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JWST499-Cetinkunt
JWST499-c07
ELECTROHYDRAULIC MOTION CONTROL SYSTEMS 519
the natural frequency of an EH axis are the compressibility of the fluid (its spring effect)
and the inertial load on the axis. The fluid spring effect is modeled by its bulk modulus and
fluid volume. The lowest natural frequency is approximated as
√
w = K∕M (7.295)
n
where M is the total inertia moved by the axis. For varying load conditions, the worst case
inertia should be considered. The spring coefficient, K, of the axis is approximated by
( 2 )
A A 2
K = he + re (7.296)
V he V re

where, A and V represents cross-sectional area and volume, he and re subscripts refer to the
head-end and rod-end of the cylinder, respectively. The fluid bulk modulus, is defined as
−ΔP
= (7.297)
ΔV∕V
5
The typical range of values for is 2to3 ⋅ 10 psi.
It is important to note that entrapped air in hydraulic fluid reduces the effective
bulk modulus very significantly, whereas dissolved air has very little effect. Furthermore,
bulk modulus is a function of the temperature, and generally reduces with increasing
4
temperature. For mineral oil type hydraulic fluid, bulk modulus is about 30 × 10 psi at
◦
◦
4
50 F, and reduces to about 15 × 10 psi at about 200 F temperature [14].
The V and V are functions of cylinder position, hence the effective stiffness is
he re
a function of the cylinder position. The natural frequency of the axis varies as a function
of the cylinder stroke. The minimum value of the natural frequency is around the middle
position of the cylinder stroke. Unless advanced control algorithms are used, closed loop
control system gains should be adjusted so that the closed loop system bandwidth stays
below 1∕3 of this open loop natural frequency. In general the natural frequency of the valve
is much larger than the cylinder and load hydraulic natural frequency. Therefore, the valve
natural frequency is not the limiting factor in closed loop performance of most applications.
When the open loop system and load dynamics has low damping, the closed loop
system bandwidth using position feedback is severly limited due to the low damping ratio,
that is to much lower values than the 1∕3 w , where w is the open loop system natural
n
n
frequency. Therefore, it is necessary to add damping into the closed loop system in order
to achieve higher closed loop bandwidth. This can be achieved in two ways:
1. By-pass the leakage orifice at the valve between two sides of the actuator. This,
however, has two drawbacks: 1. it wastes energy, 2. the static stiffness of the closed
loop system against load disturbance is reduced.
2. Velocity and/or pressure feedback in the valve control.

The standard pressure compensated flow control valve increases the effective damping in
the closed loop system by modifying the pressure-flow characteristics of the valve. The fact
that the valve affects flow as a function of pressure, that is a constant times the pressure,
it indirectly affects the velocity since flow rate and actuator velocity are closely related.
Hence, the feedback in the form of velocity or pressure adds damping. However, the cost is
the reduced static stiffness of the closed loop system. The pressure feedback alone makes the
pressure-flow (PQ) characteristics of the valve linear, which has the effect of increasing the
damping.