NONLINEAR PHENOMENA IN HYDRAULIC SYSTEMS

NONLINEAR PHENOMENA IN HYDRAULIC SYSTEMS
Satoru Hayashi
Professor Emeritus, Tohoku University, 981-3202, Sendai, Japan

ABSTRACT
Hydraulic systems include various non-linearities in
static and dynamic characteristics of their components.
Consequently, a variety of nonlinear phenomena occur
in the systems. This paper deals with intrinsic
nonlinear dynamic behaviors of hydraulic systems.
KEYWORDS
Hydraulics, Nonlinear phenomena, Hard self-
excitation, Micro-stick-slip, Chaos
INTRODUCTION
Hydraulic systems consist of various elements: pumps,
actuators, control valves, accumulators, restrictors,
pipelines and the like, which include many types of
nonlinearity, such as pressure-flow characteristics in
control valves, dry friction acting on actuators and
moving parts of valves, collision of valves against
valve seats. As a result, various types of nonlinear
phenomena arise caused by these non-linearities. It is a
marked feature of nonlinear systems that global
behaviors are sometimes quite different from local
behaviors. In such cases, results of linear analysis are
unavailable to estimate global nature of the system.
This paper focuses on the nonlinear phenomena
occurring in hydraulic systems, especially, “hard self-
excitation” [8] whose global stability drastically
changes from local one on the basis of the author’s
studies in the past [1]-[7].

HARD SELF-EXCITATION IN ASYMMET-
RICALLY UNDER-LAPPED SPOOL VALVE
[1],[2]
Spool valves are classified into three types, over-lap
valves, zero-lap valves and under-lap valves on the
basis of the relation of the land-width to the port-width.
They are used properly according to their applications.
Usually in spool valves, the supply side lap is equated
to the exhaust side lap, but the lap of the exhaust side is
often taken smaller than that of the supply side by error
in measurement in working or for stability purpose.
This type of spool valve is called ”asymmetrically
under-lapped spool valve”. Abnormal oscillations so-
called “hard self-excitation” are excited in hydraulic
servo-systems using this type of spool valve shown in
Fig. 1 [1].
“Hard self-excitation” is a kind of a self-excited
oscillation that occurs around a stable equilibrium point
by disturbances beyond a critical value and it is
distinguished from an ordinary self-excited oscillation
which occur around a unstable equilibrium point and is
called “soft self-excitation”. This situation is
demonstrated in Fig. 2, which shows the relation
between soft self-excitation and hard self-excitation by
bifurcation maps of amplitude and phase plane
trajectories of oscillations, where λ is a related system
parameter.
Fig. 1 Servo-system using asym-
metrically lapped spool valve
Fig. 2 Types of self-excitation, bifurcation

maps and phase trajectories
Fig. 3 shows responses of the cylinder of a hydraulic
system shown in Fig. 1 for different magnitudes of step
inputs given to a spool shaft of the system resting at the
neutral position, whose asymmetry lap ratio is
λ(= ε
e
/ε
s
)

= 0.047 (ε
s
=0.75mm) and the supply pressure
is P
s
= 9.5MPa. As shown here, the transient
oscillatory responses (a), (b) and (c) settle down to an
initial equilibrium position for relatively small inputs.
This shows the neutral position is locally stable.
However, the response (d) for larger inputs beyond a
critical valve develops into a finite amplitude
oscillation. This fact shows that the phenomenon is a
typical “hard self-excitation”[1].
Fig. 4 indicates a local stability map of the neutral
position of the system, which is calculated from the
following stability criterion Eq. (1) [2].
[ ]









>+
′






′
+








κκ
020
2
V
aMAABbMbB
V

(1)
and A is the cross-sectional area of the actuator, B the
damping coefficient, C
x
the leakage coefficient, M the
load mass, Q the flow rate of the valve and κ the bulk
modulus of oil.
The curve in Fig. 4 shows the critical supply
pressure against asymmetry ratio Λ(=1−λ). According
to the map, the system using a symmetrical lapped
valve λ=1 (ε
s
= ε
e
) is locally stable for the supply
pressure P
s
=5.9MPa. But for the system using a spool
valve with asymmetry lap ratio λ=0.047, the neutral
position is stable.
Equivalent asymmetry ratio (Λ=1−λ) is gradually
increases according to the increase of the spool
amplitude after the valve begins to move by input
disturbances, even though the system is stable at the
neutral position. The pressure-flow coefficient b in Eq.
(1) drastically increases as shown in Fig. 5. On the
other hand, the flow-gain a changes little. As a result,
the system becomes unstable and the oscillation is
excited. This is the mechanism of the “hard self-
excitation”. Taking into consideration this hard self-

excitation, the self-excited region is enlarged more than
locally unstable region that is between a solid line and a
dashed line as shown in Fig. 6.
Fig. 3 Responses of hydraulic servo-
system with asymmetrical spool valve for
different magnitude of step inputs
,
2
1
0
,2
0
2
0
1
,
0
where
VVV
d
C
e
Cbb
P
Q
P
Q
b
x
Q

a
==++=
′
∂
∂
=
∂
∂
−=
∂
∂
=























Fig.
4 Local stability map by asymmetri-
cal lap ratio

21
0
, PPP
P
Q
b
L
L
−=








∂
∂
=
Fig. 5 Pressure-flow coefficient
NEW DEVELOPMENTS IN PNEUMATICS

Dr. Kurt Stoll
Festo AG & Co., Ruiterstr. 82, D-73734 Esslingen, Germany
ABSTRACT
This paper dealt with the new developments of
pneumatics in the following areas:
• Pneumatic components
• Industry segment specialized applications
• Best before-sales and after-sales services
KEYWORDS: Developments, Pneumatic drive,
Servo control, Field-bus, valve terminal, modular
systems, dynamic simulation, database
INTRODUCTION
Pneumatics were first utilised at the beginning of the
fifties. Fig. 1 shows a device built in 1955, which was
fitted with single-acting aluminium die cast cylinders. A
typical pneumatic system of that time was used in this
device; it consisted of cylinders and manually operated
valves. An operator played the roll of a “logic controller”.
Fig. 1 An early pneumatic system
Fig. 2 A purely pneumatic sequence controller with 12
inputs and 12 outputs
Over the past 50 years, with the rapid developments in
science and technologies, especially in automation,
mechanical, electronic and computer technologies,
pneumatics has been experiencing a quick expansion and
development. Take automation sequence controllers as an
example, the first pneumatic control systems functioned
via valves that were actuated by driven camshafts. In the
seventies many purely pneumatically actuated sequence
controllers such as the QUICKSTEPPER (Fig. 2), which

consisted of several pneumatic logic elements, were used
in applications.
How is pneumatics applied in today’s modern world? I
would like to focus on the new developments in
pneumatics in the following areas:
• Pneumatic components
• Industry segment specialized applications
• Best before and after-sales services
NEW DEVELOPMENTS IN PNEUMATIC
COMPONENTS
o The combination of different techniques
The combining of pneumatics with electronics and of
pneumatics with mechanics became an obvious trend over
the last 10 years.
Behind this trend is the fact that more and more
pneumatic drives, sensors and valves are used in a modern
automatic machine. This means more inputs and outputs
are required in the control system. A purely pneumatic
control system is no longer suitable to meet present
demands. So in most machines today, PLCs or IPCs are
used as sequence controllers together with a large number
of electro-pneumatic converters, or solenoid valves.
As a result, the pneumatic suppliers are faced with
demands to improve the performance and to expand the
functions of pneumatic components. A pneumatic valve
should be easy to install and fast switching. A pneumatic
drive should be able to move faster and more precisely.
Sometimes an electro-pneumatic proportional valve is
required to convert a continuous electronic signal into
pneumatic signal.

