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DYNAMIC MODELING AND CONTROL OF AN ELECTROMECHANICAL

CONTROL ACTUATION SYSTEM

A THESIS SUBMITTED TO

THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES

OF

MIDDLE EAST TECHNICAL UNIVERSITY

BY

ÜMİT YERLİKAYA

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR

THE DEGREE OF MASTER OF SCIENCE

IN

MECHANICAL ENGINEERING

SEPTEMBER 2016

Approval of the thesis:



submitted by ÜMİT YERLİKAYA in partial fulfillment of the requirements for the

degree of Master of Science in Mechanical Engineering Department, Middle

East Technical University by,

Prof. Dr. Gülbin Dural Ünver

Dean, Graduate School of Natural and Applied Sciences __________________

Prof. Dr. Tuna Balkan

Head of Department, Mechanical Engineering __________________


Supervisor, Mechanical Engineering Dept., METU __________________

Examining Committee Members

Prof. Dr. Metin Akkök

Mechanical Engineering Dept., METU __________________



Assoc. Prof. Dr. İlhan Konukseven


Assoc. Prof. Dr. Yiğit Yazıcıoğlu


Assoc. Prof. Dr. S. Çağlar Başlamışlı

Mechanical Engineering Dept., Hacettepe University __________________

Date: 09.09.2016

iv

I hereby declare that all information in this document has been obtained and

presented in accordance with academic rules and ethical conduct. I also declare

that, as required by these rules and conduct, I have fully cited and referenced

all material and results that are not original to this work.

Name, Last Name: Ümit Yerlikaya

Signature :

v

ABSTRACT



Yerlikaya, Ümit

M. S., Department of Mechanical Engineering

Supervisor: Prof. Dr. Tuna Balkan

September 2016, 131 pages

Electromechanical simulators, actuators are widely used in miscellaneous

applications in engineering such as aircrafts, missiles, etc. These actuators have

momentary overdrive capability, long-term storability and low quiescent power/low

maintenance characteristics. Thus, electromechanical actuators are applicable option

for any system in aerospace industry, instead of using hydraulic actuators. In the

same way, they can be used in control actuation section of missiles to deflect flight

control surfaces. Mostly used alternatives of control actuation system (CAS) are

electromechanical, electrohydraulic and electrohydrostatic CASs. In this thesis,

electromechanical control actuation systems that are composed of brushless direct

current motor, ball screw and lever mechanism are studied. In this type of control

actuation system, there are both nonlinearity and asymmetry which are caused by

lever mechanism itself, saturation limits, Coulomb friction, backlash and initial

mounting position of lever mechanism. In order to design controller and optimize

controller parameters, all equations of motion are derived and so the detailed

nonlinear and linear mathematical models of this system are obtained. The servo

vi

drive amplifier of motor is used in current mode. Between position and current loops,

inner velocity loop is used to provide extra damping to the system and avoid

unnecessary oscillations. Therefore, three control loops are used. By using linear

model of electromechanical CAS, according to performance requirements, it is

decided that PI and P-controller are sufficient for position and velocity control,

respectively. The limitations that are imposed to controllers which have integral gain

cause a residual error, so the controllers tend to overshoot target value in order to

eliminate it. In order to solve this problem, an anti-windup method is applied. Then,

the unknown controller parameters and anti-windup coefficients are found according

to the performance requirements by using MATLAB Response Optimization Tools

on the nonlinear model. During the optimization, the nonlinear relations and

limitations on controller outputs are considered. A prototype of electromechanical

CAS with ball screw and lever mechanism is manufactured. All unknown parameters

such as dimensions, masses, inertias of components, viscous and Coulomb frictions

and backlash of the system are identified. Identified Coulomb friction values are used

for friction compensation in real-time application. Real-time tests are performed with

optimized controller parameters and anti-windup coefficient by using xPC Target

(MATLAB-Simulink). Finally, the nonlinear model of electromechanical control

actuation system is verified by making real-time tests on the manufactured prototype

with and without external load.

Keywords: Control Actuation System, Electromechanical Actuators, Fin, Control of

Brushless DC Motor, Response Optimization, PID, xPC Target

vii

ÖZ

ELEKTROMEKANİK KONTROL TAHRİK SİSTEMİNİN DİNAMİK

MODELLENMESİ VE KONTROLÜ

Yerlikaya, Ümit

Yüksek Lisans, Makine Mühendisliği Bölümü

Tez Yöneticisi: Prof. Dr. Tuna Balkan

Eylül 2016, 131 sayfa

Elektromekanik eyleyiciler uçak ve füzelerde olmak üzere birçok uygulamada

sıklıkla kullanılmaktadır. Bu eyleyiciler anlık aşırı sürme kapasitesine, uzun vadeli

depolanabilme özelliğine, pasif durumda düşük güç tüketebilme ve az bakım

gerektirme karakteristiğine sahiptirler. Bu yüzden elektromekanik eyleyiciler

havacılıktaki çoğu sistem için uygulanabilir bir seçenektir. Aynı şekilde bunlar

füzelerin kontrol bölümlerinde uçuş kontrol yüzeylerini döndürmek için

kullanılabilmektedir. En çok kullanılan kontrol tahrik sistemleri elektromekanik,

elektrohidrolik ve elektrohidrostatik alternatifleridir. Bu tez kapsamında, fırçasız

doğru akım motoru, bilyeli vida ve kaldıraç mekanizmasından oluşan bir

elektromekanik kontrol tahrik sistemi ele alınmıştır. Bu tip kontrol tahrik

sistemlerinde, kaldıraç mekanizmasının kendisinden, limitlerden, Coulomb

sürtünmelerinden, boşluklardan ve kaldıracın ilk montaj konumlanmasından

kaynaklanan bazı doğrusal olmayan durumlar ve simetri bozuklukları mevcuttur.

Kontrolcü tasarımı ve kontrolcü parametrelerinin en iyilenmesi için tüm hareket

denklemleri türetilmiş, sistemin ayrıntılı doğrusal ve doğrusal olmayan matematiksel

viii

modelleri elde edilmiştir. Servomotor sürücüsü akım modunda kullanılmaktadır.

Sisteme fazladan sönüm katmak ve oluşabilecek gereksiz salınımları engellemek için

konum ve akım döngüsü arasına eklenen hız iç döngüsü ile üç kontrol döngüsü

kullanılmaktadır. Doğrusal model kullanılarak, başarım gereksinimlerine göre konum

ve hız kontrolcüsü olarak sırasıyla PI ve P kontrolcülerin kullanılmasının yeterli

olduğuna karar verilmiştir. İntegral kazancı olan kontrolcü çıkışlarına uygulanan

sınırlar hataların artmasına sebep olmaktadır. Gerçekleşen değerin referans komutuna

varmasına rağmen, bu hatalar hemen giderilememektedir. Bu durumu ortadan

kaldırmak için “anti-windup” yöntemi uygulanmıştır. Sonrasında, belli olmayan

kontrolcü parametreleri ve “anti-windup” katsayısı, doğrusal olmayan model

kullanılarak performans gereksinimine göre MATLAB Response Optimization Tools

(cevap en iyileme araçları) yardımıyla bulunmuştur. En iyileme sırasında, doğrusal

olmayan ilişkiler ve kontrolcü çıkışlarına uygulanan sınırlamalar göz önünde

bulundurulmuştur. Kaldıraç mekanizmalı ve bilyeli vidalı elektromekanik kontrol

tahrik sisteminin prototipi üretilmiştir. Bileşenlerin boyutları, kütleleri, atalet

momentleri ve sistemin viskoz/Coulomb sürtünmeleri ve boşluk gibi bilinmeyen

parametreler belirlenmiştir. Belirlenen Coulomb sürtünme değerleri gerçek zamanlı

uygulamada sürtünme telafisi olarak kullanılmıştır. Gerçek zamanlı testler, en

iyilenen kontrolcü parametreleri ve “anti-windup” katsayısı kullanılarak xPC Target

(MATLAB-Simulink) ortamında yapılmıştır. Son olarak, üretilen prototip üzerinde

harici yük olmadan ve harici yük altında gerçek zamanlı testler yapılarak, doğrusal

olmayan benzetim modeli doğrulanmıştır.

Anahtar Kelimeler: Kontrol Tahrik Sistemi, Elektromekanik Eyleyici, Fin, Fırçasız

Doğru Akım Motor Kontrolü, Cevap Eniyileme, PID, xPC Target

ix

ACKNOWLEDGEMENTS

First of all I would like to express my sincere appreciation to my thesis supervisor

Prof. Dr. Tuna BALKAN for his guidance throughout my thesis study.

