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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