Autonomous Flight Control System (Autopilot) Design ...

Benha University Faculty of Engineering at Shoubra Electrical Engineering Department

Autonomous Flight Control System (Autopilot) Design Using Embedded Systems A Dissertation Submitted to the faculty of engineering at Shoubra in partial fulfillment of the requirements for the Degree of Doctor of Philosophy in [Electrical Engineering]

By

Eng. Ahmed ELSayed Ahmed Ali Elbanna Supervised by: Prof. Dr. Hossam El-din H. Ahmed

Prof. Dr. Hala Mohamed Abd-Elkader

Prof. of Electronics and Communication Networks P. Dean of Faculty of Electronic Engineering,

Prof. of Signal Analysis, Shoubra Faculty of Engineering, Benha University. [ ]

Faculty of Electronic Engineering, Menufiya University. [ ]

Dr. Ashraf Mohamed Hafez

Dr. Ahmed Nasr Eldin Ibrahim

Dept. of Electric Engineering, Shoubra Faculty of Engineering, Benha University.

Dept. of Electric Engineering, Military Technical College.

[

]

[ Cairo – EGYPT. 2016

]

Benha University Faculty of Engineering at Shoubra Electrical Engineering Department

APPROVAL SHEET

Autonomous Flight Control System (Autopilot) Design Using Embedded Systems Examiners Committee: Signature: …………………….…

Prof. Dr. Said Abdel Menem Wahsh Prof. of Control and Power Electronics Electronics Research Institute

Signature: …..………………...…

Prof. Dr. Hossam El-din H. Ahmed Prof. of Electronics and Communication Networks

P. Dean of Faculty of Electronic Engineering, Faculty of Electronic Engineering, Menufiya University. Signature: …………….…………

Prof. Dr. Hala Mohamed Abd-Elkader Prof. of Signal Analysis, Shoubra Faculty of Engineering, Benha University.

Signature: ………….……………

Assoc. Prof. Dr. Adly Shahat Tag ELdin Assoc. Prof. of Electronics (Communication Networks), Shoubra Faculty of Engineering, Benha University. Cairo - EGYPT 2016

ACKNOWLEDGEMENT

ACKNOWLEDGEMENT First and foremost, I'm thankful to ALLAH, the most gracious most merciful for helping me finishing this work. I would like to express my sincere gratitude to my supervisors, Prof. Hossam Eldin Hussien Ahmed, prof. Hala Mansour, Dr. Ashraf Hafez and Dr. Ahmed Nasr for their great efforts beginning with selecting the topic of research and continuing during the course of the work. I’m very thanks to Minnesota University for helping me at this thesis. I can’t continue this work without my wonderful small family; my mother, my wife, my daughters Malak and Menna, and my son Mohamed. Their support means everything to me especially. Last and surely not least, I want to thank my brothers Mohamed and Ehab. My deep appreciation for their ongoing encouragement.

i

DEDICATION

DEDICATION

To my father and my mother To my family

ii

ABSTRACT

ABSTRACT The past two decades have witnessed a dramatic increase in the utilization of the Unmanned Aerial Vehicles (UAVs). So, designing and manufacturing of UAVs are too necessary at these days. Autonomous aircrafts represent a convenient possibility for monitoring large areas with the addition of many military applications (military reconnaissance, advanced attack air vehicle for hazardous missions). Autopilot is the most important system in Small Unmanned Air Vehicle (SUAV) manufacturing. It guides the UAV during flight with no assistance from human operators. Design of Automatic Flight Control System (AFCS) is very challenging due to the limited resources available onboard and the high number of constraints including weight, space, time, energy and cost by using Commercial-Off-The-Shelf (COTS) components. So our challenge is to design a high performance AFCS with low cost and improving the level of autonomy. This thesis represents a complete design of AFCS of Ultrastick-25e. Beginning our mission with the modeling of SUAV as follows; the mathematical model of the nonlinear equations of motion is introduced, a survey with a standard method to obtain the full non-linear equations of motion is utilized and the linearization of the equations according to a steady state flight condition (trimming) is derived. Linear longitudinal and lateral models are obtained with algorithmic and a novel analytical linearization techniques. The modeling is completed with the evaluation of the linear model; check matching between the behavior of the states of the nonlinear model and the resulted linear model with applying a doublet signal at the control surfaces of the aircraft. The autopilot design is preceded first by Model in loop stage (MIL), then Software In loop (SIL) and at last Processor in Loop (PIL) to complete the design and evaluate it with many circumstances. The detailed design of autopilot and its simulation with a various flight scenarios is introduced. The first part is the design of longitudinal motion controller. Beginning with the inner loop pitch rate (q) (pitch damper) which is designed with the best value of feedback gain by root locus technique and tuning it with Safety integrity level which is defined as a relative level of risk-reduction provided by a safety iii

ABSTRACT function, or to specify a target level of risk reduction. Then pitch attitude hold controller (pitch tracker) is designed with PI-controller far away from complexity with good performance in the time domain characteristics. Linearization of the nonlinear equation of motion of altitude dynamics is derived to get a linear relation between the altitude and pitch angle (θ) under assuming of cruise speed of 17 m/s. Altitude hold controller is designed using of Pcontroller with results better than PI-controller in the Minnesota controller. Ascending scenario is tested in the non-linear model to check the all over behavior of the aircraft. The design of lateral motion controller is introduced. Most inner loop is designed with feedback gain, and then roll attitude hold controller is designed with PIcontroller far away from complexity with good performance in the time domain characteristics. The lateral motion controller design procedures are: a. Roll rate feedback. b. The roll attitude controller. c. Linearization algorithm to get a linear relation between heading angle and roll attitude according to coordinated turn flight. d. The outer loop controller is a simple P-controller. e. Yaw damper is designed with washout filter. f. Finally, the rectangular motion command is applied in the non-linear model to check the behavior of the aircraft. The environment disturbances and sensors noise are considered in the design architecture of test platform. The whole autopilot is tested under climbing turn scenario. After all the previous discussion, it's the time to implement the autopilot of SUAV. Flight computer (ArduMega 2560) is used because of its historical successfulness in many autopilots design and its simplicity. MEMS sensors are chosen in implementing (IMU (MPU6050), Magnetometer (HMC 5883L), GPS (UBLOX LEA-6H)) which are smaller and lighter than the old mechanical sensor devices, but so noisy. With implementing the state estimator with complementary and Kalman filters; the problem is finished and solved. All of the previous sensors are used for implementing Attitude and Heading reference system (AHRS). The communication iv

ABSTRACT link between autopilot and the ground station is achieved by using (3DR radio telemetry module). Processor In Loop (PIL) simulation is implemented to evaluate the pitch attitude controller by converting the continuous system to a discrete one and implementing the communication adaptation between MATLAB and flight computer. The results show us that the proposed controller strategy design is very good and convenient to our requirements. All of these designed circuits for the most important subsystems and designing the Autopilot for Ultrastick-25e aimed to maintain the system with small size, low weight, low power consumption and low cost.

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TABLE OF CONTENTS

TABLE OF CONTENTS Acknowledgement..................................................................................................... i Dedication.................................................................................................................

ii

Abstract.....................................................................................................................

iii

Table of Contents......................................................................................................

vi

Abbreviations and Nomenclature..........................................................................

x

List of Figures...........................................................................................................

vi

List of Tables....................................................................................................... List of Publications...................................................................................................

xxiv xxv

Thesis Contribution...................................................................................................

xxvi

CHAPTER 1 Unmanned Aircraft Systems And Autopilots 1.1

Introduction………………………………………………………..……………...1

1.2 UAV Types and Technologies……………………………………..……………..2 1.2.1 UAV Applications……………….…………………………..……………...4 1.2.1.1 Civilian Applications…..………...…...………….….……………...4 1.2.1.2 Military Applications……………………………..…….………….....5 1.2.2 UAV System Structure………………………………….….….…………….5 1.2.3 UAV Categories……………………………………….…….………………6 1.2.3.1 Major operating UAVs………………………..…….……………….7 1.2.3.2 UAVs Research Projects…………………….……………………..13 1.3 Automatic Flight Control System (AFCS)……………………………………….15 1.4 Survey of Various Autopilots…………………………………………………….15 1.4.1 Commercial Autopilots Review……………….……………………......…..17 a. UAV Navigation VECTOR………………….………………………......17 b. Micropilot MP2x28 Series…………………….………………………....17

vi

TABLE OF CONTENTS c. Procerus Kestrel Autopilot…………………….………………………....18 d. Cloud Cap Piccolo series……………….....…….………………………..19 1.4.2 Open Source Autopilots Review……………………………………..….19 a. APM 2.6 Autopilot…………….........................………….…..…..19 b. Openpilot……………………………………………………..…..…20 1.4.3 Comparison of various autopilots……….………………………..…..…21 a. Physical Specifications……………………………………..……….21 b. Sensor Ranges……………………………………………..……......21 c. Autopilot functions………………………………………..………...21 1.4.4 Universities Developed Autopilots..………………..………..………….22 1.4.4.1 Virginia Commonwealth University (VCU) Autopilot Research…………………………………………………..…...22 a. First generation………………………………………..…....22 b. Second generation…………………………………..………23 C. Third generation, Mini-FCS………………………..………24 1.4.4.2 AggieAir Autopilot…………………………………..………..25 1.4.4.3 Federal University of Minas Gerais, Brazil……………..…….26 1.4.4.4 Paparazzi Autopilot Versions…………………………..……..27 1.5 Summary…………………………………………………………………..………29

CHAPTER 2 SUAV Equations Of Motion 2.1 Introduction…………………………………………………………………….....31 2.2 Coordinate Transformations……………………………………………………....32 2.2.1 UAV Coordinate Frames…………………………………....……………..32 2.3 Wind Triangle……………………………………………………………………..36 2.4 Fixed Wing UAV Parameters….......................……………………..........…..38 2.4.1 Basic parameters of the UAV geometric…………………....….....………..38 2.4.2 Basic Parameters for Aerodynamics………………………......…………....39

vii

TABLE OF CONTENTS 2.4.3 Fixed Wing UAV Control Surfaces………………………...……………....41 2.5 UAV Flight Dynamics……………………………………………….…………....42 2.5.1 Kinematics and Dynamics………….....………………………..………..…43 2.5.2 Atmospheric Disturbance…………….....………………………………......44 2.6 The Final Form of Nonlinear Equations of Motion…………………………….....45 2.7 Summary………………………………………………………………………......46

CHAPTER 3 Linear Model Of SUAV (Ultrastick-25e) 3.1 Introduction……………………………………………………………………..…48 3.2 Equilibrium Point and Steady State Flight.…………………………………..……49 3.2.1 Trimming Algorithm for Ultrastick-25e………………………….……..51 3.3 Linear State Space Model…………………………………………………….…...52 3.3.1 Historical Perspective for Linear State Space Models……………..……53 3.3.2 General Linearization Technique…………………………………..……54 3.3.3 Longitudinal State Space Model…………………………………..…….54 3.3.3.1 Longitudinal Model for Ultrastick-25e………………..………57 3.3.3.2 Longitudinal Reduced Order Modes………………………..…58 3.3.4 Lateral State Space Model…………………………………………..…...59 3.3.4.1 Lateral Model for Ultrastick-25e………………………..……..62 3.3.4.2 Lateral Reduced Order Modes………………………….……..64 3.4 Validation of Aircraft Model Linearization……………………………..…...66 3.4.1 Doublet Response of the Linear and Nonlinear Longitudinal Model............66 3.4.2 Doublet Response of the Linear and Nonlinear Lateral Model…............…69 3.5 Analytical Linearization of Roll and Roll Rate……………………………….…..70 3.6 Summary……………………………………………………………………..……72

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TABLE OF CONTENTS

CHAPTER 4 Autopilot Design And Simulation 4.1 Introduction……………………………………………………………..................73 4.2 Automatic Flight Control System (AFCS) (Autopilot) Design………...................74 4.2.1 Longitudinal Motion Controller Design………………………..................76 4.2.1.1 Pitch Attitude Tracker Design………………………….................77 4.2.1.2 Pitch Attitude Tracker Simulation Tests……………….................79 4.2.1.3 Outer Loop Altitude Hold Controller……………………..............82 4.2.1.4 Altitude Hold Controller Simulation Tests…………….................84 4.2.2 Lateral Motion Controller Design………………………………...............88 4.2.2.1 Roll Attitude Tracker………………………………......................90 4.2.2.2 Roll Attitude Hold Controller Simulation Tests….…....................92 4.2.2.3 Direction Heading Controller………………………......................94 4.2.2.4 Heading Controller Simulation Tests………………....................96 4.3.3.5 Yaw Damper………………………………………….................99 4.3

Whole Autopilot Flight Scenarios Simulation Test…………………..............100

4.4 Summary………………………………………………………………................101

CHAPTER 5 Autopilot Implementation With Experimental Test Results 5.1 Introduction…………………………………………………………………....…103 5.2 Autopilot Hardware Block Diagram…………………………………………......104 5.3 Selection of Avionics and Sensors…………………………………………….....105 5.3.1 Flight Computer………………………………………………………...…106 5.3.2 SUAV Sensors………………………………………………………….....108 5.3.2.1 Inertial Measurement Unit (IMU)……………………………...…109 5.3.2.2 Magnetometer…………………………………………………......114 5.3.2.3 Global Positioning Systems (GPS)……………………………......115 5.3.3 Communication Components……………………………………………...117 ix

TABLE OF CONTENTS

5.4

SUAV State Estimator…………………………………………………………...118 5.4.1 Complementary Filter…….……………………………………………..…119 5.4.2 Kalman Filter (KF)…………………………………………………..….....119

5.5 Implementation procedures of the autopilot……………………………….........121 5.6 Processor In Loop (PIL) Simulation For SUAV………………………………....125 5.6.1 PID Controller Implementation Results………………………………...…126 5.7 Summary………………………………………………………………………....127

CHAPTER 6 Conclusions and Future Work 6.1 Conclusions............................................................................... ...129 6.2 Future Work.......................................................................... ...131

REFERENCES References....................................................................................................................132

x

ABBREVIATIONS and NOMENCLATURE

ABBREVIATIONS AAI

Aircraft Armament Incorporated Company.

ACTDs

Advanced Concept Technology Demonstrations.

ADC

Analog to Digital Converter.

AFCS

Automatic Flight Control System.

AHRS

Attitude and Heading Reference System.

APM

Ardu-Pilot Mega.

ARM

Advanced RISC Machine.

Avionics

Aviation Electronics.

AVR

Advanced Virtual RISC.

BLOS

Beyond Line Of Site.

CDL

Common Data Link.

CISC

Complex Instruction Set Computer.

COTS

Commercial Off-The-Shelf.

CPU

Central Processing Unit.

DARPA

Defense Advanced Research Projects Agency.

DCM

Direct Cosine Matrix.

DGPS

Differential GPS.

DMP

Digital Motion Processor.

DOD

Department Of Defense.

DOF

Degree Of Freedom.

EEPROM

Electrically Erasable Programmable Read-Only Memory.

EO/IR

Electro Optical/ Infra-Red.

FAA

Federal Aviation Administration.

FEUP

Faculdade de Engenharia da Universidade do Porto

FPGA

Field Programmable Gate Array.

FPSLIC

Field Programmable System Level Integrated Circuit.

GCS

Ground Control Station.

GLONASS

GLObal NAvigation Satellite System.

GPIO

General Purpose Input /Output.

GPS

Global Positioning System. xi

ABBREVIATIONS and NOMENCLATURE HALE

High Altitude Long Endurance.

HIL

Hardware In Loop.

I2C

Integrated Integrated Circuit.

IMU

Inertial Measurement Unit.

INS

Inertial Navigation System.

ISR

Intelligence, Surveillance and Reconnaissance.

IST

Instituto Superior T´ecnico.

JAUS

Joint Architecture for Unmanned Systems.

J-UCAS

Joint Unmanned Combat Aerial System.

KF

Kalman Filter.

L/D

Lift / Drag.

LAETA

Laborat ´ orio Associado de Energia, Transportes e Aeron´ autica.

LOS

Line Of Sight.

LTI

Linear Time Invariant.

MALE

Medium Altitude Long Endurance.

MAV

Micro Air Vehicles.

MB

Mega Byte.

MCE

Mission Control Element.

MEMS

Micro Electro Mechanical Systems.

MIMO

Multi Input Multi Output.

MIT

Massachusets institute of technology.

MIPS

Million Instruction Per Second.

MPU

Motion Processing Unit.

MTI

Moving Target Indicator.

MUAV

Mini Unmanned Aerial Vehicle.

NACA

National Advisory Committee of Aeronautics.

NAV

Nano UAV.

NBC

Nuclear, Biological or Chemical.

NED

North East Down.

NMEA

National Marine Electronics Association.

NPL

National Physical Laboratory.

OMAP

Open Multimedia Applications Platform.

PDA

Personal Data Assistance.

PID

Proportional Integral Differential. xii

ABBREVIATIONS and NOMENCLATURE PWM

Pulse Width Modulators.

QFN

Quad Flat No-Lead.

R&D

Research and Development.

RAM

Random Access Memory.

RC

Radio Controlled.

RISC

Reduced Instruction Set Computer.

ROM

Read Only Memory.

RPH

Remote Piloted Helicopter.

RPV

Remote Person View.

RTK

Real Time Kinematic.

SAR

Synthetic Aperture Radar.

SAS

Stability Augmentation System.

SIL

Software In Loop.

SISO

Single Input Single Output.

SPI

System Programming Interface.

SRAM

Static Random Access Memory.

SUAV

Small Unmanned Aerial Vehicle.

SWaP

Size Weight and Power.

TCDL

Tactical Common Data Link.

TV

Television.

TUAV

Medium Range or Tactical UAV.

UARTs

Universal Asynchronous Receiver Transmitter.

UAS

Unmanned Aircraft Systems.

UAV

Unmanned Aerial Vehicle.

UBI

Universidade da Beira Interior.

UCAV

Unmanned Combat Air Vehicle.

UERE

User Equivalent Range Error.

US

United States.

USA

United States Army.

USAF

United States Air Force.

USMC

United States Marine Corps.

USN

United States Navy.

VCU

Virginia Commonwealth University. xiii


VDD

Voltage Drain Drain.

VTOL

(Vertical Takeoff and Landing) Unmanned Aerial Vehicle or VUAV or VTUAV.

VVI

Velocity Vector Imaging.

WOT

War On Terrorism.

WDT

Watch Dog Timer.

xiv


NOMENCLATURE (ii, ji , ki)

Inertial frame axes

(iv, jv, kv)

Vehicle frame axes

(ib, jb, kb)

Body frame axes Attitude angles - Euler angles, rad. Magnetic heading angle measured by the compass.

α

Angle of attack.

β

Side slip angle. Course angle. Crab angle.

γ

Inertial-referenced flight path angle. Products of the inertia matrix.

ρ

Air density. Aileron deflection. Elevator deflection. Rudder deflection. Throttle deflection. Poles of the characteristic equation – Eigen values.

σ

Standard deviation.

ξ

Damping Coefficient. Constants for transfer function associated with roll dynamics Acceleration component along x-axis of body frame. Acceleration component along z-axis of body frame.

b

Wing span.

c

Mean aerodynamic chord of the wing.

CL

Aerodynamic lift coefficient.

CD

Aerodynamic drag coefficient. xv

ABBREVIATIONS and NOMENCLATURE Aerodynamic pitching moment coefficient. Aerodynamic moment coefficient along xb- axis. Aerodynamic moment coefficient along yb- axis. Cprop

Aerodynamic coefficient for the propeller. Aerodynamic moment coefficient along the zb.

CX

Aerodynamic force coefficient along xb.

CY

Aerodynamic force coefficient along yb.

CZ

Aerodynamic force coefficient along zb.

Cr

Aerodynamic moment coefficient along the body frame z-axis.

dh

Disturbance signal associated with reduced altitude dynamics. Disturbance signals associated with reduced roll dynamics. Disturbance signals associated with reduced yaw dynamics.

FD

Force due to aerodynamic drag.

FL

Force due to aerodynamic lift.

fY

Side force. Total body forces vector. Force components of the airframe projected onto xb-axis.

fg

Gravity force.

fa

Aerodynamic force.

fp

Propeller force.

Gp

Output vector of accelerometer.

Gpx, Gpy, Gpz Acceleration components of accelerometer. g

Gravitational acceleration (9.81 m/s2) .

J

The inertia matrix.

Jx, Jy, Jz, Jxz

Elements of the inertia matrix.

kmotor

Constant that specifies the efficiency of the motor.

kd_q

Feedback damping gain of pitch rate.

kp_θ

Proportional gain of pitch angle.

ki_θ

Integral gain of pitch angle.

kp_h

Proportional gain of altitude.

xvi

ABBREVIATIONS and NOMENCLATURE ki_h

Integral gain of altitude.

kd_p

Feedback damping gain of roll rate.

kp_φ

Proportional gain of roll angle.

ki_φ

Integral gain of roll angle.

kd_r

Feedback damping gain of roll rate. Proportional gain of yaw angle.

L

State-space coefficients associated with lateral dynamics.

M

State-space coefficients associated with longitudinal dynamics. Mass.

mb

External moment applied to the airframe.

l, m, n

The components of mb in Fb.

ma

Aerodynamic moment.

mp

propeller moment.

N


pn

The inertial (North) position of the aircraft along ii in Fi.

pe

The inertial (East) position of the aircraft along ji in Fi.

pd

The inertial down position (negative of h (altitude)) of the aircraft measured along ki in Fi.

p

The roll rate measured along ib in Fb.

q

The pitch rate measured along jb in Fb.

r

The yaw rate measured along kb in Fb.

Sprop

Area of the propeller.

s

Wing area.

SYSlat

State space model associated with lateral dynamics (Alat, Blat, Clat, Dlat).

SYSlon

State space model associated with longitudinal dynamics (Alon, Blon, Clon, Dlon).

tr

Rise time of step response.

ts

Settling time of step response. Trim input.

u, v, w

velocity components of the airframe projected onto xb-axis.

xvii

ABBREVIATIONS and NOMENCLATURE Va

Airspeed vector.

Vg

Ground speed vector.

Vw

Wind speed vector.

wn

Natural frequency. Trim state.

X

State-space coefficients associated with longitudinal dynamics.

Y


Z

State-space coefficients associated with longitudinal dynamics.

xviii

LIST OF FIGURES

LIST OF FIGURES Figure 1.1

Timeline of current and planned DOD UAS systems.…….....…………

3

Figure 1.2

Structure of Unmanned Aircraft System (UAS).……………....……….

6

Figure 1.3

MQ-1 Predator from various views……………………………....…......