Then I would like to thank TÜBİTAK for scholarship and financial supports which

made this project possible. I hope their endless support to science and scientists

continue to enrich our scientific heritage.

I wish to express my gratitude to Prof. Dr. Bülent E. PLATİN and Ahmet Can

AFATSUN for their guidance throughout my thesis study.

I am in debt of gratitude to Aslı AKGÖZ BİNGÖL in ROKETSAN Inc. for her

friendly support and advices.

I also owe thanks to my colleagues in my unit in ROKETSAN Inc. who helped me in

every subject throughout the years of my study.

Finally I wish to express my sincere thanks to my father Ahmet YERLİKAYA, my

mother Nigar YERLİKAYA, my sister Ayfer YERLİKAYA and lastly I dedicate this

thesis work to my lovely son, Onur YERLİKAYA.

x

TABLE OF CONTENTS

ABSTRACT ................................................................................................................ V

ÖZ ............................................................................................................................. VII

ACKNOWLEDGEMENTS ....................................................................................... IX

TABLE OF CONTENTS ............................................................................................ X

LIST OF TABLES .................................................................................................. XIII

LIST OF FIGURES ................................................................................................. XIV

LIST OF ABBREVIATIONS .............................................................................. XVIII

LIST OF SYMBOLS .............................................................................................. XIX

CHAPTER 1 ................................................................................................................. 1

1. INTRODUCTION ................................................................................................ 1

1.1 Literature Survey .............................................................................................. 1

1.1.1 Electromechanical Control Actuation Systems (EM-CASs) ................... 2

1.1.1.1 EM-CAS with Screw and Lever Mechanism ................................... 3

1.1.1.2 EM-CAS with Clutch Actuator ........................................................ 6

1.1.1.3 EM-CAS with Worm Gear ............................................................... 7

1.1.2 Electrohydrostatic Control Actuation Systems (EHS-CASs) .................. 8

1.1.3 Electrohydraulic Control Actuation Systems (EH-CASs) ....................... 9

1.2 Objective and Scope of Thesis ....................................................................... 12

1.3 Thesis Outline ................................................................................................ 13

CHAPTER 2 ............................................................................................................... 17

2 DYNAMIC MODELING OF EM-CAS ............................................................ 17

2.1 Mechanical System ........................................................................................ 17

2.1.1 Kinematic Relations ............................................................................... 18

2.1.2 Equations of Motion ............................................................................... 20

2.2 Electrical System ............................................................................................ 28

2.3 Block Diagram of EM-CAS ........................................................................... 29

CHAPTER 3 ............................................................................................................... 33

3 IDENTIFICATION OF THE SYSTEM PARAMETERS ................................. 33

3.1 System Performance Criteria ......................................................................... 34

3.2 The Components of EM-CAS ........................................................................ 35

xi

3.2.1 BLDC Motor .......................................................................................... 35

3.2.2 Servo Drive Amplifier............................................................................ 36

3.2.3 Real-time Target Machine (RTTM) ....................................................... 40

3.2.4 Incremental Encoder .............................................................................. 40

3.2.5 Fin .......................................................................................................... 41

3.2.6 Fin Shaft ................................................................................................. 42

3.2.7 Fork ........................................................................................................ 43

3.2.8 Screw and Nut ........................................................................................ 44

3.3 The Friction Characterization of EM-CAS .................................................... 45

3.3.1 Friction Measurement Test Setup .......................................................... 45

3.3.2 Viscous Friction ..................................................................................... 46

3.3.2.1 Ambient Temperature, 24ºC .......................................................... 47

3.3.2.2 Ambient Temperature, -6ºC ........................................................... 50

3.3.2.3 The Effect of Different Ambient Temperatures on Viscous Friction

........................................................................................................ 52

3.3.2.4 Curve Fitting to Viscous Friction Graph ........................................ 55

3.3.3 Coulomb Friction ................................................................................... 57

3.3.3.1 Ambient Temperature, 24ºC .......................................................... 57

3.3.3.2 Ambient Temperature, -6ºC ........................................................... 59

3.3.3.3 The Effect of Different Ambient Temperatures on Coulomb

Friction ........................................................................................................ 60

3.3.3.4 Curve Fitting to Coulomb Friction Graph ...................................... 60

3.4 Measuring Backlash in EM-CAS ................................................................... 64

3.5 Loading Test Setup ........................................................................................ 66

CHAPTER 4 .............................................................................................................. 69

4 LINEAR SYSTEM MODELING AND CONTROLLER DESIGN ................ 69

4.1 Linear System Modeling ................................................................................ 70

4.1.1 Using P-Controller in Position Control .................................................. 73

4.1.2 Using PI-Controller in Position Control ................................................ 76

4.2 Controller Design ........................................................................................... 78

4.2.1 Optimizing of Controller Parameters ..................................................... 79

CHAPTER 5 .............................................................................................................. 83

5 SIMULATION AND TEST RESULTS ............................................................ 83

5.1 Nonlinear Simulink Model of EM-CAS ........................................................ 83

5.1.1 Controllers .............................................................................................. 84

5.1.2 Motor & Drive ....................................................................................... 84

5.1.3 Screw and Nut ........................................................................................ 85

5.1.4 Fin .......................................................................................................... 86

5.2 Comparison of Linear and Nonlinear Models ................................................ 87

5.3 Real-time Test Model in xPC Target ............................................................. 89

xii

5.3.1 Homing ................................................................................................... 91

5.3.2 Setup Files .............................................................................................. 92

5.3.3 Incremental Encoder .............................................................................. 93

5.3.4 Friction Compensation ........................................................................... 94

5.3.5 Loading Model ....................................................................................... 94

5.4 Evaluation and Comparison of Test and Simulation Results ......................... 95

5.4.1 Unloaded Tests ....................................................................................... 95

5.4.1.1 Step Test ......................................................................................... 96

5.4.1.2 Modified Square Wave Test ........................................................... 98

5.4.1.3 Bandwidth (Chirp) Test ................................................................ 100

5.4.2 Loaded Tests ........................................................................................ 103

5.4.2.1 The Comparison of Simulation and Real-Time Test Results ....... 104

CHAPTER 6 ............................................................................................................. 109

6 DISCUSSION OF THE RESULTS AND CONCLUSIONS .......................... 109

6.1 Summary and Discussion ............................................................................. 109

6.2 Conclusions and Future Work ...................................................................... 113

REFERENCES ......................................................................................................... 115

APPENDIX A .......................................................................................................... 117

APPENDIX B .......................................................................................................... 129

xiii

LIST OF TABLES

TABLES

Table 1: Parameters to Calculate Frequencies ........................................................... 32

Table 2: Performance Requirements of EM-CAS ..................................................... 34

Table 3: Motor Parameters ......................................................................................... 35

Table 4: Determining Units of Current Loop of Ba-mobil ........................................ 38

Table 5: Specifications of Servo Drive Amplifier ..................................................... 39

Table 6: Required IO Modules ................................................................................... 40

Table 7: Specifications of the Fin .............................................................................. 42

Table 8: Specifications of the Fin Shaft ..................................................................... 43

Table 9: Specifications of the Fork ............................................................................ 44

Table 10: Specifications of the Screw and Nut .......................................................... 44

Table 11: Components of FMTS [18] ........................................................................ 46

Table 12: Parameters of FMTSM [18] ....................................................................... 46

Table 13: Effects of Ambient Temperatures on the Friction ..................................... 53

Table 14: Friction Parameters of EM-CAS @ 24ºC .................................................. 57

Table 15: Coefficients of Polynomials ....................................................................... 61

Table 16: Specifications of the Components of LTS [21] ......................................... 68

Table 17: Requirements of Position Controller ......................................................... 69

Table 18: Parameters to Be Optimized ...................................................................... 79

Table 19: Optimized Parameters ................................................................................ 81

Table 20: Realized Performance Values of EM-CAS.............................................. 103

xiv

LIST OF FIGURES

FIGURES

Figure 1.1: Types of Control Actuation Systems (CASs) [1] ...................................... 2

Figure 1.2: Control Actuation System (CAS) [5], [6] .................................................. 3

Figure 1.3: EM-CAS with Screw and Lever Mechanism [5], [6] ................................ 4

Figure 1.4: Ristanović's EM-CAS Simulation Model [5], [6], [7] ............................... 5

Figure 1.5: Özkan's EM-CAS Simulation Model [9], [10] .......................................... 5

Figure 1.6: Habibi's EM-CAS Simulation Model [8] .................................................. 6

Figure 1.7: EM-CAS with Clutch Actuator [3], [4] ..................................................... 7

Figure 1.8: EM-CAS with Worm Gear ........................................................................ 7