All this resulted in the combination of pneumatics,
electronics and mechanics.
By combining pneumatics with mechanics, customers will
not only save engineering time with regard to designing
and testing, but also receive an optimised solution because
the product they receive is proven and tested by the
pneumatics manufacturer.
Fig. 3 shows a swivelling/linear unit, in which a linear
cylinder is combined with a rotary drive to get
independent linear and rotational movements.
Fig. 3 A swivelling/linear unit
Fig. 4 shows pneumatic units used in an assembling
system. This includes a linear and rotary cylinder
combined with a high precision guide unit. Excellent
precision and rigidity can be achieved with this
combination of components.
The “valve terminal” concept was introduced at the
beginning of the nineties. In recent years valve terminals
have been widely used. The origin of such a product is to
meet the demands of the larger scale control system. In a
valve terminal, the valves and electronic I/Os are
integrated in accordance with specific user interfaces (Fig.
5). Customers can order a valve terminal according to the
specification of their application. They will get a complete
factory
Fig.4 Pneumatic units with several precision
mechanical parts
pre-assembled and pre-tested unit. They can link the valve
terminal to a PLC or IPC via the desired interface, such as
multipin or fieldbus. They can even order a valve terminal

with a PLC already integrated. In this way, application
engineers can easily divide their control systems into a
couple of sub-systems. They obtain the sub-systems from
the suppliers with guaranteed functionalities. That is to
say, what the customers get are not only the components,
but also the whole solution, a solution that suits their
application.
Fig. 5 A valve terminal, the combination of pneumatics
and electronics
A valve terminal equipped with fieldbus connection
makes it possible for the pneumatic system to be
integrated as a part of a factory network.
Another example of combination and integration is shown
as Fig. 6, a pneumatic unit with the combination of a
cylinder, sensors, speed control valves and direction
control valve. Where the interfaces to the sensor and
direction valve could be fieldbus or individual
connections.
Fig. 7 is a multi controlled positioning system, a
pneumatic servo-positioning axis is combined with an
electrically driven axis. In this system, we can see that
both the guided pneumatic linear cylinder DGPL and the
guided electrical axis DGEL have the same mechanical
interfaces. This makes it much easier for customers to
design their machines.
Fig. 6 Cylinder, solenoid valve, speed control valves
and sensors in an integrated unit
Fig.7 Pneumatic and electrical drives with the same
mechanical interface
o Compact performance

In many applications, a pneumatic control valve is to be
mounted together with some moving parts of the machine.
In this case, the valve should be as light and as small as
possible. On the other hand, in order to shorten machine
cycle time, the control valves should be installed as close
to the cylinder as possible.
Fig. 8 provides a direct comparison of a solenoid valve
made in 1961 with one made in 1997, both valves have
the same flow rate (400 l/min) but the new generation of
solenoid valve is only 10 mm in width, while the old type
is 40 mm.
Fig.8 In comparison, valves of 1961 and 1997, the
same flow rate, but a quarter of the width
o More intelligence is integrated into products.
Faster movement is often desired on a machine. It is not
difficult to get a cylinder to move faster. But it is more
difficult to stop a fast moving cylinder properly (without
vibrations or shocks).
Fig. 9 shows a soft-stop cylinder, in which a displacement
sensor, a 5/3 dynamic proportional valve and a smart
controller are included. With such a system, the time
taken for the cylinder to travel from one end position to
the other can be reduced by 30%. In addition, 2 freely
selectable intermediate position settings are possible.
Fig.9 Fast speed and soft stop
Fig. 10 shows a pneumatic servo positioning system. A
digital smart controller is employed in such a system.
Fig.10 Smart pneumatic positioning axes
The controller is robust and suitable for industrial
applications. Built-in intelligence enables it to find the

optimised control parameters. The user needs only to
input the essential application data, such as the load,
stroke, diameter and so on. Or even more simply, in the
case of the SPC11 controller, just to push a “teach-in”
button.
o Cutting costs with the modular product concept
In a modern highly automated machine, the control
system often has many functions. One solution is to make
such products, in which all the necessary functions are
integrated, but this may incur high manufacturing costs.
Fig. 11 A modular valve terminal with 26 solenoid
valves and various electronic interfaces
A very elegant way is to use a modular product concept.
The benefit of a modular product for customers is that
they can order the products in modules which exactly
meet their requirements. They only pay for the functions
they need.
A modular valve terminal is shown in Fig. 11. Customers
can configure or select the number and the size of the
valves, the quantity of the electronic I/Os and so on.
Fig. 12 and Fig. 13 show modular vacuum components
and modular air service unit respectively.
Fig.12 A modular vacuum system with freely
combinable suction cup holder, angle
compensator, filter and suction cup
o Innovation, the new driving principle
A new single-acting pneumatic drive - fluidic muscle - is
shown in Fig. 14. It can output 10 times more force than a
standard cylinder of equivalent diameter. Fig. 14 shows
some applications of such a drive.

Fig. 13 A modular air service unit with manual on-off
valve, compressed air filter and regulator,
lubricator, soft-start valve, distributor and
pressure switch
Fig. 14 Fluidic muscle and some typical applications
It is well known that with a pneumatic cylinder it is very
difficult to achieve slow movement without the stick-slip
effect. To overcome this disadvantage electrically driven
cylinders of the same size and with the same installation
interfaces as standard pneumatic cylinders have been
developed and applied in applications. Customers don’t
need to make mechanical modifications to their machines.
TRENDS REGARDING APPLICATIONS
With regard to pneumatic applications, one of the most
important tasks today is to develop more and more
specialized products for the various industry segments.
Fig. 15 Pneumatic components for the food and packing
industry
Fig. 15 shows cylinders and valves that have been
specially developed for the food and packaging industry,
where high corrosion resistance and ease of cleaning are
essential.
The electronics and handling and assembly industry also
need pneumatic products that can meet special
requirements. Fig 4 shows some precisely guided
pneumatic drives with very high rigidity that are suitable
for use in the handling and assembling industry. Fig. 16
shows some miniature precisely guided pneumatic
actuators that suit the applications in the electronics
industry.

Fig. 16 Components for the electronics industry
OPTIMUM SERVICES ARE DESIRED
It is not enough nowadays just to offer customers a good
pneumatic product. Customers need more and more help
with their everyday tasks. This is because they get less
and less time for designing, establishing and maintaining
their machines.
A very efficient way is to help the customer by providing
new software tools.
An electronic catalogue using the database principle
makes it possible to access product information and
drawings quickly and easily, via function searching,
image searching and other searching methods (Fig. 17).
Fig. 18 shows a software tool ProPneu, which differs
from a normal dynamic simulation software tool. ProPneu
can not only check an existing pneumatic system via
dynamic simulation but also automatically select the
components according to the performances required by
the customer. The customer needs only provide Propneu
with a limited amount of information concerning an
application.
The settings and parameters of the components, such as
the setting of the pneumatic cushioning and the flow
control valves, can be automatically optimised by
Propneu, according to the criteria the user has selected.
Propneu can also recommend the appropriate pneumatic
components for a given task, e.g. to move a defined load
in a required time and a certain distance vertically,
horizontally or any inclined installation.
Fig. 19 shows the software FluidDraw that assists

customers in creating pneumatic circuits on a CAD
system. If customers need to know whether their circuit
sequences are correct, then FluidSim is the right
simulation tool.
Fig. 17 Fast product accessing via the electronic catalogue
Fig. 18 ProPneu, an intelligent software for the selecting,
simulating and optimising of a pneumatic system
Fig. 19 Software for designing and simulating circuits
for pneumatic sequences
Fig. 20 3D CAD drawings on a Website
More and more engineers use a CAD system for
machine design, so, it is very helpful for them to get 2D
or 3D CAD drawings of the pneumatic components they
have selected. As shown in Fig. 20, they can now easily
import a 2D or 3D CAD drawing via the Internet.
REFERENCES
[1] Arnold, G., Pneumatics and Hydraulics in the History
of Energy Technology. O+P Vol, 18, 1969
[2] Stoll, Kurt, What is Pneumatics? Thesis, University
of Stuttgart, 1958
[3] Pneumatic Tips, No. 51/1994, Festo Pneumatic,
Esslingen
[4] Pneumatic World, 2000, No. 1, 2
[5] Werner Deppert, Kurt Stoll, Cutting Costs with
Pneumatics, 1988, ISBN 7-111-07456-4, in 14
Languages (including Chinese)
[6] Stefan Hesse, 99 Examples of Pneumatic
Applications, 2000
[7] Hong Zhou, A Smart Pneumatic Servo Positioning
Axis and Its Applications, 3

rd
JHPS, Proceedings of
the Third JHPS International Symposium on Fluid
Power, Yokohama, 1996
The Project Sponsored by ROC, SEM
A RESEARCH AND APPLICATION ON A NEW FNN CONTROL
STRATEGIES
*
Wang Sun’an and Du Haifeng
Xi’an Jiaotong University, 710049, Xi’an, P.R. China

ABSTRACT
As the precise model of most practical mechatronics
system cannot be obtained, the practice of typical
control method is limited. Accordingly, numerous AI
(Artificial Intelligence) control methods have been used
widely. Fuzzy control and Neural Network control have
been an important point in the developing process of the
field. However, shortcomings exist in each of these
methods. For example, the fuzzy control is unable to
learn, and the physical meanings of learning result of
the Neural Network control are not clear. Combining the
strong points of above two methods, a new control
method of FNN (Fuzzy Neural Networks) is explored in
this paper. Additionally, a problem concerning the
traditional network learning is discussed and a solution
to such a problem is obtained subsequently. The new
control strategy does not depend on the classical model
and the algorithm is simple. The results of the
experiments applying the new strategies are discussed.