8

Figure 1.4

RQ-2B pioneer UAV photograph and schematic views…………....…... 8

Figure 1.5

Global hawk UAV……………...……………………………………….

Figure 1.6

RQ-5A Hunter UAV……………………………………………………. 9

Figure 1.7

RQ-7A Shadow200 UAV……………………………………………….

10

Figure 1.8

MQ-9 Reaper UAV……………………………………………………..

10

Figure 1.9

X-47B J-UCAS…………………………………………………………. 11

Figure 1.10

Samples of SUAVs……………………………………………………...

Figure 1.11

Various models of MAVs…...………………………………………….. 12

Figure 1.12

Long endurance electric UAV…………………………………..............

Figure 1.13

University of Minnesota Ultrastick-25e UAV………………….............. 15

Figure 1.14

The basic elements of SUAV w.r.t a control system………………........ 16

Figure 1.15

VECTOR avionic system……………………………………………….

17

Figure 1.16

Micropilot Autopilots…………………………………………………...

18

Figure 1.17

Procerus kestrel autopilots versions…………………………………….

18

Figure 1.18

Cloud cap piccolo autopilots…………………………...……….............

19

Figure 1.19

Ardupilot mega autopilot pin assignment……………………................. 20

Figure 1.20

Openpilot revolution autopilot board……………………………...........

20

Figure 1.21

First generation VCU FCS………………………………………...........

23

Figure 1.22

Second generation VCU FCS...........................................................……

24

Figure 1.23

Third generation VCU FCS....................…............….............................

25

xix

9

12

14

LIST OF FIGURES

Figure 1.24

AggieAir system architecture…………………………………………...

Figure 1.25

Minas Gerais low cost UAV platform of the Federal University of

26

Minas Gerais………................................................................................. 27 Figure 1.26

Paparrazi autopilot system Archeticture………..…………………......... 28

Figure 1.27

Lisa /S smallest autopilot in the world…………………………….........

Figure 2.1

Vehicle frame (Fv) orientation is identical to earth frame……………… 33

Figure 2.2

Heading angle extracted from rotation from Fv to Fv1.............................

34

Figure 2.3

Pitch angle extracted from rotation between Fv1 to Fv2………................

34

Figure 2.4

Roll angle extracted from rotation between Fv2 to Fb…………………..

35

Figure 2.5

Rotation angles between the body frame and the wind frame………...... 36

Figure 2.6

Flight path angle ( ), and course angle ( )……………............……

37

Figure 2.7

Heading ( ), Crab ( ) angles, and wind triangle…………….......……

38

Figure 2.8

Section of airfoil and the applied lift (FL) and drag (Fd) forces………...

39

Figure 2.9

The lift coefficient as a function of α can be approximated by a linear function of α (dot-dashed)…................................................……………

28

40

Figure 2.10

SUAV control surfaces…………….............…………………………… 41

Figure 2.11

Definitions of UAV body velocities, forces, moments, and angular rates..........................................................................................................

43

Figure 3.1

Basic linear state space model derivation flowchart for simulation......... 50

Figure 3.2

Response of (

) of Ultrastick-25e model due to elevator doublet

(trim±5 degree)……………………………….....................................… 67 Figure 3.3

Response of (

) of Ultrastick-25e model due to elevator doublet

(trim±5 degree)……………………........................................................ 67 Figure 3.4

Response of (ax, az) of Ultrastick-25e model due to elevator doublet (trim+5 degree)......................................................................................... 68

Figure 3.5

Response of (h) of Ultrastick-25e model due to elevator doublet (trim±5 degree)…………………………………………………………. 68

Figure 3.6

Response of the lateral dynamics

due to 5 degree (aileron,

xx

LIST OF FIGURES rudder) deflection doublet signal......……………………………............ 69 Figure 3.7

Response of the lateral dynamics

due to 5 degree (aileron,

rudder) deflection doublet signal............…………………….................. 69 Figure 3.8

Comparison Response of the lateral dynamics

due to 5 degree

doublet signal in aileron deflection between Jacobian and analytical linearization……..................................................................................

71

Figure 4.1

Longitudinal autopilot block diagram…………………….......………...

76

Figure 4.2

MATLAB structure of pitch damper………………………………........ 77

Figure 4.3

Most inner loop root locus of pitch tracker………………………..........

78

Figure 4.4

MATLAB structure of pitch attitude hold controller…………………...

79

Figure 4.5

+5 degree doublet signal response………………………………….......

80

Figure 4.6

+5 degree doublet signal response in the existence of sensor noise…..... 80

Figure 4.7

+5 degree response in the existence of disturbance………………….....

81

Figure 4.8

Multi commanded steps of pitch attitude response…………………......

81

Figure 4.9

MATLAB Structure of altitude hold controller………………………...

83

Figure 4.10

Step response of altitude hold controller…………………………..........

84

Figure 4.11

10 [m] doublet signal response……………………………………......... 85

Figure 4.12

Effect of the noise in the altitude hold controller…………………........

85

Figure 4.13

Effect of the disturbance on the altitude hold controller……………….

86

Figure 4.14

Level climbing 100 meter altitude from the pitch………………………

87

Figure 4.15

Comparison between the classic and designed controllers applied on the approximated analytical linear model and non-linear model in the absence of noise and environment model to illustrate the differences…..................................................................................…

Figure 4.16

Figure 4.17

87

Comparison between the classic and designed controllers applied on the approximated analytical linear model and non-linear model….........

88

Lateral autopilot block diagram………………………………………...

89

xxi

LIST OF FIGURES

Figure 4.18

Roll rate feedback system………………………………………………

90

Figure 4.19

MATLAB structure of bank angle hold controller……….....…………

91

Figure 4.20

+5 degree doublet signal in roll response……………………………….

92

Figure 4.21

Effect of the noise in the roll tracker…………………………………....

93

Figure 4.22

Effect of the disturbance in the roll tracker………………………….….

93

Figure 4.23

Multi-step response of roll tracker……………………………………...

94

Figure 4.24

MATLAB Structure of the lateral autopilot…....……………………….

95

Figure 4.25

Doublet signal response of the heading hold controller………………...

96

Figure 4.26

Effect of the noise in the heading hold controller………………………

97

Figure 4.27

Effect of the disturbance in the heading hold controller………………..

97

Figure 4.28

Rectangular motion heading command and its response in linear simulation model…....…………………………....……………………..

98

Figure 4.29

Heading command rectangular motion response in SIL………………..

98

Figure 4.30

Shape of the aircraft trajectory due to rectangular motion commands in the heading angle.....................................................................................

99

Figure 4.31

Change in the bank angle due to rectangular motion in the aircraft......... 99

Figure 4.32

Climbing turn trajectory of the aircraft…………………………………

101

Figure 5.1

SUAV electronic components block diagram....………………………..

105

Figure 5.2

Open source development boards………………………………………. 106

Figure 5.3

The functional block diagram of the Arduino mega 2560 board…........

Figure 5.4

Orientation of axes descriptions of the device and mathematical calculations...............................................................................................

108 113

Figure 5.5

MPU6050 pin configuration..................................................................... 114

Figure 5.6

HMC5883L pin configuration…………………………………………..

115

Figure 5.7

Pin configuration of Ublox LEA 6H module…………………………...

117

Figure 5.8

3DR 915 Mhz radio module…………………………………………….

118

xxii

LIST OF FIGURES

Figure 5.9

Configuration of telemetry wireless module……………………………

118

Figure 5.10

Schematic diagram of flight computer with IMU………………………

121

Figure 5.11

Flight computer connections with GPS/IMU/Digital compass…………

122

Figure 5.12

Pitch angle comparison according to various state estimator techniques. 123

Figure 5.13

Roll angle comparison according to various state estimator techniques..

Figure 5.14

Heading comparison, according to various state estimator techniques… 124

Figure 5.15

Pitch, roll, and heading GUI indicator………………………………….

125

Figure 5.16

Components of a PIL Simulation……………………………………….

126

Figure 5.17

PIL simulation of +5 deg response of pitch attitude……………………

127

xxiii

123

LIST OF TABLES

LIST OF TABLES Table 1.1

Samples of Small Unmanned Aerial Vehicles…………….....................

11

Table 1.2

Physical properties of Ultrastick-25e………………….…………..........

15

Table 1.3

Physical specifications of various autopilots………………………........ 21

Table 1.4

Sensor ranges of various autopilots…………………..……………........

21

Table 1.5

Autopilot functions of various autopilots…..……………………….......

21

Table 3.1

Trimmed flight conditions for Ultrastick-25e (Thor)……….………......

52

Table 3.2

Longitudinal state space model coefficients……...…………………...... 56

Table 3.3

Poles of the longitudinal state space linear model...................................

58

Table 3.4

Lateral state space model coefficients………………..…........................

61

Table 3.5

Poles of the lateral state space linear model.............................................

63

Table 3.6

Maximum error existed in the longitudinal dynamics comparison between linear and nonlinear models.......................................................

Table 3.7

68

Maximum error existed in the lateral dynamics comparison between linear and nonlinear models...................................................................... 70

Table 4.1

Time domain analysis of pitch tracker…………………….....................

79

Table 4.2

Altitude hold controller time domain characteristics…………...............

84

Table 4.3

Roll attitude hold controller time domain characteristics……….…........ 92

Table 4.4

Heading controller time domain characteristics…………………….......

96

Table 4.5

Value of the control parameters of Ultrastick-25e autopilot..............

101

Table 5.1

Standard pseudorange error model……………………………...............

115

Table 5.2

Data results from GPS module in NMEA protocol………….................. 116

xxiv

LIST OF PUBLICATIONS

LIST OF PUBLICATIONS [01]

Ahmed EA, Hafez A, Ouda AN, Ahmed HEH, Abd-Elkader HM "Modelling of a Small Unmanned Aerial Vehicle", Adv. Robot Autom 4: 126, 2015, doi: 10.4172/2168-9695.1000126..

[02]

Ahmed EA, Hafez A, Ouda AN, Ahmed HEH, Abd-Elkader HM, " Design of a Lateral Motion Controller for a Small Unmanned Aerial Vehicle (SUAV)", 6th International Conference on Mathematical Models for Engineering Science (MMES '15), Michigan State University, East Lansing, MI, USA, September 20-22, 2015.

[03]

Ahmed EA, Ouda AN, Hafez A, Ahmed HEH, Abd-Elkader HM," Design of Longitudinal Motion Controller of a Small Unmanned Aerial Vehicle ", I.J. Intelligent

Systems

and

Applications,

DOI: 10.5815/ijisa.2015.10.05.

xxv

2015,

10,

37-47,

THESIS CONTRIBUTION

THESIS CONTRIBUTION Unmanned Aircraft Systems (UAS) are playing increasingly prominent roles in defense programs and defense strategies around the world. Technology advancements have enabled the development of it to do many excellent jobs as reconnaissance, surveillance, battle fighters and communications relays. This thesis covers the design and implementation of hardware and software for AFCS suitable for SUAV and is organized as follows: -

At chapter one, we make a survey on the various types of Unmanned Aerial Vehicles and its usage in military and civilian environments. The other part of chapter one is the survey of the autopilots, its design concepts and its specifications. The survey includes commercial autopilots, open source autopilots, and universities research's autopilots.

-

At chapter two, we previewed a standard method for deriving the nonlinear equations of motion of a fixed wing SUAV.

-

At chapter three, we used the nonlinear equations of motion to accomplish the modeling of Ultrastick-25e fixed wing UAV by linearizing these equations to extract a linear model. This linear model describes the behavior of the aircraft accurately to depend on it for autopilot design. We obtained the State Space linear models for longitudinal dynamics and lateral dynamics of aircraft. A novel analytical linearization is derived with accurate description of the behavior as soon as the state space linear model.

-

At chapter four, the full design of the autopilot with its lateral and longitudinal motion controllers is done. The design test results are compared with the Minnesota controller design. The test results assured that the proposed one is better than the Minnesota controller. The standalone Simulink model for the lateral motion controller and longitudinal motion controller is considered very useful for the design and a good contribution extracted from this thesis. The design takes into account the sensors random noises and the unpredictable disturbances.

-

Chapter five utilizes the implementation of the AFCS; flight computer, MEMS Sensors (gyroscopes, accelerometers, magnetometer, GPS), and state estimator xxvi

THESIS CONTRIBUTION with two techniques which are complementary and Kalman filters. All of the previous components formed the AHRS for assigning accurate values of the aircraft attitudes (φ, θ, ψ). The last part of this thesis is the processor in loop (PIL) stage for evaluating the implemented autopilot with aiding of the designed hardware autopilot and MATLAB environment for the model of Ultrastick-25e. The evaluation results of PIL are very good. By the last stage of this thesis we completed the AFCS with autopilot and attitude indicator software communicated with the autopilot by using the wireless telemetry link between the autopilot and the ground station.

xxvii

CHAPTER 1

Unmanned Aircraft Systems and Autopilots

CHAPTER

1


1.1 Introduction. Unmanned Aircraft Systems (UAS) are playing increasingly prominent roles in defense programs and strategies around the world. Technology advancements have enabled the aerospace engineers to develop UAS capable of doing many excellent jobs as reconnaissance, surveillance, battle fighters, and communications relays. So the need for designing a reliable Unmanned Aerial Vehicles (UAV) is very interesting nowadays. Autonomous UAV provides the possibility of performing tasks and missions that are currently hazardous or can cost humans or much money. From beginning, let's define the UAV and how to distinguish between it and other aerial systems as cruise missiles. UAV is defined as "an uninhabited reusable aircraft with aviation devices that sustain flight using onboard propulsion and aerodynamic lift". A cruise missile is defined as a "guided missile; the major proportion of whose flight path to its target is conducted at approximately constant velocity, depends on the dynamic reaction of air for lift and upon propulsive forces to balance drag" [1]. Cruise missile weapons are occasionally confused with UAV because they are both unmanned. The key discriminators are: (1) UAVs are equipped and intended for recovery at the end of their mission but cruise missiles are not. (2) Munitions carried by UAV (for military applications) are not tailored and integrated into their airframe whereas the cruise missile‟s warhead is. This distinction is clearly existed in United States Department of Defense (US DOD) Dictionary‟s definition for “UAV” [2].

1

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A powered UAV that does not carry a human operator uses aerodynamic forces to provide vehicle lift, can fly autonomously or be piloted remotely, can be expendable or recoverable, and can carry a lethal or non-lethal payload. With the previous definitions, ballistic or semi ballistic vehicles, cruise missiles and artillery projectiles are not considered UAVs.

1.2 UAV Types and Technologies. The need for replacing human pilots for performing high risk low cost missions make UAV manufacturing sector has become the most dynamic growth sector in the aerospace industry. According to a report entitled "Unmanned Aerial Vehicle (UAV) Market (2013-2018)", the total global UAV market is expected to reach over $8,000 million by 2018 [3]. UAVs have been widely used since the World War II [4] with its development being driven by military applications. However, there are several civil applications that can take advantage of UAV capabilities such as monitoring crops, wildlife, forests fires and traffic, as well as remote area delivery of medicine, aerial news and photography, TV and movie production, among others. In May 2013, there were about 4,000 UAVs operating worldwide [5], with the majority being small Intelligent, Surveillance and Reconnaissance (ISR) platforms and only a small part being of civilian application mostly in agriculture. Federal Aviation Administration (FAA) forecasts that, within five years there will be 7,500 commercial UAVs flying in the US airspace alone [6]. W.r.t. military applications, the condensed description of current and planned US DOD efforts is illustrated from Figure 1.1

2

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Figure 1.1 Timeline of current and planned DOD UAS systems [7]. UAV design strategy should be established to achieve UAS capabilities. To achieve the purpose of UAV we must know the processor capabilities, communication links, platform structure, sensor technologies, and how these technologies become available and how it can be integrated to enable the UAV requirements, there are several different tasks that need to be addressed as the following: 1. Conceptual Design overview. 2. Aerodynamic analysis. 3. Noise Prediction. 4. Propulsion System - electric propulsion system configurations are evaluated in terms of performance, overall weight and cost. 5. Structural Design and Aero-elasticity Analysis - The airframe is designed in this task, where different wing structural solutions will be evaluated. It will be considered several different materials in order to meet the goal of achieving the lightest and strong enough structure. 6. Stability and Control - During this task, the control surfaces will be designed to provide enough stability and control to the aircraft. The data gathered from wind tunnel testing to be used in developing the UAV controller.

3

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7. Multidisciplinary Design Optimization - At this Stage, all the necessary analysis tools for the propulsion, aerodynamics, structures, and controls are integrated together into a framework to improve the aircraft design. 8. Communications and Electronics - In this task the communications and electronic systems will be designed. There are several goals for this task: design and implement the autopilot hardware and software, make the aircraft systems capable of flight logging and possibly telemetry to a ground station and install all the sensors and actuators in the airframe. Aero-thermodynamic analysis for the management of thermal loads from the internal avionics to guarantee efficient cooling in the expected tight places. Telemetry equipment can be installed to monitor the aircraft behavior. 9. Flight Testing - The full-scale prototype testing will include system checks on ground, wind tunnel tests to access aerodynamic performance, static thrust under varying solar conditions and finally, flight tests. The first flight will be operated under radio controlled mode, which allows for throughout checks of the powered propulsion system. The second flight will be used to test the overall design refinement and also the autopilot hardware and software. The system that comprises all the required elements and network to control and command the UAV is also known as an Unmanned Aircraft System (UAS) [8].

1.2.1 UAV Applications. Before looking into UAV in more details, it is appropriate to list some of its applications. There are many applications; the most obvious missions are listed w.r.t. civilian and military applications as following: 1.2.1.1 Civilian Applications [9].  Electricity companies (Power line inspection).  Agriculture (Crop monitoring, spraying, etc.).  Conservation (Pollution and land monitoring).  Aerial photography (Film, video, urban feature, etc.).  Customs (Surveillance for illegal imports).  Fire Services and Forestry (Fire detection, incident control).  Coastguard (Search and rescue, coastline and sea-lane monitoring). 4

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1.2.1.2 Military Applications [10, 11]. A reconnaissance is not the only task any more. UAV shares with strike, force protection and signals collection. UAV also helps to reduce the complexity and time lag in the sensor-to-shooter chain for acting on "actionable intelligence". UAV continues to expand to cover a wide range of mission capabilities. These diverse systems range in cost from a few thousand dollars to millions of dollars, and range in capability from NAV weighing less than one pound to aircraft weighing over 40,000 pounds. UAV in general, are changing the conduct of military operations in the WOT by providing merciless pursuit without offering the terrorist a high value target, some uses at various branches of armed forces are as follows: 

For Navy - Following enemy fleets, Decoying missiles by the emission of artificial signatures, Electronic intelligence, Relaying radio signals, Protection of ports from offshore attack, Placement and monitoring of sonar buoys and possibly other forms of anti-submarine warfare.



Army - Reconnaissance, Surveillance of enemy activity, Monitoring of Nuclear, Biological and chemical (NBC) contamination, electronic intelligence, target designation and monitoring, and location and destruction of land mines.



Air Force - Long-range, high-altitude surveillance, Radar system jamming and destruction, electronic intelligence, airfield base security, airfield damage assessment and elimination of unexploded bombs.

1.2.2 UAV System Structure. UAV remote sensing system (for example) comprises six main systems, three on board the plane and three on the ground. The systems on board the plane are: 

The autopilot for autonomous control.



The imaging system for image capture.



Image processing to identify targets and characteristics.

The systems on the ground are:  The Ground Control Station (GCS) to monitor and control the aircraft through wireless data link.

5

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 The ground imaging station to receive and monitor the images and identified targets from the onboard image processing system through another data link using a high gain directional antenna.  There is a small control link system for Radio Control (RC) pilot to achieve manual control of control surfaces or downlink for telemetry data. All of these main system components are integrated as in Figure 1.2.

Figure 1.2 Structure of Unmanned Aircraft System (UAS) [12]

1.2.3 UAV Categories. UAV can be categorized depending on these characteristics (size, altitude limits, endurance or mission purpose) as follows [10]: • High Altitude Long Endurance (HALE) - With an altitude over 15000 m and over 24 hours of endurance. They are used to carry out extremely long-range surveillance and reconnaissance missions, are increasingly being armed. It's usually operated from fixed bases. • Medium Altitude Long Endurance (MALE) - They have an altitude varies from 5000 m to 15000 m and have 24 hours of endurance, usually operated from a fixed base in similar missions of HALE UAVs but with a shorter range. • Medium Range or Tactical UAV (TUAV) - They have a range between 100 km and 300 km. It's smaller and operated within simpler systems than MALE and HALE UAVs.

6

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• Close-range UAV - They usually operate at ranges of up to about 100 km and have both military and civil applications, such as reconnaissance, target designation, airfield security, power-line inspection, crop spraying, traffic monitoring. • Mini or Small UAV (MUAV or SUAV) - Are usually lighter than 20 Kg but heavier than a Micro UAV, capable of being hand-launched and operating at ranges of up to 30 Km. They are used by mobile battle groups and for many civilian purposes. • Micro UAV (MAV) – It's originally defined as being an UAV with a wing span no greater than 150 mm. principally required flying in an urban environment. It is required to fly slowly and to have the ability to be able to stop and sit on a wall or post. It's usually hand-launched. • Nano Air Vehicles (NAV) - These are very small UAVs and are proposed to be used in swarms for radar confusion. If with technological advancements it is possible to make cameras, propulsion and control systems small enough for these UAVs, they could be used for ultra-short range surveillance. • Remote Piloted Helicopter (RPH) and Vertical Take-Off UAV (VTUAV) - They are both UAVs capable of vertical take-off and landing, and also capable of hovering during a mission. • Unmanned Combat Air Vehicle (UCAV) - These UAVs are capable of launching weapons and even air-to-air combat. 1.2.3.1 Major Operating UAVs. A. MQ-1 Predator. The Air Force MQ-1 Predator is manufactured by General Atomics Aeronautical Systems Inc. It was one of the initial Advanced Concept Technology Demonstrations program (ACTDs) in 1994 and transitioned to an Air Force program in 1997. Since 1995, Predator has flown surveillance missions. In 2001, the Air Force demonstrated the ability to employ Hellfire missiles from the Predator, leading to its designation being changed from RQ-1 to MQ-1 to reflect its multi-mission capability. MQ-1 is shown in Figure 1.3 [13].

7

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Figure 1.3 MQ-1 Predator from various views. B. RQ-2B Pioneer. The Navy/Marine RQ-2B Pioneer in Figure 1.4 is manufactured by Pioneer co. it has served with Navy, Marine and Army units since 1986. Initially deployed aboard battleships to provide gunnery spotting, its mission evolved into reconnaissance and surveillance, primarily for amphibious forces. Launched by rocket assist, pneumatic launcher, or from a runway, it recovers on a runway with arresting gear after flying up to 5 hours with a 75 pound payload. It currently flies with a gimbaled EO/IR sensor, relaying analog video in real time. [14].

