Ahmed Fouad_Experimental and Theoretical Investigation for Electro-hydraulic Servovalve Systems Control_2014

A Thesis
Submitted to the Department of Machine and Equipment Engineering of
the University of Technology in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy in Mechanical Engineering
BY
AHMED FOUAD MAHDI KRIDI
(B.sc. 1992, M.Sc. 2005)
Supervisors
Republic of Iraq
Ministry of Higher Education
& Scientific Research
University of Technology
Machines & Equipment Engineering
Department
Experimental and Theoretical Investigation for
Electro-hydraulic Servovalve Systems Control
Prof. Dr. Asst. Prof. Dr.
JAFAR MEHDI HASSAN MAJID AHMED OLEIWI
Iraq / Baghdad
2014

َ‫ﺻ‬‫ـــــ‬َ‫ﺪ‬َ‫ق‬ُ‫ﷲ‬َ‫ﻌ‬‫اﻟ‬‫ـــــ‬ُ‫ﲇ‬َ‫ﻌ‬‫اﻟ‬‫ـــــ‬ْ ِ‫ﻈﲓ‬

Linguistic Certification
I certify that this thesis entitled " Experimental and Theoretical
Investigation for Electro-hydraulic Servovalve Systems Control" was prepared
by "Ahmed Fouad Mahdi", under my linguistic supervision. Its language was
amended to meet the style of the English language.
Signature
Name: Dr. Arkan Kh. Husain Al-Taie
Title: Prof.
Date: 31 / 12 /2013

Supervisors' Certification
We certify that this thesis entitled "Experimental and Theoretical
Investigation for Electro-hydraulic Servovalve Systems Control " was prepared
by "Ahmed Fouad Mahdi" under our supervision at the Department of
Mechanical Engineering, University of Technology in partial fulfillment of
the requirements for the degree of Doctor of Philosophy in Mechanical
Engineering.
Signature
Name: Dr. Jafar Mehdi Hassan
Title: Prof.
Date: 31 / 12 /2013
Supervisor
Signature
Name: Dr. Majid Ahmed Oleiwi
Title: Asst. Prof.
Date: 31 / 12 /2013
Supervisor

EXAMINATION COMMITEE CIRTIFICATE
We certify that we have read the thesis entitled "Experimental and
Theoretical Investigation for Electro-hydraulic Servovalve Systems
Control " and as an examination committee, examined the student in its
contents and in what is related with it and that in our opinion, it is
adequate as a thesis for the Degree of Doctor of Philosophy in Mechanical
Engineering.
Signature:
Name: Dr. Majid Ahmed Oleiwi
Asst. Prof. (Supervisor)
Date: / /2014
Signature:
Name: Dr. Ali Abul mohsin Hasan
Asst. Prof. (Member)
Date: / /2014
Signature:
Name: Dr. Emad N. Abdulwahab
Date: / /2014
Signature:
Prof. (Supervisor)
Date: / /2014
Signature:
Name: Dr. Adnan Naji Jameel
Prof. (Member)
Date: / /2014
Signature:
Name: Dr. Mohammed Idrees Mohsin
Date: / /2014
Signature:
Name: Dr. Arkan Kh. Husain Al-Taie
Prof. (Chairman)
Date: / /2014
Approved by the Mechanical Engineering Department
Signature:
Prof.-Dean of Mechanical Engineering Department
Date: / /2014

IIChapter One: Background and Introduction to Servovalve
Acknowledgements
Praise should first be to Almighty Allah for His most passionate blessings that
have assisted me in completing my dissertation.
My great thanks go to my dear parents and my family who have endured with
me the bitter swill of the hard times of examinations and who have eaten their hearts
out throughout this journey.
I would like to express my sincere thanks to my supervisor Prof. Dr. Jafar Mehdi
Hassan, who has lighted my journey in writing this dissertation, encouraged me to
choose this subject, supplied me with very valuable recommendations and comments
and has been very helpful in providing me with useful resources.
My thanks extend to my supervisor Assit. Prof. Dr. Majid Ahmed Olieiwi, for his
support and recommendations. Also, special thanks to Lec. Dr. Yiqin Xue, Cardiff
University / UK, for his constructive remarks which have been the cornerstone upon
which the main practical work of this dissertation has been built.
My thanks extend to my other professors of the Mechanical Engineering
Department who taught me along with other PhD students the best and the most
modern subjects in the field of mechanical power of engineering.
I am particularly grateful to my brother-in-law (M.A. Sattar Hussain) for his
support and effort in the linguistic revision. I also thank my colleagues and other
friends who have helped me during the past four years and provided me with some
useful resources.
Ahmed Fouad Mahdi
14/12/2013

IIIChapter One: Background and Introduction to Servovalve
Abstract
The control concept on the electro-hydraulic servovalve system
focuses on the pressure control, position control and velocity control. The
servovalve and the system components are needed to be considered in the
proposed control strategy. The control concepts on the electro-hydraulic
servovalve systems in this work are divided into two parts:
1. Theoretical and experimental investigation for pressure control on the
electro-hydraulic servovalve systems.
The pressure control study in this work is concerned with the modeling and
controlling of the hydraulic fluid pressure value at the end of long
transmission line (TL) by using the electro-hydraulic servovalve. The input
voltage signals to the amplifier, designed by C++
program, are used to
control the pressure reference signal at the end of TL. The electrical
analogy method is used to simulate the effect of the TL, as well as the first
order transfer function to simulate the servovalve effect. Therefore, the
whole system is represented mathematically in MATLAB m-file program.
The mathematical model is seen as a good simulation approach compared
with the experimental open loop control test. The on-line adjustable control
strategy, Ziegler & Nichols method and Astrom & Hagglund method, can
be used experimentally to find the proportional and integral control gain
values for acceptable control system behavior. The servovalve succeeds to
reduce and overcome the negative effect of the TL on the hydraulic fluid
pressure value at the chosen control point.
2. Theoretical and experimental investigation for velocity and position
control by the electro-hydraulic servovalve system.
The C++
language programs are designed to control the position and
velocity of the road simulator (single-rod, double acting linear cylinder
actuator) with variable load (quarter car suspension system). The whole

IVChapter One: Background and Introduction to Servovalve
system is analyzed mathematically and experimentally. The mathematical
model of the electro-hydraulic servovalve system is represented and
analyzed successfully by designing the SIMULINK program.
The dynamics modeling of the servovalve and the single road cylinder
actuator under variable load which are controlled as a closed loop position
control method with existence of the actuator internal leakage is done
successfully by using the SIMULINK environments. So, the transfer
function and the state-space model of the system in open and closed loop
control are presented. Also, the Bode diagram is done for the system as
well as the stability characteristics are found for the system by the Nyquist
Diagram.
The on-line adjustable PID control tuning is employed experimentally to
find the best control gain values which are applied to the system. In the
mathematical SIMULINK program, the PID gains values are tuned manually
and automatically by computing a linear model of the plant. The tuning
strategies are done automatically for the P, PI and PID strategies for three
different response time values. The comparison figures in the P strategy
show that the simulation programs give a good and accurate prediction
results and enhance the system behavior. On the other hand, the PI strategy
shows incompatible results between the actual test and the simulation
program. The PID strategy shows a good prediction results. To analyze the
actual fully system behaviors for a large spectrum frequency, the numbers
of sinusoidal voltage input signal are used with unity compensator to create
actual Bode plot. The tracking closed loop control method is done
experimentally by designing C++
program and it is done theoretically by
the SIMULINK simulation program for the system. The comparison result
with the previous research clarifies that the mathematical solution method
proposed in this dissertation shows that the prediction of the system
behavior is acceptable and improve the system behavior.

VChapter One: Background and Introduction to Servovalve
Contents
1. Chapter One: Background and Introduction to Servovalve....2
1.1 Introduction:..................................................................................... 2
1.2 Electro-hydraulic Servovalve:............................................................ 3
1.3 Basic Servovalve Systems:................................................................. 4
1.4 Servovalve Construction Types: ........................................................ 5
1.4.1 Torque Motor:............................................................................ 6
1.4.2 Double Flapper Nozzle:............................................................... 7
1.4.3 Programmable Orifice: ............................................................... 8
1.5 The Electro-hydraulic Servo Systems:................................................ 9
1.5.1 Pot-Pot servo systems: ............................................................... 9
1.5.2 Force, Pressure, and Torque Servo Systems: ............................ 10
1.5.3 Velocity Servo Systems:............................................................ 10
1.5.4 Servovalve Amplifiers: .............................................................. 10
1.6 The Aims of the Current Study: ....................................................... 11
2. Chapter Two: Literature Review................................................... 13
2.1 Transmission Line Effect Publications:............................................. 13
2.2 Fluid Power Systems and Servovalve Publications: ......................... 17
2.3 Summary of the Review of Literature and the Scope of the Present
Study:................................................................................................... 23
3. Chapter Three: Theoretical Analyses.......................................... 26
3.1 Theoretical Analyses of the Pressure Control on the Electro-
hydraulic Servovalve System............................................................... 26
3.1.1 Introduction: ............................................................................ 26
3.1.2 System Description:.................................................................. 29
3.1.2.a System hardware description: ............................................ 29

VIChapter One: Background and Introduction to Servovalve
3.1.2.b System control software description:.................................. 31
3.1.3 Servovalve construction: .......................................................... 32
3.1.3.a First stage:......................................................................... 32
3.1.3.b Second stage: .................................................................... 32
3.1.4 Servovalve Modeling: ............................................................... 33
3.1.4.a Steady State Modeling of Servovalve:............................ 33
3.1.4.b Dynamic Modeling of Servovalve: .................................. 37
3.1.5 Transmission line modeling: ..................................................... 41
3.1.6 Servovalve Gains and the Transmission Line Losses: ................45
3.1.7 MATLAB Simulation:................................................................. 47
3.2 Theoretical Analyses of the Position and Velocity Control by Electro-
Hydraulic Servovalve System. ............................................................... 53
3.2.1 Introduction: ............................................................................ 53
3.2.2 Control Systems Theory:........................................................... 55
3.2.3 Road Simulator Mathematical Modeling: ................................. 57
3.2.4 Passive Suspension Mathematical modeling: ........................... 59
3.2.5 Closed loop Control of the Road Simulator System with the
Passive Suspension System: .................................................................. 61
3.2.6 The Closed Loop Control of the Road Simulator System with
Variables Load by the MATLAB Tuning Gains: ....................................... 64
3.2.7 Nyquist Stability Criterion:........................................................ 65
4. Chapter Four: Experimental Approach:........................................ 78
4.1 Experimental Approach of the Pressure Control on the Electro-
Hydraulic Servovalve System.............................................................. 78
4.1.1 Introduction: ............................................................................ 78
4.1.2 Modeling Properties:................................................................ 78
4.1.3 Open Loop Pressure Control:.................................................... 79
4.1.4 Ultra Servovalve (4658) Transient Response: ........................... 81
4.1.5 Closed Loop Pressure Control and PID Control a Benchmark:...81
4.1.5.a. On-line adjustable PID Control: ................................. 82
4.1.5.b. Non-Model Specific Tuning: ...................................... 83
4.1.5.b.1. Ziegler and Nichols Method: ............................... 83
4.1.5.b.2. Astrom and Hagglund Method:........................... 84

