Modern Control Engineering

Example Problems and Solutions 147

Oil under

pressure

A

y

x

Figure 4–34
Hydraulic jet-pipe
controller.

mentx, the oil flows to the right side of the power piston, and the oil in the left side of the power

piston is returned to the drain. The oil flowing into the power cylinder is at high pressure; the oil

flowing out from the power cylinder into the drain is at low pressure. The resulting pressure

difference causes the power piston to move to the left.

For a small jet-nozzle displacement x, the flow rate qto the power cylinder is proportional to

x; that is,

For the power cylinder,

whereAis the power-piston area and ris the density of oil. Hence

where constant. The transfer function Y(s)/X(s)is thus

The controller produces the integral control action.

Y(s)

X(s)

=

K

s

K=K 1 (Ar)=

dy

dt

=

q

Ar

=

K 1

Ar

x=Kx

Ar dy=q dt

q=K 1 x