Figure 1.4 RQ-2B pioneer UAV photograph and schematic views. C. RQ-4 Global Hawk. The Air Force RQ-4 Global Hawk is a HALE UAS designed to provide wide area coverage. It's manufactured by Northrop Grumman. The size differences between the RQ-4A (Block 10) and RQ-4B (Blocks 20, 30, 40) models are shown in Figure 1.5. Global Hawk completed its first flight in February 1998. It carries both an EO/IR sensor and Synthetic Aperture Radar (SAR) with Moving Target Indicator (MTI) capability, allowing day/night; all-weather reconnaissance. Sensor data is relayed over 8

CHAPTER 1


various types of data links to its Mission Control Element (MCE) shelter, which distributes imagery up to seven theater exploitation systems [15].

Figure 1.5 Global Hawk UAV. D. RQ-5A/MQ-5B Hunter. The RQ-5 Hunter in Figure 1.6 is manufactured by Northrop Grumman; it was originally a joint Army/Navy/Marine Corps Short Range UAS. A gimbaled EO/IR sensor is used to relay video in real time via a second airborne Hunter over data link [7].

Figure 1.6 RQ-5A Hunter UAV. E. RQ-7A/B Shadow 200. US Army selected the RQ-7 Shadow 200 formerly tactical UAV (TUAV) which is manufactured by Aircraft Armament Incorporated Company (AAI) in December 1999 to meet the Brigade-level requirement. Its shape in Figure 1.7, it is recovered with the aid of arresting gear. Its gimbaled EO/IR sensor relays video in real time via data link. The first upgraded „B‟ model was delivered in August 2004. The RQ-7B can now accommodate the high bandwidth tactical common data link (TCDL) and features a sixteen inch longer wingspan, 7 hours endurance (greater fuel capacity), and an improved flight computer [16].

9

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Figure 1.7 RQ-7A Shadow200 UAV F. MQ-9 Reaper B. The MQ-9 shown in Figure 1.8 is a MALE UAV. Its primary mission is as a persistent hunter-killer for critical targets. The MQ-9 system consists of three subsystems; aircraft, a ground control station (GCS) and a Reaper Primary Satellite Link. The integrated sensor suite includes moving target capable synthetic aperture radar (SAR), houses EO/IR sensors, a laser range finder and a laser target designator [17].

Figure 1.8 MQ-9 Reaper UAV. G. Joint Unmanned Combat Air Systems (J-UCAS). The Air Force UCAV and Navy UCAV-N demonstrator programs were combined into a joint program under Defense Advanced Research Projects Agency (DARPA). First flights of the original prototypes of the Boeing X-45A and the Northrop Grumman X-47s which is shown in Figure 1.9 are occurred in May 2002 and February 2003 respectively. First flights of the larger X-45C and X-47B models and introduction of a Common Operating System are occurred in 2007. J-UCAS is focused on demonstrating a versatile combat network. Air and ground components are nodes that can be changed over time to support a wide range of multiple missions. The program demonstrated 10

CHAPTER 1


weapon delivery and coordinated flight in 2004. It completed its first autonomous aerial refueling. First catapult launch from the deck of an aircraft carrier and first arrested landing on the deck of an aircraft carrier [18].

Figure 1.9 X-47B J-UCAS. H. SMALL UAS [19]. - SUAV. This category of UAVs is summarized in Table 1.1 and shown in Figure 1.10 Table 1.1 Samples of Small Unmanned Aerial Vehicles.

Manufacturer Weight(pound) Length(ft) Wingspan(ft) Payload (ib) Engine Type Ceiling (ft) Endurance

Dragon Eye

FPASS

Pointer

Raven

Buster

AeroVironment

Lockheed Martin

AeroVironment

AeroVironment

Mission Technologies

4.5 2.4 3.8 1 Battery 1000 45 – 60 min

7 2.7 4.3 1 Battery 1000 1 hr

8.3 6 9 1 Battery 1000 2 hr

Note: -

1 pound (ib) = 0.45 kg.

-

1 ft = 0.305 m.

11

4 3.4 4.3 2 Battery 1000 1.5 hr

10 3.417 4.125 3 Gasoline 10000 +4 hr

CHAPTER 1


Figure 1.10b Force protection aerial surveillance system (FPASS) UAV

Figure 1.10a Dragon eye UAV

Figure 1.10d Raven UAV

Figure 1.10c FQM-151 Pointer UAV

Figure 1.10 Samples of SUAVs.

- Micro Air Vehicles (MAV). The MAV is focused on a small system suitable for backpack placement and single-man operation as (MAV/Wasp/Hornet). Honeywell was awarded an agreement to develop the MAV as part of the MAV ACTD, which pushes the UAV design in small, lightweight propulsion, new sensing and communication technologies. Some examples of these MAVs are shown in Figure 1.11.

MAV

Harnet

Wasp

Figure 1.11 Various models of MAVs. These previous analysis about some different types of UAS is a brief report about these systems. There are many and many other systems but here we make a global overview about the working UAS around the world. The next section talks about some research UAVs developed from universities and research laboratories. 12

CHAPTER 1


1.2.3.2 UAVs Research Projects. A. Long Endurance Electric UAV of LAETA [20]. A project of a long endurance electric UAV that is being developed in a collaborative project by Superior Institute of Technique (IST), Engineering College of Porto University (FEUP) and University of Beira Interior (UBI) under the sponsorship of Associate Laboratory of Energy, Transportation of Aeronautics (LAETA). It is shown in Figure 1.12. This project is designed to accomplish these specifications: •

Long Endurance - realized by green power technologies with solar power by using a high efficiency solar cells, high capacity/density batteries.

•

Autonomous Flight - realized by inserting an autopilot and navigation systems such as Global positioning System / Inertial Navigation System (GPS / INS).

•

Obstacle Avoidance - realized by implementing an obstacle avoidance technique includes detection, estimation, and avoidance planning of the obstacle.

•

High-Strength, Low-weight Structure: realized to give a good impact resistance on landing.

•

Multiple Mission - accomplished by designing a sufficiently large payload range capability and developing upgradable modular avionics, to enable an easy software upload and/or hardware Size, Weight and Power (SWaP) to meet the selected mission requirements.

Figure 1.12 Long endurance electric UAV [21].

13

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B. Ultrastick Minnesota UAVs. Ultrastick-25e vehicle has three models Ultrastick-mini, Ultrastick-25e (thor), and Ultrastick-120. We will focus on Ultrastick-25e which is shown in Figure 1.13; its hardware and sensing capabilities, and the preliminary analysis used to generate the linear model of the aircraft dynamics. The Ultrastick-25e has a conventional fixed-wing airframe with aileron, rudder and elevator control surfaces. The aircraft is also equipped with flaps. All control surfaces are actuated via servos with a maximum deflection of 25 deg. in each direction. The propulsion system consists of an electric motor. Physical properties of the airframe are summarized in Table 1.2, where the moments of inertia are calculated using swing tests. More details Ultrastick-25e platform can be found in [22, 23]. The linear model of the Ultrastick-25e flight dynamics is generated using aerodynamic data from the airframe. Control derivatives and stability derivatives associated with the body velocities are estimated from wind-tunnel tests performed with an Ultrastick-Mini. This airframe is smaller than Ultrastick-25e and fits in the wind tunnel available at the University of Minnesota. Ultrastick-25e and the Mini have similar aerodynamics but are not exact geometric scales of each other.

Figure 1.13 University of Minnesota Ultrastick-25e UAV. Stability derivatives associated with the angular rates were taken from an aerodynamic model for the Ultrastick-120 [22]. This airframe is larger than Ultrastick-25e; it has similar aerodynamics, but is not an exact geometric scale. The aerodynamic model for Ultrastick-120 was developed at NASA Langley Research

14

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Center, using both static and dynamic wind-tunnel testing [24, 25]. The linear model for the Ultrastick-25e is used as a guide to design flight experiments. Table 1.2 Physical properties of Ultrastick-25e Property Wing span (m) Wing surface area (m2) Main cord (m) Mass (kg) Inertia (kg.m2)

Symbol

The value

b S C m Jx Jy Jz Jxz

1.27000 0.30970 0.25000 1.95900 0.07151 0.08636 0.15364 0.01400

1.3 Automatic Flight Control System (AFCS). The main objective of this thesis is to design an autonomous flight control system of SUAV. Ultrastick-25e (thor) is chosen for this mission to allow it to be flown autonomously and to be remotely controlled. This system will be composed by an autopilot, a GCS and all the required equipment for data transmission between the autopilot and the GCS as in Figure 1.2. To meet this goal, there are several tasks that needed to be accomplished including the following steps: •

Survey of various autopilot solutions (Commercial, Open source, Universities developed).

•

Comparison of different technical solutions.

•

Modeling of ultrastick-25e fixed wing UAV.

•

Detailed design of the autonomous flight control system.

•

Assembly of the flight control system using off-the-shelf components.

•

Test, characterization and tuning of the flight control system in a controlled environment.

•

Field test using an available flying testbed using RPV.

•

Flight demonstration using waypoint satellite navigation.

1.4 Survey of Various Autopilots. In order to support new SUAV research activities; a new, simple, lightweight, power efficient and inexpensive AFCS is needed. An autopilot is the heart of this AFCS; it's an electric device that is used to automatically guide a vehicle without the 15

CHAPTER 1


assistance of a human operator. There has been a significant evolution of the autopilots over decades, and they have evolved from simple autopilots; that only held altitude to autopilots that are capable of complex scenarios such as landing, automatic takeoff and loiter. The first autopilot was developed in 1912 by Lawrence Sperry [26]. It allowed the aircraft to fly straight and level on a compass course without the need for the pilot to operate. This autopilot became known as "George autopilot". Modern autopilots use control software algorithms to control the vehicle and GPS for position determination. This evolution allows the autopilots to perform complex tasks such as waypoint following, even automatic take-off and landing of some air vehicles. An UAV autopilot system is a closed-loop control system that has two main parts: the controller and the state estimator. Usually, the state estimator is an inertial guidance system that includes attitude rate, acceleration, magnetic sensors, GPS and pressure sensors. The sensor measurements and GPS data is passed to software filters to generate estimates of the current state of the vehicle. These estimates are then passed to the controller that based on the control strategy employed, and then sending control inputs to the actuators as shown in Figure 1.14. For any autopilot design project it is important that the autopilot covers the following requirements: • Low price. • Reconfigurable. • Auto take-off and landing. • Small dimensions and weight. • Waypoint following capabilities.

Figure 1.14 Basic elements of SUAV w.r.t. a control system.

16

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The following sections show some examples of autopilots, beginning with the commercial autopilots.

1.4.1 Commercial Autopilots Review. There are many commercial autopilots, some of them are presented here and the main characteristics of each autopilot are discussed with their technical data. The lack of commercial autopilots can be summarized as the vendors typically provided SWaP requirements and price points but with little details about their navigation algorithms, control systems and sensors concepts. A. UAV Navigation VECTOR. VECTOR is a top of the range autonomous Flight Control unit designed for high quality target drones and UAVs. It's developed by UAV Navigation and is shown in Figure 1.15.

Figure 1.15 VECTOR avionic systems. It has a high processing power with dual 200 MIPS CPUs with 8 MB flash memory. It is capable of fully automatic take-off, flight plan execution and landing. This autopilot can control several different types of UAVs such as fixed wing Tactical UAVs, high-end subsonic drones and helicopter or multirotor platforms. A POLAR AHRS/INS unit is a basic component of the autopilot which combines all the necessary vehicle dynamics sensors and algorithms for state estimation [27]. B. Micropilot MP2x28 Series. Micropilot Company offers a series of autopilots for various applications with prices ranging from $1,500 to $8,000. The middle range autopilot MP2028g, shown in Figure 1.16 is an example of this series; its small size and light weight are the main 17

CHAPTER 1


features of this autopilot. It has GPS, 3-axis gyros/accelerometers, pressure altimeter and pressure airspeed sensors all integrated in a single circuit board. The MP2028g autopilot supports altitude hold, airspeed hold and waypoint navigation. The MP series autopilots use Proportional Integral Derivative (PID) based control loops [28] at a rate of 30 Hz. Some models support autonomous takeoff and landing. It also supports completely independent operations such as autonomous take-off, bungee launch, hand launch and landing. This model is not suitable for research purpose because of all the limitations imposed [29].

Figure 1.16 Micropilot autopilots. C. Procerus Kestrel Autopilot. Procerus Kestrel v2.4 is an autopilot specially designed for SUAVs and MAVs, weighting only 16.7 grams. It's shown in Figure 1.17. This autopilot has a complete inertial sensor set that includes: 3-axis rate gyros and accelerometers, absolute and differential pressure sensors for altitude, and airspeed measurement. Kestrel has the built-in ability to autonomous take-off and landing, waypoint navigation, speed and altitude hold and it also supports multiple UAV operations [30].

Figure 1.17 Procerus kestrel autopilots versions. 18

CHAPTER 1


D. Cloud Cap Piccolo Series. Cloud Cap company releases many versions of autopilots (piccolo SL, piccololl, piccolo Nano). Piccolo SL is an autopilot for small fixed wing UAVs and Vertical Takeoff and Landing (VTOL) applications. It's shown in Figure 1.18. It provides a complete integrated avionics solution that includes the flight control processor, inertial sensors (3-axis accelerometers and gyros), static and dynamic pressure sensors, GPS receiver, and a datalink radio. Piccolo SL supports peripherals that enhance its capabilities such as laser altimeters for more accurate altitude information, transponders, magnetometers, Real Time Kinematic (RTK) GPS with a small error, payload pass through support, among others. It is also possible to extend the autolanding performance by using Differential GPS (DGPS). With DGPS this autopilot supports autonomous taxi, rolling take-off and moving net recovery [31].

Figure 1.18 Cloud cap piccolo autopilots.

1.4.2 Open Source Autopilots. Open source autopilots are the most familiar to the researchers due to their flexibility in modification and low cost, these autopilots are released almost from universities labs as ardupilot, open pilot , LISA and so many. Here we will make a brief on ardupilot and open pilot due to their good specifications with the requirements of SUAV design. A. APM 2.x Autopilot. The APM 2.x is an open source autopilot system based on an Arduino platform. Figure 1.19 illustrates some features of APM 2.6 autopilot for example. The APM 2.x can be used with an open source Ground Control Station (GCS) application such as the Mission Planner. This software allows the user to calibrate and configure the

19

CHAPTER 1


autopilot, plan and save missions and view live flight data [32]. The last version of these types of autopilots is APM 2.8.

Figure 1.19 Ardupilot Mega autopilot pin assignment. B. Openpilot Revolution Board. Open source UAV autopilot system Openpilot shown in Figure 1.20 is capable of supporting fixed-wing UAVs, as well as multi-rotor and helicopters. The Revolution has a full INS unit onboard. The Openpilot Revolution board has a built-in modem that provides a direct telemetry link between the controller and the GCS, a barometric pressure sensor, a magnetometer and it can be connected with a GPS module. This autopilot is capable of waypoint navigation with GPS installed, position hold and automatic return to launch base. Software also provides waypoint navigation settings and telemetry functions [33].

Figure 1.20 Openpilot revolution autopilot board.

20

CHAPTER 1


1.4.3 Comparison of Various Autopilots. The tables below summarize specifications of the commercial and open source autopilots, physical specifications, sensor ranges, and autopilots functions. A. Physical Specifications. Table 1.3 Physical specifications of various autopilots Commercial

Autopilot Size (cm)

Open Source

Vector

Mp2028

g

Kestrel v2.4

Piccolo SL

APM 2.8

Revolution

6.88x4.5x7.45

10.0x4.0x1.5

5.08x3.5x1.2

13.1x5.7x1.9

7.1x4.5x1.35

3.6x3.6x1.2

Weight (gm)

300

28

16.8

110

43

14

Power

2.5W

[email protected]

500mA @ 3.3V

4W

200mA @ 5V

Is very low

Price

> $3500

$3500

$5000

> $5000

< $250

$120

Temp. (C)

-40 to 85

-40 to 85

-40 to 85

-40 to 85

I/p. voltage. V

7 to 36

4.2 to 26 v

5 – 30

5–6

5–6

4.8 – 8.4

CPU

Dual 200 MIPS

3

16 MHz

16 MHz

210 MIPS

Memory

8 MB

-

4Mb

4Mb

-

-

B. Sensor Ranges. Table 1.4 Sensor ranges of various autopilots. Autopilot

Mp2028g

Vector

Kestrel v2.4

Piccolo SL

APM 2.8

Revolution

h (m)

-600 – 9000

12000

-800 to 7000

-

-

-

amax (g)

8

2

10

6

2

-

Vamax

230 m/s

140 m/s

130 m/s

100 m/s

-

-

300 deg./sec

150 deg./sec

300 deg./sec

300 deg./sec

250 deg./sec

-

Knot = 0.5144 m/s C. Autopilot Functions. Table 1.5 Autopilot functions of various autopilots. Autopilot

Mp2028g

Vector

Kestrel v2.4

Piccolo SL

APM 2.8

Revolution

Waypoint navigation

√

√(1000 pts.)

√

√(1000 pts.)

√

√

Auto takeoff / landing

√

√

√

√

√

√

Altitude hold

√

√

√

√

√

√

Airspeed hold

√

√

√

√

√

√

Multi-UAV support

√

√

√

√

√

√

Return home

√

-

-

-

√

√

21

CHAPTER 1


The above analysis serves in the implementation of a low cost autopilot that has good quality performances and flexibility when being installed in different platforms.

1.4.4 Universities Developed Autopilots. 1.4.4.1 (VCU) Autopilot Research, USA. Autopilots developed under universities researches is very important and have many scientific facts, these autopilots are the root of any advancement in the autopilot manufacturing. VCU Autopilot from Virginia Commonwealth University [34] is a very good application for discussion. a. First Generation VCU FCS. The first generation VCU FCS was built around the Atmel FPSLIC [35]. This device combines Atmel's AT40K FPGA architecture with 20 MIPS 8-bit Reduced Instruction Set Computer (RISC) microprocessor core and numerous microcontroller peripherals. GPS was used to determine both position and heading of the aircraft. Infrared (IR) sensors were used to determine attitude information. Control of the aircraft was accomplished via a GCS developed by Visual Basic. The flight control software was written in C++ and ran on the FPSLIC's embedded AVR microcontroller. The main control loop of the AFCS ran at 20Hz. It was tasked with bidirectional communication to the ground for receiving telemetry data, perform aircraft stabilization and executing waypoint following. The output of the FCS was a set of Pulse Width Modulator (PWM) values that correspond to control surface positions. Communications to the ground was via a radio modem connected to a serial port on the microcontroller. The second serial port was used to receive GPS positioning data. The first generation VCU FCS development board is shown in Figure 1.21. This board is relatively large. Its size is 12.7x15.24 (cm). It required add-on boards connected to General Purpose Input Output (GPIO) headers to interface with external sensors and servos. Similarly, the GPS and radio modems have their own boards that have similar size. This added to the overall SWaP budget.

22

CHAPTER 1


Figure 1.21 First generation VCU FCS. b. Second Generation VCU FCS. Major modifications were made to the computing platform and sensor system [36]. The computing platform moved away from the 8-bit microcontroller design. The flight control system software ran on a Xilinx MicroBlaze soft-core. CPU is running at 50 MHz. The FPGA system board used was an Atmark-Techno Suzaku-S. FPGA hardware was based on a reference design for Xilinx's Embedded Development Kit (EDK). The second generation system used software threads to handle I/O with serial devices. It was tasked with barometric sensors (dynamic and static) to calculate airspeed and altitude, GPS information for navigation, and perform attitude control and stability using PID based controllers. The system software was also implemented Atmark-Techno's Suzaku-V platform. This platform uses Xilinx's Virtex-2 Pro [37]. Rather than using a soft-core CPU, it contains a hardcore PowerPC processor that is capable of running at higher clock speeds. The second generation FCS has an advancement that was the use of the Crossbow AHRS400-200. This AHRS allowed for more accurate attitude measurements. AHRS performance was not dependent on weather conditions as IR attitude sensors existed in 1st generation. An expansion or based board, aptly named Suzaku EX., platform was designed to interface with the various peripherals of the system. The base board shown in Figure 1.22 contains: 

3.3V regulator for the Suzaku board. 23

CHAPTER 1




Two level shifters to interface serial ports to standard RS232 serial devices.



Differential and absolute barometric sensors for airspeed and altitude measurements.



8 channel ADC connected to the Suzaku board via SPI.

Figure 1.22 Second generation VCU FCS. c. Third generation VCU FCS. Third generation has least modifications; most improvements were to the flight control algorithms to support high performance jet turbine UAVs. A few new expansion boards were developed but they all maintained the same general layout and capabilities as shown in Figure 1.23. Improved power regulators and ADCs were the main differences from the older expansion board. Support for newer and more compact IMUs were introduced, these include the MIDG and MIDGII IMUs from Microbotics [38]. Copilot IR sensors was also reintroduced to lower the overall system cost. Software improvements included waypoint navigation with cross-track error compensation, PID gain scheduling for better performance over a larger airspeed range, and some software filtering of barometric sensors. Great improvements to the GCS were also introduced. A client/server system written in C# allows multiple clients to control various aspects of the UAV. Flight log analysis and graphing tools were also developed.

24

CHAPTER 1


Figure 1.23 Third generation VCU FCS. The new miniFCS enables the use of smaller, cheaper aircraft and allow flight verification of new multi-UAV cooperative algorithms that would be cost prohibitive with other systems. 1.4.4.2 AggieAir Autopilot, USA. Utah State University presents a hardware and software architecture for low cost miniature fixed-wing autonomous UAVs. The AggieAir autopilot system is composed of three different but interdependent modules; these are the AggieCap, AggieNav and AggiePilot. The structure of the system is shown in Figure 1.24. The AggieCap is responsible for payload management and system control; it runs on a Gumstix computer. It is capable of controlling a pan and tilt camera system and relaying images to the ground over a WiFi data link. AggieCap also adds enhanced Kalman filtering to sensor data from AggieNav. The AggieNav is a navigation sensor suite that contains a 6-DoF IMU, GPS and compass module, as well as dual pressure sensors for estimation of altitude and airspeed [39]. AggiePilot is the Paparazzi autopilot system [40] with the addition of using the Joint Architecture for Unmanned Systems (JAUS) command and control messaging standard. The AggieNav system is based around the Atmel AVR32 UC3A microcontroller. It includes an Analog Devices ADIS1654 6-DoF IMU, Honeywell HMC6343 3-axis magnetic compass, Ublox LEA-5H GPS receiver, and two VTI SCP-1000 pressure sensors. 3.3V and 5.0V switching regulator are used to power all systems. Data link is implemented using a Commercial Off-The-Shelf (COTS) Bullet2-HP from Ubiquity Wireless.