VIIChapter One: Background and Introduction to Servovalve
4.1.6 The Restrictor Valve Effect on Transmission Line:.....................84
4.1.7 Time Sampling Limitation: ........................................................ 85
4.2 Experimental Approach of the Position & Velocity Control by
Electro-Hydraulic Servovalve System................................................. 95
4.2.1 Road Simulator System Test Rig Hardware Overview:..............95
4.2.1.a. Servovalve:............................................................. 95
4.2.1.b. Hydraulic Actuator: ................................................ 96
4.2.1.c. Quarter Car Suspension:......................................... 96
4.2.1.d. Control System:...................................................... 97
4.2.1.e. Linear Variable Differential Transformers (LVDTs):.97
4.2.1.f. Velocity Sensors:..................................................... 98
4.2.2 System Performance: ............................................................... 99
4.2.3 Road Input Simulator for Experiment: .................................... 100
4.2.4 Open Loop Servovalve in Closed Circuit (Transient Response):.....
............................................................................................... 100
4.2.5 Closed Loop Tracking Control: ................................................ 102
4.2.6 Internal Leakage Resistance with Experimental Test: ............. 103
4.2.7 Closed Loop Position Control with On-line Adjustable PID Control:
............................................................................................... 104
4.2.8 Closed Loop Frequency Response:.......................................... 105
5. Chapter Five: Results and Discussion: ......................................128
5.1 Results and the Discussion for the Pressure Control on the Electro-
Hydraulic Servovalve System............................................................ 128
5.1.1 Open Loop Pressure Controlled by VFG in the TL System: ...... 128
5.1.2 Pressure Control System by the DAP-card: ............................. 129
5.1.3 Time Sampling Limitation Results:.......................................... 132
5.2 Results and the Discussion for the Velocity and Position Control for
the Electro-Hydraulic Servovalve System:........................................ 140
5.2.1 The Closed Loop Control of the Road Simulator System with
Variables Load by the MATLAB Tuning Gains: ..................................... 140
5.2.2 The Automatic PID Tuning from the Mathematical Simulation
Model: 140
5.2.3 Closed Loop Frequency Response:.......................................... 144

VIIIChapter One: Background and Introduction to Servovalve
5.2.4 The Closed Loop Tracking Control: ......................................... 146
6. Chapter Six: Conclusions and Recommendations......................165
6.1 Conclusions for the Pressure Control on the Electro-Hydraulic
Servovalve System and its Recommendations................................... 165
6.1.1 Conclusions: ........................................................................... 165
6.1.2 Recommendations:................................................................. 167
6.2 Conclusions for the Velocity and Pressure Control on the Electro-
Hydraulic Servovalve System and its Recommendations: ................ 168
6.2.1 Conclusions: ........................................................................... 168
6.2.2 Recommendations.................................................................. 170
References ....................................................................................................171
7. Appendixes................................................................................................0

IXChapter One: Background and Introduction to Servovalve
Nomenclature
Latin Characters
Character Description Units
1 A1 Actuator cross-sectional area for side 1 m2
2 A2 Actuator cross-sectional area for side 2 m2
3 Ao orifice area m2
4 a Hydraulic pipeline cross section area m2
5 an Servovalve nozzle area m2
6 anx, any Nozzle cross section area m2
7 ao The spool orifice area m2
8 aso The spool orifice area for rectangular ports m2
9 as The spool cross section area m2
10 Bv The actuator fluid damping coefficient N/ms-1
11 Bs Suspension damping rate N/ms-1
12 Bsf The spool viscous damping torque coefficient Nms/rad
13 Bt Tyre damping rate N/ms-1
14 Bsv The flapper viscous damping torque coefficient Nms/rad
15 b The distance between the torque motor and flexure joint mm
16 C Controller gain (Compensator) -
17 Cd Orifice coefficient -
18 Cq, Cqn, Cqo The flow coefficients of the orifices and the nozzles -
19 C Electrical capacitance Farad
20 di Pipe internal diameter m
21 dn The nozzle diameter m
22 do The orifice diameter m

XChapter One: Background and Introduction to Servovalve
23 d Transmission line diameter m
24 e error signal volt
25 Ei Electrical inductance
26 F Frequency Hz
27 Fg Voltage input from the Voltage Function Generator Volt
28 f Darcy friction factor -
29 G Plant -
30 H Sensor controller gain -
31 I Current A
32 i The input torque motor current mA
33 Δi Input differential current mA
34 J The flapper inertia kgm/s
35 Po Number of poles of G(s) H(s) in the right-half s plane. N/m2
36 Pa, Pb Pressure at nozzle a and nozzle b N/m2
37 PLoad The pressure difference on the load N/m2
38 Pi, Px, Po Pressure in the π networks model N/m2
39 PR The return line pressure N/m2
40 Ps System pressure N/m2
; bar
41 Q Flow rate m3
/s, l/min
42 Q1, Q2 Flow rate from servovalve m3
/s, l/min
43 Qa, Qb The orifice discharge m3
/s
44 Qx, Qy The nozzle discharge m3
/s
45 Kd Derivative control gain
46 Ki Integral control gain
47 Kp Proportional control gain
48 KTL The servovalve TL gain constant m3
/s/ N/m2

XIChapter One: Background and Introduction to Servovalve
49 k Servovalve wire stiffness N/m
50 ka Flexure tube rotational stiffness Nm/rad
51 kc Servovalve flow constant related with the current
52 kf Servovalve flow constant related with the input DAP-card voltage
53 kfo The cantilever springs stiffness Nm/rad
54 kfr The flow reaction equivalent stiffness
55 km Electromagnetic spring constant of torque motor Nm/rad
56 kp1, kp2 Servovalve pressure coefficient m3
/s /N/ m2
57 ks Suspension spring stiffness N/m
58 kt Tyre spring stiffness N/m
59 kts Electromagnetic constant of torque motor Nm/Amp
60 kv1 , kv2 Servovalve linearized flow gain m3
/s /volt
61 kvp Servovalve pressure sensitivity N/ m2
/volt
62 l Hydraulic pipeline length m
63 L Electrical inductance Henry
64 Lc Corrected length m
65 Lequiv Equivalent losses length m
66 LTL Transmission line length M
67 M Chassis mass kg
68 Mt Total mass with all fraction effect in suspension system kg
69 m Tyre mass kg
70 N Number of clockwise encirclements of the (–1+j0) point.
71 R Electrical resistance Ω
72 RL Internal leakage resistance is kPa.s/mm3
73 r The distance between the nozzle center line and flexure joint m
74 t Time s

XIIChapter One: Background and Introduction to Servovalve
75 T The torque on the flexure tube N.m
76 Tc Time distance between the two peaks in the oscillation wave s
77 Ts Time sampling period s
78 Tf The resisting torque N.m
79 U The spool velocity m/s
80 U3 The output mean flow rate velocity from the servovalve m/s
81 u Control signal Volt
82 V Volume m3
83 V1 Suspension actuator volume for side 1 m3
84 V2 Suspension actuator volume for side 2 m3
85 Ve Electrical Voltage volt
86 v input voltage volt
87 ws The rectangular port gradient area m
89 x The displacement of the flapper at the nozzles mm
90 xc Chassis deflection mm
91 xd Suspension system deflection m
92 xr Road input displacement mm
93 xs The theoretical spool displacement mm
94 xt Tyre deflection m
95 xnm Flapper clearance in the mid position mm
96 y Total spring deflection mm
97 Zo Constant for the servovalve design parameter (valve characteristic) -
98 Z Number of zeros of 1+G(s) H(s) in the right half s-plane.

XIIIChapter One: Background and Introduction to Servovalve
Greek Symbols
Character Description Units
1 α Suspension angle deg.
2 βr Effective Bulk modulus N/m2
3 µ Fluid absolute viscosity kg/m.s
4 ρ Fluid density kg/m3
5 θ The rotation of the armature and flapper rad
6 θ ' Spool jet angle relative to the spool axis deg.
7 ω Frequency Hz
Subscripts
ss Steady state operation condition -
Abbreviations
1 DAP Data Acquisition Processor (Microstar Laboratories, Inc.) -
2 DCV Directional Control Valve -
3 EHSA Electro-hydraulic Servo Actuator -
4 EHSV Electro-hydraulic Servovalve -
5 EMA Electromechanical Actuator -
6 GM Gain Margin -
7 LVDT Linear Variable Differential Transformer -
8 PC Personal Computer -
9 P, PI, PID Control Strategy
10 PM Phase Margin -
11 TF Transfer Function -

XIVChapter One: Background and Introduction to Servovalve
12 TL Transmission Line -
13 TLM Transmission Line Modeling -
14 TVC Thrust Vector Control -
15 VSB Voltage Signal Builder block -

2Chapter One: Background and Introduction to Servovalve
1. Chapter One: Background and Introduction to Servovalve
1.1 Introduction:
The advantages of fluid power allow it to compete directly with other
power sources for many engineering solutions (Backe, 1993) while being
the only approach for mobile applications in agriculture and construction.
However, future usage will depend, to some extent, upon the industries
continued ability to out-perform its competitors by consistently improving
the dynamic performance, reliability and efficiency of the designs whilst
also meeting the inevitable environmental legislation, especially in large
industrial applications. The ability of fluid power systems to provide rapid
and controllable pressure and flow makes it highly suitable for the
provision of the enabling force in the many engineering processes. To
maintain and further improve performance and reliability it is necessary to
have at our disposal the facility to model behavior of components both
singularly and collectively in an overall simulation of the process. In doing
so it should be possible to optimize the design and produce the required
performance and subsequent quality of product and control.
There are several components common to most fluid power control
systems:
• Pump (for the provision of hydraulic power).
•.Valve (either servo or proportional to control pressure and
flow).Controlled by either voltage or current, the valve acts as an interface
between electrical and hydraulic systems, and is able to facilitate computer
control.
• Relief valve (to limit supply pressure).
• Actuator (typically a cylinder or motor)

In addition, and of significance here is the interconnecting pipe work
or more suitably named transmission line (TL) which in some systems can
make a significant contribution to the overall dynamic performance. The
TL allows the delivery of power over reasonably long distances and
represents another advantage of fluid power in that the power source and
associated actuator equipment may be remote to the application, such as in
mining, offshore exploration and hazardous primary processing such as the
steel industry.
Fluid power systems are employed extensively in such processes, able
to provide not only the huge forces required, but also the high level of
controllability essential to achieve the demanding product quality.
1.2 Electro-hydraulic Servovalve:
Servovalves were developed to facilitate the adjustment of fluid flow
based on changes in load motion. The range of applications for electro-
hydraulic servo systems is diverse, and includes manufacturing systems,
materials test machines, active suspension systems, mining machinery,
fatigue testing, flight simulation, paper machines, ships and
electromagnetic marine engineering, injection moulding machines,
robotics, and steel and aluminum mill equipment. Hydraulic systems are
also common in aircrafts, where their high power-to-weight ratio and
precise control make them an ideal choice for actuation of flight surfaces.
Unfortunately hydraulic systems exhibit several inherent non-linear
effects which can complicate the control problem.
The vast majority of electronic closed loop controllers are based on
simple analogue circuit designs offering robust, low cost implementations
of the well known PID control strategy. This approach works well in
systems with simple topology and limited bandwidth. However the
growing use of complex control strategies, coupled with the need to

support enhanced features, has lead to increased interest in the use of
digital processors for control of hydraulic servo-systems. Nowhere is this
more apparent than in the field of mechanical test equipment, where the use
of a programmable digital processor allows the same servo controller to be
used with a wide range of hydraulic systems (Poley, 2005).
1.3 Basic Servovalve Systems:
There are four basic servo systems as shown in Fig. 1.1.The two
servo-actuator systems are (1) valve-motor and (2) valve-cylinder. These
systems are often referred to as servo motors and servo cylinders. The
recommended procedure is to mount the valve directly on the actuator. This
avoids a column of compressed fluid in the lines and increases the natural
frequency of the system, which increases positioning accuracy.
The two servo pump systems are (3) servo pump-motor and (4) servo
pump-motor (split). Most accurate speed control is given by the servo
pump- motor, because this configuration avoids a column of compressed
fluid in the lines and thus gives a higher natural frequency for the system.
There are times, however, when the pump and motor cannot be packaged
together. The split configuration has the largest position error of the four
configurations.
The two systems under research are similar to the system (2) in Fig.
1.1. The first system will consider the negative effect (losses and delay) of
the long transmission line behind the servovalve (TL test rig).On the other
hand, the second system will consider the negative effect (the variable
load) acting on the linear actuator driven by the electro-hydraulic
servovalve in the test rig (Road simulator test rig).