Figure 1.9: EHS Top Level System Schematic [1] ...................................................... 8

Figure 1.10: An Example of EHS [25] ......................................................................... 9

Figure 1.11: Typical Valve Controlled Hydraulic Circuit [2] .................................... 10

Figure 1.12: Schematic Diagram of the Servo Mechanism ....................................... 11

Figure 2.1: Assembly State of EM-CAS .................................................................... 18

Figure 2.2: Motion State of EM-CAS ........................................................................ 19

Figure 2.3: Free Body Diagram of Motor and Screw Pairs ....................................... 21

Figure 2.4: Free Body Diagram of Screw and Nut Pairs ........................................... 21

Figure 2.5: Free Body Diagram of Aero Fin and Fork Pairs ...................................... 22

Figure 2.6: Representation of Earth’s Fixed and Missile’s Local Axes ..................... 25

Figure 2.7: Nonlinear Block Diagram of EM-CAS ................................................... 29

Figure 2.8: Details of Motor Shaft and Screw ........................................................... 31

Figure 3.1: Electromechanical Control Actuation System ......................................... 34

Figure 3.2: Torque vs Speed Graph of Motor ............................................................ 36

Figure 3.3: Servo Drive Amplifier [17] ..................................................................... 37

Figure 3.4: Motor Actual Current /Reference Analog Voltage Input, .................. 37

Figure 3.5: Modeling of Motor Drive’s Current Loop ............................................... 38

Figure 3.6: Result of Current Loop (Test and Simulation) ........................................ 39

Figure 3.7: Speedgoat® Real-time Target Machine [19] ............................................ 40

Figure 3.8: Baumer Hollow Shaft Incremental Encoder [22] .................................... 41

Figure 3.9: Initial Position of Fin w.r.t. Earth’s Fixed Frame .................................... 42

xv

Figure 3.10: Initial Position of Fin Shaft w.r.t. Earth’s Fixed Axis ........................... 42

Figure 3.11: Initial Position of Fork w.r.t. Earth’s Fixed Axis .................................. 43

Figure 3.12: Initial Position of Screw and Nut w.r.t. Earth’s Fixed Axis .................. 44

Figure 3.13: Friction Measurement Test Setup (FMTS) ............................................ 45

Figure 3.14: Changes of FMTSM Speed and Current @ 24ºC, with 50 rpm Speed

Command ................................................................................................................... 47


Command ................................................................................................................... 48


Command ................................................................................................................... 48


Command ................................................................................................................... 49


Command ................................................................................................................... 49

Figure 3.19: Changes of FMTSM Speed and Current @ -6ºC, with 50 rpm Speed

Command ................................................................................................................... 50


Command ................................................................................................................... 50


Command ................................................................................................................... 51


Command ................................................................................................................... 51


Command ................................................................................................................... 52

Figure 3.24: Friction Torque of whole EM-CAS vs FMTSM Speed @ 24ºC .......... 54

Figure 3.25: Friction Torque of whole EM-CAS vs FMTSM Speed @ -6ºC .......... 54

Figure 3.26: Effect of Ambient Temperatures on Friction Torque of whole EM-CAS

vs Motor Speed .......................................................................................................... 55

Figure 3.27: Find the Viscous Friction Torque Coefficients of EM-CAS ................. 56

Figure 3.28: Changes of Current, Speed and Position of FMTSM @ 24ºC Ambient

Temp., 25 rpm Speed Command................................................................................ 58

Figure 3.29: Coulomb Friction Torque of EM-CAS @Motor Axis vs Fin Position @

24ºC ............................................................................................................................ 58

Figure 3.30: Changes of Current, Speed and Position of FMTSM @ -6ºC Ambient

Temp., 25 rpm Speed Command................................................................................ 59

Figure 3.31: Coulomb Friction Torque of EM-CAS @Motor Axis vs Fin Position @

-6ºC ............................................................................................................................ 59

Figure 3.32: Effect of Ambient Temperatures on Coulomb Friction Torque of whole

EM-CAS vs Fin Position ............................................................................................ 60

Figure 3.33: Curve Fitting to Coulomb Friction Torque for Positive Direction ........ 62

Figure 3.34: Curve Fitting to Coulomb Friction Torque for Negative Direction ...... 62

Figure 3.35: Combination of Curve Fittings for Both Directions .............................. 63

xvi

Figure 3.36: Position of Encoders to Measure Backlash ........................................... 64

Figure 3.37: Direct and Indirect Measurements of Fin Angle and Change of

Backlash ..................................................................................................................... 65

Figure 3.38: Backlash of EM-CAS ............................................................................ 66

Figure 3.39: Design of Loading Test Setup (LTS) [21] ............................................. 67

Figure 3.40: Photo of EM-CAS Mounted Loading Test Setup .................................. 68

Figure 4.1: Linear Block Diagram of EM-CAS ......................................................... 70

Figure 4.2: Using “Anti-windup” in Position Controller ........................................... 79

Figure 4.3: Entering Controller Requirements into Simulink Block [20] .................. 80

Figure 4.4: Optimization of Design Parameters by Using Simulink Response

Optimization Tool ...................................................................................................... 81

Figure 5.1: Nonlinear Simulink Model of EM-CAS .................................................. 83

Figure 5.2: Details of "Controllers" Sub-block .......................................................... 84

Figure 5.3: Details of "Motor &Drive" Sub-block ..................................................... 84

Figure 5.4: Details of "Screw" Sub-block .................................................................. 85

Figure 5.5: Details of "Nut" Sub-block ...................................................................... 85

Figure 5.6: Details of "Fin" Block ............................................................................. 86

Figure 5.7: Details of "Nonlinear Kinematic Relation" Block ................................... 87

Figure 5.8: Comparison of Linear and Nonlinear Model Responses for 1º Step

Command ................................................................................................................... 88

Figure 5.9: Comparison of Linear and Nonlinear Model Responses for 10º and 20º

Step Command ........................................................................................................... 89

Figure 5.10: Test Prototype of EM-CAS ................................................................... 90

Figure 5.11: Real-time Test Model in Simulink-xPC Target ..................................... 90

Figure 5.12: Homing Operation Steps ........................................................................ 91

Figure 5.13: Setup Files of Controller's Modules ...................................................... 92

Figure 5.14: Settings of the Modules ......................................................................... 93

Figure 5.15: Details of "Incremental Encoder" Block ............................................... 93

Figure 5.16: Details of "Friction Compensation" Block ............................................ 94

Figure 5.17: Details of "Loading Model" Block ........................................................ 95

Figure 5.18: Unloaded Step Test ................................................................................ 96

Figure 5.19: Difference between Fin Angles of Simulation and Test Results (Step

Test) ............................................................................................................................ 97

Figure 5.20: Fin Angular Speed (Unloaded Step Test) .............................................. 97

Figure 5.21: Fin Angle Command for Modified Square Wave Test (MSWT) .......... 98

Figure 5.22: Results of MSWT (Fin Angle, Angle Difference, Angular Speeds) .... 99

Figure 5.23: Bandwidth (Chirp) Test ....................................................................... 100

Figure 5.24: Bandwidth (Chirp) Test (Zoomed) ...................................................... 101

Figure 5.25: Difference between Fin Angles of Simulation and Test Results

(Bandwidth Test) ...................................................................................................... 101

Figure 5.26: Bode Plot of Bandwidth Test ............................................................... 102

Figure 5.27: Fin Angle and Command for Loaded Tests ............................... 104

xvii

Figure 5.28: Real-time Applied Load on Fin Axis .................................................. 105

Figure 5.29: Results of Real-time Loaded Tests ...................................................... 106

Figure 5.30: Results of Real-time Loaded Tests (Zoomed) ..................................... 107

xviii

LIST OF ABBREVIATIONS

AC : Alternating Current

BLDC : Brushless Direct Current

CAS : Control Actuation System

CFD : Computational Fluid Dynamic

CM : Center of Mass

DC : Direct Current

DOF : Degree of Freedom

EH : Electrohydraulic

EHA : Electrohydraulic Actuator

EHS : Electrohydrostatic

EH-CAS : Electrohydraulic Control Actuation System

EHS-CAS : Electrohydrostatic Control Actuation System

EM-CAS : Electromechanical Control Actuation System

EMA : Electromechanical Actuator

EMF : Electromotive Force

FA : Fin Angle

FBD : Free Body Diagram

FMTS : Friction Measurement Test Setup

FMTSM : Friction Measurement Test Setup Motor

IAF : Indirect Angle of Fin

IO : Input / Output

ISF : Indirect Speed of Fin

LTS : Loading Test Setup

LTSM : Loading Test Setup Motor

MA : Motor Angle

MSWT : Modified Square Wave Test

PPR : Pulses Per Revolution

PWM : Pulse Width Modulation

RPM : Revolution Per Minute

RTTM : Real-time Target Machine

TF : Transfer Function

xix

LIST OF SYMBOLS

: Circular Cross Sectional Area of the Beam [m2]