25

CHAPTER 1


Figure 1.24 AggieAir system architecture. 1.4.4.3 Federal University of Minas Gerais, Brazil. Implementing a low cost, portable, and reliable aerial platform for ground reconnaissance is the main goal of this example research. The sensor used are one SCP1000 pressure sensor from Velocity Vector Imaging (VVI) Technologies, one 163PC01D75 differential pressure sensor from Honeywell, FMA Direct CPD4 horizon sensor for IR attitude determination, and a Garmin GPS-18 module. The system's main computer is the Personal Data Assistant device (PDA). A Palm Pilot TX with a 312 MHz Advanced RISC Machine (ARM) based processor and 128 MB of RAM was used to implement the control loops running at a rate of 5 Hz. PDA has the advantage of having significantly faster processor and RAM than most low cost microcontrollers but shortages in its I/O capabilities; it contains a single RS232 serial port for communications with all peripherals. The design improved this limitation by adding two additional microcontrollers to multiplex all sensor outputs through the single available serial port. One microcontroller is used to receive GPS data, signals from the two barometric sensors and an infrared horizon sensor. The second microcontroller is used to output PWM servo control signals and to control a multiplexer to switch from manual and autonomous flight. The whole developed system is shown in Figure 1.25. The main weakness to this approach is the large size of all components in relation to the aircraft; most components are mounted externally [41].

26

CHAPTER 1


Figure 1.25 Minas Gerais low cost UAV platform of the Federal University of Minas Gerais. 1.4.4.4 Paparazzi Autopilot Versions There are active and current autopilots designs from paparazzi autopilot Concept (ENAC University, France). Not all autopilots have the same capabilities, peripherals or features, but each has advantages in different applications w.r.t. the required application. Figure 1.26 shows the general architecture of the paparazzi autopilot. Currently, boards are designed around the STM32F1 series which is based on ARM architecture, there are future upgrades capabilities depend on the F2 and F4 series, giving way to feature rich processors with a variety of peripherals and speeds. Architecture-dependent

firmware code is

supported by libopencm3 Project.

Lisa , Krooz and LinAM autopilots use the STM32. The LPC21xx based boards use the LPC2148 and have been flying fixed wing and multi-rotors for many years. This architecture is more industrialized but at the expense of speed and extra ports available on the newer STM32 series processors, Tiny series, Booz, TWOG, YAPA, Umarim and NavGo autopilots all use the LPC2148. Some autopilots have also been designed for close integration with small singleboard computers; particularly those based on Open Multimedia Applications platform (OMAP) processors as Gumstix Overo series. The Lisa/L and Classix boards are designed depending on this series [40].

27

CHAPTER 1


Figure 1.26 paparrazi autopilot system Archeticture. Delft University developed the new Lisa autopilot from the concept technology of

paparazzi

autopilot

by

its

researchers.

The

autopilot

shown

in

figure 1.27 is the smallest one in the world, designed for Micro and Nano aerial vehicle

Figure 1.27 Lisa /S smallest autopilot in the world [42]. It has the main following features: 

1 UART port



1 CAN interface



Weight: 2.8g (0.1oz).



3 Axis Magnetometer



Barometer (Altimeter)



Onboard Ublox GPS



6 PWM (servo) outputs

28

CHAPTER 1




1 Bind/Boot tact switch



Size: 20mm x 20mm x 5mm (0.787" x 0.787" x 0.197").



Combined 3 axes Gyroscopes and 3 axes Accelerometers.



2 MOSFET switches connected to PWM output channels.



Pads to simply connect a Superbit CYRF RC and telemetry module.



72MHz 32bit ARM Cortex M3 MCU with 16KB RAM and 512KB Flash



Switching buck/boost converter allowing wide range of power input making it perfect and stable. From the previous discussion all the challenges in the autopilot design are

depending on the desired application but corresponding to SWaP number in mind, some of them differs in attitude determination techniques and other in GPS and pressure sensor but all of them do their job professionally.

1.5 Summary. This chapter investigated an overview about UAS; its definition, its categories and technologies. Then investigate the applications of UAVs from civilian to military applications. We investigate the methodology of designing SUAV. This chapter discussed some examples of major operated and universities research UAVs, the main benefit of this discussion and literature review about UAVs is to decide that the chosen UAV for designing the autopilot. UltraStick-25e is an airplane from Minnesota research lab of UAV is chosen because of its conventional structure and its data available. The second part of this chapter makes a brief review about AFCS with many types of autopilots. Beginning from Commercial autopilots (UAV Navigation VECTOR, Micropilot MP2x28 Series, Procerus Kestrel autopilot, Cloud Cap Piccolo series) and Open source autopilots (APM2.x Series, and OpenPilot), the comparison between the various autopilots is done by some tables w. r. t. (Physical specifications, sensor ranges, and autopilot functions). Last section of this chapter illustrated some examples of universities researches about autopilots design such as (VCU) autopilot research, AggieAir autopilot, Federal University of Minas Gerais, Brazil, and Paparazzi autopilot versions. The last autopilot Lisa /S is the smallest autopilot in the world, it's an evolution in aerospace

29

CHAPTER 1


technology, and very thanks to new Micro Electro Mechanical Systems (MEMS) technology which provides us with precise sensors managed the aerospace engineers to design this autopilot.

30

Chapter 2

SUAV Equations of Motion

CHAPTER

2

SUAV Equations of Motion 2.1 Introduction. This chapter presents the equations of motion which are used to obtain a mathematical model for a fixed wing UAV. First, introducing of the coordinate frame which is used to transfer any rigid body from frame to another, the Euler angles (

) which transfer any vector or rigid body from the inertial frame to the body

frame passing through intermediate frames for transferring. Then the Direct Cosine Matrix (DCM) is introduced. The frames extracted from the airspeed vector to represent it in the form of (u, v, w) which are the components of the air velocity vector in the body frame (ib, jb, kb) respectively, these frames are the stability frame which is rotated from the wind frame with a sideslip angle ( ), then rotate from the stability frame to the body frame with an angle of attack ( ). The airspeed vector is identical to i-axis of the wind frame. Third section states some beneficial properties of any fixed wing UAV which are used in the aircraft modeling (geometric properties, inertia, aerodynamic properties and control surfaces). Fourth section introduces a standard method for an aircraft modeling by converting it from a black box into the airframe (platform). This airframe has 12-state nonlinear equations called equations of motion, beginning from the kinematics then adding the forces and moments terms expressed in the body frame, the forces applied to the aircraft are the gravity forces, aerodynamic forces and propeller forces, these forces are represented in the body frame, then converted to the stability frame to get the Lift, Drag, and side forces, and the moments and momentum applied to the aircraft. Last section lists the nonlinear equations of motion resulted from all previous considerations.

31

Chapter 2


2.2 Coordinate Transformations. The starting point for the derivation of the equations of motion is the understanding how different bodies are oriented relative to each other. In the development of the rigid body equations of motion, we shall need to express any vector in different coordinate frames. The absolute reference frame for position vectors and other quantities is inertial space. An inertial frame can be defined as stationary. The aircraft orientation with respect to the inertial reference frame (earth absolute frame) must be considered. We also need to know how a sensor (e.g. Camera) is oriented relative to the aircraft. Mainly the understanding of coordinate rotation about several coordinate systems is required because of the following reasons [43, 44, and 45]. -

Newton’s equations of motion are derived w.r.t. a fixed inertial reference frame, however the motion is described in a body fixed frame.

-

The aerodynamic forces and torques act on the aircraft body are most easily described in a body-fixed frame.

-

On-board sensors like accelerometers and rate gyros measure information w.r.t. the body frame. Alternatively, GPS receivers provide position, ground speed, and course angle w.r.t. the inertial frame (Global Coordinates) [46].

-

Most mission scenarios, as loiter, flight track trajectory, and path planning are specified in the inertial frame.

2.2.1 UAV Coordinate Frames. In aerospace applications, we commonly need to express a given vector in terms of a new Cartesian coordinate frame, where the new frame has the same origin as the old frame, but orientation is different. In this section the various coordinate frames will be defined and described, starting with Inertial frame which is identical to vehicle frame, but the origin of the two frames are not at the same point, so they are related by translation only. The other frames are related or transferred by rotation. The angles relating the transfer from the vehicle frame to the body frame are the yaw ( ), pitch ( ), and roll ( ). These angles describe the attitude of the aircraft and commonly called Euler angles.

32

Chapter 2


The angles relating the rotation between the body and the stability frame, and Stability frame and wind frame are called angle of attack ( ), and sideslip angle ( ) respectively. All the above coordinates will be studied briefly as follows. -

The inertial frame (Fi).

-

The vehicle frame (Fv).

-

Vehicle-1 frame (Fv1).

-

Vehicle-2 frame (Fv2).

-

Body frame (Fb).

-

Stability frame (Fs).

-

Wind frame (Fw).

- The Inertial Frame (Fi). This frame is an earth-fixed coordinate. The vector ii directs to north, ji directs to east, and ki directs to the center of the earth or down. This frame is sometimes called North-East-Down (NED) frame. -

Vehicle Frame (Fv). The axes of the vehicle frame are aligned with the axes of the inertial frame, but

the origin of the frame is at the center of mass of the aircraft as in Figure 2.1.

Figure 2.1 Vehicle frame (Fv) orientation is identical to earth frame.\ - Vehicle-1 Frame (Fv1). The origin of the vehicle-1 frame (Fv1) is identical to the vehicle frame (Fv) and the frame is rotated about kv axis with the heading angle ( ) right handed is positive as in Figure 2.2.

33

Chapter 2


Figure 2.2 heading angle extracted from rotation from Fv to Fv1. - Vehicle-2 Frame (Fv2). The origin of the vehicle-2 frame (Fv2) is identical to the vehicle-1 frame (Fv1) and the frame is rotated about jv1 axis with the pitching angle ( ) right handed is positive as in Figure 2.3.

Figure 2.3 Pitch angle extracted from rotation between Fv1 to Fv2. - Body Frame (Fb). The origin of the body frame is identical to the vehicle-2 frame (Fv2) and the frame is rotated about iv2 axis with the rolling angle ( ) or called as bank angle, right handed is positive as in Figure 2.4.

34

Chapter 2


Figure 2.4 Roll angle extracted from rotation between Fv2 to Fb. The transformation matrix from the vehicle frame (Fv) to the body frame (Fb) is a function of the Euler angles (

which is described in equation (2.1) and finally

DCM matrix is described in equation (2.2). ( (

(

(

(

(2.1).

) (

) (

(

)

)

(2.2)

Where The rotation sequence

is commonly used for aerospace applications

and is just one of several Euler angle systems in use [47]. Euler angles representation suffer from a singularity (θ = ± π/2) also known as the “gimbal lock”. In practice, this limitation does not affect the fixed wing UAV in normal flight mode [48]. - Stability Frame (Fs). The stability frame is described as follows, the is-axis points along the projection of the airspeed vector onto ib-kb plane, js is identical to the jb, and the ks is constructed to make a right-handed coordinate system. To generate lift, the wings of the airframe must fly at a positive angle w.r.t. the airspeed vector. This means that (α) must be positive; the angle of attack is defined as the angle between the projection of the air velocity vector (i-axis of Stability Frame (is)) and the i-axis of the body frame (ib). The airspeed velocity (Va) is the velocity of the aircraft relative to the surrounding air.

35

Chapter 2


- Wind Frame (Fw). The angle between the velocity vector and the ib-kb plane is called the side-slip angle and is denoted by β. Figure 2.5 illustrates the angles extracted from rotation of the body frame to the stability frame to the wind frame (α, β) respectively. The total transformation matrix from the body frame to the wind frame is given by equation (2.4). ( (

(

(

(2.3)

) (

(

)

)

(2.4)

Figure 2.5 Rotation angles between the body frame and the wind frame. Note: - I, j, and k axes detonation can be called X, Y, and Z axes respectively.

2.3 Wind Triangle. The significant effect of the wind is very important in SUAV. From the wind triangle described in Figure 2.6, we can extract some relations and definitions which can be considered in the navigation of the SUAV. If the wind triangle is projected on the vertical plane, some definitions can be extracted; two main angles to transform from body frame to flight path frame (

) [49] as in Figure 2.6.The flight path angle ( ) is

the angle between the horizontal plane and the ground velocity (Vg)

36

Chapter 2


Figure 2.6 Flight path angle ( ), and course angle ( ). The direction of the traveling SUAV with respect to the ground is shown by the velocity vector (Vg). The angle between the inertial north (ii) and the velocity vector projected on the horizontal plane is called the course angle ( ). The definition of course, is the line of flight taken by an aircraft. The ground track is the projection of the line of flight onto the surface of the earth. If there is a constant ambient wind, the aircraft will need to crab into the wind. The crab angle (

is defined as the difference between the course angle and the

heading, these definitions illustrated obviously in Figure 2.7. For the existence of the wind, equation (2.5) determines the relation between airspeed (Va), ground velocity (Vg), and wind velocity (Vw). (2.5)

37

Chapter 2


Figure 2.7 Heading ( ), Crab ( ) angles, and wind triangle. Notes: In the absence of wind, -

The crab angle ( ) equal zero.

-

The sideslip angle ( ) equal zero.

-

Va =Vg.

2.4 Fixed Wing UAV Parameters. This section presents the basic used parameters of the Ultrastick-25e (thor). As discussed from the previous chapter, it has a conventional fixed-wing airframe with aileron, rudder and elevator control surfaces. The maximum deflection of servo actuators equals 25 deg. in each direction [22, 23].

2.4.1 Basic parameters of the UAV geometric. The mathematical model extracted for SUAV to be controlled must contain the aerodynamic data of the assigned aircraft. The shape of the airfoil determines its aerodynamic properties, and some of its geometrical parameters. Some of aerodynamic parameters are shown in Figure 2.8.

38

Chapter 2


FD

Figure 2.8 Section of airfoil and the applied lift (FL) and drag (Fd) forces. The chord line (c) is a straight line drawn from the leading edge to the trailing edge, the mean curved line is a line drawn from the leading edge to the trailing edge midway between the upper and lower surface. The difference between the mean line and the chord line determine the amount of camber. The shape of the upper and lower surfaces, the amount of camber, the thickness, and the leading edge radius are combined to determine the aerodynamic properties. There are other important parameters such as wing area (s) which is dependent on the shape of the wing. The wing span (b) which is defined as the distance between the wing tips of an aircraft. Aspect ratio (AR) which is important for low speed aircrafts since a high aspect ratio generates high lift at low speed. Aspect ratio determine the relation between wing span and wing area as in equation (2.6). (2.6)

2.4.2 Basic Parameters for Aerodynamics. The aerodynamics of the UAV is decomposed into longitudinal and lateral dynamics; each of them has some aerodynamic non-dimensional coefficients affect the stability of the aircraft. These coefficients are parameters in the aerodynamic forces and moments equations, and influenced by the airfoil design. These coefficients will be discussed briefly with respect to longitudinal and lateral dynamics [50, 51, and 52]. -

Longitudinal aerodynamic coefficients: The distance between Center of gravity and the aerodynamic center affects the longitudinal dynamics stability; this distance is

39

Chapter 2


changed due to the change of the load. The longitudinal motion acts in the ib-kb plane which is called pitch plane and affected by the lift force (FL), Drag force (FD), and pitch moment (m). The effectiveness of these forces and moments are measured by lift coefficient (CL), drag coefficient (CD), and pitch moment coefficient (Cm). These coefficients influenced by the angle of attack (α), pitch angular rate (q), and elevator deflection (

), but they are nonlinear in the angle of attack; For small α

the flow over the wings remain laminar. So, no stall conditions will be happened and the equations can be linearized about this linear zone as in Figure 2.9.

Figure 2.9 The lift coefficient as a function of α can be approximated by a linear function of α (dot-dashed). -

Lateral aerodynamic coefficients: the lateral motion which is responsible of the yaw and roll motions. It’s affected by the side force (fY), yaw moment ( ), and roll moment ( ). The effectiveness of these forces and moments are measured by side force coefficient (CY), yaw moment coefficient (Cn), and roll moment coefficient (Cl). These coefficients influenced by the sideslip angle ( ), yaw angular rate (r), roll angular rate (p), aileron deflection (

), and rudder deflection ( ), but they are

nonlinear in these parameters. All of these coefficients should be determined by wind tunnel. Linear approximations for these coefficients and their derivatives are acceptable for modeling

40

Chapter 2


purposes and accurate, the linearization is produced by the first-Taylor approximation, and non-dimensionalize of the aerodynamic coefficients. [51]. Notes: - Reynolds number and Mach number effects can be neglected because they are approximately constant and low due to low speed [52]. - The distance between Center of gravity and the aerodynamic center affects the longitudinal dynamics stability; this distance is changed due to the change of the load.

2.4.3 Fixed Wing UAV Control Surfaces. At first; we must know the type of the UAV that we want to design; rotary or fixed wing UAV? Everyone has its own controls to do different scenarios as takeoff, landing, loiters, and straight flight. As said earlier the designed UAV in this thesis is a standard fixed wing UAV with a standard control surfaces; the elevator, the rudder, the aileron, and the thrust

,

,

, and

respectively, the

input controls are shown in figure 2.10.

Figure 2.10 SUAV control surfaces. The positive deflection when: -

Trailing edge of the rudder goes to the left of the ib-kb plane; the moment is created about kb-axis.

-

Trailing edge of the elevator goes to down of ib-jb plane; the moment created about jb-axis.

The aileron deflection is calculated by a relation between the left and right ailerons and has a specific property; the basic principle is to modify the span lift

41

Chapter 2


distribution so that the moment is created about ib-axis. The aileron deflection can be calculated with this equation [53]. (

(2.7)

2.5 UAV Flight Dynamics. First, we will investigate decomposition of the Mechanics (kinematics, statics, dynamics and control). Kinematics is the general description of an object’s motions without regard to the forces or torques that may induce change. Statics addresses the balance of forces and torques with inertial effects to produce equilibrium. An aircraft can achieve static equilibrium when it is moving, as long as neither translational nor angular momentum is changing, this implies un-accelerated flight. Dynamics deals with accelerated flight, when momentum is changing with time. While it is possible to achieve a steady, dynamic equilibrium (as in constant-speed turning flight), the dynamics problem concerns with continually varying motions in response to a variety of conditions, such as non-equilibrium initial conditions, disturbance inputs, or commanded forces and torques [54]. This section will focus on a standard method for deriving the full nonlinear equations of motion of a fixed wing aircraft. To begin, several major assumptions must be considered [55]. First, the aircraft is rigid. Second, the earth is an inertial reference frame. Third, aircraft mass properties are constant throughout the simulation. Finally, the aircraft has a plane of symmetry. The first and third assumptions allow for the treatment of the aircraft as a point mass. In developing the equations of motion, 12-state variables are introduced which are separated as translational (3-positions, 3- linear velocities) and rotational (3-attitudes, 3angular rates) these states are related with the axes of motion. These terms is shown in Figure 2.11 are summarized as follows. First: Axes of motion. -

Lateral y-axis (rotation around this axis is done by

-

Longitudinal x-axis (rotation around it is done by

and affects the roll).

-

Vertical z-axis (rotation around it is done by

and affects the direction)

42

or

and affects the pitch)

Chapter 2


Second: 12-states of aircraft pn = the inertial (North) position of the aircraft along ii in Fi, pe = the inertial (East) position of the aircraft along ji in Fi, pd = the inertial down position of the aircraft measured along ki in Fi, u = the body frame velocity measured along ib in Fb, v = the body frame velocity measured along jb in Fb, w = the body frame velocity measured along kb in Fb, = the roll angle defined with respect to Fv2, = the pitch angle defined with respect to Fv1, = the yaw angle defined with respect to Fv, p = the roll rate measured along ib in Fb, q = the pitch rate measured along jb in Fb, r = the yaw rate measured along kb in Fb.

Figure 2.11 Definitions of UAV body velocities, forces, moments, and angular rates. The derivative of the attitudes can't be considered to be the attitude rates due to the nonlinearity of the system which make the attitudes is obtained from intermediate frames but attitude rates is in the body frame. But in some cases to approximate the linear model of the state equations, it can be assumed that they are equal.

2.5.1 Kinematics and Dynamics. The kinematics is obtained by the relations between the linear positions and velocities, angular positions (roll angle , pitch angle θ, and heading angle body frame angular rates (

).

43

) and the

Chapter 2


UAV is subjected to external forces and moments due to gravity, propulsion, and aerodynamics, after applying the newton’s second law for translational motion, the applied forces are combined and expressed in the body frame due to equation (2.7). (

)

(2.7)

For rotational motion, the applied moments are combined and expressed in the body frame as in equation (2.8). For moments, (

(2.8)

And momentum which is defined as the product of inertia matrix j and the angular velocity vector, due to symmetry of the aircraft about the plane ib-kb, the only inertia used in the modeling is jx, jy, jz, and jxz, however jxy = jyz = 0 because of symmetry of aircraft. We have obtained six degrees of freedom 12-state. The modeling of the forces and moments can be utilized to get finally the nonlinear 12- state equations of motion. The gravity (fg), aerodynamic (fa), and propeller (fp) forces are the composition of the total forces applied on the body frame (

). Aerodynamic (ma), and

propeller (mp) moments are the compositions of the total moments applied on the body frame (

), there are no moments produced by the gravity. These forces will be

represented in the stability frame to get FL, and FD [56].

2.5.2 Atmospheric Disturbance. At the existence of wind, the atmospheric disturbances can be modeled with its two components (steady ambient wind, and wind gusts); the steady ambient wind is modeled as a constant wind field, the wind gusts is modeled as a turbulence which is generated by passing white noise linear time invariant filter, the Dryden gust model approximations considered in the modeling as MIL-F-8785C [57].

44

Chapter 2


2.6 The Final Form Nonlinear Equations of Motion. After this brief discussion about the flight dynamics and modeling of the fixed wing aircraft, we will get the equations of motion for UAV which are fairly complicated. Set of 12 nonlinear, coupled, first-order and ordinary differential equations. We get the following equations of motion [52]. ( ̇

(

( (2.9)

( ̇

(

( (2.10)

̇

(2.11) ̇

[

(

(

(

]

(

(2.12)

̇

[ ]

(2.13)

̇

[

(

(

(

]

(2.14)

̇

(2.15)

̇

(2.16) ̇

(2.17)

̇

[

] (2.18)

̇

̇

(

[

]

[

(2.19) ] (2.20)

45

Chapter 2


Notes: -

The lift and drag terms is nonlinear in (α),

-

The propeller thrust is nonlinear in the throttle command.