Fig. 1.1 Four basic servovalve systems: (1) valve-motor, (2) valve-cylinder, (3) servo pump-motor, and
(4) servo pump-motor (split) (John, 2002).
1.4 Servovalve Construction Types:
This section gives some details on the construction of servovalves. It
is important to remember that a servovalve is really just a carefully
machined spool-type directional control valve. The spool is shifted with a
torque motor mounted on top of the valve or another way a solenoid
mounted at the end of the spool.
There are three types of servovalves.
1. Single-stage. This valve has one spool. The torque motor must
supply enough torque to shift the spool against the pressures that act on the
spool.
2. Two-stage. In this valve, the first stage is called the pilot stage. The
torque motor shifts the pilot spool, which directs flow to shift the second
stage. The second stage supplies flow to the actuator.

3. Three-stage. In this valve, the pilot stage shifts the second stage,
which shifts the third stage. Three-stage valves are used for applications
with high flow and high pressures. Large forces are required to shift the
third stage, which directs the high-volume flow to the actuator.
1.4.1 Torque Motor:
As shown in Fig. 1.2, a torque motor consists of an armature, two
coils, and two pole pieces. When current is supplied to the coils, the
armature rotates clockwise or counterclockwise, depending on polarity
produced in the armature. Current in the opposite direction produces the
opposite polarity and the opposite rotation.
A key to the operation of the torque motor is the mounting of the
armature to a flexure tube. This mount bends as the armature turns. The
armature stops pivoting when the torque produced by magnetic attraction
equals the restraining torque produced by deflection of the flexure tube.
This design prevents the armature from touching the pole pieces.
The torque motor coil can be immersed in oil, classified as a wet
torque motor, or operated dry. Even though a wet torque motor has the
advantage of cooler operation, most servovalves use dry torque motors,
because the magnets tend to attract metal particles circulating in the fluid,
and this eventually causes failure.
Fig. 1.2 Construction of a torque motor (John, 2002).

1.4.2 Double Flapper Nozzle:
A diagram of the double flapper nozzle is shown in Fig. 1.3. Pressure
is supplied to the points identified with supply pressure (Ps). Fluid flows
across the fixed orifices and enters the center manifold. Orifices are formed
on each side between the flapper and the opposing nozzles. As long as the
flapper is centered, the orifice is the same on both sides and the pressure
drop to the return line is in the same value. Pressure at A equals the
pressure at B, and the spool is in force balance. Suppose the torque motor
rotates the flapper clockwise.
Fig. 1.3 Spool valve, flapper & nozzle as a first stage for a two-stage servovalve (Watton J. , 2009).
Now, the orifice on the left is smaller than the orifice on the right, and
the pressure at A will be greater than the pressure at B. This pressure
difference shifts the spool to the right. As the spool shifts, it deflects a
feedback spring. The spool continues to move until the spring force
produces a torque that equals the electromagnetic torque produced by the
current flowing through the coil around the armature. At this point, the
armature is moved back to the center position, the flapper is centered, the
pressure becomes equal at A and B, and the spool stops. The spool stays in
this position until the current through the coil changes. Because of the

feedback spring, the spool has a unique position corresponding to each
current through the coil ranging from 0 to rated current. At rated current,
the spool is shifted to its full open position.
A cutaway of a two-stage valve with double flapper nozzle for the first
stage is shown in Fig. 1.4 Note that the spool slides in a bushing. It is the
relationship between this bushing and the spool that establishes the opening
to Ports A and B.
Fig. 1.4 Cutaway of two-stage servovalve with double flapper nozzle for a first stage, courtesy of Moog Inc.
An adjustment, known as the null adjust, is provided to slide this
bushing left or right and bring it into precise alignment with the spool when
no current is supplied to the valve. This adjustment ensures that the valve is
mechanically centered.
1.4.3 Programmable Orifice:
To define the dynamics of fluid flow through an orifice, it is important
to note that whenever the pressure differential is large for all operating
points of interest, it can be safely assumed that the flow always has a large
enough Reynolds number. So, it can be calculated using the turbulent flow
equation (Merritt, 1967).

Servovalves are rated by the manufacturer at a given pressure drop,
typically 70bar. Rated current is applied so that the valve is in its full open
position. Pump speed is increased until a 70bar ΔP is measured across the
servovalve. Once the 70bar ΔP is obtained, the flow is measured, and this
flow is used to specify the valve size (John, 2002).
1.5 The Electro-hydraulic Servo Systems:
Additional flexibility and versatility can be obtained by using an
electrical input. This kind of servo systems is commonly referred to as a
pot-pot servo.
1.5.1 Pot-Pot servo systems:
The pot-pot servo gets this name from the fact that the command and
feedback signals are obtained from potentiometers. The command is a
voltage obtained by rotating the command potentiometer. This command
voltage is compared to a voltage obtained from the potentiometer mounted
adjacent to the manufacturing work table, known as the feedback
potentiometer. As the work table moves, it slides the wiper along this
potentiometer to change the feedback voltage. The difference between the
command and feedback voltages is the "error" voltage, and this voltage is
the input to an amplifier. The amplifier produces a milliamp current
proportional to the error voltage, and this current is the input current to the
servovalve torque motor.
The servovalve opens to direct hydraulic fluid to the actuator cylinder,
which moves the work table. The table moves, and thus moves the wiper on
the feedback pot, until the feedback voltage equals the command voltage.
Each table position corresponds to a unique command voltage.
For the systems used in modern manufacturing, the input voltage is
typically a series of voltages produced by a digital-to-analog converter.

This converter converts a series of computer instructions to the needed
command voltages. A work-piece mounted on the table is positioned to be
machined in accordance with the computer instructions. A series of
operations, often with several actuators, are controlled in this manner.
1.5.2 Force, Pressure, and Torque Servo Systems:
Force servo systems use the signal from a force transducer as the
feedback signal. In like manner, a pressure servo uses the signal from a
pressure transducer and a torque servo the signal from a torque transducer.
For example, the force servo systems have a force transducer mounted
between the cylinder and the load. In this case, the cylinder increases the
force on the load until the transducer output voltage (feedback voltage)
equals the command voltage. The system then holds this force until the
command signal is changed. It is possible to cycle the force and program
various force duration times by inputting the correct command voltage vs.
time function.
1.5.3 Velocity Servo Systems:
Velocity servo systems are used to control both linear and rotational
velocities. These servo systems are widely used in manufacturing to draw
wire, buff steel sheets to a required finish, run printing presses, and for a
variety of other applications where the rotational velocity of a drive is
controlled to provide a certain linear velocity.
1.5.4 Servovalve Amplifiers:
A servovalve amplifier card has two main functions:
1. It provides a mA current proportional to an input voltage. Typical
designs fall in the range 5mA/Volt - 100mA/Volt.

2. It saturates at the rated current of the servovalve. The amplifier is
designed so that it cannot deliver enough current to the torque motor to
burn out the coils.
1.6 The Aims of the Current Study:
In order to identify the reciprocal influences between the servovalve
and the system under control mathematically, many internal servovalve
coefficients (flow coefficients, magnetic coefficients, and spool, orifice,
and nozzle dimensions…etc) should be available. Unfortunately, the
internal servovalve coefficients change from one valve to another and it is
not easy to find them experimentally. Also, this information is not available
in manufacturer data sheet. So, many assumptions and experimental tests
should be considered and evaluated to find the servovalve mathematical
model. Therefore, the data should be taken from the input and output
servovalve signal to evaluate the unknown coefficients for the
mathematical model. This helps to make a comparison between the
experimental work and mathematical model. Furthermore, the
mathematical model will help to make enhancements on the actual system
behavior by finding new control gain value.
Foregoing, the data acquisition is needed to collect and record the sensors
reading as well as to design the voltage input signal in different shapes and
values by using C++
language. So, the DAP-card (Microstar Laboratories)
will be use to design the control voltage value and record the data for the
system. This data acquisition is a useful tool to generate unlimited control
voltage input signal shapes.

12
Chapter
Two
Literature Review

13Chapter Two: Literature Review
2. Chapter Two: Literature Review
2.1 Transmission Line Effect Publications:
Hydraulic transmission lines have received considerable deal of
attention with regard to the understanding and prediction of dynamic signal
transmissions in a range of applications with gas, water and oil which are
used as the working fluid.
Regarding the hydraulic transmission lines, consideration has been
given to both frequency domain and time domain analyses using a variety
of approximations and explanations of the fundamental distributed
parameter equations.
Hsue and Hdleoder (1983) have developed and represented the
modal approximations and accuracy considerations for the distributed
parameter laminar flow model for circular, rigid wall hydraulic and
pneumatic transmission line. The approach is based on a technique for
formulating rational polynomial approximations using product series for
both Bessel functions and hyperbolic functions. This approach accounts for
real poles of these functions, in addition to the dominant second order zeros
recognized by other researchers. There is a requirement for including these
real poles and real zeros in model approximations.
Kitsios and Bowher (1986) investigated the transmission line
modeling (TLM) method. They showed how lumped dynamic components
can be represented by equivalent lines. A hydraulic position control system
was modeled by the TLM method, requiring mechanical and fluid
transmission line models and a special ‘integrator’ line. The TLM
technique fundamentally utilizes the loss less and dispersion less of
transmission line model and requires detailed consideration of other
dynamic components within the system and the mathematical linking to the

suitable transmission line termination equations. The theoretical responses
to step inputs are compared with experimental ones and the researchers had
a good agreement.
In Watton J. (1988), discussed the method of model approximation to
the distributed friction transmission line functions via frequency-domain
analysis has been discussed. A specific form is then derived a matter which
allows time-domain analysis to be easily pursued using a digital simulation
package approach. The method is applied to a highly non-linear servovalve
controlled motor system and a good comparison between experiment and
theory is shown. A comparison is also made with previous work using the
method of characteristics, and natural frequency predictions are also
compared with some common lumped parameter approximations.
Longmore and Schlesinger (1991) claim that measured relationships
between the vibration and pressure fluctuation at the input and output ends
of hydraulic hoses are generated by a pump and transmitted to the
subsequent circuit. This relation can be described satisfactorily by two
types of wave involving the contained fluid, together with bending and
torsional wave motion. The values of the wave properties required to do
this are presented for four representative hose constructions. The
relationship of the properties to the construction is discussed, and it has
been proved to be highly effective in problems involving pressure ripple
propagation.
Sanada et al. ( 1993) suggest that a finite element technique may
alleviate some of the computational problems, such as numerical instability
and variable time steps. The resulting equations are expressed in state-
space theorem. Solutions have been obtained for a blocked line where the
mathematical modeling requires the consideration of the range of
undamped natural frequencies in advance. Results for the loss less line case

