Page 488 - Mechatronics with Experiments

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that is the outlet pressure of compensator valve is smaller or equal to the input pressure, and
similarly, the output pressure of the flow control valve is smaller or equal to the pressure at
its input. The p fb2 pressure is determined by the load conditions downstream. The task of
the compensator pressure is to maintain a constant pressure differential between the input–
output ports of the main flow control valve, labeled as the adjustable orifice in Figure 7.54,

Δp = p − p (7.195)
set fb1 fp2
by controlling the intermediate pressure p fb1 through the movement of the compensator
valve spool,

k spring ⋅ (x preload +Δx ) = p fb1 ⋅ A − p fb2 ⋅ A 2 (7.196)
1
cs
p fb1 = p − K vp ⋅ Δx cs (7.197)
s
where Δx is the spool displacement of the compensator valve. Again, if we eliminate the
cs
Δx from the above equations, and note that K ≫ k , and let A = A for simplicity,
cs vp spring 1 2
it can be shown that
k spring k spring
⋅ (p − p fb1 ) = (p fb1 − p fb2 ) − ⋅ x preload (7.198)
s
K A A
vp 1 1
k spring
p ≈ p + ⋅ x (7.199)
fb1 fb2 preload
A
1
k spring
where the left hand-side of the above equation is approximated as zero since ≈ 0.0.
K vp
If load pressure p increases, so does the p by reducing the pressure drop relative to
fb2 fb1
p , in order to maintain a constant pressure drop across the main flow control valve as long
s
as p ≤ p . When p = p ,if p continues to increase, the compensator valve saturates
fb1 s fb1 s fb2
and cannot maintain the pressure differential. If the load pressure (p ) is so large that the
fb2
pressure differential between p and p is less than the desired pressure differential, then
s fb2
the compensator valve modulation saturates and it tries to do its best by making p as
fb1
close as possible to p (minimizes the restriction). Hence, when supply pressure is constant
s
and the load pressure increases to a level so large that the desired pressure differential
between two ports is not possible, the compensator valve fully opens, trying to minimize
the pressure drop,
p ≈ p (7.200)
fb1 s
ΔP ≈ p − p ≤ ΔP (7.201)
v s fb2 set
This is the condition where pump pressure supply has reached its maximum (saturation)
level and load pressure is very high.
The post-compensator configuration (Figure 7.55) uses two pressure feedbacks to its
spool: input port pressure feedback to one side and output (i.e., maximum load) pressure
feedback to the other side.
The spool movement of the compensator valve is controlled by the following rela-
tionship (Figure 7.55),

k spring ⋅ (x preload +Δx ) = p ⋅ A − p ⋅ A 2 (7.202)
l
1
cs
c
p = p − K vp ⋅ Δx cs (7.203)
c
s