Modern Control Engineering

Problems 153

B–4–2.Consider the liquid-level control system shown in
Figure 4–43. The controller is of the proportional type. The
set point of the controller is fixed.
Draw a block diagram of the system, assuming that
changes in the variables are small. Obtain the transfer func-
tion between the level of the second tank and the distur-
bance input qd. Obtain the steady-state error when the
disturbanceqdis a unit-step function.

C 2

R 1

C 1 h 2

R 2

Q+qi

qd

Q+q 0

H

Proportional

controller

Figure 4–43

Liquid-level control system.

R

C

A

X+x

P+po

P+pi

k

Figure 4–44

Pneumatic system.

B–4–3.For the pneumatic system shown in Figure 4–44,

assume that steady-state values of the air pressure and the

displacement of the bellows are and respectively.

Assume also that the input pressure is changed from to

wherepiis a small change in the input pressure. This

change will cause the displacement of the bellows to change

a small amount x. Assuming that the capacitance of the bel-

lows is Cand the resistance of the valve is R, obtain the

transfer function relating xandpi.

P

–

+pi,

P

X –

–

P ,

–