diagram of a force-distance type of pneumatic proportional controller;
(b) flapper mounted on a fixed point; (c) flapper mounted on a feedback bellows;
(d) displacement xas a result of addition of two small displacements;
(e) block diagram for the controller; (f) simplified block diagram for the controller.