: Bandwidth [Hz]

: Coulomb Friction on Fin Axis [Nm]

: Coulomb Friction on Motor Axis (CCW) [Nm]

: Coulomb Friction on Motor Axis (CW) [Nm]

: Average Coulomb Friction on Motor Axis [Nm]

: Equivalent Inertia of EM-CAS [kg.m2]

: Equivalent Damping Coefficient of EM-CAS [Nm.rad/s]

: Moment Arm [m]

: Equivalent Disturbances of EM-CAS [Nm]

: Diameter of the Beam [m]

: Elastic Modulus of the Beam [Pa]

: Resolution of the LTS's Encoder [PPR]

: Force on Nut by Motor [N]

: Equivalent Coulomb Friction of EM-CAS [Nm]

: Load on Nut by Thrust of Missile [N]

⃗ : Load Vector by Thrust of Missile on the Fin [N]

⃗ : Load Vector by Thrust of Missile on the Fork [N]

⃗ : Load Vector by Thrust of Missile on the Fin Shaft [N]

⃗ : Load Vector by Thrust of Missile on the Nut [N]

xx

: Load on Nut by Gravity [N]

⃗ : Load Vector by Gravity on the Fin [N]

⃗ : Load Vector by Gravity on the Fork [N]

⃗ : Load Vector by Gravity on the Fin Shaft [N]

⃗ : Load Vector by Gravity on the Nut[N]

⃗ : Gravity Vector [m/s2]

: Shear Modulus of the Beam [Pa]

: Controller of Current Loop of Drive [V/A]

: TF of Motor Electrical Part [A/V]

: TF of EM-CAS [rad/ Nm s]

: Speed Controller of EM-CAS [V.s/rad]

: Position Controller of EM-CAS [1/s]

: TF of Integral Operation [s]

: Current of EM-CAS's Motor [A]

: Second Moment of Inertia of the Beam [m4]

: The Inertia of Screw [kg.m2]

: Equivalent Inertia on the Motor Axis [kg.m2]

: Inertia of Fin Around Hinge Axis [kg.m2]

:

:

Total Inertia at Fin Axis [kg.m2]

: Actual Current of FMTSM [A]

: Inertia of Fork Around Hinge Axis [kg.m2]

: Inertia of Fin Shaft Around Hinge Axis [kg.m2]

: Inertia of EM-CAS's Motor [kg.m2]

xxi

: Total Inertia at Motor Axis [kg.m2]

: LTSM Actual Current/Analog Reference Signal[A/V]

: Back EMF Constant of EM-CAS's Motor [V.s/rad]

: Equivalent Stiffness of the Beam in Tension [N/m]

: Equivalent Stiffness of the Beam in Torsion [Nm/rad]

: Integral Gain of Current Loop in Servo Drive [V/A.s]

: Proportional Gain of Current Loop in Servo Drive [V/A]

: Integral Gain of Position Loop EM-CAS [rad/rad.s2]

: Proportional Gain of Position Loop of EM-CAS [rad/rad.s]

: Proportional Gain of Speed Loop of EM-CAS [V.s/rad]

: Torque Constant of EM-CAS's Motor [Nm/A]

: Torque Constant of FMTSM [Nm/A]

: Torque Constant of LTSM[Nm/A]

: EM-CAS's Motor Actual Current/Analog Reference Signal [A/V]

: EM-CAS's Motor Current Offset [A]

: LTSM Motor Actual Current/Analog Reference Signal [A/V]

: Forward Gain of EM-CAS in Illustration of TFs [Nm/A]

: Feedback Gain of EM-CAS in Illustration of TFs [V.s/rad]

: Inductance of EM-CAS's Motor [H]

: Length of the Beam [m]

: Equivalent Mass on the Ball Screw [kg]

: Mass of Fin [kg]

: Mass of Fork [kg]

xxii

: Mass of Fin Shaft [kg]

: Mass of Nut [kg]

: LTS Transmission Ratio

: Pole Number of EM-CAS's Motor

: Pitch Rotational Matrix

: Resistance of EM-CAS's Motor [Ohm]

: Roll Rotational Matrix

⃗ : Position Vector of Reference Point at Hinge Axis [m]

⃗ : Position Vector of CM of Fin [m]

⃗ : Position Vector of CM of Fork ,while is zero [m]

⃗ : Position Vector of CM of Fin Shaft [m]

: Approximate Transport Delay in EM-CAS's Servo Drive [ms]

: Aerodynamic Load Applied Fin Axis [Nm]

: Torque of EM-CAS's Motor [Nm]

: Nominal Torque of EM-CAS's Motor [Nm]

: Nominal Torque of LTSM [Nm]

: Rise Time [s]

: Settling Time [s]

: Stall Torque of EM-CAS's Motor [Nm]

: Nominal Torque of LTSM [Nm]

: Coulomb Friction Torque of FMTSM [Nm]

⃗⃗ : Load Vector on Fin Axis by Thrust of Missile (Fin, Fin Shaft and

Fork) [Nm]

: Load on Fin Axis by Thrust of Missile (Fin, Fin Shaft and Fork) [Nm]

xxiii

: Load on Fin Axis by Gravity (Fin, Fin Shaft and Fork) [Nm]

⃗⃗ : Load Vector on Fin Axis by Gravity (Fin, Fin Shaft and Fork) [Nm]

: Input Torque of Nut [Nm]

: Voltage of EM-CAS's Motor [V]

: Viscous Friction Coefficient on Fin Axis [Nm.rad/s]

: Viscous Friction Coefficient on Motor Axis(CCW) [Nm.rad/s]

: Viscous Friction Coefficient on Motor Axis(CW) [Nm.rad/s]

: Average Viscous Friction Coefficient on Motor Axis [Nm.rad/s]

: Maximum Speed of EM-CAS's Motor [rpm]

: Maximum Speed of LTSM [rpm]

: Nominal Speed of EM-CAS's Motor [rpm]

: Nominal Speed of LTSM [rpm]

: Viscous Friction Coefficient of FMTSM [Nm/ krpm]

: Yaw Rotational Matrix

: Linear Displacement of Nut [m]

̇ : Linear Speed of Nut [m/s]

̈ : Linear Acceleration [m/s2]

: Initial Displacement of Nut Because of Angle [m]

: Overshoot [%]

: Natural Frequency [Hz]

: Natural Frequency of the Beam in Tension [Hz]

: Natural Frequency of the Beam in Torsion [Hz]

⃗ : Acceleration Vector of Missile [m/s2]

xxiv

: Damping Ratio

: Fin Angle [rad]

̇ : Fin Angular Speed [rad/s]

̈ : Fin Angular Acceleration [rad/s2]

̇ : Angular Speed of FMTSM [rpm]

: Initial Assembly Angle of Fork [rad]

: Motor Angle [rad]

̇ : Motor Angular Speed [rad/s]

̈ : Motor Angular Acceleration [rad/s2]

: Pitch Angle of Missile [rad]

: Lead of Ball Screw [m/rad]

: Roll Angle of Missile [rad]

: Yaw Angle of Missile [rad]

º : Degree

1

CHAPTER 1

1. INTRODUCTION

1.1 Literature Survey

One of the most important subsystems of guided missiles is the control actuation

systems (CASs), in other words fin (wing) actuators. The aim of CASs is to steer the

missile towards target according to command signal that comes from the autopilot of

the missile [9], [10], [11]. The autopilot defines the fin deflection angle demand

during flight and simultaneously sends this demand to the control actuation system.

After receiving the command, aero fins (control surfaces) are deflected to desired

angles under the effect of aerodynamic loads acting on these surfaces, as well as

viscous and Coulomb friction, backlash and etc. [11]. There are several types of

CASs which are widely used in aerospace applications such as Electromechanical

Control Actuation Systems (EM-CASs), Electrohydrostatic Control Actuation

Systems (EHS-CASs) and Electrohydraulic Control Actuation Systems (EH-CASs)

[1], [2], [3], [4], [8]. These systems and their components are shown as simple

diagrams in Figure 1.1.