Through different researches on control system, which
model is unacquainted, the reasonableness, effectiveness
and applying universality of the new control strategies is
proved.
INTRODUCTION
The mechatronics system becomes more and more
complicated. According to the Incompatibility Principle
[1], the higher complicacy of the system is, the lower
ability to describe becomes. So the typical control
methods based on the precise model cannot meet the
need. AI offers new strategies for the mechatronics
control system.
Since the AI Project was launched at MIT in 1957, it
has achieved great success in many fields. It attracts
more and more attention to AI and many AI methods
have been put forward

[2]. Fuzzy and NN (Neural
Networks) are important aspects in AI, simulating
different functions of the human brain. The former
simulates the macroscopical functions, such as
syllogisms, but the latter simulates the associatron,
classification, memory by way of imitating the
microcosmic structure. But the Fuzzy cannot learn and
the NN cannot deduce. In addition, the Fuzzy can be
understood and the learning results of the NN cannot
[3]. The new AI method, FNN , which integrated the
good qualities of the two methods, has been the hotspot
in AI fields.
Firstly, this paper will discuss a new object function of

FNN learning and a problem in NN control system.
Then a new FNN control structure will be put forward
based on them. Finally, some conclusions will be
acquired, supported by related experiments.
THE OBJECT FUNCTION
Object function is very important for the control system.
∫e
2
dt is usually taken as the Object function in time
fields. The smaller the area, like figure 1, which
surrounded by the phase track in the phase space is, the
better performance of the system is. So the integrated
object function can be defined as
deedteJ
∫
+
∫
=
&
βδ
2
(1)
where e is the error between the sysytem’s real output
and the reference input.
e
&
is the differential coefficient
of e . ∫e
2
dt is the general object function,

∫
dee
&
is the
area. δ and β are the weighted coefficients.
Fig. 1 A example of phase space
On second thoughts

( )
dtedt
dt
de
dt
de
de
dt
de
dee
2
&&
=∗∗==
(2)
 dtedee
∫ ∫
=
2
&&
(3)
The area surounded by the phase track is the integration
of the error’s differential coefficient. So the error and its

differential coefficient are synthetically considered in
the new object.
A PROBLEM IN NN CONTROL
NN control just applies the NN’s approximating ability.
A typical NN control system likes figure2.
System
f(U)
u
e
e
&
+
-
W
r
y
a
Fig. 2 The typical structure of NN
Where y is the real output, r is the reference input,
u is the NN’s output, and e is the system error. The
object of the control is made y=r, namely e becomes 0.
The learning method adopted is usually Gradient
Search. Obviously, the error is the main parameter in
this method.
In theory, the error which is needed by the NN
learning is e’, defined as
o
uue −= (4)
Where u
o

is the NN’s desired output. u
o
can be
obtained:
)(
1
rfu
o
−
= (5)
So the general object function can be defined as:
21
))(( rfuJ
e
−
∗
−=
(6)
Then
w
rf
rfu
w
J
e
∂
∂
−−=
∂
∂

−
−
∗
)(
))((
1
1
(7)
Because the precise model of the system can not be
obtained, even though the precise model is obtained,
most practical mechatonics system is very complex.
Therefore, the equations cannot be solved. So u
o
is not
known. Practically, y usually is used to replace u
o
, as a
result, the object function is defined as
2
)( yrJ
e
−=
(8)
So

w
y
yr
w
J

e
∂
∂
−−=
∂
∂
)(
(9)
Generally the following equation is not true.
w
rf
rfu
w
y
yr
∂
∂
−=
∂
∂
−
−
−
)(
))(()(
1
1
(10)
In fact, the signs are different from each other between
these at the two sides of the “=”. So the NN can not

approach the desired value, even the NN’s astringency
can not be guaranteed.
THE NEW CONTROL STRUCTURE
Based on the above discussion, a new control structure
of FNN can be put forward. It looks like figure 3.
Where the network NN1 is FNN network and NN2 is
the RBF network. W is the weight of NN1 and W’ is the
weight of NN2. NN1 is employed to obtain the control
output u. NN2 is just as the system’s inverse model, it is
used to acquire the u
o
, u’s desired output.
System
f(u)
u
e
e
&
+
_
W
r y
a
W'
a'
NN1
NN2
the learning
algorithm
u1

+
_
adjust
adjust
e
e
&
e
u
Fig. 3 The structure of the new FNN
There are lots of types of FNN, but generally they can
be classified two kinds. One is the NN which directly is
constructed by the Fuzzy’s rule,another is the NN which
is fuzzied from the unfuzzy NN.
In this paper, The FNN has two layers. Its topical
structure is achieved by the Fuzzy, and the fuzzy
learning ability becomes strong by taking advantage of
NN. The number of NN’s hidden layer’s nodes is just
the same with that of the fuzzy’s section and the accept
function of the nodes is corresponding to the
membership function of the Fuzzy section.
So define the object function again:
∫
+
∫
+
∫
= dtedtedteJ
u
2

22
γβδ
&
(12)
THE ALGORITHM
The new algorithm’s detail process is the following:
(1) Partition the fuzzy section according to e and
e
&
(2) Initial the network
(3) Calculate
T
Wu *α=
where ) (
21 m
aaa £¬£¬=α is the accept
functionm is the number of the nodes
(4) Modify the weight W and W’
For the j th node, because:
dtegraddtegradJgrad
jjj
www
∫
+
∫
=
22
**
&
βδ

dtegrad
uw
j
∫
∗+
2
γ
(13)
dtegraddtegradJgrad
jjj
www
∫
+
∫
=
22
'''
**
&
βδ
dtegrad
u
w
j
∫
∗+
2
'
γ
(14)


)()(
T
Wfrufryre α−=−=−=
TT
u
WWuue αα −=−= ''1

T
j
TT
j
u
WW
w
e
αα
α
αα
)''(
2
−−=
∂
∂
T
j
TT
j
u
WW

w
e
''
'
)''(
'
2
αα
α
αα −=
∂
∂
jj
w
u
u
uf
ufr
w
e
∂
∂
∗
∂
∂
∗−−=
∂
∂ )(
)]([
2

αα
α
T
j
u
uf
ufr ∗
∂
∂
∗−−=
)(
)]([
u
uya
uyydtegrad
j
T
j
jRw
j
∂
∂
∗−−=
∫
)(
))((
2
αα
jjj
w

u
u
y
yr
w
y
yr
w
e
∂
∂
∗
∂
∂
∗−−=
∂
∂
∗−−=
∂
∂
&
&&
&
&&
&
][][
2

T
j

u
y
yr
αα
α
∗
∂
∂
∗−−=
&
&&
][

(15)
At the k th sample time:

)()1(
)()1()(
kuku
kyky
u
uf
−+
−
+
≅
∂
∂
tkuku
kykyky

u
y
∆∗−+
−
+
∗
−
+
≅
∂
∂
)]()1([
)1()(2)1(
&
yr
t
yr
t
e
e
tt
&&&
−=
∆
−
=
∆
=
→∆→∆ 00
limlim

t
kyky
t
krkr
tt
∆
−
+
−
∆
−
+
=
→∆→∆
)()1(
lim
)()1(
lim
00
t
∆
is the interval of sample time
))(1)((
''
)1()(2)1(
]
)()1()()1(
[
)]()([
)()1(

)()1(
*)()1(
'
kuku
t
kykyky
t
kyky
t
krkr
kykr
kuku
kyky
kwkw
T
j
T
j
jj
−∗
+



∆
−+∗−+
∗
∆
−+
−

∆
−+
∗
+−



∗
−+
−+
∗
∗+=+
αα
α
γ
β
δ
αα
α
η
))()(1(
''
'*)()1(
'
''
kukukwkw
T
j
jj
−+=+

αα
α
η
(16)
In this way, plenty of information is used in the learning
process for the NN1, and the damp of the system is
increase, which is useful for the stability of the system.
This point is proved in the experiments.
(5) If J supplies the demand, then stop, else go to (3).
Experiment
Some experiments using the above methods have been
done.
A three order system’s open-loop model is the
following:
sss
sG
322
2
10*31
1
*
975.4*975.4*041.0*2
975.4
)(
−
+++
=
Its step response likes figure 4. The result that is used
the new FNN control is also shown as figure 4.
Fig 4. The result of the physical emulational experiment

The result is obtained after six times learning.
Apparently it is better than that of PID and BP (The
result of PID and BP is not given). It is found in the
experiment that δ and β are very important for the result
Motor is the typical mechatronics system, but its precise
mathematics model cannot be obtained. Regulating the
motor’s speed is the normal work in the practice, and a
lot of methods in such an aspect have been brought
forward [4][5][6]. Figure 5 is the result of the
experiment about regulating the motor’s speed.
Fig. 5 The result of the experiment about motor
Fig 6. The result of the PID control
The result of the new FNN is obtained after three times
learning. Comparing the results of the experiments, the
strengths of the new FNN are outstanding. In addition,
PID’s parameter is confirmed hardly. The PID
optimized result shown in Fig.6, which is caused by
regulating again and again. According to the
experiments, the availability of the new FNN proposed
above is proved.
SUMMARY AND OUTLOOK
At first, a new object function based on the phase space
is defined, then a problem about NN’s learning is
discussed and a new FNN control Strategies is
proposed, at last two related experiments are practised.
Through the experiments, some results can be obtained:
(1) The new FNN is available.
(2) The new FNN does not need the precise
mathematics model of the system.
(3) The new object function is valid.