-

For small angle of attack a linear relation can be approximated.

As we interested in modeling UAV flight under low angle of attack conditions, so simpler linear model can be utilized and approximated as seen in Figure 2.9 for: ( ( By these above 12 equations we have described the dynamic behavior of the UAV in response to inputs (throttle, aileron, rudder, and elevator). These equations are the core of the UAV simulation nonlinear model. The Euler-angle representation of attitude is preferred than the quaternion for the reduced-order. Furthermore, the gimbal-lock singularity is far removed from the flight conditions that will be considered subsequently, and thus will not cause issues with the models to be developed. At the end of this standard section, the 12- state equations of motion can be utilized. These equations are nonlinear and will be linearized, then evaluating the new linear model by making the comparison between the nonlinear and linear model.

2.7 Summary. This chapter is considered as the first part of SUAV modeling which extracts the nonlinear equations of motion. To understand how these equations are derived we must recognize some concerned features; these features compromise the various sections of this chapter. Euler angles are extracted from the coordinate transformations from inertial frame to the body frame. Angle of attack and sideslip angles are extracted from rotations between wind frame and body frame. Wind triangle is very important in the navigation and wind speed considerations. Fixed wing UAV parameters are considered important components of the derivation, these parameters includes geometric parameters, aerodynamic parameters and control surfaces of SUAV.

46

Chapter 2


Forces and moments applied on the aircraft due to gravity and aerodynamics and thrust are included. Atmospheric disturbances must be considered. All of the previous considerations are used to extract the 12- states SUAV nonlinear equations of motion. The second part of the modeling is continued in chapter 3 to extract the linear model of Ultrastick-25e which is used in the autopilot design.

47

Chapter 3

Linear Model of SUAV (Ultrastick-25e)

CHAPTER

3


3.1 Introduction. The main task of this chapter is the linearization of the nonlinear state equations of motion about an equilibrium point (trimming). Investigating how to calculate the trimmed values according to the steady state flight condition, dynamic equations will be decomposed into two separated groups one for longitudinal dynamics, another for lateral dynamics. The linearization technique will be applied on Ultrastick-25e for every group separately to derive a linear state space model for longitudinal motion (Alon, Blon, Clon, Dlon), and a linear state space model for lateral motion (Alat, Blat, Clat, Dlat) according to straight and leveling flight trim conditions. A novel analytical linearization technique for aircraft states are derived step by step to get the linear state equations. To evaluate the resulted model, a comparison between the behavior of nonlinear and linear models will be done by applying many different types of signals as a reference and check the response to analyze the matching between the two models. Model linearization is based on a small disturbance theory. According to the theory; analysis is done under small perturbations of motion characteristics [58]. SUAV equations of motion will be decoupled and linearized to produce a reduced linear transfer functions or state space models describing the nonlinear UAV airframe. Inner and outer control loops of autopilot for SUAV will be designed using This Linear Time Invariant (LTI) system.

48

Chapter 3


3.2 Equilibrium Point and Steady State Flight. Aircraft modeling is so amazing, but with some difficulties. We must decompose the dynamics, and bring the model under control by finding a combination of values of the state and control variables that correspond to a steady-state flight condition [44], then analyzing the dynamics of the aircraft about steady state scenarios or equilibrium points; actually is called trimming technique. The linear equations will be derived by taking a more general approach, starting with implied state equations in the general form. ( ̇

)

Where f is a vector of n elements nonlinear functions The linearization is done at the condition which makes ̇

or constant.

With these conditions the system is called to be at rest (all derivatives are equal to zero), then examine the behavior of the system near the equilibrium point by slightly perturbing some of the variables. Steady state aircraft flight can be defined as a condition in which all of the motion variables are constant or zero. The following assumptions will be considered: -

Flat earth.

-

The mass of the aircraft is constant.

-

All acceleration components are zero.

-

Linear and angular velocities are constants or zero.

-

Neglecting of the change of atmospheric density due to altitude.

This definition is available for some aircraft basic scenarios [44]. -

Steady wings level flight.

-

Steady turning flight.

-

Steady wings level climb.

-

Climbing turn.

For steady state flight: ̇ ̇ ̇ ̇

̇

̇

̇

49

̇ ̇

Chapter 3


With the following additional constraints according to the flight condition: 1-

Steady wings level flight: ̇ ̇

2-

̇

Steady turning flight: ̇ ̇

3-

Steady pull-up flight: ̇

4-

̇

̇ ̇

Steady climbing turn: ̇

̇ ̇

Figure 3.1 illustrates the flowchart or the procedures for the rigid body to a suitable linear model.

Figure 3.1 Basic linear state space model derivation flowchart for simulation. For a fixed wing UAV: The states are: The inputs:

. .

The problem is how actually calculating the states and control surface deflections that satisfy the required scenario. It must be done by numerical algorithm which iteratively adjusts the independent values till a solution criterion is met. The solution is an approximation but close to the exact solution, it may not be unique.

50

Chapter 3


The general trim program executes to the nonlinear model and produces a file containing the steady state values for the states and control inputs for use in the linearization. We must know how to specify the steady state condition; how many of the state and control variables may be chosen independently, and what constraints exist on the remaining variables. In the process of performing trim calculations for SUAV the wind effects is treated as an unknown disturbance, so the wind speed is assumed to be zero. The trim calculation algorithm output trim states and inputs values according to the steady state condition [59]. 3.2.1 Trimming Algorithm for Ultrastick-25e. The main task of the algorithm is to assign the trimmed value for some parameters due to various flight conditions. These parameters are used in the transfer functions and state space models for lateral and longitudinal dynamics. The algorithm [22] is programmed and executed by using MATLAB program as follows. 1- Initial condition assignment for inputs and states. 2- Specify the flight conditions. 3- Create an operating point object for the simulation. 4- Trim the aircraft, according to a specific flight condition. We will state these steady state flights according to Ultrastick-25e as follows. a- Steady Straight and Level flight.

b- Level Climb.

c- Level Turn. ̇ d- Climbing Turn. ̇

51

Chapter 3

Linear Model of SUAV (Ultrastick-25e) e- Level steady heading sideslip.

So the trimmed outputs and controls are summarized in Table 3.1 which represents a set of trimmed conditions for the Ultrastick-25e model. These values will be used to get the numerical lateral and longitudinal state space models, and then used in the autopilot simulations as initial values according to the desired flight scenario. Table 3.1 Trimmed flight conditions for Ultrastick-25e (Thor). A 0.569 -0.0963 0.00317 0.01 17 3.72*10-22 0.054 100 -0.00172 0.054 2.71 5.09*10-27 -7.56*10-23 -1.03*10-24 -9.8*10-17

B 0.721 -0.102 0.00436 0.0138 17 3.56*10-25 0.0529 Don’t care -0.00239 0.14 2.71 5.21*10-28 1.12*10-26 -8.32*10-28 0.0873

C 0.582 -0.125 -0.00748 0.0186 17 -1.51*10-20 0.0646

D 0.731 -0.131 -0.00607 0.0253 17 5.8*10-20 0.0633

E 0.577 -0.0983 0.0301 -0.0174 17 0.0873 0.0561

0.544 0.0553 2.71 -0.0193 0.181 0.298 -1.23*10-09

0.547 0.141 2.71 -0.0492 0.18 0.295 0.0873

0.116 0.0659 2.71 1.53*10-21 1.6*10-21 -5.5310-22 2.73*10-12

3.3 Linear State Space Model. This section derives the linear state-space models for both longitudinal and lateral motions by linearizing non-linear equations of motion about trimming conditions according to Figure 3.1. After obtaining nonlinear 12-state equations of motion from chapter 2 and obtaining the trimmed value of different flight conditions at this chapter; we will search and make a linearization technique to linearize the equations. Finally, the state space models for longitudinal and lateral dynamics are obtained. Calculating the Jacobian matrices for LTI equations directly from the nonlinear model are done by assigning the state and control variables from the steady state conditions, and numerically evaluating the partial derivatives in the Jacobian matrices. The Jacobian matrices may therefore be determined for any steady state flight condition [60]. The linearization is done to determine A, B, C, and D of the state space model.

52

Chapter 3


Finally, longitudinal state space model and its reduced order modes including the short-period and the phugoid are described.

Then the lateral model with its roll,

dutch-roll, and the spiral-divergence modes are described. 3.3.1 Historical Perspective for Linear State Space Models. In early 1897, Fredrick Lanchester was studying the motion of gliders. He concluded that his glider fly along a straight path if they were launched at “natural speed”. Launching it at a lower speed or higher speed will cause oscillatory motion. He also found that if the glider at natural speed, then disturbed from its flight path, the glider will begin to oscillate along its flight trajectory. Lancaster called the oscillatory motion as the “phugoid motion”. This word means in Greek “to fly”. The term “phugoid” is still used to describe the long period slowly damped ((zeta=0. 01, .06, .1, etc.). At step response the curve is oscillating about the value oscillations associated with the longitudinal motion of an airplane [61, 62]. Then Brian took on his mind the consideration and the results of the Lanchester experiments and made a significant contribution to the analysis of the vehicle motions, he recognized that the equations of motion can be separated into symmetrical longitudinal motion and an unsymmetrical lateral motion, but his actions were too complex to be analyzed [63]. Bairstow and B. M. Jones of National Physical Laboratory (NPL) in England made researches to determine estimates of the aerodynamic stability derivatives used in Bryan’s theory. In addition of determining stability derivatives from wind-tunnel tests of scale models is achieved. Bairstow and Jones non-dimensionalized the equations of motion and showed that, with certain assumptions, there were two independent solutions (one longitudinal and one lateral). At the same time Jerome Hunsaker and his group at Massachusets institute of technology (MIT) were continued wind tunnel studies of scale models of several flying airplanes. In the late 1930s national advisory committee of aeronautics (NACA) conducted an extensive flight test program with the pilot’s opinion of its handling characteristics. These experiments were the foundation of the modern flight researches. In 1943 NACA published a list of specifications which could be used in designing an airplane. If the

53

Chapter 3


design complied with the specifications, that’s sure the airplane would have a good flying qualities [63]. 3.3.2 General Linearization Technique. From the beginning, a brief discussion about linearization technique is introduced. Given the general nonlinear system equation (3.1) is the root of the derivation. ̇

(3.1)

….. The state and ….. The control vector. ̇ ……… Trim state ……… Trim input Let

̅ ̇̅ ̇

̇

= = ̅

=

̅

Using the Taylor series expansion technique for the first term about the trim state, we get: ̇̅ ̅ ̅

̅ ̅.

(3.2)

According to equation (3.2), the linearized dynamics are determined by finding evaluated at the trim conditions. 3.3.3 Longitudinal State Space Model. Due to the complexity of the full linear model to be analyzed, the dynamics of aircraft are normally separated into two decoupled; one of the longitudinal axis and another for the lateral-directional axes. The longitudinal state equations are given by:

54

Chapter 3

Linear Model of SUAV (Ultrastick-25e) ̇

And the input (control) vector is defined as:

Expressing equations (2.12), (2.14), (2.19), (2.16), and (2.11) in terms of and

, Assuming that the lateral states are zero (i.e., φ = p = r = β = v = 0) and the

wind speed is zero. Jacobian matrices are given by: ̇

̇

̇

̇

̇

̇

̇

̇ ̇

̇ ̇

̇

(

̇ ̇

̇

̇ ̇

̇

̇

̇

̇

̇

,

̇ ̇

̇

̇

̇ ̇

̇

̇ ̇

̇ ̇

)

̇

(

̇

)

By calculating the derivatives, the following linearized state-space equations are resulted. ̅̇ ̅̇ ̅̇ ̇̅ ( ̅̇ )

̅ ̅ ̅ ̅ ) (̅)

(

( (

̅ ̅

)

)

Equation (3.3) is the longitudinal state space model with Alon and Blon matrices where there coefficients are given in Table 3.2 [44, 52, 45, 64].

55

Chapter 3


Table 3.2 Longitudinal state space model coefficients. Lon. Coeffs.

The formula [

]

1

[

]

2

3 4 5 6

[

]

7

[

]

8 9 [

]

[

]

10

11

12 13

56

Chapter 3


The longitudinal equations are often given in terms of α instead of w from the following equation we have:

Where we assume β = 0 due to its smallness, the second assumption that the linearization algorithm about the trim condition (straight wings level), so the equation will be the following form. ̅̇

̅̇

Hence the linearized ̅̇ can be obtained from equation (3.4). ̅̇

̅̇

3.3.3.1 Longitudinal Model for Ultrastick-25e. State space longitudinal model has 5 States ( (

), and seven Outputs (

, two Inputs ). The longitudinal linear state

space model is SYSlon which has (Alon, Blon, Clon, Dlon).

(

)

(

)

(

)

Dlon

57

Chapter 3


The eigenvalues can be determined by finding the eigenvalues of the matrix Alon |

|

Longitudinal Poles are listed in Table 3.3. Table 3.3 Poles of the longitudinal state space linear model. Eigen value -0.159 ± 0.641i -11.7 ± 10.0i

Damping 0.241 0.759

Frequency

The mode phugoid short period

0.66 15.4

) response due to ̅ input represented

- The linearized outputs (

in polynomial form as in equations (3.5), (3.6), (3.7), (3.8), (3.9), (3.10), (3.11). ̅̅̅̅ ̅

.

̅ ̅

(3.5) .

̅ ̅

(3.6) .

̅

(3.7)

̅

.

(3.8)

̅ ̅

.

(3.9)

̅̅̅̅ ̅ ̅̅̅̅ ̅

.

(3.10)

.

(3.11)

3.3.3.2 Longitudinal Reduced Order Modes. The traditional literatures on aircraft dynamics and control define several openloop aircraft dynamic modes. These include the short-period mode, and the phugoid mode for longitudinal dynamics. The classical phugoid and short-period aircraft modes are derived from the longitudinal linear state space model resulted above. The eigenvalues of the state matrix have some considerations; it was found that there are two parts (two modes); the first part is fast and damped mode (short period mode) and the second part is slow and lightly damped mode (phugoid mode). The system can be separated into two approximated modes to be likely familiar with the analysis. We assume (h = const. and

).

58

Chapter 3


- Short Period Mode. This approximated mode is effective. It's assumed that maintaining

changes while

constant, so u is constant due to the constant aircraft speed so: ̅̇

̅ Notes:

1- The short period mode is fast response (Ts=1/f) and damped ( =0.761). 2- The short period mode is well damped and fast response, so that the aircraft response to the elevator commands is acceptable. - Phugoid Mode (Long Period). The long period mode is characterized by changes in pitch attitude, altitude, and velocity at nearly constant α for level flight ̅

̅̇ α= α*

Notes: 1- The long period (phugoid) mode is slow response (Ts=1/f) and lightly damped ( = 0.241). 2- To improve the damping of the phugoid motion, the designer of the airframe should reduce the lift-to-drag ratio (L/D) of the airplane [65]. But it may be found that the choice is unacceptable and would look for another alternative, such as an automatic stabilization system to provide the proper damping characteristics. 3.3.4 Lateral State Space Model. Lateral directional equations of motion consist of the side force, rolling moment and yawing moment equations of motion. For the lateral state-space equations, the state is given by: ̇ And the input (control) vector is defined as:

Expressing equations (2.13), (2.18), (2.20), (2.15), and (2.17) in terms of

, we get The Jacobians of equations are given by

59

Chapter 3

Linear Model of SUAV (Ultrastick-25e) ̇

̇

̇

̇

̇

̇

̇

̇

̇

̇ ̇

̇

̇

(

̇

̇ ̇

̇

̇

̇

̇

̇

̇

̇

̇ ̇

̇

, ̇

̇

̇

̇

)

(

̇

̇ ̇

̇

̇

)

By working out the derivatives, and assuming that jxz = 0, the equations of motion reduced to be the following linearized state-space equation (3.12) as follows [52]. ̇̅ ̇̅

̅ ̅ ̅ ̅ ) ( ̅)

̇̅ ̅̇ ( ̅̇ )

(

( (

̅ ̅

)

)

Lateral state space coefficients are listed in Table 3.4

60

Chapter 3


Table 3.4 Lateral state space model coefficients [52]. Lat. Coefficients

The formula *

1

+ √

2

3

4

5

* 6

+

√

7 8 9 10 * 11

+

√

12 13

61

Chapter 3


Table 3.4 to be continued Lat. Coefficients

The formula

14

15 The lateral equations can be in terms of ̅ Instead of ̅

Linearizing around

, this implies the equation (3.13). ̇̅

̇̅

3.3.4.1 Lateral Model for Ultrastick-25e. The lateral-directional model has five state six outputs

, two inputs

, and

. The lateral state space model is SYSlat with (Alat, Blat, Clat,

Dlat).

(

)

(

)

(

)

Dlat

62

Chapter 3


The null column in the Alat matrix shows that the state

is not coupled back to

any other states, and it can be omitted from the state equations when designing the Stability Augmentation System (SAS). The eigenvalues can be determined by finding the eigenvalues of the matrix A. |

|

Lateral-Directional Poles are listed in Table 3.5. Table 3.5 Poles of the lateral state space linear model. Eigen value - .0138 - 1.84 ± 5.28i - 16.1

Damping 1.00 0.329 1.00

Frequency 0.0138 5.59 16.1

The mode spiral mode Dutch roll Roll mode

In general; it was found that the roots of the lateral-directional characteristic equation composed of two real roots and a pair of complex roots. These roots will characterize the airplane response. The linearized outputs (

) response due to

̅ input are the equations

(3.14), (3.15), (3.16), (3.17). ̅

(3.14)

̅ ̅

(3.15)

̅ ̅

(3.16)

̅ ̅

(3.17)

̅

And the linearized outputs (

) responses due to

̅ input are the equations

(3.18), (3.19), (3.20), (3.21): ̅

(3.18)

̅ ̅

(3.19)

̅ ̅

(3.20)

̅ ̅

(3.21)

̅

63

Chapter 3


3.3.4.2 Lateral Reduced Order Modes. Lateral motion of an airplane disturbed from its equilibrium state is a complicated combination of rolling, yawing, and side slipping motions. There are three lateral dynamic instabilities of interest to the airframe designer; roll subsidence, spiral divergence, and Dutch roll oscillations [65]. - Roll Mode Approximation. From the linear state space lateral model in equation (3.12), equation (3.22) can be extracted from 2nd state we can get ̅̇ Equation as follows: ̅̇

̅ ̅

̅ ̅

̅

(3.22)

By assuming that ̅

̅ ̅

The roll moment equation will be ̇̅

̅ ̅

Then the transfer function is therefore ̅

̅̅̅

(3.23)

From equation (3.23), the eigenvalue

A highly convergent motion, called the rolling mode. Is usually highly damped and will reach the steady state rapidly, the mode stability depends on the choice of value in the design. -

Spiral Mode Approximation. The airplane enters a gradual spiraling motion. The spiral becomes tighter and

steeper as time proceeds and can result in a high speed spiral if the correct action is not taken. Directional divergence can be occurred when the airplane doesn’t possess directional stability; it can rotate increasing the side slip angle. The undesired motion can be avoided by the proper design of the vertical tail surface to ensure directional stability. This mode is naturally unstable. By assuming roll rate equal zero

64

Chapter 3

Linear Model of SUAV (Ultrastick-25e) ̇̅ ̅ ̅

From the linear state space lateral model in equation (3.12), equation (3.24) can be extracted from 2nd and 3rd state equations; so the transfer function of ̅ from ̅ is in the following equation:

̅

(

̅

) (

(3.24)

)

Eigenvalue is the pole of the characteristic equation

The stability derivative

(

) and

usually negative quantities. On the other hand,

(

), are

(

) and

are generally positive quantities. If the derivatives have the usual sign, then the condition for a stable spiral mode is:

Increasing the dihedral effect

or yaw rate damping

can be used to make the

spiral mode stable [66, 67, and 68]. - Dutch roll mode Approximation. The Dutch roll oscillation is a combination of rolling and yawing oscillations. Its period is from 3 to 15 seconds, so that if the amplitude of the disturbance is appreciable the motion can be very annoying. Its motion can be expressed as weaving motion of an ice skater. It’s a lightly damped oscillatory motion having a low frequency [08]. Hence its dependence mainly on side slipping and yawing motions, so we can neglect the rolling moment equation. From the linear state space lateral model in equation (3.12), equation (3.25) can be extracted. ̇̅ ( ) ̇̅

(

̅ )( ) ̅

65

(

) ̅

(3.25)

Chapter 3


The characteristic equation will be given by the following formula. |

|

The characteristic equation is

The poles of the Dutch roll mode are approximated by √(

)

Equations (3.26) and (3.27) are the transfer functions of ( ̅ ̅ ) by input (̅̅̅) respectively. ̅ ̅̅̅ ̅ ̅̅̅

3.4 Validation of Aircraft Model Linearization. After getting the model, the evaluation of the model can be done by checking the Ultrastick-25e (thor) longitudinal dynamic response to (elevator) deflection and lateral dynamic responses to (aileron, rudder) deflections of linear and nonlinear models. A doublet pulse signal (it's a symmetric pulse about its reference level (the trim setting)) will be applied to the control inputs to see the response of the various outputs. 3.4.1 Doublet Response of the Linear and Nonlinear Longitudinal Model. The longitudinal dynamics (

) of the linear model and nonlinear

model due to Doublet signal of the control input ( ) are shown in the following Figures 3.2, 3.3, 3.4 and 3.5.

66

Chapter 3

Figure 3.2 Response of (


) of Ultrastick-25e model due to elevator doublet (trim±5 degree).

Figure 3.3 Response of (

) of Ultrastick-25e model due to elevator doublet (trim±5 degree).

67

Chapter 3


Figure 3.4 Response of (ax, az) of Ultrastick-25e model due to elevator doublet (trim±5 degree).

Figure 3.5 Response of (h) of Ultrastick-25e model due to elevator doublet (trim±5 degree). From the above figures, the comparison between longitudinal states in linear and nonlinear models is much closed with very small not effective errors existed in a few places in the time axis. These errors are listed in Table 3.6. Table 3.6 Maximum error existed in the longitudinal dynamics comparison between linear and nonlinear models.

State Airspeed Pitch angle Angle of attack Pitch rate x-axis (body) acceleration z-axis (body) acceleration

Symbol va θ α q ax az

Errors 0.20 m/s 0.40 deg. 0.05 deg. 1.00 deg./s 0.45 deg./s2 1.50 deg./s2

68

Chapter 3


3.4.2 Doublet Response of the Linear and Nonlinear Lateral Model. Doublet response of the lateral dynamics (

) response due to

of

the linear model and nonlinear model are shown in the following Figures 3.6, and 3.7.