were compared with a further theoretical solution using the method of
characteristics (Watton J. , 1988).
Burton et al. (March 1994), hydraulic systems are characterized by a
transport delay in the pipelines connecting physical components. This is
due to the propagation of waves at the speed of sound through the fluid
medium. The transmission delay allows component models to be decoupled
for the current time step, enabling a parallel solution; the inputs to each
component model are delayed outputs from connected models. Burten
describes a simulation environment suitable for the simulation of hydraulic
system performance, using the transmission line modeling approach for the
pipelines and decoupling the component models in a hydraulic circuit
simulation.
In Krus (1995), a dynamic simulation of systems, is proposed where
the differential equations of the system are solved numerically. It is an
important tool for analysis of the detailed behavior of a system. In his paper
Krus shows how flexible joints based on transmission line modeling (TLM)
with distributed parameters can be used to simplify modeling of large
mechanical link systems interconnected with other physical domains,
which is the case in hydraulic system applications. The introduction of
transmission line elements in mechanical link system simulation shows a
great potential in simplifying the system description at the equation level,
since subsystems interconnected through TLM-joints can be described
completely independently from each other.
In Watton J. and Hawkly (1996), an approach is developed utilizing
measurements of transient pressure and flow rate at the inlet and outlet of
the line. A time series analysis technique is used in such a way that the
number of unknown coefficients to be estimated is minimized. For three
different line configurations and a range of operating conditions. There is
an accurate prediction which is shown for three different line

configurations and a range of operating conditions. The evaluation of just
two transmission line functions then allows a simple model structure to be
used for the simulation of fluid power circuits incorporating long lines.
Krus and Nyman (2000), have demonstrated the actuation system
control surfaces with transmission line simulated using a flight dynamics
model of the aircraft coupled to a model of the actuation system. In this
way the system can then be optimized for certain flight condition by "test
flying” the system. The used distributed modeling approach makes it
possible to simulate this system faster than real time on a 650 MHz PC.
This means that even the system optimization can be performed in a
reasonable time. This approach was adopted for simulation of fluid power
systems with long lines in the HYTRAN program.
Ayalew and Kulakowski (2005), used analytical results obtained in the
frequency domain. A cording to these results, the modal approximation
techniques are employed to derive transfer function and state-space models
applicable to a pressure input-flow rate output causality case of a
transmission line. However, the modal approximation results presented
apply also to other cases where the linear friction model is considered
applicable. It is highlighted that the results presented can reduce the overall
order of the hydraulic system model containing the transmission line being
considered.
Dong, Zhu, and Lu (2010) proved that the long pipeline in hydraulic
system has some influence on system performances and causes the system
to become unstable. They targeted a hydraulic servo system with long
transmission line between hydraulic power supply and servovalve. A
mathematical model considering pipeline effect is established by means of
the theories of transmission line dynamics and hydraulic control systems in
which pipeline characteristics are depicted by lumped-parameter model.
Dong uses AMESim (a software for modeling, simulation and dynamic

analysis of hydraulic and mechanical system based on bond graph and
which is a production of imagine corporation of France) to simulate the
impact on system dynamic behaviors which were investigated theoretically.
In addition the influences of pipeline structural parameters on hydraulic
system dynamic characteristics were also analyzed.
Yang and Moan (2011) studied a heaving-buoy wave energy converter
equipped with hydraulic power take off. This wave energy converter
system is divided into five subsystems: a heaving buoy, hydraulic pump,
pipelines, non-return check valves and a hydraulic motor combined with an
electric generator. A dynamic model is developed by considering the
interactions between the subsystems in a state space form. The simulation
results show that transmission line dynamics play a dominant role in the
studied wave energy converter system. The length of the pipeline will not
only affect the amplitude of the transient pressures but also the converted
power transformed in the generator.
2.2 Fluid Power Systems and Servovalve Publications:
Electro-hydraulic servo-systems have been a subject of an extensive
study. They are widely used in many industrial applications because of
their high (power/weight) ratio, high stiffness and high payload capability
at the same time, achieve by that fast responses and high degree of both
accuracy and performance.
The standard textbook that deals with the fluid power topics is written
by Merritt (1967), where the main control component of the hydraulic
system is the servovalve in which the modeling and the work on spool
valves and flapper nozzle valves are mostly found. He explains in detail the
effects of some nonlinearity on the servovalve behavior, and describes the
following phenomena: flow forces on a spool and a flapper, torque motor
nonlinearities (magnetic hysteresis and saturation), friction forces on the

spool valve (dry and viscous), etc. He also defines and describes the
functions of the mentioned phenomena.
Watton and Braton (1985) examine the hydraulic actuation with
further contributions to the response and stability of electro-hydraulic servo
actuators with unequal areas. This expands the overview of the research
done on the modeling of a servo-hydraulic system.
S. LeQuoc, R. Cheng and A. Limaye (1987) proposed an electro-
hydraulic configuration, in which the drain line is connected to the tank
through a direction control valve, a metering valve and a relief valve which
allow external adjustment of the drain, orifice and back pressure. Servo
systems with the conventional servovalve and the new servovalve
configuration are modeled and simulated for step input to various values of
system parameters. The simulation results demonstrated that the servo
system with this new configuration would offer a higher steady state
velocity, a lesser settling time and a lower percent overshoot when the
drain line orifice opening and the back pressure are properly tuned. In
addition, they executed out experiments to validate the simulation results
and it has been demonstrated that the mathematical model is relatively
proper to portend the performance of the two servo systems.
Arafa, H. and Rizk, M. (1987), worked on an experiment to design
and investigate electro hydraulic servovalves with mechanical feedback,
excluding the effects of lap conditions and flow forces on the spool.
Evidence is furnished that the feedback wire stiffness must not be constant.
The parameters used to describe this non-linearity are accurately
determined by computer simulation. Furthermore, this phenomenon is
found to account for anomalies observed in the no-load flow gain
characteristics of similar valves.

A non-linear mathematical model based on physical quantities is
developed by Wang et al. (1995). This model includes non-linear relations
for the torque motor dynamics and a flow force on the flapper and fluid
compressibility. The first stage control volume is change due to a spool
movement, the first stage leakage and flow forces. These scientific articles
usually include experimental verification of established models.
Karan et al (1996) describes the servovalve dynamics as a second
order transfer function. He supposes the servovalve to be dependent on the
dynamic characteristics of a system that contains the servovalve. The
values of time constants, undamped natural frequencies and damping ratios
are calculated from the experimentally determined servovalve frequency
characteristics which are found in the catalogues of the manufacturer.
Many researchers as (Lee, 1996; van Schothorst, 1997; Tawfik, 1999)
present the theoretical, or theoretical and experimental modeling, and make
the linearization about some characteristic working region (the most
popular is the null position) in order to obtain linear mathematical models.
However, certain phenomena or physical quantities that are considered to
be of less importance are neglected.
M. Montanari et al (2003) analyze a hydraulic actuated clutch control
system for commercial cars. The design of closed-loop controller is
presented based on a simplified system model. A physical full-order model
is also described and used to assess, through computer simulations, the
dependence of the closed-loop system performances on some plant and
controller key parameters. Selected performance indexes are gear shift
timing and position tracking error and these are mostly affected by two key
parameters: oil pipeline length and controller sampling time. The resulting
dependencies can be used to set performances and cost specifications for
both plant configuration and electronic control unit. Experimental tests
performed with different plant and controller configurations are reported.

They closely match the simulation results, showing the effectiveness of the
proposed approach.
Beshahwired A. et al (2005), present a model of an electro-hydraulic
fatigue testing system that emphasizes components upstream of the
servovalve and actuator. Experiments showed that there are significant
supply and return pressure fluctuations at the respective ports of the
servovalve. The model presented allows prediction of these fluctuations in
the time domain in a modular manner. An assessment of design changes
was done to improve test system bandwidth by eliminating the pressure
dynamics due to the flexibility and inertia in hydraulic hoses. The model
offers a simpler alternative to direct numerical solutions of the governing
equations and is particularly suited for control oriented transmission line
modeling in the time domain.
Olaf Cochoy et al (2006), tried to move towards the more electric
aircraft, a hybrid actuator configuration. In which an electromechanical
actuator (EMA) and an electro-hydraulic servo actuator (EHSA) operate on
the same control surface. This provides an opportunity to introduce
electromechanical actuators into primary flight controls. In this mode the
EMA is controlled in a way that it actively follows the movement of the
control surface without carrying external air loads, thereby reducing power
dissipation compared to active/active mode and failure transients compared
to active/passive mode. However, force fighting will occur if both actuators
are actively controlled. The control concepts for a hybrid configuration,
extending the original actuator control loops, are presented, enabling
active/active as well as active/no-load operation. Nonlinear as well as linear
models for an EMA, an EHSA, and a control surface structure are derived
from technical data for an airworthy EHSA and combined with a model of
the hybrid configuration. These models are used for matching the actuator
dynamics and simulation of the developed control laws.

In Ristanovic, and Milan R. (2007), the thrust vector control (TVC) of
rocket engines is used when the aerodynamic surfaces are inadequate to
control vehicles or when a greater agility may be required of a missile. The
TVC was gimballed nozzle assembly controlled by an electro-hydraulic
servo system, where two linear hydraulic servo actuators gimbals the
engine. Each servo actuator is controlled by an electro-hydraulic
servovalve. The thrust vector direction is a result of the motion of both
servo actuators. The position feedback is provided by measuring the
direction of the thrust vector, instead of measuring the displacements of the
servo actuators. A linear model of the servo system has been developed and
simulated. Therefore, the proposed control concept has experimentally
been validated in the TVC test bench.
Ghasemi, S.A. et al (2008) present a theoretical analysis of a two-
stage electro-hydraulic servovalve with a spool position feedback which is
carried out by two main probable effects, under-lap and back pressure.
These analyses are based on fundamental laws of electromagnetism, fluid
and general mechanics and rectangular ports to simplify the equations. A
detailed mathematical model of servovalve with circular ports is developed
to improve the accuracy of the model. Besides, the back pressure in the
pilot region of the flapper nozzle servovalve is considered. The effects of
the under-lap spool and the back pressure on the performance, stability and
response of the whole system are investigated through solving the
governing equations in MATLAB-SIMULINK.
Fahmy, M. et al (2011) describe the dynamic performance of a two
stage electro-hydraulic servovalve. Nonlinear Non-dimensional
mathematical model is developed. The system main equations could be
derived in minimal symbolic forms a matter which facilitates a subsequent
numerical simulation in order to investigate the static and dynamic
behaviors. In addition to a step response, ramp and sinusoidal inputs

responses are investigated. The model has been coded in the software
package SIMULINK. The mathematical model presented can be used to
investigate dynamic characteristics of a two stage electrohydraulic
servovalve based on hydraulic system such as that under investigation, and
to illustrate the effect of the various parameters on the hydraulic system
performance.
According to Li, M et al (2012) the simulation model of the two stage
flapper-nozzle electro-hydraulic servovalve with the hydraulic component
design libraries has been done where the AMESet secondary development
of modeling is found in AMESim simulation environment. By adjusting the
parameters of the model, the performance of the servovalve are analyzed.
At the same time, the characteristic curve of the servovalve is discovered.
These characteristic curves can describe the static and dynamic
characteristics of the valve which can greatly guide the study and design
the servo systems. The various methods have advantages and
disadvantages, but the solution technique in most cases is based upon
distributed parameter theory with its restriction to laminar flow and
uniform fluid properties. In reality, this is unlikely to be the case for lines
with large pressure and flow rate fluctuations. A method is suggested using
the modal analysis technique as the foundation theory to establish the form
of a set of discrete equations relating pressures and flow rates at both ends
of the line and at the servo system. The unknown coefficients of each time
domain equation may then be determined for the experimental test using
measured transient pressure and flow rate data.