(4) The new FNN is good for overcoming the problem
in NN control.
It is very easy for the control rules to be mined from the
New FNN. There are some papers concerning this point
[7][8].
Finally, we would like to point out that both real time
ability of this new control and astringency are the
further work we will explore.
REFERENCE
[1] Sugeno M, K Tanaka, A fuzzy-logic-based
approach to qualitative modeling. IEEE Trans on Fuzzy
Systems, 1993, 1(1): 7-13.
[2] Daniel G.Bobrow, J.Michael Brady, Artificial
Intelligence 40 years later, Artificial Intelligence, 1998,
(103) 1∼4.
[3] Li Shaoyuan, Xi Yugeng, Chen Zengqiang, Yuan
Zhuzhi, The new progresses in Intelligent Control (I),
Control and Decision, 2000, 15(1): 1-5, (in Chinese).
[4] N.C. Sahoo, S.K. Panda, P.K. Dash, A current
modulation scheme for direct torquecontrol of switched
reluctance motor using fuzzy logic, Mechatronics ,
2000, 10 353370.
[5] Ma Hongtao, Wei Zeding, Zhai Cheng, The new
control system for alternating voltage adjusting and
practice, Journal of Hebei Academy of Sciences, 1997
(1): 12-14, (in Chinese).
[6] Xiang Jun, Li Shiwne, A PLL Motor-Speed control
system, Journal of South-West Jiaotong University,
1998, 33(6): 705-709, (in Chinese).
[7] Chen Ming, Wang Jing, Shen Li, Research on

Automatic Fuzzy Rule Acquisition Based on Genetic
Algorithms, Journal of Software, 2000,11(1): 85-90 (in
Chinese).
[8] Hou Yuanhui, Lu Yuchang, Shi Chunyi, Using two-
phase approach to extract knowledge from artificial
neural network, Journal of Qinhua University, 1998,
38(9): 96-99, (in Chinese).
A STUDY OF THE INFLUENCES OF PIPE ON VALVE CONTROL
HYDRAULIC SYSTEM
Kong XiaowuQiu Minxiu, Wei Jianhua, Wu Genmao
State Key Laboratory of Fluid Power, Zhejiang University, Hangzhou, Zhejiang, 310027,P.R.China

ABSTRACT
The accurate mathematical model of valve control
hydraulic system with long pipeline is constructed
through theoretical analysis. The influences of long
pipeline on valve control hydraulic system are
investigated. A series of conclusions were obtained,
which are important to the design and analysis of valve
control hydraulic system.
INTRODUCTION
Large-sized construction machinery usually has tens of
actuators. All of them get power from a central
hydraulic source. Some are far away from the hydraulic
source. The long pipeline between actuator and
hydraulic source is essential sometimes. It causes many
problems to electro-hydraulic system. This paper studies
the influences of long pipeline on valve control system
and comes to some simply and valuable conclusions.
TRANSFER FUNCTION OF VALVE

CONTROL SYSTEM
In order to analyze the characteristics of valve control
system with long pipeline, The transfer function of
valve control system must be established. Fig.1 shows
the principle of valve control system with long pipeline
Fig.1 The principle of valve control system
(1) Pipe Dynamic Characteristics
Equation
[2][4]





Γ+Γ=
Γ+Γ=
)()(
)(
1
)()()(
)()()()()()(
221
221
sshsP
sZ
schsQsQ
sshsQsZschsPsP
C
C
Assume that the hydraulic source supply constant

pressure oil, the return pressure is zero and the length of
in-line and return line is equal, then we obtain
0)()()()()(
0)()()()()(
00
=Γ−Γ
=Γ+Γ
sshsQsZschsP
sshsQsZschsP
vCv
svCsv

)2(
)1(
where
)(
s
Γ
—propagation operator

)(sZ
c
characteristic impedance
(2) Four-way Slide valve Dynamic Equation
If orifice area of slide valve is matching and symmetric,
then the flow-pressure equation is
ρρ
vfsv
d
vfsv

dL
PPP
AC
PPP
ACQ
0
2
0
1
−+
−
−−
=
(3)

ρρ
vfsv
d
vfsv
dvsv
PPP
AC
PPP
ACQQ
0
2
0
10
−+
+

−−
==
(4)
where





−≤
−≥⋅+
=
W
A
X
W
A
XXWA
A
V
VV
10
10
10
1
,0
,






≥
≤⋅−
=
W
A
X
W
A
XXWA
A
V
VV
20
20
20
2
,0
,
1
A
is the orifice area of
AP
→
or
TB
→
,
2

A
is the
orifice area of
BP
→
or
TA
→
,
10
A
and
20
A
are the
orifice area of operating point,
W
is the area gradient,
v
X
is the relative motion of spool to operating point.
d
C
is the flow coefficient. The Laplace transforms of
Eq. (3) and Eq. (4) are as follows
)6()()()()()(
)5()()()()()(
00
00
sPKsPKsPKsXKsQ

sPKsPKsPKsXKsQ
vSsvSSfCSvQSsv
vsvSfCvQL
++−=
+
+
−
=
where







=⋅
≠⋅
−−
−++−−
=
∂
∂
=
0
0
,
,
)||(
)(

2010
2010
0
00
AA
AA
PPP
WC
PPPPPP
WC
X
Q
K
vfsv
d
vfsvvfsv
d
v
L
Q
ρ
ρ
f
L
C
P
Q
K
∂
∂

=







=⋅
≠⋅
−−
+
−+
+
−−
=
0
0
,
,
)
||
(
2
)(
2
2010
2010
0
2010

0
20
0
10
AA
AA
PPP
AAC
PPP
A
PPP
AC
vfsv
d
vfsvvfsv
d
ρ
ρ











=≥

−−
−
=≥
−−
≠⋅
−+
−
−−
=
∂
∂
−=
00,
||2
00,
||2
0,)(
2
1020
0
20
2010
0
10
2010
0
20
0
10
AA

PPP
AC
AA
PPP
AC
AA
PPP
A
PPP
AC
P
Q
K
vfsv
d
vfsv
d
vfsvvfsv
d
f
S
CS
ÇÒ
ÇÒ
ρ
ρ
ρ










=≥−−−
=≥−−
≠⋅−+−−−
=
∂
∂
=
00,||
00||
0)(
10200
20100
201000
AAPPP
WC
AAPPP
WC
AAPPPPPP
WC
X
Q
K
vfsv
d

vfsv
d
vfsvvfsv
d
v
S
QS
ÇÒ
ÇÒ£¬
£¬
ρ
ρ
ρ
CS
L
CS
S
L
S
K
P
Q
KK
P
Q
K −=
∂
∂
==
∂

∂
=
0
0
,
C
S
SC
S
S
SS
K
P
Q
KK
P
Q
K −=
∂
∂
==
∂
∂
=
0
0
,
(3) The Continuity Equation and Force
Balance Equation of Cylinder
)8()(

)7()(
4
2
2
EquationBalanceForce
FXK
dt
dX
B
dt
Xd
mPA
EquationContinuity
PC
dt
dP
E
V
dt
dX
AQ
Ltt
t
t
t
tft
fsl
f
y
tt

tL
+++=
⋅+⋅+=
where
t
A
and
t
X
are the area and motion of hydraulic
cylinder piston respectively,
Y
E
is the equivalent
volume elastic modulus,
t
V
is the general volume of
hydraulic cylinder,
sl
C
is the general leakage
coefficient. Eqs. (1), (2), (5), (6) together with the
Laplace transforms of Eq. (7) and Eq. (8) composed a
set equations, from which we can obtain the transfer
function of system as follows
v
t
X
X

sG
•
=)(
)9(
)1
2
()(2)1
2
(
)(2
'
2
2
1
2
2
1
+++++
+
=
s
s
KsGs
s
sGKK
h
h
h
C
h

h
h
vpv
ω
ξ
ωω
ξ
ω
where

))((
))((
)(
1
sch
sshZ
sG
C
Γ
Γ
=

tt
ty
h
Vm
AE
2
4
=ω

ty
t
t
t
t
ty
t
slC
h
mE
V
A
B
V
mE
A
CK
4
)(
+
+
=ξ
t
ty
Ct
CS
hh
V
mE
KA

K
2
'
−=ξξ

t
Q
v
A
K
K =

t
CSQSCQ
vp
A
KKKK
K
−
=
THEORETICAL ANALYSIS OF THE
INFLUENCES OF PIPE ON VALVE
CONTROL HYDRAULIC SYSTEM
When the influence of pipe is neglected
ssv
PP =
=constant
0
00
== PP

v

)(
1
sG
=0
The transfer function of system is
1
2
)(
2
2
'
++
==
•
s
s
K
X
X
sG
h
h
h
v
v
t
ω
ξ

