ahmed fouad_experimental and theoretical investigation for electro-hydraulic servovalve systems...

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

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 Asst. Prof. (Member) Date: / /2014

Signature:

Name: Dr. Jafar Mehdi Hassan Prof. (Supervisor) Date: / /2014 Signature:

Name: Dr. Adnan Naji Jameel Prof. (Member) Date: / /2014 Signature:

Name: Dr. Mohammed Idrees Mohsin Asst. Prof. (Member) Date: / /2014 Signature:

Name: Dr. Arkan Kh. Husain Al-Taie Prof. (Chairman) Date: / /2014 Approved by the Mechanical Engineering Department Signature: Name: Dr. Jafar Mehdi Hassan Prof.-Dean of Mechanical Engineering Department Date: / /2014

II Chapter 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

III Chapter 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

IV Chapter 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.

V Chapter 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

VI Chapter 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

VII Chapter 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

VIII Chapter 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

IX Chapter 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

X Chapter 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 i 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 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

XI Chapter 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

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

XII Chapter 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.

XIII Chapter One: Background and Introduction to Servovalve

Greek Symbols

Character Description Units

1 Suspension angle deg.

2 r Effective Bulk modulus N/m2

3 Fluid absolute viscosity kg/m.s

4 Fluid density kg/m3

5 The rotation of the armature and flapper rad

6 ' Spool jet angle relative to the spool axis deg.

7 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 -

XIV Chapter 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 -

Chapter One

Introduction

2 Chapter 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 P is measured across the

servovalve. Once the 70bar P 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 dimensionsetc) 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

13 Chapter 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

26 Chapter 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).

= + ( ) = (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 :

=( + ), = + ( + ) & = (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 can be deduced (Watton J. , 1989):

= ( ) ( + )

+ ( + )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:


= + 1, = ( ), = 2, = ( + ); (3.5)

= 2( )

, =

2( )

; (3.6)

= 2 , =

2 ; (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:

=1

1 + (1 )2 =

, =1

1 + (1 + )2=

,

=

; (3.8)

= 16(

)2(

)2 (3.9)

Then the differential pressure is given by:

=4

[1 + (1 + )2][1 + (1 )2], (3.10)

Considering the null condition where = 0 and = 0; that leads to:

= =1

(1 + ) (3.11)

And the null gain condition is:

( )

=4

(1 + )2 (3.12)

Because flapper operation is designed to be around the central (null)

position, the pressure difference generated may be simply written as:

( ) =

(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:


( ) = + 22[ ], = (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:

=(1 )

( )

+ ( + )(1 )

. . . (3.15)

=( + )

(3.16)

= + ( + )2 +2

(3.17)

= 22 ( ) (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,


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:

= ( ) + ( ) + [ + ( + )]( + ) +

+

2

2 (3.20)

For flapper-nozzle resistance bridge flow, apply the continuity equation on

each side gives:

2( )

2 = +

+

(3.21)

2( )

2 =

+

(3.22)

Where:

= ( ), = ( + ) & =

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:

( ) = [ + ( + )]

+ 22 cos[ ] + 1

2

+

+ 2 (3.23)

Where:

1 = 2( 1)

,2 =

22 & = 1 2 . . (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).

1 = ( 1) & 2 = 2 . . (3.24)

Where: =

(+)2

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:

= ( , ) . . (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:

1 = 1

(0),(0)

+ 11

(0),(0)

1 &

2 = 2

(0),(0)

+ 22

(0),(0)

2 . . (3.25)

1 = 1 + 1 1 & 2 = 2 + 2 2 . . (3.25)

The servovalve equation could be written as:

1 = ( 1) & 2 = 2

1 =1

= 1 =1

. . (3.25)

2 =2

= 2 =2

. . (3.25)

1 =11

=

2 1

=2

2( 1) . . (3.25)

2 =22

=

22=

22(2)

. . (3.25)

=

=

=

=2( 1)

=22

, . . (3.25)

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 m

ahmed fouad_experimental and theoretical investigation for electro-hydraulic servovalve systems...

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