Figure 3.6 Response of the lateral dynamics

due to 5 degree (aileron, rudder)

deflection doublet signal.

Figure 3.7 Response of the lateral dynamics

due to doublet trim±5 degree

(aileron, rudder) deflection doublet signal.

69

Chapter 3


From the above figures, the comparison between lateral states in linear and nonlinear models is much closed also as longitudinal with very small not effective errors existed in a few places in the time axis. But we have some considerable errors existed in yawing due to (rudder) deflection. All the lateral states errors are listed in Table 3.7. Table 3.7 Maximum error existed in the and nonlinear models. State Symbol Side slip angle β Roll rate p Yaw rate r Roll angle φ Yaw (heading) angle

lateral dynamics comparison between linear Errors in aileron 0 deg. 0 deg./s 0 deg./s 0 deg. 2 deg.

Errors in rudder 0 0 0 1 10

3.5 Analytical Linearization of Roll and Roll Rate. For lateral dynamics, the interested variables are (β, p, , r, control surfaces are (

) and the interested

). The roll and roll rate transfer functions can be extracted

from the nonlinear equations of motion as follows: First: roll or bank angle ( ) Equation (2.15) can be considered to be linearized from this main assumption which is logic for most flight conditions; the pitch angle ( ) is a small this means that the primary influence on ̇ equation is the roll rate (p) as in equation (3.27), so ̇

(3.27)

Second: differentiate the above equation we get: ̈ ̇

̇

Third: substitute ̇ by equation (2.18) and the equation (3.27) we will get the equation (3.28) as follows: ̈

̇

(3.28)

Where: -

Are the coefficients of the roll dynamics, they are variables in the aircraft parameters and the trimmed values.

-

Can be considered as a disturbance on the system.

Fourth: by taking a Laplace transfer to the equation (3.28) the result is as follows:

70

Chapter 3


(

)

(

)

Fifth: the final numerical transfer function of roll ( ) for

as input is the equation

(3.29) as follows:

Sixth: roll rate (p) can be approximately considered as the differentiation of the roll angle as in equation (3.30).

Comparison between the analytical linearization and state space linearization is shown in Figure 3.8.

Figure 3.8 Comparison Response of the lateral dynamics

due to doublet (trim±5

degree) aileron deflection between Jacobian and analytical linearization. From Figure 3.8, the error in the matching of the roll and roll rate between analytical linear model and state space linear model is much closed. This error not exceeds than 5 deg. in the region of change of aileron deflection sign.

71

Chapter 3


3.6 Summary. Chapter three talks about the linearization of SUAV Equations of motion. It's beginning with assigning the trim values of the aircraft by a trimming algorithm; the trim values are changed according to the desired flight scenario. The nonlinear state equations are decoupled into longitudinal and lateral dynamics which are ( (

)

) respectively. Longitudinal state space model coefficients (Alon, Blon, Clon,

Dlon) are derived and the lateral (Alat, Blat, Clat, Dlat) too. The evaluation of the linear model is done by applying a doublet response test to the open loop states of linear and nonlinear models; the matching between them is too close. By applying doublet signal test it can be decided that the linear model is accurate to design the autopilot of the Ultrastick-25e. At the end of the chapter, an analytical linearization of the roll and roll rate is done and checked also with the nonlinear model to be used in the autopilot design.

72

Chapter 4

Autopilot Design and Simulation

CHAPTER

4

Autopilot Design and Simulation 4.1 Introduction. In general terms, the autopilot is a system used to guide an aircraft without the assistance of a pilot. For manned aircraft, the autopilot can be as simple as a single axis wing-leveling autopilot. A full complete complicated autopilot as a full flight control system that controls the position (altitude, latitude, longitude) and attitude (roll, pitch, yaw) during the various phases of flight (e.g., take-off, climbing, level flight, descent, landing, and loiter). This chapter presents the design of the whole autopilot (lateral and longitudinal) of SUAV. The designed autopilot is applied to an Ultrastick-25e UAV depending on state space linear models (lateral and longitudinal) and analytic linear model of a coordinated turn derivation with trimmed values of a straight and leveling scenario. The lateral motion controller design starts with the design of the most inner loop (roll rate feedback / roll damper) of the lateral system, then roll tracker design with a Proportional Integral (PI) controller. The guidance and control system is related to the design of heading direction controller with Proportional (P) controller. Yaw damper is designed with the washout filter to maintain a zero sideslip angle. The second part of the autopilot design is the design of the longitudinal motion controller. The longitudinal motion controller design starts with the design of the most inner loop (pitch rate feedback / pitch damper) of the longitudinal system, then pitch tracker design with PI controller. The guidance

73

Chapter 4


and control system is related to the design of altitude hold controller with Pcontroller as an example of outer loop controller design. The performance of two classic controller approaches for the design of the autopilot are compared and evaluated for both linear and non-linear models. The designed one is chosen in design due to its higher performance than the first one.

4.2 Automatic Flight Control System (AFCS) (Autopilot) Design. Autonomous

UAVs

are

located

in

a

particular

interest

to

many

researchers around the scientific society, as they are relatively inexpensive, offer the ability to address a plenty of autonomous flight research applications that once seemed out of reach. The more autonomous ability of UAV, the more complex its guidance and control system, advanced guidance algorithms development are essential and necessary for meeting new requirements with increasing the area of UAV applications and for future UAV concepts and associated critical technologies. SUAV control and stabilization is more difficult than a larger one due to several factors including the low mass of the vehicle, lower Reynolds numbers, and light wing loading. These factors make it more difficult to design a flight control system [69]. Automatic

Flight

Control

System

(AFCS)

presents

a

very

complete

treatment of UAV control and related technologies. The inherently unstable nature

of

typical

open

loop

UAV

configurations

necessitates

a

rigorous

approach to the analysis and design of UAV control systems, as well as a thorough understanding of stability issues. The complete state of the UAV comprises its position, airspeed (Va), attitudes (roll (

), angle-of-attack ( ), sideslip angle ( ),

and attitude rates (roll (p), pitch (q), and yaw (r)). Position, airspeed, and attitudes are also known as the navigation states [70]. Control on these states provides full control on the vehicle movements with six degrees of freedom. The requirements of control are to ensure that the dynamics are “fast” and to ensure that the oscillations die out quickly, and also the requirements on

74

Chapter 4


a good tracking of command input with minimum steady state errors. Since the open-loop dynamics of the vehicle rarely satisfy these requirements. So, the typical approach is to use linear and nonlinear feedback control to modify the pole locations and loop gains [71]. MATLAB is one of the most important software programs used in aircraft autopilot design. From the beginning; the aircraft modeling, designing of an autopilot, evaluating the performance of an accurate autopilot in linear and nonlinear models, Software in the Loop (SIL) Simulation, and processor in Loop, and at last Processor In the Loop (PIL) Simulation. Root Locus technique and Conventional PI and Proportional Integral Derivative (PID) controllers

are

used

to

design

the

autopilot

and

hence

to

improve

its

performance characteristics. By converting Multi Input Multi Output (MIMO) linear model of aircraft into a Single Input Single Output (SISO) transfer functions which can be controlled by appropriate P, PI or PID controllers [72, 45, and 73]. The desired Pole-Zero locations affect the stability of the system by a varied gain which can be observed by root locus plot. For SUAVs, the autopilot is in complete control of the aircraft during all phases of flight. The design of the autopilot is separated into two separate motion controllers express the longitudinal and lateral motion controllers [74]. Autopilot

is

designed

from

the

linearized

Ultrastick-25e (Thor) [75]. For the longitudinal dynamics

model

of

(forward speed,

pitching, and climbing / descending motions) are considered. For the lateral dynamics (rolling, and yawing motions) are considered also. This design concept simplifies the development of the autopilot with accurate results. The whole autopilot is designed, beginning with the design of the longitudinal motion controller of SUAV (longitudinal autopilot), then lateral motion controller. Longitudinal and lateral states can be represented by various transfer functions of UAV. Unit-step, doublet response, noise effect, and ability to disturbance rejection tests are executed to check the performance of autopilot in linear and nonlinear models.

75

Chapter 4


4.2.1 Longitudinal Motion Controller Design. The inner and outer loops of longitudinal autopilot are designed to achieve

the

tracking

command

requirements.

For

historical

successfulness

Several design requirements for inner loop performance that the closed loop rise time should be less than 1 Second, and the overshoot has to be smaller than 5% in outer loop, but in pitch attitude is in between 7% to increase the response and decrease the settling time. The achievement of above requirements assured the successfulness in Ultrastick-25e flights. Proportional-Integral

blocks

for

the

inner

loop

controller,

while

for

attitude rates a non-unity feedback is introduced (dampers). For outer loops controllers, a proportional gain is chosen for altitude controller, and for a cruise speed controller PI-controller is used. If the integral term of controller causes overshoot that degrades its performance causing coming out of saturation, an anti-windup scheme is implemented to check the saturation of the actuator on the current time step, if this case is happened, an anti-windup algorithm stop the integration [76]. The throttle commands go directly to the aircraft model without any modification of the inner loop. Pitch angle ( ) has to remain between 20◦. Throttle command is limited between the range of 0 and 1. Elevator and throttle is the inputs for the longitudinal motion controller. The elevator is used to control inner loops (pitch , and pitch rate q) and outer loop height (h), while the throttle ( ) is used in the outer loop to control vehicle speed [77]. The closed loop longitudinal autopilot is executed in two stages. First, the inner pitch tracked is designed, and second is altitude hold controller and cruise speed controller. These stages are illustrated in Figure 4.1.

Figure 4.1 Longitudinal autopilot block diagram.

76

Chapter 4


The response of the altitude loop (outer loop) is simulated by climbing scenario to the desired altitude (h), and then executes the scenario of straight and leveling flight. The response of the velocity loop is simulated with the same manner. From SIL stage, PID structure outlined in the design of longitudinal motion controller can adequately control the altitude and velocity of the aircraft to achieve the guidance and control system. 4.2.1.1 Pitch Attitude Tracker Design. The design of the pitch damper is the most inner loop of the longitudinal motion controller (Stability Augmentation System (SAS)), this is done to provide satisfactory natural frequency and damping ratio for the short period mode. This mode involves the variable pitch rate, and feedback of it to the elevator control to provide a good natural frequency and damping. Pitch rate feedback provides virtually a complete control of position of the short period poles. The closed loop of this most inner loop has an actuator and gyro sensor illustrated in Figure 4.2.

δe

+ -

Elevator Servo

Aircraft dynamics

Rate gyro

q

kd_q k Figure 4.2 MATLAB structure of pitch damper. The linearized transfer function of (q/δe) is fed back and the root locus technique can be applied to determine the effect of gain kd_q. The approximated short period transfer function is in Equation (4.5): (4.5) The Eigenvalues are (-11.7 ± 9.97i) with damping ratio ξ = 0.761 and natural frequency wn = 15.4 rad/sec. The value of damping ratio is too good but the effect of actuator will get the response slower, so the choice of the gain is to increase the damping [78]. Figure 4.3 illustrates that the chosen gain

77

Chapter 4


kd_q = -0.065, this gain increases the damping and shift the poles to the left hand side plane. This value is the best value after the test of the whole longitudinal autopilot, increasing this value make ripples in the response. Finally it must be noted that the feedback gain is negative, this means that an increasing of pitch angle gives the elevator a positive displacement. Alpha feedback is designed under the condition of the existing of right hand pole [44], so a desirable short period poles location is achievable with pitch rate feedback only.

Figure 4.3 Most inner loop root locus of pitch tracker. The second inner loop is Pitch attitude controller. This controller can be used when the plane is in wings level flight or climbing, the main job of pitch tracker or pitch attitude hold is to maintain the value of pitch attitude (θ) matched with the reference commanded pitch. The design can be performed using the short period approximation for aircraft dynamics, then adding an integrator to approximately obtain pitch from pitch rate. PI controller is used to determine the values of kp_θ, ki_θ. P controller alone is not sufficient due to some steady state error ( constant disturbance) resulting from the coupling between pitch attitude (θ) and pitch rate (q), it can be eliminated by adding integrator, so PI controller is used.

78

Chapter 4


Determining the values of gains depend on the concept Ziegler-Nichols tuning method as initial values, then by fine tuning; the exact values of gains are obtained to make a good pitch tracking as seen in the results.

Figure 4.4 MATLAB structure of pitch attitude hold controller. Figure 4.4 shows the simulated linear Simulink for pitch tracker. With the aid of MATLAB, the designed new parameters assured that performance of the attitude tracker is better than the assigned parameters used in the simulated program of the research group of Minnesota University [22]. The

Minnesota

parameters

are

(Kd_q =

-0.08,

kp_θ

=

-0.84,

and

ki_θ = -0.23), and the second is the designed one (Kd_q = -0.065, kp_θ = -1.1, and ki_θ = -0.8). 4.2.1.2 Pitch Attitude Tracker Simulation Tests. The first

checked

parameters

in

pitch tracker

is

the

time

domain

characteristics which are listed in Table 4.1 then figures from Figure 4.5 to Figure 4.8. A. Time domain analysis of pitch tracker. Table 4.1 Time domain analysis of pitch tracker. The property tr [sec] ts [sec] Max. O.S. [%] Peak

Minnesota controller 0.6832 15.3072 0 0.9993

79

Designed controller 0.4333 6.7472 6.7287 1.0673

Chapter 4


B. θ_ref doublet signal response in linear simulink.

Designed controller Minnesota controller

Figure 4.5 ±5 degree doublet signal response. From Figure 4.5 we can say that the differences between the two controllers are that the response time for the designed controller is better. The overshoot of the response in designed controller is higher this design rule is required as will be seen in the multi-step tracking. C. The effect of noise (0.001 rad) in the designed control system.


Figure 4.6 ±5 degree doublet signal response in the existence of sensor noise. Figure 4.6 illustrates that the effect of noise (these noise can be considered as the sensors noise) with the standard deviation not more than 0.001 rad in the designed controller is too small.

80

Chapter 4


C. The ability of the system to reject the disturbance.


Figure 4.7 +5 degree response in the existence of disturbance. The system can be exposed to any temporary disturbances. The simulated disturbance is applied to the system by applying a pulse with magnitude + 5 degree for a short time after the response goes to stability. From Figure 4.7 the designed controller response are so fast and go to stability quickly. D. Multi steps response. Designed controller Minnesota controller

Figure 4.8 Multi commanded steps of pitch attitude response. Multi step tracking assured that the controller must be designed with maximum overshoot greater than 5% to enable the controller to track these many commands in a short time. As seen in Figure 5.8 the designed controller tracks the command at any step without any steady state error.

81

Chapter 4


4.2.1.3 Outer Loop Altitude Hold Controller. From the non-linear equations of motion we can get a linear relation between the altitude and pitch attitude at constant airspeed which is controlled by elevator. Equation (2.11) in chapter two can be called now to linearize it with some assumptions compatible with longitudinal motions. ̇ With this equation, the pitch angle can directly influence the climbing rate of the aircraft at constant airspeed (cruise speed). By the following steps the linearized equation is obtained. First: add and subtract the term (va θ). ̇ ̇

(4.6)

Where: In straight and level flight condition, where v ≈ 0, w ≈ 0, u ≈ va, φ ≈ 0, and θ is small, so we have dh ≈ 0. As assumed earlier the airspeed is constant, and by converting the equation (4.6) to the Laplace domain, the linearized equation is as follows: (

)

(4.7)

So, the structure block diagram as in Figure 4.9

82


Minnesota Parameters

Designed Parameters

Chapter 4

Figure 4.9 MATLAB structure of altitude hold controller.

83

Chapter 4


The executed tests illustrated that the designed controller is better than the Minnesota one as will be seen in the following section. The Minnesota control parameters are (Kd_q = -0.08, kp_θ = -0.84, ki_θ = -0.23, kp_h = 0.021, and ki_h = 0.0017), and the designed parameters are (Kd_q = -0.065, kp_θ = -1.1, ki_θ = -0.8, kp_h = 0.05, and ki_h = 0.00). 4.2.1.4 Altitude Hold Controller Simulation Tests. The first category of tests on the altitude hold controller after time domain analysis is executed to evaluate the controller in linear model.

Time domain

characteristics are listed in Table 4.2, the figures from Figure 4.10 to Figure 4.16. A. Time domain with unit step response analysis. Table 4.2: Altitude hold controller time domain characteristics. The property tr [sec] ts [sec] Max. O.S. [%] Peak

Minnesota controller 4.0431 31.1408 13.0716 1.1397

Designed controller 2.1814 4.8717 0.5006 1.005 Designed controller Minnesota controller

Figure 4.10 Step response of altitude hold controller. From Figure 4.10 the unit step response showed that the designed controller is obviously better in rise time and maximum overshoot and settling time.

84

Chapter 4


B. 10 [m] Altitude doublet signal response.


Figure 4.11 10 [m] doublet signal response. C. The output changes against noise (0.001m).


Figure 4.12 Effect of the noise in the altitude hold controller.

85

Chapter 4


D. The ability of the system to reject the disturbance. We test the disturbance in the step response after very steady state. We make a zoom in time from 58 sec. to 85 sec.

Designed controller Minnesota

Figure 4.13 Effect of the disturbance on the altitude hold controller. By the previous tests, the basic tests of the controller were executed under linear model. The results of these tests assured that the designed controller is better in rise time, maximum overshoot, disturbance rejection and noise effects. The next category of tests were executed to check the whole sensors noise and environment model on the basic scenarios of the aircraft as straight and leveling, and level climbing for state space linear, analytical linear, and non-linear models. E. Climbing Scenario response. Applying climbing scenario 100 [m] then straight and leveling in the two controllers in the state space linear model, the response is seen in Figure 4.14

86

Chapter 4



Figure 4.14 Level climbing 100 meter altitude from the pitch. F. Level climb (10 m) comparison between analytical linear model and nonlinear model.

Analytical lin. Model designed con. Analytical lin. Model Minnesota con.

Non-lin. Model Minnesota con. Non-lin. Model designed con.

Figure 4.15 Comparison between the Minnesota and designed controllers applied on the approximated analytical linear model and non-linear model in the absence of noise and environment model to illustrate the differences. The following Figure 4.16 is the Level climb comparison between analytical linear model and nonlinear model in the existence of sensors noise and environmental disturbances of nonlinear model.

87

Chapter 4


Analytical lin. Model designed con. Analytical lin. Model Minnesota con.

Non-lin. Model Minnesota con. With noise effect Non-lin. Model designed con. With noise effect

Figure 4.16 Comparison between the Minnesota and designed controllers applied on the approximated analytical linear model and non-linear model.

4.2.2 Lateral Motion Controller Design. The lateral autopilot uses the rudder and ailerons to keep the aircraft flying in a coordinated turn and following a commanded turn rate (including a zero turn rate for a straight flight), it consists of inner loops and outer loops to manage the lateral scenarios of the aircraft as the heading control and zero sideslip angle control, the dynamics affected the lateral autopilot begin with the body axis roll rate which is fed back to the ailerons to modify the damping of the roll mode,

and yaw rate to modify the damping of the dutch roll mode, but

yaw rate feedback only is not sufficient due to coupling between yaw and roll which results a steady state yaw rate component during turns, a simple solution to this problem is to use a washout filter on the output of the yaw rate sensor. The high pass filter action of the washout filter is to remove this steady state component. The output of the washout approximates affects the yaw rate which is suitable feedback for the dutch roll mode [79]. For large angle of attack another problem can be appeared which is that the roll pole coupled with the spiral pole to form a complex pair, the solution of this is to deal with the system as multi input multi output system due to the coupling between the inputs and the outputs at high angle of attack, or we can assume that the maximum angle of attack is 20 degree. The last assumption is

88

Chapter 4


good and suitable for laminar conditions because great values of angle of attack can cause turbulent so the stolen condition will be happened to fail the flight of the aircraft [80]. The

PI

controller

of

roll

attitude

(bank

angle

hold

controller)

is designed starting from the roll rate inner loop (roll damper). The last controller is the outer loop which is used for controlling the heading and direction of aircraft with P-controller only which satisfies the design requirements. The whole lateral autopilot block diagram as shown in Figure 4.17

Figure 4.17 Lateral autopilot block diagram. So, the influenced states of Lateral motion controller are ( the lateral input controls ( The

outer-loop

) by

). is

designed

to

achieve

the

tracking

command

requirements. The inner loops are designed to track roll attitude reference signals are

required

introduced

for

the

against

the

outer inner

loop.

loop

Several

performance

design that

the

goals closed

loop rise time should be less than 1 second, and the overshoot has to be smaller than

5%

in

some

cases.

Root

locus

technique

and

PI-controller

were

tuned using the two linearized models of the aircraft, then using SIL to evaluate the design and make the pre-final recommendations [81]; Roll angle reference is constrained at 45◦. The

procedures

of

lateral

motion

controller

design

is

organized

as

follows; 1st is the design of the inner loops of lateral motion controller, 2nd

89

Chapter 4


shows the inner loops design results, 3rd is the design of the heading direction controller, 4th is the design of the yaw damper, 5th shows the performance of the whole lateral motion controller in the scenario of rectangular motion command to the aircraft. 4.2.2.1 Roll Attitude Tracker. Roll rate feedback is designed to increase the damping of roll rate and is the most inner loop of the roll attitude (bank angle) hold controller. The analytical open loop linearized transfer function of roll rate from aileron is used to design the roll rate damper then bank angle tracker then heading controller. By calling equation (3.30) from chapter three to design roll damper, this equation determines the relation between roll rate and ailerons control.

The chosen pole will move from -16.09 to the left to be -24.8 with kd_p = -0.055, the value of this gain affects the trajectory of the response of the roll tracker which makes the trajectory has many ripples or smooth. The structure is as in Figure 4.18.

δa

+ -

Elevator Servo

Aircraft dynamics

Rate gyro

p

kkdp Figure 4.18 Roll rate feedback system. After that, the next inner loop is the roll angle tracker. Integrating the roll rate transfer function to approximately extract the roll attitude, and design the controller using PI- controller as in the following structure in Figure 4.19.

90



Designed Parameters

Chapter 4

Figure 4.19 MATLAB structure of bank angle hold controller.