2.3 Summary of the Review of Literature and the Scope of the
Present Study:
The literature review of this study consists of two important parts
which deal with the TL effect and the servovalve effects as follows:
The first concentrates on the transmission line effects on the hydraulic
systems. Many methods that deal with the TL effect are presented. These
methods simulate the TL effect numerically or mathematically in different
ways and by special software's.
In the second part deal with, the servovalve and its effect and
mathematical model are presented by two different approaches used for
obtaining linear mathematical models that describe the behavior of electro-
hydraulic servovalves. According to the first, the servovalve dynamics is
neglected or described with the first, second or, even, third order transfer
function, depending on the dynamic characteristics of a system that
contains the servovalve. The values of time constants, undamped natural
frequencies and damping ratios are calculated by the experimentally
determined servovalve frequency characteristics that could be found in the
catalogues of the manufacturer. The second approaches involves
theoretical, or theoretical and experimental modeling, and make the
linearization about some characteristic working region in order to obtain
linear mathematical models. However, certain phenomena or physical
quantities that are considered to be of less importance are neglected.
Because of that, researchers propose higher order models presented in the
form of transfer functions or state-space.
Although available linear models of electro-hydraulic servovalves
could give preliminary insight of their operation, they are not able to
adequately explain and truly predict the response of servovalves over the
wide operating range. A review of the experimental frequency responses

that every manufacturer provides with their equipment clearly points out
the existence of nonlinearities.
This study aims to finding a comprehensive view on the control of the
electro hydraulic servovalve systems by focusing on the pressure control,
velocity control and the position control, by using the voltage input signal
which supplied to the servovalve amplifier and designed by using the PC in
the C++
language.
In pressure control part, the researcher aims to overcome the negative
transmission line (losses and delay action) effect on the hydraulic system
by using servovalve properties with an efficient control behavior. The
servovalve and its effects on the system are researched experimentally and
theoretically.
On the other hand, it is aimed to find how the velocity and position of
the linear hydraulic actuator are controlled efficiently by the servovalve
with a negative effect of a variable load. The effects of the servovalve on
the performance, stability and the response of the whole system are
investigated experimentally and theoretically through solving the governing
equation in MATLAB.

Chapter
Three
Theoretical Analyses

26Chapter Three: Theoretical Analyses
3. Chapter Three: Theoretical Analyses
The control concept on the electro-hydraulic servovalve system
focuses on the pressure (force), velocity and position control which depend
on the demand of the manufacturing processes and the nature of the system.
Therefore, the servo system and its components are needed to be
considered in the proposed control strategy. Consequently, this work is
divided into two parts:
3.1 Theoretical Analyses of the Pressure Control on the Electro-
hydraulic Servovalve System.
3.1.1 Introduction:
Servovalves are developed to facilitate the adjustment of fluid flow
based on changes in load motion. The twin nozzle flapper servovalve is a
high quality part combined from mechanical, electrical and hydraulic
technology and has the advantages of large power ratio, fast response and
high level of control precision. (Poley, 2005).
Although they are commonly placed as close as possible to the device
to which they are supplying fluid in some applications, it is not possible to
place servovalves close to the actuator due to the plant conditions. This is
seen commonly in the steel rolling industry (Le Bon. A., 1996).
The purpose of this section is to provide a description of the
objectives, procedures and results for the project "Pressure control of a
servo-hydraulic system". It focuses on the experimental applications of
such a system in order to explain the purpose of the experimental work
before exploring the theoretical tools available for analysis of servovalves
and transmission lines of considerable length. A modeling approach will be
based on electrical analog. The data will be collected to validate this

approach and this model will be applied on ideal controller Non-Model
Specific (Ziegler & Nichols and Astrom & Hagglund). This method is
applied to provide an improvement on system control over standard closed
loop control (Le Bon. A., 1996). This section is presented in order to
discuss the derivation of governing dynamic and fluid equations of the
valve operation. Linearization technique of these equations leads to a
transfer function between input (Voltage applied) and output (Pressure
required) variables.
The system's dynamic characteristics have been tested by using a
Personal Computer (PC) equipped with a data acquisition processor (DAP-
card). This will allow data based modeling to be carried out, allowing
prediction of the system's response to a given control output.
An important feature of the transient response of the system is the
delay that occurs between the application of a current to a servovalve, and
the effect in terms of pressure being detected at the end of the transmission
line. This is shown graphically in Fig. 3.1 & Fig. 3.2. This is due to the
time it takes for the servovalve to respond, and more significantly the time
that the pressure increase takes to propagate along the transmission line.
This time delay is usually within the feedback loop of a closed loop
control system, and this causes degradation in the quality of the system's
response to a control input. Application of predictive control is expected to
improve this behavior, although it cannot shorten the length of this time-
delay since it is an intrinsic function of the system. The object of this
section is to build up a theoretical model of a servovalve which control the
pressure at the end of a long transmission line by using the experimental
data. It is worth to mention that P1 is the system pressure supplied by the
power unit, P2 is the pressure behind the servovalve, P3 is the pressure at
the end of the TL and P4 is the pressure return line. The negative effects

-5
0
5
10
15
20
25
3900 4100 4300 4500 4700 4900
P bar, u Volt
ms
P1 bar/10
P2 bar
P3 bar
P4 bar
u-Control*10
-2
0
2
4
6
8
10
12
14
16
3500 4000 4500 5000 5500
P bar, u Volt
ms
P1 bar/10
P2 bar
P3 bar
P4 bar
u-Control*10
(pressure drop and the pressure signal delay) of the TL are clearly seen in
experimental test shown in Fig. 3.1and Fig. 3.2.
Fig. 3.1 Effect of System Delay. Fluid Power Laboratory / Cardiff University /UK. Open Loop
Ps=100bar Fr=1.0Hz, Square-wave, Am=10bar, Time sampling =1ms.
Fig. 3.2 Effect of System Delay. Fluid Power Laboratory/ Cardiff University /UK. Open Loop
Ps=100bar Fr=1.0Hz, Sine-wave, Am=10bar, Time Sampling=1ms.

3.1.2 System Description:
3.1.2.a System hardware description:
As shown in Fig. 3.3, the pressure supply line delivers hydraulic fluid
from big power unit supply to the test rig at a pressure up to 150bar. A
variable pressure relief valve is installed in the rig, so the desired pressure
can be achieved on the rig as the researcher needs. There is a temperature
and flow meters on the supply line to the servovalve. The valve to be used
is an Ultra servovalve from Moog, of type (4658-249-810), shown in Fig.
3.4. The valve consists of two-stage, nozzle/flapper and dry torque motor
unit.
As shown in Fig. 3.3, the service port B is blocked rather than feeding
to the annulus side of the actuator as might be expected. The service port A
is the exit to the servovalve, where the second flow meter and pressure
transducer are located. The servovalve provide the hydraulic pressure via a
long transmission line. This line is expected to have an important input to
the dynamic response of the system due to its considerable length. The
actuator illustrated in Fig. 3.3 is fixed into a specific position - it cannot
move. This is allowable because the system is used to provide adequate
force to counteract roll bending under load ('work roll bending' system).
The actual displacement of these actuators in the roll bending system is
small, and would ideally be zero. Hence, when modeling this system it is
considered reasonable to ignore the small actuator movements. The PC
records the Data Acquisition Processor (DAP-card), which is connected to
the transducers display and amplifier units as shown in Fig. 3.3.

Fig. 3.3 Schematic of the transmission line system set up Cardiff University Laboratory.

3.1.2.b System control software description:
The DAP-card is connected to the PC and has its own operating
system and it is provided with a program called DAP-view through which
control of the DAP-card is built. This program starts and stops collecting
data, as well as outputting signals and logging every event. This project
requires the use of custom written control commands, which will collect
input signals to the card, process them in accordance with the desired
Fig. 3.4 Ultra /Moog servovalve type 4658 and its cross sectional view.

control method, and pass them back to the DAP-view program to be sent to
the equipment. Custom commands are written in C++
language and have to
be compiled and downloaded into the DAP-card. C++
programs can only be
changed by the PC, so any adjustments to the custom commands require
the removal of previous custom commands and recompilation and
installation on the DAP-card (Microstar, 2004).
3.1.3 Servovalve construction:
The servovalve is an interface between low energy electrical signals
and high-level hydraulic power. Servovalves are electrically operated
proportional directional control valves. They are usually four port units
which control the quantity of fluid to pass, as well as the direction. Most
common servovalves are made in the form of a two stage device (Cundiff,
2002).
3.1.3.a First stage:
The first stage contains a torque motor which operates an armature
and this armature pivots a 'flapper', which is situated between two fixed
nozzles. By applying a current to the torque motor, the armature is rotated,
and this moves the flapper toward one nozzle, and away from the other.
The flapper is located within the valve and hence is surrounded by
hydraulic fluid. To keep the torque motor free from oil the flapper is
encased within a flexible 'flexure tube'.
3.1.3.b Second stage:
Second stage is typically a four-way spool valve that controls the fluid
flow to two service ports. There is commonly a mechanical feedback
system in the form of a feedback spring attached to the spool which acts to
oppose the action of the torque motor on the flapper. See Fig. 3.4.

3.1.4 Servovalve Modeling:
3.1.4.a Steady State Modeling of Servovalve:
When an electrical current is applied to the coils of the torque motor, a
torque is generated on the armature. The armature and flapper are
supported on the flexure tube or sleeve, which separates the electro-
magnetic and hydraulic parts of the valve which also provides a low
friction pivot. Four forces components are considered in the torque motor.
These are a positive function of the applied current and the rotation. These
forces are opposed by a torque from the stiffness of the flexure tube, and
the net hydraulic force acting on the flapper element (Watton J. , 1989).
𝑇 = 𝑘 𝑡𝑠 ∆𝑖 + 𝑘 𝑚 𝜃 − 𝑘 𝑎 𝜃 − (𝑃𝑎 − 𝑃𝑏)𝑎 𝑛 𝑟 = 𝑇𝑓 … … … … (3.1)
The mechanical feedback element is one of the types of servovalve
being considered. The torque of this feedback spring can be considered as
follows for small values of θ:
𝑇𝑓= 𝑘 𝑓𝑜 𝑦(𝑟 + 𝑏), 𝑦 = 𝑥 𝑠 + (𝑟 + 𝑏)𝜃 & 𝑥 = 𝑟𝜃 … … … … (3.2)
Atonement equation (2) in (1) gives the total torque on the torque
motor Fig. 3.5, flapper and spring combination, noting that the torque is
zero at steady state; the angle θ can be deduced (Watton J. , 1989):
𝜃 =
𝑘 𝑡 𝛥𝑖 − 𝑎 𝑛 𝑟(𝑃𝑎 − 𝑃𝑏) − 𝑘 𝑓𝑜(𝑟 + 𝑏)𝑥 𝑠
𝑘 𝑎 − 𝑘 𝑚 + 𝑘 𝑓𝑜(𝑟 + 𝑏)2
… … … … (3.3)
Fig. 3.5 Feedback spring free body diagram (Watton J. , 1989).