2

Figure 1.1: Types of Control Actuation Systems (CASs) [1]

1.1.1 Electromechanical Control Actuation Systems (EM-CASs)

The use of electromechanical actuation is becoming increasingly popular in

aerospace industry because of their momentary overdrive capability, low quiescent

power/low maintenance characteristics and long-term storability [5], [6], [7], [9],

[12], [13]. After developing servomotors these systems start to become prominent

and more used in defense industry. However, modeling of electromechanical actuator

is subjected to some uncertainty because of several reasons such as, electrical noises,

frictions, backlash, changing of operating point, external disturbances (ex: external

loads), parametric variations due to temperature changes, asymmetric behavior and

non-modeled dynamics [12], [13], [14].

3

To steer missiles towards to target, CASs are used to deflect fin angle and direct the

missiles. Aero fins are illustrated in Figure 1.2. As mentioned before, CASs may be

electromechanical or electrohydraulic.

Figure 1.2: Control Actuation System (CAS) [5], [6]

There are some electromechanical CAS types which can be implemented into the

missile control section. Mounting servomotor directly to the fin axis is difficult due

to volume restriction and torque-speed characteristic of the actuators. Therefore,

there should be gearing mechanisms (or transmission mechanisms) both to change

rotational axis (about 90º) and to adjust the whole system to desired torque-speed

region. Types of EM-CASs are as follows.

1.1.1.1 EM-CAS with Screw and Lever Mechanism

As seen in Figure 1.3, CAS is composed of DC Motor, Planetary gear, Screw shaft,

Encoder, Grid fin and Lever mechanism [5], [6], [9]. In this type, ball screws are

frequently used instead of acme screw due to their great efficiency which is generally

more than %95. To convert linear displacement of the ball screw, nut, lever

mechanisms (fork mechanism) are used. On the lever mechanism, there is a

longitudinal slot which lets pin of nut to slip through. Moreover, the ratio between

4

motor and fin angle is not constant and it changes with tangent of fin angle.

Therefore, this situation causes system to be nonlinear. In this study, this kind of

CASs will be investigated, mathematically modeled and a controller designed for

them.

Figure 1.3: EM-CAS with Screw and Lever Mechanism [5], [6]

Modeling of EM-CAS in Literature:

In the literature, dynamic modeling of EM-CAS with Screw and Lever Mechanism

has some differences. Ristanović used a brush DC motor in his work and therefore

PWM control was chosen as the control strategy [5], [6], [7]. As seen in Figure 1.4,

in his model there was no current loop and back EMF voltage was not included.

Also, whole system parameters, such as inertias, viscous and Coulomb frictions were

reduced to the motor shaft with constant gear ratio assumption. Moreover, there were

also rate saturation for speed due to absence of current loop and voltage limitation in

that model. Kinematic saturations could cause some oscillations or overshoot for

position control. Also, a torsional bar was used where the load increases if the angle

of fin increases in order to simulate aerodynamic loads.

5

Figure 1.4: Ristanović's EM-CAS Simulation Model [5], [6], [7]

In the Özkan's EM-CAS Simulation Model, a brushless DC motor was used instead

of a brush one. There is not much information given about the motor drive. As seen

in Figure 1.5, it was assumed that the current loop of motor drive is ideal one;

therefore no back EMF voltage exists like as in Ristanović's model. Also, whole

system parameters, such as inertias, viscous and Coulomb frictions are reduced to the

motor shaft with constant gear ratio assumption [9], [10]. Another difference from

Ristanović's model is that the shaft of the motor was modeled as a flexible body.

Figure 1.5: Özkan's EM-CAS Simulation Model [9], [10]

The different points from the other modeling, in Habibi's EM-CAS model, current,

velocity and position loops are constructed and a Backlash model is included as

shown in Figure 1.6. Also all components which are used in CAS were assumed as

rigid bodies [8]. In Habibi's model similarly whole system parameters, such as

inertias, viscous and Coulomb frictions were reduced to the motor shaft with constant

gear ratio assumption.

6

Figure 1.6: Habibi's EM-CAS Simulation Model [8]

In this study EM-CAS is modeled similarly like Habibi's model [8]. However, whole

system parameters, such as inertias, viscous and Coulomb frictions are not reduced to

the motor shaft and constant gear ratio is not assumed. Also viscous and Coulomb

friction which can change with respect to fin position is measured and modeled. The

backlash in whole CAS will be measured and decided if it can be ignored. After that,

control strategy is determined and controller parameters optimized by using

MATLAB Response Optimization Tools [20]. At least loading test is performed and

all results are compared.

1.1.1.2 EM-CAS with Clutch Actuator

This second type is nearly same with first one with exception of including clutch in

the system [3], [4]. During flight of missiles, aerodynamic loads work sometimes

against the motor, sometimes together with motor. The case of working against the

motor is not a problem but for other situation there occurs some regenerative energy

on the motor and motor drive due to requirement of braking. As seen in Figure 1.7

clutch mechanism can be implemented into CAS to ensure that the CAS is not

affected by regenerative energy that is caused by external disturbances.

7

Figure 1.7: EM-CAS with Clutch Actuator [3], [4]

1.1.1.3 EM-CAS with Worm Gear

In this alternative worm gear is used as transmission mechanism due to low backlash

and linear behavior. The gear ratio between motor and fin angle are constant and it

does not change with fin angle which makes the mechanism linear. Moreover, worm

gears have self-locking property which protects servomotor actuators from the

regenerative energy. However, self-locking means low efficiency where efficiency of

worm gear is around %50 and it decreases with increasing gear ratio. Therefore,

optimization should be made between locking and efficiency.

Figure 1.8: EM-CAS with Worm Gear

8

1.1.2 Electrohydrostatic Control Actuation Systems (EHS-CASs)

The electrohydrostatic control actuation systems, in other words, pump controlled

hydraulic systems are composed of both electric and hydraulic actuation attributes.

As seen in Figure 1.9, these systems consist of servomotor, pump, relief valves,

reservoir, hydraulic cylinder, filters, bypass valve and etc. Hydraulic transmissions

are more attractive than mechanical transmission which has potential mechanical

jamming [1], [2], [8].

Figure 1.9: EHS Top Level System Schematic [1]

In EHS system which is illustrated in Figure 1.10, the number of turns of servomotor

is proportional to the position of the hydraulic cylinder. To measure the piston

displacement, position feedback transducers are generally used which sends position

information back to the flight control computer. Also EHS contains internal fluid

reservoir which provides a minimum pressure to make flow of hydraulic fluid easier

into the suction port of the pump [1], [2].

9

Figure 1.10: An Example of EHS [25]

EHS has similar advantages and attributes to electromechanical actuation for

aerospace applications, but it also has leakage concerns and fluid contamination. [2]

Advantages [2]:

In this actuation there is no backlash or lost motion and it behaves similarly

to a conventional hydraulic system.

They are more reliable because of their jam proof attitude.

Return porting and hydraulic supply is self-contained; therefore the

requirement of hydraulic maintenance is little or none.

1.1.3 Electrohydraulic Control Actuation Systems (EH-CASs)

There are two types of hydraulic transmissions which are often used in industry due

to their high performance quality, one of them is valve controlled (EH) and other is

pump controlled (EHS) [2]. The pump controlled systems are already discussed in

section 1.1.2. A typical valve controlled circuit is presented in Figure 1.11.

10

Figure 1.11: Typical Valve Controlled Hydraulic Circuit [2]

EH (valve controlled) systems are generally composed of hydraulic cylinder, control

valve (servovalve or proportional valve), accumulator, filter, check and relief valves,

pump, electric motor, cooler and oil tank. While the hydraulic pump rotates at

constant speed (i.e. gives a constant flow rate), EH systems use a hydraulic valve as a

control element and this valve directs the oil flow that is generated by a pump to

hydraulic actuator (a hydraulic cylinder or motor). If the control element of the EH

systems would be servovalve, then the best performance can be obtained. This

system usually requires large oil reservoir that is exposed to the atmospheric

pressure. The efficiency of the system can reach values under 30% that is the

disadvantage of the circuit because of throttle losses at the valve [2]. As seen in

Figure 1.12, EH systems (valve controlled) can be used in CAS of aircraft and

missiles in order to deflect the control surface at desired angles.

11

Figure 1.12: Schematic Diagram of the Servo Mechanism

There are some transmission mechanisms such as four bar mechanism between the

Piston Connection and Control Surface. While hydraulic cylinder piston is moving,

the control surface starts to rotate.

12

1.2 Objective and Scope of Thesis

The objective of this thesis is to obtain a detailed mathematical model of an

electromechanical control actuation system which is composed of a ball screw-lever

mechanism and a brushless direct current motor and also to design its controller.

EM-CAS with ball screw and lever mechanism has some nonlinearity such as

Coulomb friction, backlash, rate saturations, external loads and etc. Also the gear

ratio between input and output shaft of this system is not constant and it changes with

respect to their position. This situation adds some extra nonlinearity to the system.