91

Chapter 4


Again the Minnesota controller parameters (kd_p = -0.07, kp_φ = -0.52, and ki_φ = -0.2) and the designed controller parameters (kd_p = -0.055, kp_φ = -0.89, and ki_φ = -0.45). 4.2.2.2 Roll Attitude Hold Controller Simulation Tests. The performance tests between the two controllers in linear and nonlinear models are discussed in this subsection. The first test is the step response analysis in time domain, then the figures from Figure 4.20 to Figure 4.23 to illustrate the comparison between the two controllers. A. Time domain analysis. Table 4.3 Roll attitude hold controller time domain characteristics. The property tr [sec] ts [sec] Max.o.s [%] Peak



From the table 4.3 the designed controller is better in rise time and maximum overshoot. The settling time can be considered good in two controllers. B. Doublet signal response.


Figure 4.20 ±5 degree doublet signal in roll response. As known, doublet signal response is related to the change of direction of signal applied to the aircraft to measure the behavior of it due to these changes. From

92

Chapter 4


Figure 4.20 the designed controller changes with the input signal quicker than Minnesota controller. This response is very useful to the requirements of aircraft design. C. The effects of sensors noise in the response. We will check the effect of noise existence by assigning standard deviation σ = 1.0*10-03 rad. The noise influences are not effectiveness in the designed controller as seen from Figure 4.21.


Figure 4.21 Effect of the noise in the roll tracker. D. The effect of disturbance in the doublet response. The behavior of the system is tested at the existence in disturbance in the output. The designed controller has an overshoots higher than the Minnesota controller. The designed controller goes to stability faster than the Minnesota controller as seen in Figure 4.22. Designed Minnesota

Figure 4.22 Effect of the disturbance in the roll tracker.

93

Chapter 4


E. Multi-step of roll attitudes response.


Figure 4.23 Multi-step response of roll tracker. By the previous tests, the roll tracker of the designed controller assures that it has a good performance and good capability against noise and is capable of rejecting the disturbance. It’s closely matched with the desired requirements. The next loop is the direction heading controller, it’s considered as an outer loop of the roll tracker and related with the guidance and control navigation system. 4.2.2.3 Direction Heading Controller. From equation (2.17), ̇ The heading rate pitch attitude

̇ is related with the pitch rate q and yaw rate r and

and roll attitude . From this equation we can get a new

simplified linear relation between the heading angle and the roll angle, this relation is obtained from the coordinated turn assumption [81] During a coordinated turn, in the absence of wind or sideslip, we have that va =vg, and . ̇

̇

(4.8)

Equation (4.8) can be rewritten as:

94

Chapter 4

Autopilot Design and Simulation ̇

By expressing the equation in Laplace form (

)

(4.9)

Equation (4.9) is the last expression can be used to control the heading from roll


Designed Parameters

attitude; Figure 4.24 illustrates the structure block diagram of the lateral autopilot.

Figure 4.24 MATLAB Structure of the lateral autopilot.

95

Chapter 4


4.2.2.4 Heading Controller Simulation Tests. After designing the lateral autopilot, the several tests are executed to check its performance; the comparison between the Minnesota and designed controllers is matched so much. The first test is the time domain specs, then linear analysis in figures from Figure 4.25 to Figure 4.27, and the nonlinear analysis in figures from Figure 4.28 to Figure 4.34 with a scenario of rectangular motion. A. Time Domain Analysis. Table 4.4 Heading controller time domain characteristics. The property tr [sec] ts [sec] Max. O.S. [%] Peak



From table 4.4 the step response test is operated in linear model of ultrastick-25e. The maximum overshoot of Minnesota controller is higher than the designed controller, but this disadvantage is disappeared in SIL. B. Doublet signal from standalone Simulink model. Designed controller Minnesota controller

Figure 4.25 ±5 doublet signal response of the heading hold controller.

96

Chapter 4


C. The effect of sensor noises. The noise test is executed under the noise at sigma σ = 1*10-3 rad.


Figure 4.26 Effect of the noise in the heading hold controller. D. The effect of disturbance (the capability to disturbance rejection).


Figure 4.27 Effect of the disturbance in the heading hold controller. In the test platform linear simulation the executed scenario is the rectangular motion, the command and response as in Figure 4.28.

97

Chapter 4



Figure 4.28 Rectangular motion heading command and its response in linear simulation model. The following test is the rectangular motion response in SIL which is applied in the non-linear model of aircraft. Figure 4.29 illustrates the response of heading angle due to rectangular motion command. Figure 4.30 shows the relation between the latitude and longitude. Figure 4.31 shows the roll change which makes the rectangular motion.


Figure 4.29 Heading command rectangular motion response in SIL.

98

Chapter 4


Figure 4.30 Shape of the aircraft trajectory due to rectangular motion commands in the heading angle.

Designed con. Minnesota con.

Figure 4.31 Change in the bank angle due to rectangular motion in the aircraft. 4.2.2.5 Yaw Damper. Yaw damper is designed to regulate the yaw rate to be zero, control of yaw rate w. r. t. rudder. Yaw rate is fed back to the rudder to improve the dutch roll mode.

The purpose of the stability augmentation of the yaw rate feedback

is to use the rudder to generate a yawing moment that opposes any yaw rate that builds up from the dutch roll mode. The resulting feedback is zero yaw rate with zero command input [82].

99

Chapter 4


Washout filter is used on the output of the yaw rate sensor to remove the steady state components of the yaw rate during turns. Washout

filter

time constant

is

a

compromise;

too

large value

is

undesirable since the yaw damper will then interfere with the entry into turns [44]. Too small value will reduce the achievable dutch roll dumping. Time constant ( ) was chosen to be 0.5 s. The transfer function of yaw rate loop can be found by using a rootlocus technique to get the gain value which damp the rate and make it suitable for maintaining yaw rate from rudder to be zero. Yaw damper is designed with washout filter as mentioned above. From the lateral state space linearized model in chapter three, the linearized transfer function of yaw rate to rudder (equation (3.20)) was called to be used. ̅ ̅ The lateral model has two pair complex poles (- 1.84 ± 5.28i) with a lightly damping ratio (0.329) and natural frequency (5.59 rad/sec). The purpose of the damper is to increase this damping ratio. The controlled system is designed by assigning the gain kd_r = 0.065, and the washout filter with transfer function: (4.10) Time constant

4.3 Whole Autopilot Flight Scenarios Simulation Test. The last test is to check the whole performance of the autopilot in the Climbing Turn scenario. The command is the altitude from 100 to 600 meter and the heading in rectangular motion. -

Simulation time 120 s

-

Turn in 4 steps 0 deg. to 90 deg. and then and then

-

Alt command 500 m direct.

100

Chapter 4


Figure 4.32 shows the trajectory of airplane due to the climbing turn scenario.

Figure 4.32 Climbing turn trajectory of the aircraft. We can summarize the controllers' parameters of the whole autopilot in the Table 4.5 Table 4.5 Value of the control parameters of Ultrastick-25e autopilot.

q h P

Dampers

P

Gain

p

Minnesota

designed

-0.08

-0.065

-0.07

Minnesota

PI P

I

designed

Minnesota

designed

Minnesota

designed

-1.1

-0.23 0.0017

-0.8

0.05

-0.84 0.021 -0.52

-0.89

-0.2

-0.45

-0.055 1.2

1.25

4.4 Summary. Chapter four introduces the detailed design of autopilot and its simulation with a various flight scenarios. The first part is the design of longitudinal motion controller. Beginning with the inner loop pitch rate (q) (pitch damper) which is designed with the best value of feedback gain by root locus technique and tuning it with the nonlinear simulator, and

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then pitch attitude hold controller (pitch tracker) which is designed with PI-controller far away from complexity with good performance in the time domain characteristics. Linearization of the nonlinear equation of motion of altitude dynamics is derived to get a linear relation between the altitude and pitch angle at assumption of cruise speed of 17 m/s. Altitude hold controller was designed using of P-controller with results are better than PI-controller in the Minnesota controller. Ascending scenario is tested in the non-linear model to check the all over behavior of the aircraft. The second part of this chapter is the design of lateral motion controller. Most inner loop was designed with feedback gain, and then roll attitude hold controller was designed with PI-controller far away from complexity with good performance in the time domain characteristics. The lateral motion controller design procedures are: a. Roll rate feedback. b. The roll attitude controller. c. Linearization algorithm to get a linear relation between heading angle and roll attitude. d. The outer loop controller is a simple P-controller. e. Yaw damper is designed with washout filter. f. Finally, the rectangular motion command is applied in the non-linear model to check the behavior of the aircraft. The environment disturbances and sensors noise are considered in the design architecture of test platform. At last, the evaluation and check of the behavior of the whole autopilot by applying climbing turn scenario is executed. The results of the checks met our requirements.

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Chapter 5

Autopilot Implementation with Experimental Test Results

CHAPTER

5

Autopilot Implementation with Experimental Test Results 5.1 Introduction. The great researches in UAVs enable us to stimulate new ideas for manufacturing advanced SUAVs with low cost. In recent years the focus has shifted from special qualified components to COTS hardware which can be slightly adapted or modified to provide adequate reliability in flight. After the completion of design and test SUAV autopilot in chapter four; it's the time to implement Ultrastick-25e autopilot according to this introduced design parameters. First section introduces an introduction of implementing Ultrastick-25e autopilot. Second section introduces the block diagram of a SUAV focusing on autopilot components and some supported components. Third section introduces the Selection of Avionics and sensors of SUAV required for stability and executing the various flight scenarios such as inertial Measurement

Unit

(IMU),

magnetometers,

and

Global

Positioning

System

(GPS). The autopilot components are chosen to achieve low cost components with

COTS

components

and

high

performance.

Flight

computer

is

the

ARDUINO MEGA 2560, IMU is MPU6050, Magnetometer is the digital compass HMC5883L, and GPS is U-Blox LEA-6H. Fourth section talks about the State estimation techniques which are now required due to new sensor technologies depending on low cost, but so noisy.

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These MEMS technologies provide the possibility to shrink the size and weight of the SUAV. These noises can be an eliminated by state estimator techniques as Kalman Filter (KF) or complementary filter for attitudes and navigation states estimation [83, 84]. Fifth components

section

introduces

are connected to

the

implementation

the flight

of

computer to

the

autopilot.

construct

The

the high

precision autopilot with state estimator and flight code to implement the longitudinal and lateral motion controller. The last section introduces PIL Simulation to evaluate the autopilot. This step is very important, it depends on replacing the emulated hardware under test or the controller strategy in the simulation model with real hardware that interacts with the models designed with the computer simulation programs.

5.2 Autopilot Hardware Block Diagram. Due to the small size of the Ultrastick-25e, many tasks must be handled and managed by a powerful processor to be capable of the management between the different subsystems of the aircraft. Figure 5.1 illustrated nearly all of the SUAV electronic components. These electronic components are grouped into seven main areas: -

The flight computer.

-

Components specific to the scientific payload of the aircraft.

-

Components specific to aircraft INS.

-

Components specific to communications with a ground station.

-

Components provide fundamental electrical support.

-

Components specific to the aircraft power subsystem.

-

Components specific to the UAV propulsion and control subsystem.

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Chapter 5


Figure 5.1 SUAV electronic components block diagram.

5.3 Selection of Avionics and Sensors. Electronic sets operated on missiles, aircraft and spacecraft are usually summarized as "Avionics", which is the acronym of aviation electronics, these electronic sets Since the 1970s, composed of digital processing modules and communication buses, supporting more avionic applications such as flight control, flight scenario management, flight telemetry, etc. There are direct basic components wanted for autopilot installation such as navigation set, IMU and supported components. There are other avionics are not directly the contents of the autopilot, but interact with it as communication, power systems, and engine thermal monitoring. Hence, avionic architectures have become a central component of an aircraft. They have to ensure an enormous variety of important requirements such as safety, robustness to equipment failures and real-time. In response to these requirements, aircraft manufacturers have proposed several design metrics. The next generation of avionic architectures involves

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reconfiguration capabilities and integrating COTS processing equipment such as multi-core processors. These two challenges will be central to this next generation of Avionics architectures (called Integrated Modular Avionic 2G (IMA-2G or IMA 2nd generation) [85].

5.3.1 Flight Computer. Nearly all UAVs have at least one flight computer devoted to performing all processing on-board UAV. This credit card sized single-board-computer can be chosen from commercial products and is built around a Complex Instruction Set Computer (CISC) or RISC microprocessors [86, 87]. Flight Computer has a number of features including: Flash as (ROM), RAM memory, nonvolatile flash storage to save all the data of telemetry of the UAV and payload collected data, communication ports, many channels of analog input, many general purpose input/output lines, power output lines, built in latch up protection, and a built-in hardware WatchDog Timer (WDT). Nearly all of the hardware subsystems onboard UAV interface to the flight computer and must be controlled by it. There are many open source boards can be adapted to perform this flight computer as ARM based boards (Arduino due [88], beaglebone black

[89], Raspberry pi

[90]), AVR

based boards

(Arduino

MEGA 2560 [91]), INTEL based boards (INTEL Galileo [92]). Figure 5.2 shows some examples of these boards.

Figure 5.2 Open source development boards.

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Chapter 5


The chosen embedded system of our autopilot implementation is the Arduino MEGA 2560 [91] which is seen in Figure 5.3, due to its simplicity ,low

cost,

high

efficiency,

and

historical

use

in

open

(Ardupilot APM2.x series) it has the following main features briefly: -

Microcontroller ATmega2560.

-

Operating voltage 5V.

-

Input voltage (recommended) 7-12V.

-

Digital I/O pins 54 (of which 14 provide PWM output).

-

Analog input Pins 16.

-

DC current per I/O pin 40 mA.

-

DC current for 3.3V pin 50 mA.

-

Flash memory 256 KB of which 8 KB used by bootloader.

-

SRAM 8 KB.

-

EEPROM 4 KB.

-

Clock Speed 16 MHz.

-

Communication ports. 

I2C (inter integrated circuit) ports (for IMU).



SPI (Serial Peripheral Interface).



4 UARTs serial ports.

107

source

autopilots

Chapter 5


Figure 5.3 The functional block diagram of the Arduino mega 2560 board.

5.3.2 SUAV Sensors. For

automatic

machines

as

unmanned

aircraft

or

other

autonomous

vehicles, navigation is very important. The navigation states of the aircraft are obtained and estimated according to many techniques such as AHRS, INS, and the full complete state estimation by GPS/INS technique [93]. Our interest lies in

integrating

IMU

consisting

of

a

triad

accelerometer

and

gyros,

and

magnetometers to estimate the attitudes of the aircraft. With these tools the construction of AHRS is implemented. GPS is used to provide the best possible aircraft position in terms of the latitude, longitude and height above the surface of the earth, also it provides ground heading and velocity. Gyroscopes and Accelerometers chips can be integrated on a small board and can effectively give the attitude of the vehicle concerned. With the advent of MEMS technology, all this can be done at extremely low cost, but with errors. These errors can be considered a negligible problem because of the estimation techniques which will be explained in the following sections AHRS can be developed and implemented in a microcontroller or a digital

signal

processor.

The

state

estimator

estimated attitude of the aircraft.

108

algorithm

would

return

the

Chapter 5


Due to (the development of the sensor technology based on MEMS which provide small and accurate sensors such as accelerometers, Gyroscopes, pressure sensors, the development of small global positioning systems (GPS), computationally

capable

microcontrollers

and

more

powerful

batteries)

the

capabilities of SUAVs have gone from being purely radio controlled (RC) by pilots on the ground to highly autonomous systems in a few years. The sensors used for guidance, navigation and control of the aircraft will be considered in details. These sensors are listed below: • Accelerometers. • Rate gyros. • Magnetometers. • GPS. 5.3.2.1 Inertial Measurement Unit (IMU). A. Accelerometer. Accelerometer

sensors

measure

the

difference

between

any

linear

acceleration in the accelerometer’s reference frame and the earth's gravitational field vector. In the absence of linear acceleration, the accelerometer output is a measurement of the gravitational field vector and can be used to determine the pitch and roll orientation angles. Due to the sequence of frames rotation from the inertial frame (Fi) to the body frame (Fb), the attitude angles are appearing. The most common order is the aerospace sequence (as discussed in chapter two) of yaw then pitch and finally a roll rotation. -

The x-axis is aligned along the ib of body frame (Fb) of the aircraft.

-

The z-axis points downwards as kb of body frame (Fb) so that; it is aligned with gravity when the aircraft in a straight and leveling flight.

-

The y-axis is aligned at right angles and is aligned along jb of body frame (Fb).

The three accelerometers are mounted near the center of mass of the aircraft, with the sensitive axis of one accelerometer aligned with each of the body axes. Accelerometers measure the difference between the acceleration of

109

Chapter 5


the aircraft and the gravitational acceleration. The output of the accelerometers (Gp) is given in equation (5.1). (

(

)

)

(5.1)

Direct Cosine Matrix (DCM) can be recalled from the equation (2.2) to express the R matrix, which is the rotation matrix describing the orientation of the aircraft body frame ( Fb) relative to the earth coordinate frame Fi, . The

aircraft

accelerometer

output

Gp

(measured

in

the

native

accelerometer units of g is: (

(

)

)

( )

( )

( )

(5.2)

( )

(5.3)

(

)( )

( The

accelerometer

) output

(5.4) has

three

components,

but

the

vector

magnitude must always equal 1g in the absence of linear acceleration. The above rotation sequence in equation (5.3) depends only on the roll (

) and

pitch( ) angles and can be solved. So the above procedures are done to extract roll and pitch attitudes from accelerometer to make fusion between accelerometers and gyroscopes sensors to estimate an accurate values of roll and pitch attitudes. All

accelerometers

are

completely insensitive

to

rotations

about

the

gravitational field vector and cannot be used to determine heading, so it's

110

Chapter 5


conventional to select either the rotation sequence Rxyz or the sequence Ryxz to eliminate the yaw rotation and allow solution for the roll and pitch angles. The unknown

yaw

angle

represents

the

aircraft

rotation

from

north,

but

its

determination requires the addition of a magnetometer sensor to create a Compass. Equation (5.2) can be rewritten in the form of an equation (5.5) relating the roll and pitch angles to the normalized accelerometer reading [94] Gp:

‖

‖

(

) ⇒

(

√

)

(

)

(5.5)

Solving for the roll and pitch angles from equation (5.5) to give equation (5.6) and equation (5.7): (

)

(

(5.6) )

(5.7)

√

B. Rate gyroscopes. Rate gyroscopes can be used to determine attitude rates of aircraft, MEMS rate gyros typically operate based on the principle of the Coriolis acceleration. There some types of gyroscopes as following [95, 96]. - Coriolis gyros (Coriolis Effect). - Optical gyros (Sagnac Effect). - Ring laser gyros (very accurate but very expensive). - Interferometric Fiber Optic Gyros (FOG) (Sagnac Effect). These MEMS gyros have many kinds of errors. It can be briefed in the fixed bias or offset, bias drift (which is usually modeled as random walk) and Bias vibration from one turns to another (thermal effect).

111

Chapter 5


It is common to measure the angular rates about each of the body axes using three gyros by aligning the sensitive axis of a gyro along each of the ib, jb, and kb axes of the SUAV. These rate gyros measure the angular body rates p, q, and r. C. MPU 6050 IMU from InvenSense [97]. The MPU-6050 is an IMU has an embedded 3-axis MEMS gyroscopes, 3-axis MEMS accelerometers, Digital Motion Processor (DMP), an embedded temperature sensor range from -40 °C to +85 °C, an auxiliary I2C port that interfaces to 3rd party digital sensors such as magnetometers, delivers a complete 9-axis Motion Fusion output to its primary I2C. It's also designed to interface with multiple non-inertial digital sensors, such as pressure sensors connected on its auxiliary I2C port. It has three 16-bit analog-to-digital converters (ADCs) for digitizing the gyroscope outputs and three 16-bit ADCs for digitizing the accelerometer outputs. For precision tracking of both fast and slow motions, the parts feature a user-programmable gyroscope full-scale range of

±250,

±500,

±1000,

and

±2000°/sec,

and

a

user-programmable

accelerometer full-scale range of ±2g, ±4g, ±8g, and ±16g. The

MPU-6050

enables

low-power

Motion

Processing

in

portable

applications with reduced processing requirements for the system processor, for power supply flexibility, operates from VDD power supply voltage range of 2.375V to 3.46V, and Communication with all registers of the device is performed using either I2C at 400 kHz. Small package size with a new footprint of 4x4x0.9mm (QFN) Quad Flat no, while providing the highest performance, lowest noise, and the lowest cost semiconductor packaging required for handheld consumer electronic devices. It has programmable low-pass filters for the gyroscopes, accelerometers. ThreeAxis MEMS Gyroscope has the following additional features: -

Enhanced bias and sensitivity temperature stability reduces the need for user calibration.

-

Gyroscope operating current: 3.6 mA.

-

Standby current: 5 μA.

-

Factory calibrated sensitivity scale factor.

112

Chapter 5


-

Sensitivity scale factor:

131

-

Sensitivity scale factor tolerance:

±3 % at 25°C

-

Total RMS noise:

0.05 º/s

at FS_SEL = 0

The DMP can be used as a tool in order to minimize power, simplify timing, simplify the software architecture, and save valuable MIPS on the host processor for use in the application. Auxiliary I2C serial interface is used for communicating to a 3-Axis digital output magnetometer or other sensors. This bus has two operating modes. -

I2C Master Mode: The MPU-6050 acts as a master to any external sensors connected to the auxiliary I2C bus.

-

Pass-Through Mode: The MPU-6050 directly connects the primary and auxiliary I2C buses together, allowing the system processor to directly communicate with any external sensors. Orientation

fabrication

sequence

is

designed

as

in

Figure

5.4.

The

mismatch between fabrication design orientation and mathematical orientation description can be treated during writing the flight code. Pin diagram also is showed in Figure 5.5

-X

Figure 5.4 Orientation of axes descriptions of the device and mathematical calculations.

113

Chapter 5


Figure 5.5 MPU6050 pin configuration. 5.3.2.2 Magnetometer. The compass is a device measures the direction of the magnetic field locally and provides an indication of heading relative to magnetic north, ψm. The earth’s magnetic field is three dimensional, with north, east, and down components that vary with location along the earth’s surface. Modern digital compasses use three axes magnetometers to measure the strength

of

the

magnetic

field

along

three

orthogonal

axes.

In

UAV

applications, these axes of measurement are usually aligned with the body axes of the aircraft. There are many libraries associated with calculation of heading with three axes magnetometers. A. HMC5883L Digital compass. The Honeywell HMC5883L [98] is a low-cost digital compass that has many benefits to be used in autopilot implementation; offset cancellation, a 12bit ADC that enables 1° to 2° compass heading accuracy, small size for highly integrated

products,

production,

enables

compatible

for

low-cost battery

functionality powered

test

after

applications,

and

assembly

in

compassing

heading. Figure 5.6 shows the shape of HMC5883L with its pin configuration. HMC5883L compass has the following main features: -

12-Bit ADC coupled with low noise.