Fig. 3.6. Schematic of a double flapper/nozzle amplifier used to move a spool
(Watton J. , 2009).
As seen in Fig. 3.6, there is a hydraulic 'bridge circuit' which is
supplied with system pressure. A small amount of fluid can flow out
through the fixed orifice and onward to the two variable orifices created by
the nozzle/flapper interface, ultimately returning to the tank.
Flapper/nozzles in conjunction with a pair of orifices used to generate
a pressure difference by small movements of the flapper positioned
midway between the nozzles, as shown in Fig. 3.6.
The spool area and velocity are as, U respectively. Typically the
nozzle diameter is dn= 0.5mm, the flapper clearance in the mid-position
xnm= 0.03mm, and the orifice diameter do = 0.2mm. It is common for such a
device to be used in servovalves as a mechanical feedback; the pressure
difference generated being used to move the spool. It will be immediately
clear from Fig. 3.6 that at the flapper mid position, often called the null
position, the maximum leakage flow back to tank will exist, hence
producing a small inherent power loss. As an example, the flapper is
moved to the left, by electromagnetic means then pressure P1 will increase
and pressure P2 will decrease, thus providing a pressure difference across
the spool which will then move unless restrained in some way. The flow
losses and power loss will decrease as the flapper position is changed
(Watton J. , 2009). To analyze the flapper-nozzle bridge, the conventional
restrictor flow equations are appropriate and given by:

𝑄 𝑎 = 𝑄 𝑥 + 𝐴1 𝑈, 𝑎 𝑛𝑥 = 𝜋𝑑 𝑛(𝑥 𝑛𝑚 − 𝑥),
𝑄 𝑏 = 𝑄 𝑦 − 𝐴2 𝑈, 𝑎 𝑛𝑦 = 𝜋𝑑 𝑛(𝑥 𝑛𝑚 + 𝑥); … … … … (3.5)
𝑄 𝑎 = 𝐶 𝑞𝑜 𝑎 𝑜�
2(𝑃𝑠 − 𝑃𝑎)
𝜌
, 𝑄 𝑏 = 𝐶 𝑞𝑜 𝑎 𝑜�
2(𝑃𝑠 − 𝑃𝑏)
𝜌
; … … … (3.6)
𝑄 𝑥 = 𝐶 𝑞𝑛 𝑎 𝑛𝑥�
2𝑃𝑎
𝜌
, 𝑄 𝑦 = 𝐶 𝑞𝑛 𝑎 𝑛𝑦�
2𝑃𝑏
𝜌
; … … … … (3.7)
At condition in which the spool motion is negligible, the steady-state
performance of the double flapper-nozzle amplifier may be derived from
equating Qa = Qx and Qb = Qy. This gives:
𝑃�𝑎 =
1
1 + 𝑍 𝑜(1 − 𝑥̅)2
=
𝑃𝑎
𝑃𝑠
, 𝑃�𝑏 =
1
1 + 𝑍 𝑜(1 + 𝑥̅)2
=
𝑃𝑏
𝑃𝑠
,
𝑥̅ =
𝑥
𝑥 𝑛𝑚
; … … … (3.8)
𝑍 𝑜 = 16(
𝐶 𝑞𝑛
𝐶 𝑞𝑜
)2
(
𝑑 𝑛
𝑑 𝑜
)2
… … … … (3.9)
Then the differential pressure is given by:
𝑃�𝑎 − 𝑃�𝑏 =
4𝑍 𝑜 𝑥̅
[1 + 𝑍 𝑜(1 + 𝑥̅)2][1 + 𝑍 𝑜(1 − 𝑥̅)2]
, … … … … (3.10)
Considering the null condition where 𝑥̅ = 0 and𝑃�𝑎 − 𝑃�𝑏 = 0; that leads to:
𝑃�𝑎 = 𝑃�𝑏 =
1
(1 + 𝑍 𝑜)
… … … … (3.11)
And the null gain condition is:
𝑑(𝑃�𝑎 − 𝑃�𝑏)
𝑑𝑥̅
=
4𝑍 𝑜
(1 + 𝑍 𝑜)2
… … … … (3.12)
Because flapper operation is designed to be around the central (null)
position, the pressure difference generated may be simply written as:
(𝑃𝑎 − 𝑃𝑏) = �
𝑥
𝑥 𝑛𝑚
� 𝑃𝑠 … … … … (3.13)
Spool displacement is then determined from the force balance across
the spool which is dominated by the feedback wire force and the spool flow
reaction force:

(𝑃𝑎 − 𝑃𝑏)𝑎 𝑠 = 𝑘𝑦 + 2𝐶 𝑞
2
𝑎 𝑠𝑜 𝑐𝑜𝑠𝜃′[𝑃𝑠 − 𝑃𝐿𝑜𝑎𝑑], 𝑎 𝑠𝑜 = 𝑤𝑠 𝑥 𝑠 … (3.14)
Where, as is the spool end cross section area, the spool orifice area aso
for rectangular ports have an area gradient ws and Pload= P1-P2. By
combining these equations the relationship between spool displacement and
input current is as follows:
𝑥 𝑠 =
(1 − 𝛾)𝑘 𝑡 𝑖
𝛽
(𝑘 − 𝑘 𝑓𝑟)𝑥 𝑛𝑚
𝑟𝑃𝑠 𝑎 𝑠
+ 𝑘(𝑟 + 𝑏)(1 − 𝛾)
… … . . . … (3.15)
𝛾 =
𝑘(𝑟 + 𝑏)𝑥 𝑛𝑚
𝑟𝑃𝑠 𝑎 𝑠
… … … … (3.16)
𝛽 = 𝑘 𝑎 − 𝑘 𝑚 + 𝑘(𝑟 + 𝑏)2
+
𝑎 𝑛 𝑟2
𝑃𝑠
𝑥 𝑛𝑚
… … … … (3.17)
𝑘 𝑓𝑟 = 2𝐶 𝑞
2
𝑤 𝑐𝑜𝑠𝜃′ (𝑃𝑠 − 𝑃𝑙𝑜𝑎𝑑) … … … … (3.18)
The spool displacement will be proportional to input current provided
that the denominator of Eq. (3.15) is positive. The flow reaction equivalent
stiffness kfr will probably be much smaller than the wire stiffness k, so that
the effect of load pressure difference Pload may not present a problem. In
practice, γ << 1 and can be neglected. Notice also that the destabilizing
magnetic constant -km, the magnitude of which can be varied during
manufacture, the process known as detuning. In particular, β can be
detuned to a very small value by magnetically increasing km and Eq. (3.15)
then becomes:
𝑥 𝑠 ≈
𝑘 𝑡 𝑖
𝑘(𝑟 + 𝑏)
… … … … (3.19)
The input electrical torque is balanced by the wire feedback torque
because of spool position, and the flapper will return to its central position
between the nozzles (Watton J. , 2009). Clearly, for the same servovalve,
the value of k, r and b are constants. The spool displacement which can be
proportional to current is dominated.

3.1.4.b Dynamic Modeling of Servovalve:
The steady state performance of the valve will need to be augmented
by a model for the transient response, and also for the transient response of
the fluid transmission line. This will allow predictive control to be used.
The servovalve requires a finite time to change its spool position as a
response of changing applied current. The combination of these issues
means that the design of both open-loop and closed-loop control systems
should take into account these dynamic issues.
For the Ultra/servovalve type (mechanical feedback) shown in Fig.
3.7, it is clear what components contribute toward the overall dynamic
performance. The use of a voltage-feedback servovalve-amplifier means
that the voltage-build-up characteristic is extremely fast when compared
with other elements of the servovalve.
The dynamic effect caused by the time required to generate the drive
current can be ignored. However, there are effects produced from the
flapper inertia and fluid viscosity (Watton J. , 2009). Considering the
Fig. 3.7 Contribution to force-feedback servovalve dynamic behavior.

steady state servovalve operation, the current build-up and the dynamic
torque equations have the following types:
𝑘 𝑡 𝑖 = (𝑘 𝑎 − 𝑘 𝑚)𝜃 + (𝑃𝑎 − 𝑃𝑏)𝑎 𝑛 𝑟 + 𝑘[𝑥 𝑠 + (𝑟 + 𝑏)𝜃](𝑟 + 𝑏) + 𝐵 𝑣𝑓
𝑑𝜃
𝑑𝑡
+
𝐽
𝑑2 𝜃
𝑑𝑡2
… … … … (3.20)
For flapper-nozzle resistance bridge flow, apply the continuity equation on
each side gives:
𝐶 𝑞𝑜 𝑎 𝑜�
2(𝑃𝑠 − 𝑃𝑎)
𝜌
− 𝐶 𝑞𝑛 𝑎 𝑛𝑥�
2𝑃𝑎
𝜌
= +𝑎 𝑠𝑜
𝑑𝑥 𝑠
𝑑𝑡
+
𝑉𝑎
𝛽
𝑑𝑃𝑎
𝑑𝑡
… … … … (3.21)
𝐶 𝑞𝑜 𝑎 𝑜�
2(𝑃𝑠 − 𝑃𝑏)
𝜌
− 𝐶 𝑞𝑛 𝑎 𝑛𝑦�
2𝑃𝑏
𝜌
= −𝑎 𝑠
𝑑𝑥 𝑠
𝑑𝑡
+
𝑉𝑏
𝛽
𝑑𝑃𝑏
𝑑𝑡
… … … … (3.22)
Where:
𝑎 𝑛𝑥 = 𝜋𝑑 𝑛(𝑥 𝑛𝑚 − 𝑥), 𝑎 𝑛𝑦 = 𝜋𝑑 𝑛(𝑥 𝑛𝑚 + 𝑥) & 𝑥 = 𝑟𝜃
And, Va and Vb are the internal small volumes on either side of and
within the flow resistance bridge. The flapper displacement at the nozzle is
x, and its maximum displacement is xnm.
The static force balance at the spool, including the flow reaction force,
is now modified to include the dynamic flow reaction force, the spool
viscous damping and acceleration effects:
(𝑃𝑎 − 𝑃𝑏)𝑎 𝑠 = 𝑘[𝑥 𝑠 + (𝑟 + 𝑏)𝜃]
+ 2𝐶 𝑞
2
𝑤𝑠 𝑥 𝑠 cos 𝜃′[𝑃𝑠 − 𝑃𝑙𝑜𝑎𝑑] + 𝜌 𝑙 �
𝑑𝑄1
𝑑𝑡
−
𝑑𝑄2
𝑑𝑡
� + 𝐵𝑠𝑓
𝑑𝑥 𝑠
𝑑𝑡
+ 𝑚
𝑑2
𝑥 𝑠
𝑑𝑡
… … … … (3.23)
Where:
𝑄1 = 𝐶 𝑞 𝑤𝑠 𝑥 𝑠�
2(𝑃𝑠 − 𝑃1)
𝜌
, 𝑄2 = 𝐶 𝑞 𝑤𝑠 𝑥 𝑠�
2𝑃2
𝜌
& 𝑃𝑙𝑜𝑎𝑑 = 𝑃1 − 𝑃2 . . (3.24)
Obviously, the defining equations of servovalve are nonlinear, and the
solution also requires the load specification so that the load pressure
difference (P1 - P2) can be derived. Considering the equations presented, it

will be seen that a valve dynamic performance depends not only on
electrical-electromagnetic-geometry parameters but also on the load it is
supplied Pload and, hence, on the load flow rate, the supply pressure Ps, and
the magnitude of the input current.
The tank (return line) pressure is usually neglected in comparison to
the line pressures. The port opening area (wsxs) is proportional to spool
displacement which is also proportional to the current applied to the
electromagnetic first stage. Servovalve manufacturers also quote the rated
flow at the valve rated current and with a valve pressure drop of 70bar, that
is, the total pressure drop across both ports. Consequently the servovalve
equations could be rewritten in the following form (Watton J. , 2009).
𝑄1 = 𝑘 𝑐 𝑖�(𝑃𝑠 − 𝑃1) & 𝑄2 = 𝑘 𝑐 𝑖� 𝑃2 . . … (3.24𝑎)
Where: 𝑘 𝑐 = 𝐶 𝑞 𝑤𝑠
𝑘 𝑡
𝑘(𝑟+𝑏)
�
2
𝜌
From the previous equations and the contribution of dynamics
behavior was shown in Fig. 3.7, the amount of hydraulic fluid flow from
the servovalve depends on the pressure and the current value coming to
servovalve amplifier. In the steady state condition, both of the
electromagnetic and mechanical properties are considered constant.
The effect of the dynamic behavior of the amplifier can be considered
as a constant at steady state operation condition (New assumption). This
assumption permits the equation (3.24a) to convert the amplifier input
current replaced by the voltage value coming from the DAP-view programs
to the servovalve amplifier. In other words, the hydraulic flow rate coming
from the servovalve (Q) can be considered as a function of the input DAP-
card voltage value and the pressure effect on the servovalve will be as
follows:
𝑄 = 𝑓 ( 𝑣 , 𝑃 ) … . . (3.25)