ω
The influences of pipe on system can be measured by
the difference between
)(
sG
and
)(
'
sG
.
While the difference in amplitude frequency and phase-
frequency characteristic is expressed by
|)(|
||)(||)(||
)(
'
ω
ωω
ω
jG
jGjG
e
A
−
=
and

|))(())((|)(
'
ωϕωϕω

ϕ
jGjGe −=
respectively, we can reach the following conclusion.
If
1|)(|)2(2
1
<<≤− EjGK
K
K
K
CS
Q
QS
C
ω
then
Ee
A
≤)(ω
and
Ee ≤)(ω
ϕ
The certification is neglected here
If we define
|)(|)2(2)(
1
ωω jGK
K
K
Ke

CS
Q
QS
C
−=
,
then
)(
ω
e
can be used to measure the influences of pipe
on system approximately
When slide valve is in different operating position, the
influences of pipe to system are discussed as follows
(i) Zero position
When slide valve is in zero position,
0==
CSC
KK
,
0)(
=
ω
e
. Pipe has a little influence on the dynamic
characteristics of system. The actual value of
c
K
and
cs

K
aren’t zero but very small. So, the influence of pipe
to system is minimal under the condition
(2) Nonzero position
When slide valve is in nonzero position,

QSQ
KK =
,
CSC
KK =
,
|)(|2)(
1
ωω jGKe
C
=
It will be seen that if
C
K
is small enough, the influences
of pipe on system can be neglected. According to the
theory of fluid transmission lines,
|)(|
1
ωjG
reaches
maximal point at resonance frequency and fluctuates
periodically as frequency ascends. Accordingly,
)(

ω
jG
fluctuates periodically relating to
)(
'
ωjG
. The
fluctuation frequency is proportional to the length of
pipe. The fluctuation amplitude descends as frequency
ascends.
SIMULATION STUDY
It will be seen that the influences of pipe on hydraulic
system are related to the steady-state point of slide
valve. Slide valve is in zero position in position
control system and in nonzero position in velocity
control system. The following is the simulation study
of them.
(1) Position Control System
The simulation parameters are as follows:
2.137
=
h
ω
1−
s

11
102.4
−
×=

C
K

12
102.3
−
×=
CS
K

5.0
=
=
QSQ
KK

5.0
=
h
ξ

495.0
'
=
h
ξ

250
=
v

K

9
107.9
−
×=
vp
K

Fig.2 presents the frequency response characteristics of
valve control hydraulic system under different pipe
length. The simulation result shows:
 the frequency response curve of system exists
periodic fluctuation
 the fluctuation frequency is proportional to the length
of pipe.
 the fluctuation amplitude reaches maximum near the
natural frequency of system and is smaller in low-
frequency and high-frequency stage
 The frequency response is generally approximate to
second-order system.
 Fig.2 The frequency response characteristic of system
when slide valve is in zero Position
Fig.3 The frequency response characteristic of system
when slide valve is in nonzero position
50 100 150 200 250 300 350 400 450 500
-180
-160
-140
-120

-100
-80
-60
-40
-20
0
Phase-frequency characteristics
¦Ø£¨1/s£©
¦Õ£¨¦Ø£©
L=25m
L=50m
L=0m
50 100 150 200 250 300 350 400 450 500
-40
-30
-20
-10
0
10
20
30
40
50
Amplitude frequency characteristic
¦Ø£¨1/s£©
A£¨¦Ø£©£¨dB£©
L=0m
L=50m
L=25m
50 100 150 200 250 300 350 400 450 500

-250
-200
-150
-100
-50
0
50
100
Phase-frequency characteristic
¦Ø£¨1/s£©
¦Õ£¨¦Ø£©
L=25m
L=50m
L=0m
50 100 150 200 250 300 350 400 450 500
25
30
35
40
45
50
55
Amplitude frequency characteristic
¦Ø£¨1/s£©
A£¨¦Ø£©£¨dB£©
L=25m
L=50m
L=0m
(2) Velocity Control System
The simulation parameters are as follows

2.137
=
h
ω
1−
s

11
102.4
−
×=
C
K

12
102.4
−
×=
CS
K

5.0
=
=
QSQ
KK

5.0
=
h

ξ

495.0
'
=
h
ξ

250
=
v
K

0
=
vp
K

Fig.3 presents the frequency response characteristics of
valve control hydraulic system under different pipe
length.
The simulation result shows:
the frequency response of system fluctuates
periodically.
 the fluctuation amplitude descends when the
frequency ascends
 the fluctuation frequency is proportional to the length
of pipe.
 If the length of pipe or the value of
C

K
isn’t small
enough, the system can’t be considered as second-
orde system.
CONCLUSION
This paper has presented an accurate mathematical
model for valve control hydraulic system with long
pipeline. On the basis of the analysis to it, some
conclusions are reached.
1. The influences of pipe on system can be measured
approximately with the frequency domain criterion
|)(|)2(2)(
1
ωω jGK
K
K
Ke
CS
Q
QS
C
−=
2. For given pipe parameters,
c
K
decides the influences
of pipe on system in terms of ideal zero lap slide
valve.
3. Pipe makes the frequency response of system
fluctuating periodically. The fluctuation frequency is

proportional to the length of pipe. The fluctuation
amplitude is decided by valve coefficient, pipe elastic
modulo and pipe inner diameter.
4. The influences of pipe are greater to velocity control
system than to position control system.
REFERENCES
[1] T.J.Viersma, A.A.Ham, “Hydraulic Line
Dynamics”,1979.
[2] 
1986
[3] H.E.1
976
[4] “
”1987
[5] .“
”
CAD
[6] .“
”
CAD
[7] “
”94
[8] Chen, Jine, “Theoretic solution of the transient flow
of liquid in the pipe with fluid Machinery”, Journal
of Hydrodynamics, v 4 n 4 Oct 1992. p 119-126
A STUDY ON THE CONTROLLABILITY OF FLOW-PRESSURE
RELATIONSHIP OF THE PILOT OPERATED PRESSURE RELIEF VALVE
Wu Wanrong,Qiu Minxiu,Wei Jianhua,Wu Genmao
Institute of Mechatronic Control Engineering, Zhejiang University, and Hangzhou 310027 P.R.China
ABSTRACT

The flow-pressure relationship is an important external
characteristic of the pilot operated pressure relief valve.
Many research efforts have been put on this topic for its
significant impact on the overall hydraulic system.
Some of the researches focused on the influences of the
hydraulic bridge to the main stage, while the others
attempted to analyze the influence of difference pressure
measurement (direct or indirect) of the system pressure
using control theories. In this project, a novel method
has been adopted. The basic idea is to find out the
correlation between the pilot flow and the overflow of
the main valve, and use this relative function as a
criterion to compensate for the force bore on the valve
poppet. The flow-pressure curve of the relief valve can
be bent upwards(under-compensated), flat, or
downwards(over- compensated). The above scheme has
been utilized in the manufacture’s product catalogs.
Key words: variable hydraulic resistance, force
compensating, relief valve, controllability
INTRODUCTION
In pilot operated pressure relief valve, the main valve is
actually controlled by the pilot hydraulic bridge. On the
other hand, the pilot hydraulic circuit and the main
valve port hydraulic circuit form parallel hydraulic
network. The current researches show that the steady-
state override pressure is related to the control pattern of
the pilot valve and varied with where the pressure
exerting on the pilot valve and where the pressure sign
coming from[1]. This paper intends to find the
correlationship between the pilot flow and the main

overflow of the relief valve, and to control the flow-
pressure characteristic of the pilot operated pressure
relief valve by compensating for the force bore on the
pilot poppet according to the correlationship.
THE CORRELATIONSHIP BETWEEN THE
PILOT FLOW AND THE MAIN
OVERFLOW OF THE RELIEF VALVE
Fig.1 shows the structure and the principle of the relief
valve with compensating for the force bore on the pilot
poppet. And the flow equations and force equilibrium
equations under steady-state are described below.
The related flow equations of the pilot hydraulic circuit
are as follows:

pp
c
q
21
1
1
−= (1)

pp
y
b
q
32
2
2
−= (2)

p
c
q
3
3
3
= (3)
Neglecting the steady-sate hydrodymatic force, the
force equilibrium equation of the pilot poppet:
a
p
a
py
y
k
3
3
2
21
2
)( +=+ (4)
The flow equation of the main valve port:

p
x
b
q
x 1
1

= (5)
the force equilibrium equation of the piston:

p
x
b
A
p
A
p
x
xk
1
02
2
1
1
11
)( −−=+ (6)
Fig. 1 The structure and principle of the relief valve with
compensating for force bore on the pilot poppet
Where 2
11
1
1
ρ
µ
ac
= , 2
13

3
3
ρ
µ
ac
= ;
µ
1
,
µ
3
are
the flow coefficient of orifice r
1
and r
3
respectively,
ρ
is fluid mass density, a
11
and a
13
are the cross-area
of r
1
and r
3
respectively
;
b

