Modern Control Engineering

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

Engine

Oil under

pressure

k

b

z e

y

a 2 a 1

v

Figure 4–35

Speed control

system.

+

E(s) Y(s)

Z(s)

a 2

a 1 + a 2

K

s

a 1

a 1 + a 2

bs

bs+ k

Figure 4–36

Block diagram for

the speed control

system shown in

Figure 4–35.

A–4–8. Explain the operation of the speed control system shown in Figure 4–35.

Solution.If the engine speed increases, the sleeve of the fly-ball governor moves upward. This

movement acts as the input to the hydraulic controller. A positive error signal (upward motion of

the sleeve) causes the power piston to move downward, reduces the fuel-valve opening, and

decreases the engine speed. A block diagram for the system is shown in Figure 4–36.

From the block diagram the transfer function Y(s)/E(s)can be obtained as

If the following condition applies,

the transfer function Y(s)/E(s)becomes

The speed controller has proportional-plus-integral control action.

Y(s)

E(s)



a 2

a 1 +a 2

a 1 +a 2

a 1

bs+k

bs

=

a 2

a 1

a 1 +

k

bs

b

2

a 1

a 1 +a 2

bs

bs+k

K

s

(^2)  1
Y(s)
E(s)

=

a 2

a 1 +a 2

K

s

1 +

a 1

a 1 +a 2

bs

bs+k

K

s

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