At steady state operating condition ( vss, P1ss, P2ss, Q1ss, Q2ss), the first
linear term of the Taylor series expansion for a nonlinear function will be
employed. Consequently, small changes in each parameter lead to:
𝛿𝑄1 =
𝜕𝑄1
𝜕𝑣𝑠𝑠
�
𝑣(0),𝑃(0)
𝛿𝑣𝑠𝑠 +
𝜕𝑄1
𝜕𝑃1
�
𝑣(0),𝑃(0)
𝛿𝑃1 &
𝛿𝑄2 =
𝜕𝑄2
𝜕𝑣𝑠𝑠
�
𝑣(0),𝑃(0)
𝛿𝑣𝑠𝑠 +
𝜕𝑄2
𝜕𝑃2
�
𝑣(0),𝑃(0)
𝛿𝑃2 … . . (3.25𝑎)
𝛿𝑄1 = 𝑘 𝑣1 𝛿𝑣𝑠𝑠 + 𝑘 𝑝1 𝛿𝑃1 & 𝛿𝑄2 = 𝑘 𝑣2 𝛿𝑣𝑠𝑠 + 𝑘 𝑝2 𝛿𝑃2 … . . (3.25𝑏)
The servovalve equation could be written as:
𝑄1 = 𝑘 𝑓 𝑣�(𝑃𝑠 − 𝑃1𝑠𝑠) & 𝑄2 = 𝑘 𝑓 𝑣� 𝑃2𝑠𝑠
𝑘 𝑣1 =
𝜕𝑄1
𝜕𝑣 𝑠𝑠
= 𝑘 𝑓� 𝑃𝑠 − 𝑃1𝑠𝑠 =
𝑄1𝑠𝑠
𝑣 𝑠𝑠
𝐹𝑙𝑜𝑤 𝐺𝑎𝑖𝑛 . . … (3.25𝑐)
𝑘 𝑣2 =
𝜕𝑄2
𝜕𝑣𝑠𝑠
= 𝑘 𝑓� 𝑃2𝑠𝑠 =
𝑄2𝑠𝑠
𝑣𝑠𝑠
𝐹𝑙𝑜𝑤 𝐺𝑎𝑖𝑛 … . . (3.25𝑑)
𝑘 𝑝1 =
𝜕𝑄1
𝜕𝑃1
=
𝑘 𝑓 𝑣𝑠𝑠
2� 𝑃𝑠 − 𝑃1𝑠𝑠
=
𝑄2𝑠𝑠
2(𝑃𝑠 − 𝑃1𝑠𝑠)
𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 … . . (3.25𝑒)
𝑘 𝑝2 =
𝜕𝑄2
𝜕𝑃2
=
𝑘 𝑓 𝑣𝑠𝑠
2� 𝑃2𝑠𝑠
=
𝑄2𝑠𝑠
2(𝑃2𝑠𝑠)
𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 . . … (3.25𝑓)
𝑘 𝑣𝑝 =
𝜕𝑃
𝜕𝑣𝑠𝑠
= −
𝜕𝑄
𝜕𝑣𝑠𝑠
𝜕𝑄
𝜕𝑃
=
𝑘 𝑣
𝑘 𝑝
=
2(𝑃𝑠 − 𝑃1𝑠𝑠)
𝑣𝑠𝑠
=
2𝑃2𝑠𝑠
𝑣𝑠𝑠
, 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑠𝑒𝑛𝑠𝑖𝑣𝑖𝑡𝑦 … . . (3.25𝑔)
In this application, the single action operation will be considered, so
the port B (number 2 in previous equations) has been cancelled, see Fig.
3.3. Thus, it is needed to consider the segment of the first port to find the
value of flow gain and pressure coefficient equations (3.25c & 3.25de) at
steady state condition.

Practically, the dynamic characteristic is often specified by the
manufacturer as a frequency-response diagram for the spool position
(input) and the flow rate (output) for a typical performance range. The
frequency response is obtained usually with the output ports connected at
the no-load condition. It therefore represents the best performance that can
be expected from the servovalve.
Indeed, in this experimental work the servovalve is not new, so there
is wear effects on the flexure tube, and erosion effects around the ports and
nozzles. Whilst a clear understanding may be gained by consideration of
such theory, the experimental work will rely on data based modeling
techniques. Before addressing data-based modeling, analytical
consideration will be given to transmission line modeling.
3.1.5 Transmission line modeling:
Hydraulic pipelines, when of significant length, have an important
effect upon the performance of many systems. The electrical analogy is a
useful mechanism for understanding this approach (Watton J. , 2009).
Considering linear characteristics and a slug of fluid, (a) is cross sectional
area and the length is (l).
a. Fluid resistance: The pressure drop ΔP, along the fluid element for
laminar flow, is given by:
∆𝑃 =
128𝜇𝑙
𝜋𝑑4
𝑄 → ∆𝑉𝑒 = 𝑅𝐼, … . . (3.26𝑎)
Hydraulic resistance Electrical resistance
b. Fluid compressibility:
∆𝑄 =
𝑉
𝛽
𝑑𝑃
𝑑𝑡
→ ∆𝐼 = 𝐶
𝑑𝑉𝑒
𝑑𝑡
, … . . (3.26𝑏)
Fluid compressibility Electrical capacitance

c. Fluid inertia: The pressure drop that is due to fluid acceleration is
given by:
∆𝑃𝑎 = 𝜌𝑙𝑎
𝑑𝑈
𝑑𝑡
, ∆𝑃 =
𝜌𝑙
𝑎
𝑑𝑄
𝑑𝑡
→ ∆𝑉𝑒 = 𝐿
𝑑𝐼
𝑑𝑡
, … . . (3.26𝑐)
Fluid mechanical mass Electrical inductance
𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 → 𝑅 =
128𝜇𝑙
𝜋𝑑4
, 𝐼𝑛𝑑𝑢𝑐𝑡𝑎𝑛𝑐𝑒 → 𝐿 =
𝜌𝑙
𝑎
&
𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑎𝑛𝑐𝑒 → 𝐶 =
𝑉
𝛽
… . . (3.26𝑑)
If a system is expected to have a frequency component that is
comparable with this frequency, line dynamics must be modeled with some
accuracy. The issue is how to distribute R, L and C in the line and how
many "lumps" should be used (Watton J. , 2009). This work shows a two-
lump approximation using a pair of π networks as shown in Fig. 3.8.
The set of equations using this approximation, and working from left
to right, may then be written as follows:
𝑄𝑖 − 𝑄 𝑎 =
𝐶
4
𝑑𝑃𝑖
𝑑𝑡
, 𝑄 𝑎 − 𝑄 𝑏 =
𝐶
4
𝑑𝑃𝑥
𝑑𝑡
, 𝑄 𝑏 − 𝑄 𝑜 =
𝐶
4
𝑑𝑃𝑜
𝑑𝑡
. . … (27𝑎)
𝑃𝑖 − 𝑃𝑥 =
𝑅
2
𝑄 𝑎 +
𝐿
2
𝑑𝑄 𝑎
𝑑𝑡
, 𝑃𝑥 − 𝑃𝑜 =
𝑅
2
𝑄 𝑏 +
𝐿
2
𝑑𝑄 𝑏
𝑑𝑡
… … … … (27𝑏)
Fig. 3.8 The line dynamics approximation using lumped π elements for laminar mean flow (Watton J. ,
2009).

These equations can be resolved when the input and the output
pressure flow relationships have been included to close the solution. So the
pressure and flow meter sensors are needed in the test rig to record the
overall pressure difference between the input and output for the
transmission line, as shown in Fig. 3.3 and Fig. 3.9. This pressure
difference can be used to calculate the losses that occur in the TL and the
fittings which include such as bends, elbows, restricted valves and sudden
expansion or contraction and other minor losses.
To solve the previous equations, it is necessary to make some
experimental experiences to achieve steady state condition, through
collecting this kind of data. The values of unknown constants mentioned in
equations (3.25) such as flow and pressure gains can be calculated, as well
as the losses that occur in transmission line.

(a)Top view of The Transmission line System. (b) The Supplied Fluid Power Unit
(c) Side view of The Transmission Line System. (d) The Pressure Control Unit For the System.
(e) The Sensor Unit in TL System. (f) The Flow Meter. (g) The Pressure Transducer.
Fig. 3.9 The Fluid Power System and The Transmission Line Test Rig in THe Fluid Power Laboratory,
W20/ School of Engineering / CARDIFF UNIVERSITY/ UK.