1
b
2
the coefficient of the main valve port and
pilot valve port respectively;
b
0
the coefficient of the steady-sate
hydrodymatic force of the main valve port;
A
1
A
2
the effective area of the piston on the
lower end and upper end respectively;
a
2
a
3
the effective area of the different part of
the pilot poppet;
k
1
k
2
spring stiffness
x
1
y
1

the precompression quantity of spring.
The function between q
2
and q
x
can be solved by
formulas (1)~(6), but result is very complex. To
simplify the result, change formulas (1)~(6) into
increment equations. Considering q
1
=q
2
=q
3
, at a steady-
state point(q
20
q
x0
x
0
y
0
) the increments equations
are as follows:
)(
2
21
20
2

1
2
pp
q
c
q
∆−∆=∆ (7)

)(
2
21
20
2
0
2
2
0
20
2
pp
q
y
b
y
y
q
q ∆−∆+∆=∆ (8)
p
q
c

q
3
20
2
3
2
2
∆=∆ (9)

a
p
a
p
y
k
3
3
2
2
2
∆+∆=∆ (10)

p
q
xb
x
x
q
x
q

x
x 1
0
2
0
2
1
0
0
2
∆+∆=∆ (11)
x
xb
q
b
k
p
A
p
xbA
x
∆+=∆−∆− )()(
2
0
2
1
2
0
0
1

2
2
1
00
1
(12)
From equations (7)~(12), the following equation can be
derived.

(
)
( )
q
m
q
cAmm
q
q
a
y
bkxcc
q
q
x
x
xx
∆
+
+
=∆

3
2
0
2
1
2
21
20
2
0
2
3
0
2
2
20
2
3
2
1
0
2
2
2
13
Where
ca
q
ca
q

mm
2
1
3
2
20
2
3
2
2
20
41
22 −+= (14)

xbxb
q
A
q
m
xx
3
0
2
1
00
2
0
1
2
0

2
22 +−= (15)

b
y
kc
y
ka
q
m
2
2
2
0
2
2
30
23
2
20
3
2 −−= (16)
)(
2
3
2
1
2
2
2

0
2
2
3
2
1
0
24
ccb
y
kcc
y
km
++= (17)
The first part (m4) in right hand of formula (14) can be
omitted when compared with the others, so do the last
two parts in equations (15) and (16).Therefore, formula
(13) can be rewritten as follows:
Fig.2 The emulation curve of pilot flow varying with
the changing of the main overflow
(
)
[ ]
q
acAAcaA
qq
q
a
y
bkxcc

q
x
x
x
∆
−+
+
≈∆
3
2
1
12
2
3
2
1
3
200
2
0
2
3
0
2
2
20
2
3
2
1

2
)(4
2
(18)
Generally, A

A

, and each of parameters in formula
(18) is positive, consequently, the pilot flow increases as
the main overflow increases. The theoretical and
experimental relationship of the pilot flow and the main
overflow are shown in Figs 2-3, from which it can be
seen that they coincide very much. Figs 2-3 also show
that the changing amplitude of the pilot flow follows
with the varying of the main overflow under different
system pressure. It can be proven that the results can
meet all pilot operated pressure relief valve with
different structure.
Fig.3 The experimental curve of the pilot flow
varying with the overflow under different system
pressure
THE COMPENSATING FOR THE
FORCE BORE ON THE PILOT POPPET
The disadvantage of general relief valve is that the
system pressure increases with the increasing of the
overflow, and the higher the system pressure, the
greater the override pressure (Fig.4 shows).
Fig.4 The experimental curve of the override pressure
changing with the overflow under different system

pressure
According to the results above, the override pressure of
the relief valve can be compensated by attaching
hydraulic resistance in the pilot hydraulic circuit. The
compensating method is to connect the pilot poppet with
the compensating piston which consists of an orifice
(Fig.1), when fluid flow through the orifice, cause a
pressure difference in it, thus modifying the equilibrium
2
1
30
25
20
15
10
5
P
1
(Mpa)
q
x
(L/min)
)
q
2
(L/min)
)
200100
0 50 100 150 200
0.0

0.2
0.4
0.6
0.8
1.0
1.2
P
1
=10MPa
P
1
=15MPa
P
1
=20MPa
q
2
(L/min)
q
x
(L/min)
0
P
1
(Mpa)
30
20
10
0
0 100 200

q
x
(L/min)
state of force bearing on the pilot poppet and reducing
the resistance of the variable hydraulic resistance of the
pilot valve port to fluid. This results in compensating
the unfavorable effects to system pressure causing by
the factors of the pilot valve, such as hydrodymatic
force, spring force, etc., when the main overflow varies.
Compensating force F
c
:

a
p
F
c 3
3
= 19
According to equation (2), the hydraulic resistance of
the pilot valve port under a steady-state point is as
follows[2]:

y
b
pp
q
d
pd
R

a
aa
a
a
2
32
2
2 −
=
∆
=
In order to discuss the general hydraulic resistance
property of the pilot valve port, the above equation can
be rewritten:

y
b
pp
R
2
32
2 −
= 20
Transform the formula (19) and (20) into increment
equations:

p
a
F
c

3
3
∆=∆ (21)

y
y
b
q
q
pp
R ∆−
∆
−
∆
=∆
3
0
2
2
10
20
21
2
(22)
Solve equations (7)~(10) and (22), we can get:
q
y
bka
q
c

aa
q
y
bka
qy
b
y
bka
q
R
2
3
0
2
2
22
2
20
2
3
32
2
20
3
0
2
2
22
2
20

2
0
2
2
2
0
2
2
22
2
20
)
2
(
)(8
)
2
(
24
∆








+
+

+
+
−
−=∆
(23
Where the latter part of the numerator in the first
fraction can be omitted when compared with the former
part, the other parameters in formula (23) are positive,
therefore, the hydraulic resistance of the pilot valve port
decreases with the increasing of the pilot flow. The
second part of the square bracket of the formula (23)
results from the compensating force, which results in
more reducing the hydraulic resistance of the pilot valve
port with the increasing of the pilot flow. The greater
the parameter a
3
or the smaller the parameter c
3
, the
greater the compensating force and the decreasing
amplitude of the pilot valve port hydraulic resistance.
From formulas (9) and (21), get:

q
c
a
q
F
c
2

2
3
3
20
2
∆=∆ 24
Consequently, compensating force increases with the
increasing of the pilot flow. The variation of the
compensating force with the changing of the pilot flow
has something to do with the pilot flow of the steady-
state point and changes with the different structural
parameters a
3
c
3
, Fig.5 shows the theoretical
relationship of the compensating force and the pilot
flow with the different structural parameter c
3.
Fig. 5 The emulation curve of the compensating force
varying with the changing of the pilot flow
THE CONTROLLABILITY OF THE
FLOW-PRESSURE CHARACTERISTIC
OF THE RELIEF VALVE
Because the changing amplitude of the compensating
force with the varying of the pilot flow is mainly
dependent on the structural parameters a
3
and c
3

according to formula (24), it is reasonable to change the
hydraulic resistance property which varies with the
changing of pilot flow. According to the formula
(7)~(10) and (21):

F
p
c
∆=∆ λ
1
25

)2(
2
2)(
3
0
2
0
2
2
20
3
2
1
2
1
3
2
20

2
3
2
2
20
2
3
2
1
3
0
2
2
2
2
3
2
1
0
2
y
bk
q
ac
ca
q
ca
q
cc
y

bkcc
y
k
+
−+
+
+
=λ
26
From formula (25), it can be seen that different
λ
will
results in different characteristic of the control
pressure p
1
varying with the compensating force:
λ
>0p
1
increases with the increasing of the
compensating force, this is under-compensated
;
λ
=0p
1
keeps constant, and does not change with
the compensating force, right-compensated;
λ
<0p
1

decreases with the increasing of the
compensating force, over-compensated.
Meanwhile, the value of
λ
is only dependent on the
structural parameters and pilot flow. In formula (26),
the value of denominator is positive, so, whether the
value of
λ
is positive, zero or negative is decided by
the value of the numerator. The first two parts of the
numerator in the formula (26) can be omitted when
compared with the others, so the value of
λ
is
mainly dependent on the last two parts , i.e.

caca
2
1
3
2
3
2
− >0
λ
>0

caca
2

1
3
2
3
2
− =0
λ
=0

caca
2
1
3
2
3
2
− <0
λ
<0
Consequently, the value of
λ
is mainly dependent on
the arrangement of the parameters a
2
, a
3
, c
1
, c
3

, When
the parameters a
2
and c
1
are fixed, the value of
λ
is
decided by a
3
and c
3
. Fig.6 shows the theoretical
relationship of the control pressure varying with the
compensating force under different parameter value
of a
3
(or c
3
), i.e.
λ
.
0 2 4 6 8 10 12
0
10
20
30
40
0 0.2 0.4 0.6 0.8 1.0 1.2
c

