Modern Control Engineering

156 Chapter 4 / Mathematical Modeling of Fluid Systems and Thermal Systems

B–4–8.Figure 4–49 shows a flapper valve. It is placed

between two opposing nozzles. If the flapper is moved slight-

ly to the right, the pressure unbalance occurs in the nozzles

and the power piston moves to the left, and vice versa. Such

a device is frequently used in hydraulic servos as the first-

stage valve in two-stage servovalves. This usage occurs

because considerable force may be needed to stroke larger

spool valves that result from the steady-state flow force. To

reduce or compensate this force, two-stage valve configura-

tion is often employed; a flapper valve or jet pipe is used as

the first-stage valve to provide a necessary force to stroke

the second-stage spool valve.

diagram of the system of Figure 4–50 and then find the trans-

fer function between yandx, where xis the air pressure and

yis the displacement of the power piston.

x

y

Oil under

pressure

Oil under

pressure

y

Flapper

x

Figure 4–49Flapper valve.

u

f

l

a

b

Oil under

pressure

Figure 4–51

Aircraft elevator

control system.

B–4–9.Figure 4–51 is a schematic diagram of an aircraft

elevator control system. The input to the system is the de-

flection angle uof the control lever, and the output is the el-

evator angle f. Assume that angles uandfare relatively

small. Show that for each angle uof the control lever there

is a corresponding (steady-state) elevator angle f.

Figure 4–50

Schematic diagram of a

hydraulic servomotor.

Figure 4–50 shows a schematic diagram of a hydraulic

servomotor in which the error signal is amplified in two

stages using a jet pipe and a pilot valve. Draw a block

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