3.1.6 Servovalve Gains and the Transmission Line Losses:
To find the properties of flow inside the transmission line, the steady
state conditions have been created to record the values of pressure and flow
rate inside the TL. By using these data, the servovalve gain could be found
from the Excel-file that has been recorded by employing the equations
(25b, 25d & 25f). At 1.5 degree opening restrictor valve, the pressure inside
the TL is accumulated. 50bar as a pressure line system is supplied with a
direct control using the voltages function generator. The results come from
the square-wave voltage illustrated in Fig. 3.10 and Fig. 3.11.
The noise and the oscillations of the signal are shown in Fig. 3.11, for
the values of flow rate result from the nature of flow meter design. As
mentioned previously there is an error should be dealt with and reduced by
subtracting the offset value and depending on the average values to solve
the mathematical equations.
Through the act of the experimental test, the nature of the flow rate
has been checked as a laminar flow by calculating the Reynolds number
and the velocity from recorded flow. The relation between the voltage and
the spool position inside the servovalve considered as a first order. That is
clearly seen in the transient response test and the Moog literary
recommendation (Moog Controls Limited, 25th March, 2011) and with
supporting by Eq.(3.19). It can be considered that, the input (voltage v) and
the output (theoretical spool position xs) relationship is given by:
𝑥 𝑠
𝑣
=
𝐾 𝑇𝐿
1 + 𝜏 𝑠
… . . (3.28)
Taking the inverse Laplace transformation of Eq. (3.28)
𝑥 𝑠(𝑡) + 𝜏 ∗
𝑥 𝑠(𝑡) − 𝑥 𝑠(𝑡 − 1)
𝑇𝑠
= 𝐾 𝑇𝐿 ∗ 𝑣(𝑡) … . . (3.28𝑎)

The transfer function constant (τ=1/2πf) has been found at break point
frequency from Bode diagram supported by manufacturer data sheet, see
{Appendix A} and the final relation illustrated below:
𝑥 𝑠(𝑡) =
1
�1 +
𝜏
𝑇𝑠
�
∗ ��𝐾 𝑇𝐿 ∗ 𝑣(𝑡)� + 𝑥 𝑠(𝑡 − 1) ∗ �
𝜏
𝑇𝑠
�� … . . (3.28𝑏)
This relation can be used in MATLAB program to find the flow rate
values by the effect of the movement of servovalve spool position with
supporting by equation (3.24) at the small time constant Ts. The servovalve
gain constant (KTL) is found from the experimental test rig at steady state
condition.
The fluid power unit of the laboratory supplies many test rigs. So, it
was difficult to find out the miner losses through the line supply, the
fluctuation effect on the test benches which have been used. The minor
losses mean the pressure drop which happens due to elbows, junction,
reducers, valves and hoses…etc. The major losses occurring in TL can be
calculated from the equation below (White, 2005):
∆𝑃 𝑚𝑎𝑗𝑒𝑟 = 0.5𝑓(𝜌 ∗ 𝑈3
2) �
𝐿 𝑇𝐿
𝑑𝑖3
� , 𝑤ℎ𝑒𝑟𝑒: 𝑈3 =
𝑄3
𝑎3
. . … (3.28𝑐)
An experimental test has been used to find the total losses ( ΔPTotal)
between point 2 & 3 as located in Fig. 3.3, where:
∆𝑃𝑇𝑜𝑡𝑎𝑙 = ∆𝑃 𝑚𝑎𝑗𝑒𝑟 + ∆𝑃 𝑚𝑖𝑛𝑜𝑟 … . . (3.28𝑑)
Then:
∆𝑃 𝑚𝑖𝑛𝑜𝑟 = 0.5𝑓(𝜌 ∗ 𝑈3
2) �
𝐿 𝑒𝑞𝑢𝑖𝑣
𝑑 𝑖3
� … . . (3.28𝑒)
So the equivalent length Lequiv = 18.46m, and the corrected total TL
length become:
𝐿 𝑐 = 𝐿 𝑇𝐿 + 𝐿 𝑒𝑞𝑢𝑖𝑣 … . . (3.28𝑓)

The total corrected length (Lc=l) has been used in equations (3.28f) to
solve the mathematical model.
3.1.7 MATLAB Simulation:
To find a mathematical model for the TL equations (3.27a and 3.27b)
and the servovalve flow rate equations (3.24) supported by the voltage
linearization equations (3.25b, 3.25d & 3.25f) that mentioned
before, MATLAB program can be used to represent the transmission line
effect after converting to electric analogy.
To overcome the complexity of the pressure signal of the hydraulics
system in the fluid power laboratories in Cardiff University which is
represented in the large size of the power unit system as well as the length
of the pipes connected with TL test rig. Some assumptions have been taken
into account such as: the pressure provided by the supplied pressure line
which delivers the fluid to the servovalve was considered as constant
pressure in MATLAB program. This will neglect the fluctuation of the
pressure value caused by system complexity. The MATLAB program can be
seen in {Appendix B} which employ the theoretical equations to simulate
the effect of the transmission line pressure drop. However, it is essential to
find the values for the gain and the constant properties needed.
The sample was taken from the calculated data, which represent a step
input supplied by the artificial function generator build the voltage signal in
MATLAB designed program.
As shown in figures (3.12-13-14) which represent the square wave
pressure signal acting on the TL system. The pressure values are measured
in three points. The first act on the input servovalve port and the second
measured in the output servovalve port while the third measured in the end
of the transmission line. Point three makes apparent the delay effect of the
loss in TL. Fig.3.13 shows the values of the instant flow rate in the long TL

in the same three positions mentioned before with the changing in the
voltage signal generation. The theoretical spool position displacement
calculated from the first order transfer function the servovalve spool
displacement is shown in Fig. 3.14. It is an important to mention that this
servovalve is working in the single acting direction, so the voltage always
in the positive value.
By using the flexibility of the MATLAB, many shapes of the voltage
signal can be generated as the demand of the manufacturing process.
Therefore, an extra two shapes of the voltage signal are generated in
MATLAB. As illustrated in Fig. 3.15 the sine wave voltage signal was
applied to the servovalve to generate a sine wave pressure form in the end
of the TL with starter voltage 3volt and with amplitude 1.5volt. The delay
in the pressure value is obviously seen in the end of TL at P3 and the
instantaneous flow rate can be seen in Fig. 3.16. Also the theoretical spool
position displacement can be seen in Fig. 3.17. The third voltage signal
form generated in this work is the saw-tooth wave and the effect of this
kind of voltage wave form can be seen in Fig. 3.18, Fig. 3.19 and Fig. 3.20
at starter voltage 5volt and with amplitude 2volt.
The MATLAB program can create various shapes of input voltage
value (sine-wave, square-wave or saw tooth-wave…etc). This will be
useful to understand and calculate the effect of the loss inside the TL and
also find the way to avoid the distortion in the pressure wave which
generated by the servovalve. Therefore, the open loop control method is not
sufficient to this kind of the pressure control process. So it is important to
study the closed loop control method to overcome the loss effect and
provide the pressure signal in the end of the TL at the same designed value.
This feature will be discussed in the next chapter using the experimental
way.

Fig. 3.10 Experimental Pressure Values in Open Loop controlled by C
++
program (1.5 degree Opening
from the Restrictor Valve), Square-wave, P1=50bar, Fr=0.25Hz.
Fig. 3.11 Experimental Flow Values in Open Loop controlled by C
++
program (1.5 degree Opening from
the Restrictor Valve), Square-wave, P1=50bar, Fr=0.25Hz.
-10
0
10
20
30
40
50
60
70
3000 3500 4000 4500 5000 5500 6000 6500 7000
P bar, v Volt
ms
P1 bar
P2 bar
P3 bar
P4 bar
Pr bar
v-
Volt*20
-5
0
5
10
15
20
3000 3500 4000 4500 5000 5500 6000 6500 7000
Q L/min, v Volt
ms
Q1 l/min
Q2 l/min
Q3 l/min
Q4 l/min
v Volt*10

Fig. 3.12 Mathematical Pressure Values. Open loop done by MATLAB artificial voltage function
generator P1=50bar, Frequency = 1 Hz, Amplitude=1.5volt, Start Voltage=3volt, Time= 3 s.
0 0.5 1 1.5 2 2.5 3
0
10
20
30
40
50
60
time s
Pressurebar,vVolt
(Input, output) Pressure on Servovalve & Input voltage signal
P1 bar
P2 bar
P3 bar
v Volt
Fig. 3.13 Mathematical Flow Rate Values. The Flow Rate in Open Loop done by MATLAB
P1=50bar, Freq. = 1 Hz, Time= 3 s.
0 0.5 1 1.5 2 2.5 3
0
1
2
3
4
5
6
x 10
-4
time s
flowratem3/s&vVolt/105
Flowrate through servovalve & input voltage signal
Q1 m3
/s
Q2 m3
/s
Q3 m3
/s
v Volt/105
Fig. 3.14 Mathematical Spool Position. Spool Position in Open Loop done by MATLAB P1=50bar,
Freq. = 1 Hz, Time= 3 s.
0 0.5 1 1.5 2 2.5 3
0
1
2
x 10
-4
time s
displacementmm
Servovalve spool displacement
Xs

Fig. 3.15 Mathematical Pressure Values. Open Loop Sine wave Pressure Signal done by MATLAB
artificial voltage function generator P1=50bar, Frequency = 0.25 Hz, Amplitude=1.5volt, Start
Voltage=3volt, Time= 3s.
0 0.5 1 1.5 2 2.5 3
0
10
20
30
40
50
60
time s
Pressurebar,vVolt
P1 bar
P2 bar
P3 bar
v Volt
Fig. 3.17 Mathematical Spool Position. Spool Position in Open Loop done by MATLAB P1=50bar, Freq.
= 1 Hz, Time= 3s.
0 0.5 1 1.5 2 2.5 3
0
1
2
x 10
-4
time s
displacementmm
Xs
Fig. 3.16 Mathematical Flow Rate Values. The Flow Rate in Open Loop Sine wave Pressure Signal done
by MATLAB P1=50bar, Time= 3 s.
0 0.5 1 1.5 2 2.5 3
0
1
2
3
4
5
6
x 10
-4
time s
Q1 m3
/s
Q2 m3
/s
Q3 m3
/s
v Volt/105

Fig. 3.19 Mathematical Flow Rate Values. The flow rate values in open loop servovalve done by
MATLAB P1=50bar, sine wave, Time= 3s.
0 0.5 1 1.5 2 2.5 3
0
1
2
3
4
5
6
x 10
-4
time s
Q1 m3
/s
Q2 m3
/s
Q3 m3
/s
v Volt/105
Fig. 3.18 Mathematical Pressure Values. The pressure values in open loop servovalve done by MATLAB
P1=50bar, Sawtooth wave, Amplitude=2 volt, Start Voltage=5volt, Time= 3s.
0 0.5 1 1.5 2 2.5 3
0
10
20
30
40
50
60
time s
Pressurebar,vVolt
P1 bar
P2 bar
P3 bar
v Volt
Fig. 3.20 Mathematical Spool Position. Spool Position in Open Loop done by MATLAB P1=50bar, Freq.
= 1 Hz, Time= 3s.
0 0.5 1 1.5 2 2.5 3
0
1
2
3
4
x 10
-4
time s
displacementmm
Xs

3.2 Theoretical Analyses of the Position and Velocity Control by
Electro-Hydraulic Servovalve System.
3.2.1 Introduction:
The mathematical analysis of electro-hydraulic servovalve model for
controlling the position and velocity of road simulator with variable load
(suspension system) will be analyzed. The servovalve is connected to a
single rod double acting liner actuator to control the position of the wheel
support dish under a suspension system unit.
The system's dynamic characteristics will then be tested using a PC
equipped with data acquisition processor (DAP-card). This will allow data
to be collected and will allow the prediction of the system's response to be
given a suitable control gain constant.
A road simulator system is shown in Fig. 3.21 and its purpose is for
experimental study. It is developed by using a hydraulic actuator providing
road input to a passive suspension system via a wheel unit. The description
of the road simulator system is described in Chapter 4. A schematic
diagram of the road simulator system is shown in Fig. 3.22.
The road simulator system is designed to generate step, sine-wave and
square-wave input signal to the passive suspension system by using C++
programs. The step and square-wave road input are intended for use in time
domain studies whilst sine-wave input is intended to be used in frequency
domain studies, i.e. frequency response tests. Displacement and velocity
outputs of the road simulator system become disturbance inputs for the
suspension system. Therefore, both systems are dynamically related and the
dynamic behavior of the road simulator system becomes an important
factor in this study, and must be investigated.

Fig. 3.21 Side View for The Road Simulator System Test Rig, Fluid Power Laboratory, W19/ School of
Engineering / CARDIFF UNIVERSITY/ UK.

Ahmed Fouad_Experimental and Theoretical Investigation for Electro-hydraulic Servovalve Systems Control_2014

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