31
<c
32
<c
33
c
33
c
32
c
31
F
c
(N)
q
2
(L/min)
0 5 10 15
16000000
18000000
20000000
22000000
16
22
20
18
p
1
(MPa)
F

c
(N)
2.5233
×10
-20
-1.9842
×10
-20
-1.4763
×10
-21
( a
2
c
3
2
-a
3
c
1
2
)
Fig.6 The emulation curve of the control pressure
varying with the changing of the compensating force
From formulas (24) and (25):

q
c
a
q

p
2
2
3
3
20
1
2
∆⋅=∆ λ 27
According to formulas (18) and (27), it can be seen that
the flow-pressure relationship of the relief valve is also
dependent on the value of
λ
, i.e. there exists different
flow-pressure characteristic of the relief valve with
the different matching of the parameters a
2
, a
3
, c
1
, c
3
:
under-compensated,
λ
>0, the pressure increases with
the increasing of the overflow; right-compensated,
λ
=0the pressure

keeps constant, and does not change with overflow;
over-compensated,
λ
<0the pressure decreases
with the increasing of the overflow.
EXPERIMENT ON FLOW-PRESSURE
CHARACTERISTIC OF THE RELIEF
VALVE
Fig.1 shows the structure of the experimental valve
(NG10), the relational structural parameters are as
follows[3]: d
r1
=0.6mm, a
2
=12.566mm
2
, a
3
=164.15mm
2
,
A
1
=76.2mmm
2
, A
2
=78.54mm
2
. Fig.7 shows the

experimental results of the pressure varying with the
overflow under d
r3
=1.0mm, d
r3
=1.1mm, d
r3
=1.2mm.
d
r3
=1.0mm, the pressure reduces with the increasing
of the overflow in Fig 5c; d
r3
=1.1mm, the pressure
keeps constant, it does not change with the increasing
or decreasing of the overflow in Fig. 5b; d
r3
=1.2mm,
the pressure increases with the increasing of the
overflow in Fig. 5a. There exists different flow -
pressure characteristic of the relief valve with the
different of d
r3
(or
λ
).
Consequently, it is reasonable to obtain the flow-
pressure characteristic required according to the
different parameters of the pilot hydraulic circuit.
Some kinds of pressure valves have been

manufactured by applying the above principle by
Roxroth Ltd. Fig.8 shows one of the products, a pilot
operated pressure relief valve[4].
Fig.8 The structure and principle of the relief valve of
Roxroth Ltd.
CONCLUSIONS
(1) The pilot operated pressure valve is made up of
parallel hydraulic network which formed by the
hydraulic circuit of the pilot valve and that of the main
valve port. The pilot flow increases with the increasing
of the main overflow, and the greater the system
pressure, the more the variation of the pilot flow varying
with the overflow.
(2) The flow-pressure characteristic of the pilot
operated pressure valve can be compensated by
altering the equilibrium state of the force bore on the
pilot poppet through attaching hydraulic resistance in
the pilot poppet.
(3)There exists different flow-pressure characteristic
with different compensating degree of the force bore on
the pilot poppet: under-compensated, the flow-
pressure curve will be bent upwards; right-
compensated, kept flat; over-compensated, bent
downwards.
(4) The principle of compensating the override pressure
of the relief valve by attaching a hydraulic resistance in
the pilot circuit is actually to compensate the variable
hydraulic resistance of the pilot hydraulic bridge, which
is suited for other pressure valves controlled by, for
example, B half bridge.

P
1
(MPa)
20 (a)
0 50 100 150 200
P
1
(MPa) q
x
(L/min)
20 (b)
0 50 100 150 200
P
1
(MPa) q
x
(L/min)
20 (b)
0 50 100 150 200
q
x
(L/min)
Fig.7 The experimental curves of the flow-
pressure characteristic of the relief valve
REFERENCES
[1] Tang Quanbo, Li Zhaomin, Li Zhangyun. The
analysis on the override pressure of relief valve,(in
Chinese). Machine tool and hydraulics. 1989(6):21~23
[2] Backé W, Zhu Wen. Hydraulic resistance circuit
systemology, (in Chinese). Beijing: China

machinery press. 1980
[3] Wu GenmaoVorgesteuertes
Druckbegrenzungsventil DB10 Serie 30
Versuchsbericht V932Mannesmann Rexroth
GmbH1984
[4] Rexroth. Induetrieventile und Zubehör.
RD00101/09.92, ss.165
ISO/TC 131/SC 1 N XXX – 2002-07– replaces ISO/TC 131/SC 1 N 151 [CD 5598 (R) 1997-06]
3
Source English Français Deutsch
N 38 - done
abrasion
Wearing, grinding or rubbing away of
material in mechanical elements.
NOTE – The products of abrasion
will be present in the system as
generated particulate contamination.
abrasion (f)
Usure, émoulage ou frottage de
matériaux dans des éléments méca-
niques.
NOTE – Les produits de l’abrasion
seront présents dans le système en
temps que contamination particu-
laire générée.
Abrieb (m)
Abnutzen, abschleifen oder abscha-
ben von Material an mechanischen
Teilen.
ANMERKUNG: Der Abrieb ist als

erzeugte Feststoffverschmutzung in
der Anlage vorhanden.
done
absolute pressure
Pressure using absolute vacuum as
a reference. (See figures 1 and 2.)
pression (f) absolue
Pression utilisant le vide absolu
comme référence (voir figures 1 et
2).
Absolutdruck (m)
Druck bezogen auf das absolute
Vakuum. (Siehe Bilder 1 und 2.)
N 38 - done
absorbent separator (P)
Separator that retains certain solu-
ble and insoluble contaminants by
molecular adhesion.
séparateur (m) par absorption
Séparateur qui retient certains con-
taminants solubles et insolubles par
adhérence moléculaire.
absorbierender Abscheider
(m)
Abscheider, der bestimmte lösliche
und nichtlösliche Verschmutzung
durch molekulare Adhäsion zurück-
hält.
4.6.1.26 - done
active output

Output the power of which in all pos-
sible states of the device is derived
from supply power.
sortie (f) active
Sortie de puissance d’un appareil
dont tous les états possibles ne
dépendent que de l’énergie d’ali-
mentation.
aktiver Ausgang (m)
Ausgang, der seine Energie in allen
Schaltzuständen des Gerätes nur
von der Energieversorgung bezieht.
4.6.1.24 - done
active valve (P)
Valve that requires a power supply
independent of the value of input
signals.
distributeur (m) actif
Distributeur qui nécessite une ali-
mentation indépendante de la valeur
des signaux d’entrée.
aktives Ventil (n) (P)
Ventil, das unabhängig von der
Größe der Eingangssignale eine
Energieversorgung erfordert.
done
actual component
temperature
Temperature of a component mea-
sured at a specified point at a given

time.
température (f) réelle d’un
composant
Température d’un composant mesu-
rée en un point déterminé à un
instant donné.
Bauteil-Isttemperatur (f)
Temperatur eines Bauteiles gemes-
sen an einem bestimmten Punkt zu
einer bestimmten Zeit.
ISO 8625-3 -
done
actual fluid temperature
Temperature of the fluid measured
at a specified point in a system at a
given time.
température réelle (f) d’un
fluide
Température d’un fluide mesurée en
un point déterminé d’un système à
un instant donné.
Fluid-Isttemperatur (f)
Temperatur eines Fluids gemessen
an einem bestimmten Punkt in der
Anlage zu einem bestimmten Zeit-
punkt.
done
actual pressure
Pressure existing at a particular
point at a particular time.

pression (f) réelle
Pression existant en un point parti-
culier à un instant déterminé.
Istdruck (m)
Zu einem bestimmten Zeitpunkt an
einem bestimmten Ort vorhandener
Druck.
4.1.2.5 - done
actuated position
Final position of the valving element
under the influence of the actuating
forces.
position (f) commandée
Position finale dans laquelle se
trouve un élément de manoeuvre de
distribution sous l’action des forces
de commande.
geschaltete Stellung (f)
Position die das Schaltelement unter
Einwirkung der Betätigungskräfte
eingenommen hat.
2.2.9.4.1 - done
actuated time
Time during which the component is
actuated.
temps (m) d’actionnement
Temps durant lequel le composant
est actionné.
Einschaltdauer (f)
Zeit, während der das Bauteil

geschaltet ist.
ISO 1219-2 and
EN 983 - done
actuator
Component (e.g. motor, cylinder)
that transforms fluid energy into
mechanical work.
actionneur (m)
Composant (par exemple, moteur,
vérin) qui transforme l’énergie d’un
fluide en énergie mécanique.
Antrieb (m)
Bauteil, das die Energie des Druck-
mediums in mechanische Energie
umwandelt (z.B. Motor, Zylinder).
ISO/TC 131/SC 1 N XXX – 2002-07– replaces ISO/TC 131/SC 1 N 151 [CD 5598 (R) 1997-06]
4
N 37- done
adaptor
Device that allows connection of
parts whose interfaces are incompa-
tible.
adaptateur (m)
Dispositif permettant de relier des
pièces dont les interfaces sont
incompatibles.
Adapter (m)
Gerät zum Verbinden von Teilen mit
unterschiedlichen Anschlüssen/
Anschlußbildern.

