Section 4–4 / Hydraulic Systems 125
x
y
qq
p 0 ps p 0
p 1 p 2
4123
(a)
x
(b)
1 2
ps
x 0
2 +x
x 0
2 – x
Load
m b
Figure 4–17
(a) Hydraulic servo
system; (b) enlarged
diagram of the valve
orifice area.
age improves both the sensitivity and the linearity of the hydraulic servomotor. In the
following analysis we shall make the assumption that the ports are made wider than
the valves—that is, the valves are underlapped. [Note that sometimes a dither signal, a
high-frequency signal of very small amplitude (with respect to the maximum
displacement of the valve), is superimposed on the motion of the pilot valve. This also
improves the sensitivity and linearity. In this case also there is leakage through the valve.]
We shall apply the linearization technique presented in Section 2–7 to obtain a lin-
earized mathematical model of the hydraulic servomotor. We assume that the valve is
underlapped and symmetrical and admits hydraulic fluid under high pressure into a
power cylinder that contains a large piston, so that a large hydraulic force is established
to move a load.
In Figure 4–17(b) we have an enlarged diagram of the valve orifice area. Let us
define the valve orifice areas of ports 1, 2, 3, 4 as A 1 ,A 2 ,A 3 ,A 4 ,respectively. Also, define
the flow rates through ports 1, 2, 3, 4 as q 1 ,q 2 ,q 3 ,q 4 ,respectively. Note that, since the
