Aerospace and Electronic Systems Magazine September 2017 - 24
Power by Wire Thrust Vector Control System
qs = qp + qa
(33)
where qa is the output rate of the accumulator.
For the adiabatic process, the balance equation of the accumulator is
p0V0a1.4 = psV1a1.4
(34)
where p0 is the precharge pressure of accumulator, V0a is volume of
the accumulator, and V1a is volume of the accumulator when inlet
pressure is ps.
The volume change of the accumulator ΔV is
(35)
ΔV = V0a − V1a
where nmax is the maximum speed of the pump and ξp and ωnp are
damping coefficient and natural angular frequency of the pump
speed control system.
When uc is negative, we have
qp = qR = Dp
n maxη pv
s + 2ξ pωnp s + ωnp 2
2
uc
pL = pe
(42)
(43)
The highest pressure of a system is limited by a high-pressure
safety valve, therefore
pLmax = pRmax = psmax
(44)
And the flow rate of the accumulator is
The input torque of the pump is
qa = ΔV = −V1a
(36)
Tinput = Dp pL − pR η pm + T0
By the continuity equation of fluid, the system pressure is
Vs dps
= qp − qs
β e dt
(37)
The Vs is volume between pump, accumulator, and servo valve,
and it is given by
(38)
Vs = Vs0 + ΔV
where Vs0 is initial volume.
The maximum pressure of the system is limited by the safety
valve, therefore
ps ≤ psmax
(39)
where psmax is the set pressure of the safety valve.
Based on (17)-(39), the model of valve control PBW system
can be established.
PUMP CONTROL PBW SYSTEM MODELING
Because a filling-oil circuit made up by check valves is used to fill
the oil to the suction side, the pressure at the inlet side of the pump
can be approximately the constant filling-oil pressure pe.
In a pump control system, the actuator is controlled by speed
and direction of a bidirectional fixed displacement pump. The input flow rate of the actuator equals to the output flow rate of the
pump. Therefore, when uc is positive, the flow rate and pressure at
right chamber of the pump are
qp = qL = Dp
pR = pe
24
n max η pv
s 2 + 2ξ pωnp s + ωnp 2
uc
(40)
(41)
(45)
By (17)-(21), (27)-(28), (32), and (40)-(45), the model of a pump
control system can also be established.
NEW PBW SYSTEM MODELING
The model of the new PBW system is consistent with the valve
control system, except that the pressure control method of the system is different and the accumulator is only used to absorb hydraulic impact.
In the system, a shuttle valve is used to choose the larger pressure in two chambers as the load pressure. The model of shuttle
valve is expressed by
pLoad = max( pL , pR )
(46)
Based on the working principle of load sensing theory, the differential pressure is compared in the pressure control valve, and controlling the displacement of the pump to keep the ps is Δp higher
than pLoad. And this dynamic process can be simplified as
up =
1
(1 − ( ps − pLoad ) Δpset )
Ta s + 1
(47)
where Δpset is set value of differential pressure.
It is important to note that the precharge pressure of the accumulator is far higher than the pressure used in the valve control
system, and the volume of the accumulator is smaller than the accumulator used in a valve control system. Therefore, to distinguish
two different accumulators, the precharge pressure and volume of
the accumulator in a new PBW system are expressed by p01 and
V01a.
By (17)-(39) and (46)-(47), the model of a new PBW system
can be established.
IEEE A&E SYSTEMS MAGAZINE
SEPTEMBER 2017
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