Therefore, the detailed mathematical model of EM-CAS will be nonlinear. In order

to decide which controller should be used to satisfy performance criteria, the block

diagram which is composed of all transfer functions is utilized after linearizing

mathematical model of EM-CAS by making necessary assumptions.

The linear model is only used to decide controller type and check if controller

satisfies the performance criteria. Then, in order to determine controller parameters,

MATLAB Response Optimization Tools are used on the nonlinear model of EM-

CAS which has all nonlinearities including external disturbances.

In order to verify the detailed nonlinear mathematical model, a prototype of EM-

CAS with ball screw and lever mechanism is manufactured. After manufacturing, all

uncertain parameters such as friction, backlash and conversion coefficients between

components, the unknown parameters of servo drive amplifier are found by making

real-time tests and embedded into nonlinear model. In this manner, the overall

identification of system parameters of the prototype is handled.

Moreover, after obtaining controller parameters by optimizing, the performance test

of overall prototype of EM-CAS is conducted for both without external load and

under external load whether if the performance criteria is satisfied and the results of

simulation and real-time tests are overlapped.

13

1.3 Thesis Outline

In the first chapter an introduction to control actuation systems is made by presenting

what types of CASs are used in aerospace industry. Three types of CAS are mostly

used which are electromechanical, electrohydraulic and electrohydrostatic CASs.

The advantages and disadvantages of each CAS are given in detail. After developing

servomotors electromechanical actuators start to become prominent and more used in

defense industry. There are three different electromechanical control actuation

systems which transmission mechanisms are different from each other. In the scope

of this thesis, EM-CAS with ball screw-lever mechanism is studied. The

mathematical models of EM-CAS in literature are investigated and the differences

between these models and the model studied in this thesis are presented.

In the second chapter of the study, all equations of motion are derived after

determining kinematic relations between positions, velocities and accelerations of

input and output shafts. By adding the electrical system to the mechanical system, the

nonlinear model of all system is obtained. At the end of second chapter, by using all

derived equations, block diagram of EM-CAS is presented.

In the third chapter, the performance requirements of the desired CAS are given.

Accordingly, a prototype of electromechanical control actuation system which is

composed of BLDC motor, ball screw and lever mechanism is manufactured in order

to satisfy performance criteria and verify developed nonlinear model. Afterwards, all

system parameters that are used in nonlinear mathematical model are identified in

this chapter. These parameters are necessary dimensions, positions of CM, inertias

and masses of components, also viscous, Coulomb frictions, backlash and etc. In

order to use Coulomb friction torque of EMCAS as friction compensation, “curve

fitting” method is used and a 6th

order polynomial is fitted to the test data. The

backlash in whole EM-CAS is measured and it is decided that backlash can be

ignored because its value is much smaller than position accuracy limit. At the end of

third chapter, loading test setup (LTS) is explained clearly which is used to apply

external load to the EM-CAS.

14

The fourth chapter of the study is dedicated to linearized model of electromechanical

control actuation system and controller design. By making small angle assumption

for fin angle after assuming that the EM-CAS is symmetric with respect to home

position, the nonlinear equations of motion which are obtained in the second chapter

are linearized. In order to ensure that the EM-CAS is affected by inner dynamics of

servo drive amplifier as little as possible, torque mode is decided to use which has

minimum loop inside.

In this study, in order to provide some extra damping to the system and prevent the

possible oscillations during controlling, the inner velocity loop is created between

current and position loops. By combining these three loops with linearized equations,

the linear model of EM-CAS is obtained. Therefore, the transfer function between

any two variables can be found. According to controller requirements, by using Final

Value Theorem (FVT) it is found that PI and P-controller are sufficient for position

and velocity control respectively with and without external load. Also “anti-windup”

method is used due to limitation on the controller output which has integral gain.

At the end of fourth chapter, the steps during controller design are presented.

Controller parameters are found by using MATLAB Response Optimization Tools.

Both controller parameters , , and anti-windup coefficient are

selected as design parameters and optimized according to the controller’s

performance requirements by using Simulink block which is named "Check Step

Response Characteristics".

In the fifth chapter, the nonlinear mathematical model of EM-CAS is constructed in

Simulink by using all mechanical and electrical equations. Afterwards, linear and

nonlinear models are compared which behave similarly for small reference

commands (< 3°). However, for large reference command the responses differ from

each other as expected and nonlinear model is slower than linear model due to

limitations imposed on the controller’s output. Thereafter real-time test software is

explained in detail which is constructed in MATLAB/Simulink as well.

At the end of fifth chapter, several real-time tests are performed without and under

external loads if prototype satisfies performance criteria. Three unloaded tests are

15

done which are step test, modified square wave test and bandwidth test. Also loaded

test is done under applying 100 Nm external load on fin axis. After performing these

all performance tests, it is seen that simulation results and real-time test results are

very similar and consistent.

The concluding remarks and future works are presented in Chapter 6 as a conclusion.

17

CHAPTER 2

2 DYNAMIC MODELING OF EM-CAS

The detailed mathematical model of Electromechanical Control Actuation System

(EM-CAS) consists of two parts which are mechanical and electrical systems.

Mechanical modeling is created by using the equations of motion after determining

the kinematic relationship between mechanisms. Besides, electrical model consist of

the model of brushless motor, inner loops of motor drive and real-time controller

which are used in EM-CAS. After combining of all equations, nonlinear and linear

mathematical model of EM-CAS is obtained.

2.1 Mechanical System

The models of all mechanical components including stator of BLDC motor are

explained. First of all, the kinematic relations between mechanisms are defined and

then the equations of motion are written.

18

2.1.1 Kinematic Relations

In order to transfer all moments of inertias and viscous frictions in EM-CAS to the

mathematical model, it is necessary to know the relationships between the

angular/axial accelerations, speeds and positions of components. For the systems

which have no volume restriction, the angle which is shown in Figure

2.1, can be zero and therefore the system can be symmetric for positive and negative

aspects w.r.t. hinge axis. Otherwise, if this angle is not zero, the system would be

asymmetric, as in this study.

As seen in Figure 2.1 fin-fin shaft-fork and motor shaft-screw are fixed to each other

and nut is not allowed to rotate around any axis. Therefore, when motor starts to

rotate, screw rotates also and nut of ball screw moves forward/backward along

screw’s axis due to rotation of screw. There is a slotted connection between fork and

nut components. Thus when nut starts to move, the fork and fin shaft components

rotate around hinge axis. Finally, the desired motion of fin is obtained with tilting

fork.

Figure 2.1: Assembly State of EM-CAS

19

As shown in Figure 2.2 the fin of EM-CAS is tilted clockwise (- direction). The

distance between the fin axis of rotation and the ball screw axis is constant and about

“d”. When the fin moves, the slotted connection between nut and fork is provided the

elongation requirements of the fork which avoids locking.

Figure 2.2: Motion State of EM-CAS

The kinematic equations are as follows;

( )

(2.1)

(

) (2.2)

(2.3)

( ) (2.4)

Putting equations (2.3) and (2.4) into equation (2.1), the relation between fin and

motor angles are found as in equation (2.5).

20

[ ( ) ] (2.5)

By differentiating equation (2.5), the relation between angular speeds of fin and

motor are obtained as in equation (2.6) .

̇

[

( )] ̇ (2.6)

By differentiating equation (2.6) which gives ratio of motor and fin angular speeds,

the relation between their angular accelerations can be found as equation (2.7).

̈

[ ̈

( ) ̇ ( )

( )] (2.7)

As seen in equation (2.7) the relation between accelerations of motor and fin is not

linear and the ratio between them depends on initial angle of fork, instantaneous

angular velocities and positions.

2.1.2 Equations of Motion

In order to create all equations of motion, all components of EM-CAS are examined

separately, piece by piece and then all equations are combined. First of all, the force

couples of motor stator and screw pair are shown and equations are written. As seen

in Figure 2.3 motor stator and screw behave as a single piece and act together.

21

Figure 2.3: Free Body Diagram of Motor and Screw Pairs

If the elasticity of the screw is considered to be very low due to its short length, the

rotational angles of motor and screw would be almost equal. The total moment of

inertia on the motor axis is the summation of inertias of motor and screw as in

equation (2.8). The torque applied by screw on the nut is written in equation (2.9).

(2.8)

( ̇ ) ̈ ̇ (2.9)

When screw rotates, nut starts to move along screw’s axis and also nut is not allowed

to rotate around any axis (Figure 2.4).

Figure 2.4: Free Body Diagram of Screw and Nut Pairs

22

The force applied by nut on the fork is written in equation (2.10).