10.2.14 - done
additive (H)
Chemical added to a hydraulic fluid
to impart new properties or to
enhance those which already exist.
additif (m) (H)
Substance chimique ajoutée à un
fluide hydraulique pour lui conférer
de nouvelles propriétés ou améliorer
celles déjà existantes.
Wirkstoffzusatz (m) (H);
Additiv (n) (H)
Der Druckflüssigkeit zugesetzte
Chemikalie, um ihr neue Eigen-
schaften zu verleihen oder um
bereits bestehende Eigenschaften
zu verbessern.
4.4.1.2 - done
adjustable restrictor valve
Flow control valve with a restrictable
flow path between the inlet and out-
let ports. The cross-sectional area of
the restrictable flow path can be
varied within limits.
réducteur (m) de débit
réglable
Régulateur de débit à voie réduite
entre les orifices d’entrée et de sor-
tie. La section de passage restreinte
peut varier entre certaines limites.

einstellbares Drosselventil (n)
Stromventil, in dem zwischen Ein-
und Ausgang eine veränderbare
Drosselstelle ist, deren Querschnitt
innerhalb von Grenzen verändert
werden kann.
N 38- done
adjustable stroke cylinder
Cylinder in which the position of a
stop can be changed to permit the
length of the stroke to be varied.
vérin (m) à course réglable
Vérin dans lequel la position d’arrêt
peut être modifiée pour permettre un
changement de longueur de course.
Zylinder (m) mit einstellbarem
Hub
Zylinder mit eingebauten einstellba-
ren Endanschlägen.
ISO 6149-2,
6149-3, 8434-2,
8434-3, 1179-3
and 11926-2
and -3 - done
adjustable stud end connector
Stud end connector that allows spe-
cific orientation before final tighte-
ning.
connecteur (m) à extrémité
orientable

Connecteur dont l’extrémité permet
une orientation spécifique avant le
serrage final.
richtungseinstellbarer
Einschraubzapfen (m)
Anschlußteil, mit dem die Ver-
schraubung vor dem endgültigen
Festziehen der Gegenmutter ausge-
richtet werden kann.
done
aeration (H)
Process by which air is entrained in
the hydraulic fluid.
entrée (f) d’air (H)
Processus par lequel l’air est ent-
raîné dans le liquide hydraulique.
Lufteintrag (m) (H)
Vorgang, bei dem Luft in die Druck-
flüssigkeit eingetragen wird.
N 38 - done
agglomerate
Group of two or more particles com-
bined, joined or clustered by any
means.
agglomérat (m)
Combinaison, juxtaposition ou
regroupement par n’importe quel
moyen de deux ou plusieurs particu-
les.
Agglomerat (n)

Zwei oder mehr Teilchen, die irgend-
wie miteinander verbunden sind.
5.2.4.7 - done
air bleed
Means of purging air from a system
or component.
purge (f) d’air
Dispositif servant à éliminer l’air d’un
système ou d’un composant.
Entlüftung (f)
Vorrichtung zum Entlüften von Anla-
gen oder Bauteilen
from 96-03 mee-
ting - done
air breather
Device that allows the exchange of
air between a component (e.g.
reservoir) and the atmosphere.
reniflard (m)
Dispositif qui permet l’échange d’air
entre un composant (par exemple,
réservoir) et l’atmosphère.
Belüfter (m)
Vorrichtung, die den Austausch von
Luft zwischen einem Bauteil (z.B.
Behälter) und der Atmosphäre
erlaubt.
5.3.8 and from
96-03 meeting -
done

air breather capacity
Measure of air flow rate through an
air breather.
capacité (f) en débit d’un
reniflard
Mesure du débit d’air à travers un
reniflard.
Belüfterkapazität (f)
Luftvolumenstrom durch einen
Belüfter.
N 38 - done
air compressor (P)
Sub-system that converts mechani-
cal energy into pneumatic fluid
power.
compresseur (m) d’air (P)
Sous-système qui convertit l’éner-
gie mécanique en énergie pneuma-
tique.
Kompressor (m) (P)
Teilanlage, die mechanische Ener-
gie in pneumatische Energie wan-
delt.
Source English Français Deutsch
ISO/TC 131/SC 1 N XXX – 2002-07– replaces ISO/TC 131/SC 1 N 151 [CD 5598 (R) 1997-06]
5
8.4 - done
air conditioning unit (P)
(pref.); FRL unit (P) (sec.)
Assembly usually comprising a filter,

a pressure regulator and a lubrica-
tor, intended to deliver compressed
air in suitable condition.
ensemble (m) de
conditionnement d’air (préf.);
ensemble FRL (P) (sec.)
Ensemble comprenant un filtre, un
régulateur de pression et un lubrifi-
cateur, destiné à fournir un air com-
primé dans des conditions
appropriées.
Druckluft-Wartungseinheit (f)
(P); FRL-Einheit (f) (P)
Baugruppe, die aus einem Filter,
einem Druckregelventil und einem
Öler besteht und aufbereitete Druck-
luft liefert.
2.2.4.29 - done
air consumption (P)
Air flow required to perform a given
task or volume of air used over a
stated period of time.
consommation (f) d’air (P)
Flux d’air nécessaire pour réaliser
une tâche donnée ou volume d’air
utilisé sur une période de temps
déterminée.
Luftverbrauch (m) (P)
Für eine bestimmte Aufgabe benö-
tigter Luftvolumenstrom oder benö-

tigtes Luftvolumen während einer
bestimmten Zeit.
5.5.7 - done
air dryer (P)
Equipment for reducing the moisture
vapour content of the compressed
air.
sécheur (m) d’air (P)
Équipement permettant de réduire le
contenu en vapeur humide de l’air
comprimé.
Lufttrockner (m) (P)
Gerät zur Reduzierung des Feuch-
tigkeitsgehaltes der Druckluft.
5.2.4.4 - done
air exhaust port (P)
Port which provides passage to the
exhaust system.
orifice (m) d’échappement
d’air (P)
Orifice qui fournit un passage vers
un système d’échappement.
Abluftanschluß (m) (P)
Austrittsöffnung für die Druckluft
(Gas) zur Atmosphäre.
5.5.2 - done
air filter (P)
Component the function of which is
the retention of contaminants from
atmospheric air.

filtre (m) à air (P)
Composant ayant pour fonctions de
retenir les polluants et d’enlever
l’eau contenue dans l’air comprimé.
Luftfilter (m) (P)
Bauteil, dessen Funktionen die
Zurückhaltung der Verschmutzungs-
stoffe aus der Druckluft und die
Abscheidung von Wassertröpfchen
ist.
from comment
on CD
air fuse (P)
Type of flow control valve that, under
normal circumstances, allows free
flow in both directions, but that, in
the event of a piping failure on either
side of the component, will reduce
the flow rate to a very low value.
NOTE – Full flow conditions will not
be restored until the failure is recti-
fied. An air fuse may be used as a
safety component and/or to reduce
air wastage.
N 38 - done
air inclusion (H)
Volume of air in a system’s fluid.
NOTE – Air inclusion is expressed in
percentage of volume.
inclusion (f) d’air (H)

Volume d’air dans le fluide d’un
système.
NOTE – L’inclusion d’air est expri-
mée en pourcentage de volume.
Luftgehalt (m) (H)
Volumen der Luft in der Druckflüs-
sigkeit.
ANMERKUNG: Der Luftgehalt wird
in Volumenprozent angegeben.
3.2.1 - done
air motor (P)
Continuous rotation motor that is
actuated by compressed air.
moteur (m) à air(P)
Moteur qui est actionné par de l’air
comprimé.
Druckluftmotor (m) (P)
Motor, der durch Druckluft betätigt
wird.
from 96-03 mee-
ting
air purifier (P)
Compressed air filter used where a
very clean air supply is necessary.
purificateur (m) d’air (P)
Filtre à air comprimé comportant un
élément filtrant à haute efficacité, uti-
lisé lorsqu’il est nécessaire d’avoir
une alimentation en air très propre.
Luft-Feinfilter (m,n) (P)

Druckluftfilter mit einem Filterele-
ment, das einen hohen Abscheide-
grad hat.
10.3.4 - done
air release capacity (H)
Ability of a hydraulic fluid to release
air bubbles dispersed there in.
pouvoir (m) de désaération (H)
Aptitude d’un fluide hydraulique à se
libérer les bulles d’air dispersées
qu’il contient.
Luftabscheidevermögen (n)
(H)
Fähigkeit einer Druckflüssigkeit,
Luftblasen abzuscheiden.
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