̈ (2.10)

̈ ̈ (2.11)

Putting equation (2.11) into equation (2.10), the equation of motion of these

components can be found as in equation (2.12).

̈ (2.12)

By moving nut along axis of screw as seen in Figure 2.4, the pins on nut are sliding

through slotted connection between fork and nut. Therefore this motion provides fork

to rotate around hinge axis as seen in Figure 2.5.

Figure 2.5: Free Body Diagram of Aero Fin and Fork Pairs

The total moment of inertia on the hinge axis is summation of inertias of fork, fin and

fin shaft as in equation (2.13).

(2.13)

23

If the equation of motion is written with respect to hinge axis;

( ̇ ) ̇ ̈ (2.14)

Taking F term from equation (2.14),

[ ( ̇ ) ̇ ̈ ] (2.15)

So, that all equations of motion of EM-CAS are obtained separately. If these

equations are written again by equating similar terms, the equation of motion can be

rewritten in terms of a single equation as shown below.

Putting term which is given in equation (2.9) into equation (2.12), equation (2.16)

can be obtained.

( ̇ ) ̈ ̇

̈

(2.16)

By equating equations (2.15) and (2.16), the nonlinear equations of motion of all

system can be found as in equation (2.17).

( ̈ ̇ ) [ ̈ ̇ ]

( ̇ ) ( ̇ )

[ ( )]

(2.17)

The directions of rotation are same for both motor and fin, therefore;

( ̇ ) ( ̇ )

24

Linearization of Equation of Motion

By making small angle assumption for fin angle ( ) after assuming that the EM-

CAS is symmetric w.r.t. home position (i.e. is zero), the equation (2.5)

can be linearized and rewritten as in equation (2.18), its first and second time

derivatives can also be obtained as in equations (2.19) and (2.20), respectively.

(2.18)

̇

̇ (2.19)

̈

̈ (2.20)

By putting equations (2.18), (2.19) and (2.20) into equation (2.17), equation of

motion can be linearized as in equation (2.21).

[

] ̈ (

) ̇ ( ) ( ̇ )

[ ( )]

(2.21)

[

] (2.22)

(

) (2.23)

[( ) ( ̇ )] (2.24)

[ ( )] (2.25)

Term in equation (2.22) and term in equation (2.23) represent “equivalent

moment of inertia” and “equivalent coefficient of viscous friction torque”,

respectively. Term in equation (2.24) and term in equation (2.25) represent

“Coulomb friction torque” and “equivalent disturbances on motor axis”, respectively.

25

By using these abbreviations, equation of motion can be rewritten in the familiar

form as in equation (2.26).

̈ ̇ (2.26)

The parameters which are used in equation (2.24) are Coulomb friction torques. This

torques will be found by making friction measurement tests and used to feed output

of inner-loop velocity controller as friction compensation.

The disturbances can be separated in three different classes. One of them is thrust

caused , other gravity caused and last one is aero

dynamic load caused . These disturbances can change with depending on

accelerations, velocities and positions of the systems, also environmental conditions.

In order to see how big these loads are, some calculations can be done. For example,

in order to calculate aerodynamic loads , some CFD analysis of the flight must

be done.

The loads on the components of the EM-CAS which are caused by gravity and

accelerations of the system can be found by using static equations [10]. The

representations of both Earth’s Fixed Axis and the Missile’s Local Axis are shown in

Figure 2.6.

Figure 2.6: Representation of Earth’s Fixed and Missile’s Local Axes

26

In order to pass from Earth’s Fixed Axis to the Missile’s Local Axis, the basic

rotation matrices for the rotations about the yaw, pitch and roll axes are defined as in

equations (2.27), (2.28) and (2.29), respectively [10].

[

] (2.27)

[

] (2.28)

[

] (2.29)

Gravitational acceleration is in the ⃗⃗ direction of Earth’s Fixed Axis.

⃗ [ ] (2.30)

To separate gravitational acceleration into the components of missile’s local axis, three

rotational matrices need to be used. So, that weight vectors of fin, fork and fin shaft

are given in equations (2.31), (2.32) and (2.33), respectively.

⃗ ( ) ( ) ( ) ⃗⃗⃗ (2.31)

⃗ ( ) ( ) ( ) ⃗⃗⃗ (2.32)

⃗ ( ) ( ) ( ) ⃗⃗⃗ (2.33)

By cross multiplying the weight vectors of components and distance vectors between

center of masses and hinge axis, the torque vectors which occur on hinge axis can be

obtained as in equation (2.34) [10].

27

⃗⃗ ( ⃗ ⃗ ) ⃗ ( ⃗ ⃗ ) ⃗ ( ⃗ ⃗ ) ⃗ (2.34)

However, it needs to take into account second element of the torque vector as in

equation (2.35), because only the component in the ⃗⃗ direction can provide fin to

rotate.

⃗⃗ (2.35)

On the other hand, some disturbances also occur on the components of EM-CAS

because of missile’s acceleration by thrust force and vibrations.

There are only one DOF between EM-CAS and missile itself which is pitch rotational

angle. Therefore, in order to see the effects of missile’s accelerations, only pitch

rotational matrix, needs to be used in the equations.

⃗ [ ] (2.36)

Due to missile’s accelerations in equation (2.36), the loads on fin, fork and fin shaft

can be calculated as in equations (2.37), (2.38) and (2.39), respectively.

⃗ ⃗⃗⃗ ( ) (2.37)

⃗ ⃗⃗⃗ ( ) (2.38)

⃗ ⃗⃗⃗ ( ) (2.39)

By combining these three equations, torque vector which occurs due to missile’s

thrust, can be written as in equation (2.40). However, it needs to take second member

of the torque vector as in equation (2.41), because only the component in the ⃗⃗

direction can cause fin to rotate.

28

⃗⃗ ( ⃗ ⃗ ) ⃗ ( ⃗ ⃗ ) ⃗ ( ⃗ ⃗ ) ⃗ (2.40)

⃗⃗ (2.41)

The force vectors that acting on the nut due to gravitational acceleration and missile’s

accelerations can be calculated as in equations (2.42) and (2.43), respectively.

⃗ ⃗⃗⃗ ( ) ( ) (2.42)

⃗ ⃗⃗⃗ (2.43)

It needs to take first member of the force vector of the equations (2.42) and (2.43) as

given in the equations (2.44) and (2.45), because only the component in the ⃗⃗

direction can provide the nut to move.

⃗⃗ (2.44)

⃗⃗ (2.45)

2.2 Electrical System

The electrical section of EM-CAS consists of brushless DC motor and servo drive

amplifier. The brushless DC motor and servo drive amplifier couple can be modeled

as a brushed DC motor. The equations that can be applied to such electric motors are

given below.

̇ (2.46)

(2.47)

The current drawn by the motor can be found by using the relation in the equation

(2.46). The motor torque is proportional to the current drawn by the motor as seen in

the equation (2.47) and the ratio between them is the torque constant ( .

29

The servo drive amplifier has two modes named current and velocity. The mode

which is used on the motor drive varies according to the mechanism and the

application used. In this study motor drive is used in the current mode, because the

units of controller parameters that are used in drive’s software are not known. In

order not to make so many tests to figure out the controller units, drive is used in the

current mode which has only one loop. Otherwise there would be more than one

loop. Therefore velocity and position loops are constructed out of the servo drive

amplifier by Speedgoat® real time target machine (RTTM) controller. The controller

parameters and their units of the current loop will be identified in the section 3.2.2.

2.3 Block Diagram of EM-CAS

The mechanical and electrical portions are combined and therefore the block diagram

of EM-CAS is obtained as in Figure 2.7. The current loop of motor drive and

velocity and position inner loops of controller are not yet in this block diagram. In

the block diagram the flow of force and torque can be followed easily.

Figure 2.7: Nonlinear Block Diagram of EM-CAS

As seen in the Figure 2.7 on the feedback paths there are some inertia that we are not

familiar with. The reason is that the mechanical components (i.e. motor shafts, screw,

fin etc.) are modeled as rigid bodies instead of elastic modeling. The maximum

operating frequency demand is expected to be lower than natural frequency of the

30

components, that’s why the mechanical components are not modeled as elastic

bodies. On the motor shaft and screw pair there can be both tensile and torsional

loads. Therefore it needs to check how big the natural frequencies are. The cross

sectional area of a circular rod and its second moment of inertia are given below.

(2.48)

(2.49)

The tensile and torsional stiffness of a rod can be found by using the relations which

are given in the equations (2.50) and (2.51), respectively.

(2.50)

(2.51)

In order to calculate natural frequency in tension, the equivalent mass on the motor

shaft and screw must be found as follows.

(2.52)

√

(2.53)

In the same way, in order to calculate natural frequency in torsion, the equivalent

inertia on the motor axis must be found.

(2.54)

31

√

(2.55)

If both axial and torsional frequencies are much higher than bandwidth requirement,

then the components need to be modeled as rigid bodies. Otherwise, in order to

increase the accuracy of the model, the elasticity of components of EM-CAS has to

be considered. The precondition for rigid modeling is given below.

The detail information about dimensions of motor shaft and screw are given in

Figure 2.8.

Figure 2.8: Details of Motor Shaft and Screw

The length and diameter of motor shaft and screw pairs can be accepted as 278.5 mm

and 12 mm for worst case. For this rod, the parameters to calculate frequencies are

obtained as in Table 1.

32

Table 1: Parameters to Calculate Frequencies

Parameters Values Units

0.012 [m]

210 109

[Pa]

80 109 [Pa]

3 10-4

[kg.m2]

0.2785 [m]

476 [kg]

10 [Hz]

By using these parameters, the frequencies are found as below.

Therefore, the components don’t need to be modeled as elastic bodies, because the

natural frequencies are 42 to 139 times higher than bandwidth requirement.

33

CHAPTER 3

3 IDENTIFICATION OF THE SYSTEM PARAMETERS

The Electromechanical Control Actuation System (EM-CAS) is composed of

brushless DC motor, servo drive amplifier, fin, fin shaft, fork, screw and its nut as

seen in the Figure 3.1. In order to identify parameters of EM-CAS all components

are examined individually. The system’s performance requirements, Coulomb and

viscous frictions, backlash and constants which are used in the mathematical model

are determined. The dotted line and black reference point in Figure 3.1 represent the

rotation axis of fin and origin point, respectively. This origin point is used to

calculate moments which occur on hinge axis to tilt fin. The lengths given in the

⃗⃗

does not affect the calculations of moment on the hinge, because the moments

that provide fin to tilt occur around ⃗⃗

axis. Therefore the coordinates of

components in the ⃗⃗

direction can be chosen the same and the EM-CAS can be

considered as 2D.

34

Figure 3.1: Electromechanical Control Actuation System

3.1 System Performance Criteria

The performance requirements for EM-CAS are determined as in Table 2. These

criteria are obtained by making aerodynamic analysis in order to allow missile to

have desired maneuver ability. As a result of this thesis, the performance of EM-CAS

will be measured.

Table 2: Performance Requirements of EM-CAS

Operating Range of Fin ±20º

Position Accuracy of Fin ±0.2º

Unloaded Fin Angular Speed ≥220º/s

Loaded Fin Angular Speed @100Nm ≥200º/s

Bandwidth ≥10 Hz

35

3.2 The Components of EM-CAS

There are motor, servo drive amplifier, real-time controller, hollow shaft incremental

encoder, fin, fin-shaft, fork and screw nut pair in the EM-CAS which is studied in

this thesis. The components of EM-CAS are determined and identified in this section

individually.

3.2.1 BLDC Motor

As motor of EM-CAS, brushless motor is selected which is easier and more efficient

than other motors in position controlled systems. The parameters of motor that is

supplied from a domestic electric motor producer, FEMSAN Motor Company are

given in Table 3.

Table 3: Motor Parameters

FEMSAN - 5C1108009M

Nominal Torque [N.m]

Stall Torque [N.m]

Nominal Speed [rpm]

No Load Speed [rpm]

Number of Pole -

Motor Inertia [kg.m

2]

Voltage (Drive’s Supply) [V]

Back EMF Constant [V.s/rad]

Torque Constant [N.m/A]

Motor Resistance [Ohm]

Motor Inductance [H]

The torque vs. speed graph of BLDC motor is given as in Figure 3.2 for both

continuous and short term operation.

36

Figure 3.2: Torque vs Speed Graph of Motor

3.2.2 Servo Drive Amplifier

The servo drive amplifier is taken from Unitek GmbH [17]. The drive named

Bamobil-D3 receives 39 V DC with nominal 60 Amperes and converts it into Pulse-

Width Modulated (PWM) signal to send the electric motor as seen in the Figure 3.3.

This servo drive amplifier has two operating modes, which are speed and torque

(current). Speed or torque control of the electric motor can be succeeded by the

control signal for PWM by ±10 V analog input reference signal. In these loops

(speed, current) PI-controller are used. In order not to be affected by drive dynamics,

minimum loops will be used in the control of EM-CAS. Therefore it is decided to use

only current loop in the servo drive amplifier. Also it is capable to work on four

quadrant operations. It means that it is used to drive or brake in both directions and

can make energy recuperation to the power supply [17].

37

Figure 3.3: Servo Drive Amplifier [17]

The set values of the servo drive amplifier’s performance parameters; control mode,

input and output type can be reached and adjusted by the connection interface of

RS232 and CAN-BUS via software on a computer. In order to calculate the gain of

actual current of motor over a given analog input reference signal, some tests are

done. As a result of these tests, the gain is determined as in the Figure 3.4.

Figure 3.4: Motor Actual Current /Reference Analog Voltage Input,

-4 -3 -2 -1 0 1 2 3 4-40

-30

-20

-10

0

10

20

30

40

Reference Analog Voltage Input (V)

Moto

r C

urr

ent

(A)

Motor Current / Reference Analog Voltage Input, Kv

y = 8.19*x - 0.015

TestData

CurveFitting

38

Only current loop is used in the servo drive amplifier. Speed and position loops are

constructed out of drive in the real-time controller. The units of controller parameters

of current loop are not known. In order to use these parameters into dynamic model

of EM-CAS, the units are found in SI units by performing some tests. Also by doing

these tests, the approximate transport delay in the servo drive amplifier is

determined.

As mentioned before, PI-controller is used in the current loop. First, integral gain is

made zero in the drive’s software, then tests are performed to calculate the unit of P

gain. Then this process is repeated for I gain. The current loop is modeled in

Simulink as in the Figure 3.5.

Figure 3.5: Modeling of Motor Drive’s Current Loop

After doing current loop tests, the Unitek unit gains are determined as in Table 4.

According to this table, if the PI-controller parameters of current loop are multiplied

by 0.208 and 0.018 respectively, then the numbers are converted into SI units.

Table 4: Determining Units of Current Loop of Ba-mobil

P Gain Conversion Coeff. 0.208 [ ⁄ ]

I Gain Conversion Coeff. 0.018 [ ⁄ ]

After determining the Unitek unit gains, some real-time tests are performed. By

holding PI gains 5 [ ⁄ ] and 0.1 [

⁄ ], and transport delay 3.7 ms, the response of

39

drive and simulation result are obtained and compared for a given reference analog

input. As seen in the Figure 3.6 the results are overlapped.

Figure 3.6: Result of Current Loop (Test and Simulation)

The ratio of motor actual current over analog reference input, controller parameters

of the current loop and approximate transport delay of the servo drive amplifier are

specified as in the Table 5.

Table 5: Specifications of Servo Drive Amplifier

Motor Current Demand / Analog Reference Input [

⁄ ]

Current Offset [ ]

Approximate Transport Delay in Drive [ ]

Proportional Gain of Drive’s Current Loop in SI Unit [ ⁄ ]

Integral Gain of Drive’s Current Loop in SI Unit [

⁄ ]

40

3.2.3 Real-time Target Machine (RTTM)

In position controlling of EM-CAS, a real-time target machine (RTTM) of

Speedgoat® is used as seen in Figure 3.7. MATLAB, Simulink and xPC Target are

used in the controller as software [19].

Figure 3.7: Speedgoat® Real-time Target Machine [19]

The required input/output modules are tabulated in the Table 6.

Table 6: Required IO Modules

Speedgoat® Real-time Target Machine

IO401 Quadrature and SSI Decoding Module

IO110 Analog Voltage Output Module (max ±10 V)

IO106 Analog Voltage Input Module (max ±10 V)

3.2.4 Incremental Encoder

Including on the fin shaft and motor shaft two hollow shaft incremental encoders are

used as seen in Figure 3.8. Both angles of motor and fin can be measured directly

and individually. By utilizing encoders both the backlash in the EM-CAS is

measured and speed-position loops are closed on the controller.

41

Figure 3.8: Baumer Hollow Shaft Incremental Encoder [22]

The incremental encoders are taken from Baumer GmbH. The identical encoders

named G0M2H. They have 2048 pulse per revolution. [22]

IO401 module of real-time machine has 1x, 2x and 4x options where the pulses of

encoders are multiplied by the number front of x. In order to obtain high resolution,

4x option should be chosen. Therefore, encoders

dynamic modeling and control of an ...etd.lib.metu.edu.tr/upload/12620583/index.pdfdoğru akım...

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