-

Built-in self-test.

-

Low

voltage

operations

(2.16

consumption (100 μA) -

I2C Digital interface.

114

to

3.6V)

and

low

power

Chapter 5


Figure 5.6 HMC5883L pin configuration. 5.3.2.3 Global Positioning Systems (GPS). The Global Positioning System (GPS) is a satellite-based navigation system that provides 3-D position information and velocity for objects on or near the earth’s surface [84, 99]. The key component of the GPS system is the constellation of 24 satellites that continuously orbit the earth at an altitude of 20,180 km [87]. GPS Measurement has some kinds of errors that can be briefed in Dilution Of Precision (DOP) factor [100, 52], Ephemeris Data errors in the range of 1 to 5 m, Satellite Clock errors is introducing an error of maximum 3.5 m, Ionosphere errors are typically between 2 and 5 m, Troposphere introduces range errors of about 1 m and Receiver measurements error is about is 0.5 m for maximum due to increasing of the technology. Table 5.1 illustrates the total device errors briefly. The cumulative effect of each of these error sources on the pseudorange measurement is called the user-equivalent range error (UERE) Table 5.1 Standard pseudorange errors model of a conventional GPS [52]. Error source (m)

Bias

Random

Total

Ephemeris data

2.1

0

2.1

Satellite clock

2.0

0.7

2.1

Ionosphere

4.0

0.5

4.0

Troposphere monitoring

0.5

0.5

0.7

Multi path

1.0

1.0

1.4

Receiver measurement

0.5

0.2

0.5

Filtered UERE, rms

5.1

0.4

5.1

115

Chapter 5


As indicated in Table 5.1, these errors consist of statistically independent slowly varying biases and random noise components. New techniques such as differential GPS [101] can be used to reduce the bias error components of GPS position measurements to much smaller values. GPS measurements are commonly available at 1 Hz. New systems suitable for SUAV implementations provide GPS measurements at 5 Hz updates. GPS

modules

information,

under

typically something

outputs

a

called

series

the

of

National

standard Marine

strings

of

Electronics

Association (NMEA) protocol (one of the famous protocols). Each of these sentences contains a wealth of data. NMEA is illustrated via this example of received data from GPS which is emphasized in Table 5.2. ( $GPRMC,220516,A,5133.82,N,00042.24,W,173.8,231.8,130694,004.2,W*70).

Table 5.2 Data results from GPS module in NMEA protocol. Data

Illustration

225446 A 4916.45,N 12311.12,W 173.8 231.8 191194 004.2 W *70

1 2 3 4 5 6 7 8 9 10 -

Time of fix 22:54:46 UTC Navigation receiver warning A = Valid position, V = Warning

Latitude 49 deg. 16.45 min. North Longitude 123 deg. 11.12 min. West Speed over ground, Knots Course Made Good, degrees true Date Stamp Easterly var. Subtracts from true course East/West Checksum

U-Blox-6H GPS module [102]. The LEA-6h module series is a high performance GPS module. It can be

upgraded

using

U-center

program,

ready

for

GLONASS

(Russian)

and

GALILEO (European) satellites. U-Blox LEA 6H has been designed with low power

consumption

and

lower

cost.

A

standalone

receiver

combines

an

extensive array of features with flexible connectivity options. Their ease of integration results in a popularity for a wide range of industrial applications,

116

Chapter 5


especially SUAV autopilot applications as paparazzi and APM 2.8 autopilots. Pin configuration of U-Blox LEA-6H is shown in Figure 5.7.

Figure 5.7 Pin configuration of U-Blox LEA-6H module.

5.3.3 Communication Components. The

next

step

of

the

autopilot

implementation

is

the

design

the

communication subsystem to construct the down link telemetry data and uplink commands, there are two groups of communications connected between UAV and ground (man pilot, payload and telemetry data transmitted from the UAV to ground station). 3DR radio telemetry module V1 with 915 MHz [103], which is shown in Figure 5.8 is used for telemetry communication purposes due to its small size and light weight, It's designed as an open source radio set, offering a lower price, long range (about 500 m) and can be extended to several kilometers with a small Omni antenna, The system provides a full-duplex link.

Figure 5.8 3DR 915 Mhz radio module.

117

Chapter 5


Now we will configure the telemetry module with the configuration program from 3drobotics, Figure 5.9 is a screen shot of the configuration platform (3DR Radio Config 1.3.2) of the two transceivers at baudrate (115200).

Figure 5.9 Configuration of telemetry wireless module.

5.4 SUAV State Estimator. The availability of using new sensor technologies gives the aerospace engineers the opportunity to design SUAV sensors depending on MEMS. which are smaller and lighter than the old mechanical sensor devices. It provides the possibility to shrink the size and weight of the UAV to a new milestone. MEMS are low cost, but as noisy as discussed earlier. The solution for defeat the noise and obtain precise results for attitudes and navigation states is to design: -

A good controller.

-

Make a good analysis.

-

Using state estimator depends on good estimators. KF is one of the best state estimators. It's involved with most of the

navigation techniques [83, 84]. In this section we will discuss the state estimator techniques by complementary filter and KF. The better estimator is the chosen on in the estimation of SUAV attitudes.

118

Chapter 5


5.4.1 Complementary Filter. The attitude angles from the gyros, accelerometers, and magnetometers are estimated in this subsection by a complementary filter. It's used to combine them in a way that the resulted data is a stable and accurate. The gyro raw data are very good and stable for the short term, but they can quickly drift and become inaccurate, the accelerometer gives a good raw data over a longer period of time, but in the short run they can be noisy and also it has many ripples. So the data output from gyros and accelerometers can be combined in the following manner to give us the concept of a complementary filter. Often, there are cases where you have two different measurement sources for estimating one variable and the noise properties of the two measurements are such that one source gives good information only in first time region (gyro) while the other is good only in the extended measurement time region (accelerometer) but with some ripples, so You can use a complementary filter [104]. The math calculations of a complementary filter are much simpler, because it only works in one step. The optimal key equation (5.8) for implementing the filter is: Angle = AG * (angle + gyro* dt) + AA * acc

(5.8)

Where: -

Angle ... is the estimated Attitude.

-

AG ....... is the gyro measured factor (for our case = 0.93).

-

gyro ..... is the data measured from the gyroscope.

-

AA ....... is the accelerometer measured factor (for our case = 0.07).

-

Acc .... is the data extracted from accelerometer according to equation (5.6) for roll angle (φ) or according to equation (5.7) for pitch angle (θ).

5.4.2 Kalman Filter (KF). The modern filter theory began with N. Wiener’s work in the 1949s. His work was based on minimizing the mean-square error, so this branch of filter theory is sometimes referred to at least-squares filtering [105]. In 1960 R.E. Kalman considered the same problem that Wiener had dealt with earlier, but in his paper in 1960 [106], he considered the noisy

119

Chapter 5


measurement to be a discrete sequence in time in contrast to a continuous-time signal. Engineers, especially in the field of navigation, are quick to see the Kalman technique as a practical solution to some applied filtering problems. Also, the rapid advances in computer technology that occurred in the 1960s certainly contributed to popularizing Kalman filtering as a practical means of separating signal from noise. It is an optimal combination, in terms of minimization of variance, between the prediction of parameters from a previous time instant and external observations at a present time instant (recursive concept). KF is an extremely effective and versatile procedure for combining noisy sensor outputs (gyros and accelerometers) to estimate the state of the aircraft with uncertain dynamics. Noisy sensor outputs include output from the GPS and INS. state of the system may include the position (latitude, longitude, height), velocity, attitude (φ, θ, ψ) and attitude rates (P, q, and r) of a vehicle. And

uncertain

dynamics

include

unpredictable

disturbances

in

the

sensor

parameters or disturbances caused by a human operator or a medium (like wind). Briefly we can say that, KF has been just a computer algorithm for processing

discrete

measurements

(the

input)

into

optimal

estimates

(the

output). After some 56 years now, KF is still alive and well. There are some newer extensions of basic Kalman filtering that have been introduced in recent years that are also important such as extended, unscented, and particle filters [107]. Research in Kalman filtering is still quite active, so it is reasonable to expect to see further extensions and variations on the basic filter in the years ahead. KF here is applied to estimate good values of attitudes of the aircraft by eliminating

the

errors

introduced

by

the

gyros,

magnetometers. According to discrete KF the state space equations are:

120

accelerometers,

and

Chapter 5

Autopilot Implementation with Experimental Test Results Xk = A Xk-1 + B Uk + Wk-1

(5.9)

With an output equation (5.10) Zk = H Xk + Vk

(5.10)

The variables Wk and Vk represent the process and measurement noise respectively. They are assumed to be independent of each other, white, and with normal probability distributions. P(w) = N(0, Q), P(V) = N(0, R). The key parameters in KF design is the noise covariance (Q) and measurement covariance (R). The covariance matrices (R, Q) must be evaluated; R should typically be the square of the standard deviation of the Gyro. It should be there in the data sheet,

or

you

could

just

keep

things

stationary and

log

the

data

for

about 5 minutes, Calculate the mean and standard deviation.

5.5 Implementation Procedures of The Autopilot. From the beginning, we will power our flight computer and connect IMU as shown in Figure 5.10.

Figure 5.10 Schematic diagram of flight computer with IMU. Then

testing

of

IMU

(MPU6050)

is

implemented

successfulness of mpu6050 connection with the flight computer.

121

to

check

the

Chapter 5


The proceeding is continued to Read raw data from sensors, Converting to accelerations from

(accelerometers) and angular rates from

gyroscopes,

converting data output from accelerometers to roll and pitch attitudes according to equations (5.6) and (5.7) respectively, reading data (pitch and roll) from complementary filter algorithm and showing the results, Reading data (pitch and roll) from KF algorithm and showing the results. As discussed earlier, yaw angle is so drifted and all the time from many tests beginning from zero and drift, so we combined another device with MPU6050. Magnetometer can be combined to measure the heading of the aircraft if the value is not accurate, we will combine the two results of the gyroscope and magnetometer with each other. After connecting Honeywell compass HMC5883L, I2C ports are scanned to assure that the compass is right connected. That's well, we have two devices connected to our flight computer from I2C port 0x68 for MPU6050 and 0x1E for magnetometer, the next step is calibrating the magnetometer. After calibration of magnetometer, the results are approximately stable and accurate but with some ripples, so heading output from magnetometer will be combined with the value of gyroscope to filter it. Figure 5.11 shows the integration of the flight computer with GPS, MPU 6050, and Magnetometer.

Figure 5.11 Flight computer connections with GPS/IMU/Digital compass. Till now we can stop for a while to analyze the previous work, then decide which state estimator will be chosen in the autopilot design, from the analysis we have three resulted figures that determine the comparison between

122

Chapter 5


the attitudes with and without filtering as will be seen in Figure 5.12 for pitch estimation comparison, Figure 5.13 for roll, and Figure 5.14 for yaw.

Figure 5.12 Pitch angle comparison according to various state estimator techniques.

Figure 5.13 Roll angle comparison according to various state estimator techniques.

123

Chapter 5


Figure 5.14 Heading comparison according to various state estimator techniques. The previous figures are done to aid us to decide which state estimator can be used to give us the best performance. So KF is so efficient for our requirements for assigning roll and pitch, and Complementary filter data will be used in the assigning of heading. After that, the communication link between autopilot and ground control station wireless are established by connecting our telemetry module 3DR robotics. Then checking the communication between the ground station and autopilot as in Figure 5.15

124

Chapter 5


Figure 5.15 Pitch, roll and heading GUI indicator. Till that moment we finished from attitudes state estimator and tested it wired and wireless with excellent performance. The next step is to design the roll tracker and pitch tracker.

5.6 Processor in Loop (PIL) Simulation for SUAV. Depending

on

software

simulation

alone

is

not

sufficient

in

the

evaluation of the real system behavior, but is a basic step in the design. So the need for evaluation of the autopilot is completed by adding PIL simulation. One way to underestimate the gap between simulated and real systems which is the PIL simulation. PIL-simulation technique is used in many industries e.g. automotive industry, in marine and aircraft industry to test autopilots. So, it will be used to complete the design of the autopilot. This step increases the realism of the simulation, and provides access to the hardware features currently not available in software-only simulation models. It reduces the risks of discovering an error in the very last stage of on-the-field testing [108]. Today’s SUAV autopilot design is becoming increasingly complex. PIL tests and simulation for various components and control systems of SUAV can facilitate the design of an efficient autopilot passing on all manufacturing

125

Chapter 5


stages. It can greatly increase safety, enhance quality, save time and save money [109] The I/O signals between PC and hardware Controller can be conditioned and adapted to match the connectivity between them. PIL testing step is the last step of the SUAV autopilot, it focuses on one component (controller) rather than the entire system. The rest of the system is simulated by computers (airframe model) which use real time data acquisition systems to read inputs and respond like the real system (real SUAV model). The controller under test is implemented in the controller hardware (SUAV Flight Computer) and the simulator has to run in real time, the simulation time develops as real time. This real time simulation is obtained by setting the simulation algorithm cycle time equal to the simulation time step (sampling time in Ultrastick-25e autopilot is chosen to be 0.02 Sec).

Figure 5.16 Components of a PIL Simulation. As shown in Figure 5.16 the PIL simulator is generally contained of a PC (On this PC a simulation environment is installed, which is used to simulate the plant model), and the hardware control system with I/O matching or signal conditioning

circuit.

The

simulation

environment

provides

the

proper

communication between the plant model and the I/O.

5.6.1 PID Controller Implementation Results. The SUAV autopilot design structure was discussed in chapter 4. The inner loops and outer loops of the autopilot with its longitudinal and lateral motion

controllers

was

designed

by using

126

various

control

strategies.

It's

Chapter 5


evaluated in linear and nonlinear models. In this section the implementation of these strategies are done with the results, PID algorithm will be implemented to make the inner loops (pitch, roll), and outer loops (yaw, height). For example, of results Figure 5.17 shows the results +5 deg response of the pitch attitude hold a controller after implementation in flight computer, the comparison between the proposed controller [110, 111] and the Minnesota [112]. As seen the proposed one continued to be better than the Minnesota as we expected.


Figure 5.17 PIL simulation of +5 deg response of pitch attitude

5.7 Summary. The objective of this chapter is to implement the autopilot of SUAV. During the sections, we construct the block diagram of the autopilot. Flight computer (ArduMega 2560) is chosen because of its historic successfulness in autopilot design and its simplicity, MEMS sensors are the chosen sensors for implementing IMU (MPU6050), Magnetometer (HMC 5883l), GPS (UBLOX lea-6h).

With

implementing

the

state

estimator

with

complementary

and

KALMAN filters; the problem is finished and solved. All of the previous sensors are used for implementing Attitude and Heading Reference System (AHRS). The communication link between autopilot and the ground station is achieved

by

implemented

using to

(3DR

evaluate

radio the

pitch

telemetry attitude

module).

PIL

controller

by

simulation converting

is the

continuous system to a discrete one and implementing the communication

127

Chapter 5


adaptation between MATLAB and flight computer. The results show us that the proposed controller strategy design is very good and convenient to our requirements.

128

Chapter 6

Conclusion and Future Work

CHAPTER

6

Conclusion and Future Work 6.1 Conclusion This thesis gives a complete design of AFCS for SUAV. Collects housekeeping data from the aircraft subsystems and communicates these data to the ground station for subsequent processing, displaying, recording, and analyzing. The thesis has given the experience of designing, analyzing, building, and testing flight hardware. This type of researches is providing new ideas and inventing new technologies for the growing SUAV field. The thesis has provided new ideas for analytical linearization of the aircraft depending on the flight approximately assumptions. Designing the autopilot with its longitudinal and lateral motion controllers. Finally designing and implementing autopilot with chosen hardware COTS components due to their availability. The development of the SUAV market is making it more affordable and practical. A software program on MATLAB versions (2012, 2015) are constructed for making a test and simulation on our proposed Model of autopilot design for SUAV. At the end of this thesis, we conclude that: -

Development of an accurate mathematical model for SUAV. The resulted mathematical model is an efficient and very compatible for designing an accurate autopilot with various phases of flights. The nonlinear equations of motion extraction are focused. With these equations the linear longitudinal and lateral models are obtained. An analytical linearization technique is also derived to obtain the linear transfer function of the Ultrastick-25e states.

-

The methodology of getting the linear models is validated by comparing between two linearized models and the nonlinear model. The linearized model can approximately describe the behavior of the nonlinear dynamics of SUAV.

129

Chapter 6 -


The design of autopilot is utilized with the detailed design of longitudinal motion controller. Beginning with the inner loop pitch rate (q) (pitch damper), and then pitch attitude hold controller (pitch tracker) which is designed with PIcontroller far away from complexity with good performance in the time domain characteristics. Linearization of the nonlinear equation of motion of altitude dynamics is derived to get a linear relation between altitude and pitch angle at assumption of constant air speed. Altitude hold controller was designed using of P-controller with results are better than PI-controller in the classic controller. Ascending scenario is tested in the non-linear model to check the behavior of the aircraft.

-

The detailed design of lateral motion controller. Most inner loop was designed with feedback gain, and then roll attitude hold controller was designed with PIcontroller far away from complexity with good performance in the time domain characteristics. The design procedures began with roll rate feedback, the roll attitude controller, Linearization of the nonlinear equation of motion of heading rate is derived to get a linear relation between heading angle and roll attitude. The outer loop controller is a simple P-controller. Yaw damper was designed with washout filter. At last a rectangular motion command is applied in the nonlinear model to check the behavior of the aircraft. The environment disturbances and sensors noise are modeled and the performance of the system is checked in the existence of them. Longitudinal motion controller is in the development stage to design the whole

- The environment disturbances and sensors noise are considered in the design architecture of test platform. The whole autopilot is tested under climbing turn scenario. -

the autopilot design is done by using Flight computer (ArduMega 2560) because of its historic successfulness in autopilot design and its simplicity, MEMS sensors are the chosen sensors for implementing IMU (MPU6050), Magnetometer (HMC 5883l), GPS (UBLOX lea-6h), which are smaller and lighter than the old mechanical sensor devices, but so noisy.

-

With implementing the state estimator with complementary and KALMAN filters; the problem is finished and solved, all of the previous sensors are used for implementing Attitude and Heading reference system (AHRS). The

130

Chapter 6


communication link between autopilot and the ground station is achieved by using (3DR radio telemetry module). -

PIL simulation is implemented to evaluate the pitch attitude controller by converting the continuous system to a discrete one and implementing the communication adaptation between MATLAB and flight computer. The results show us that the proposed controller strategy design is very good and convenient to our requirements.

6.2 Future Work. During this thesis, a few aspects can be improved further. These are highlighted in the following points: -

Modeling techniques will be improved to model a high speed UAVs.

-

Control strategy will be modified to design an aircrafts with heavy loads.

-

Using advanced embedded systems with 32-bits with achieving real time operating systems concepts.

-

The need for the cooperation with an establishment interest in our work to construct our proposed system and aerospace labs to have a real results specially the coefficients of most advanced aircrafts from their wind tunnels to aid us in developing our design.

131

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REFERENCES [108] B. Lu, X. Wu, H. Figueroa, and A. Monti, "A Low-Cost Real-Time HardwareIn-the-Loop Testing Approach of Power Electronics Controls", IEEE Transactions on Industrial Electronics, Vol. 54, No. 2, April 2007. [109] A. Bittar, N. M. F. de Oliveira, and H. V. de Figueiredo, "Hardware-In-theLoop Simulation with X-Plane of Attitude Control of a SUAV Exploring Atmospheric Conditions", J. Intell. Robot. Syst., Vol 73, Issue 1-4, DOI 10.1007/s10846-013-9905-8, 2014. [110] A. E. Ahmed, A. Hafez, A.N. Ouda, H.E.H. Ahmed, and H.M. Abd-Elkader, "Design of a Lateral Motion Controller for a Small Unmanned Aerial Vehicle (SUAV)", 6th International Conference on Mathematical Models for Engineering Science (MMES '15), Michigan State University, East Lansing, MI, USA, September 20-22, 2015. [111] A. E. Ahmed, A.N. Ouda, A. Hafez, H.E.H. Ahmed, H. M. Abd-Elkader, "Design of Longitudinal Motion Controller of a Small Unmanned Aerial Vehicle", I.J. Intelligent Systems and Applications, Vol. 7, No. 10, 37-47, DOI: 10.5815/ijisa.2015.10.05, 2015. [112] A. Dorobantu, P. J. Seiler, and G. J. BALAS, "Test Platforms for ModelBased Flight Research", University of Minnesota, USA, 2013.

140

‫يهخص انشعبنت‬

‫مــلخــص الــرسـالــة‬ ‫حهؼب أَظًت انطبئشاث بذٌٔ ط‪ٛ‬بس (‪ )UAS‬ف‪ ٙ‬انؼقٕد األخ‪ٛ‬شة أدٔاسا ببسصة بصٕسة يخضا‪ٚ‬ذة ف‪ٙ‬‬ ‫بشايش ٔاعخشاح‪ٛ‬ض‪ٛ‬بث انذفبع عٕل انؼبنى‪ٔ .‬قذ يكُج انخطٕساث انخقُ‪ٛ‬ت يٍ حطٕ‪ٚ‬شْب نهق‪ٛ‬بو ببنؼذ‪ٚ‬ذ يٍ‬ ‫انٕظبئف انًًٓت ٔانخ‪ ٙ‬قذ حخغى ببنخطٕسة ػهٗ اإلَغبٌ يزم ػًه‪ٛ‬بث اإلعخطالع ٔانًشاقبت ٔانًقبحالث‬ ‫انغشب‪ٛ‬ت انشبغ‪ٛ‬ت ٔخ‪ٛ‬ش يزبل ػهٗ أداء ْزِ انًٓبو بُضبط انطبئشة انًقبحهت انًضُغت (‪ٓٚٔ .)X-45B‬ذف‬ ‫انبغذ إنٗ حصً‪ٛ‬ى ٔحُف‪ٛ‬ز انُظبو ا‪ٜ‬ن‪ ٙ‬نهغ‪ٛ‬طشة ػهٗ انط‪ٛ‬شاٌ نٓزا انُٕع يٍ انطبئشاث انًٕصٓت بذٌٔ‬ ‫ط‪ٛ‬بسػٍ طش‪ٚ‬ق دساعت نُظى انغ‪ٛ‬طشة ا‪ٜ‬ن‪ ّٛ‬ػهٗ انط‪ٛ‬شاٌ يغ دساعت بؼض إَٔاع انط‪ٛ‬بس ا‪ٜ‬ن‪ٔ ٙ‬يفبْ‪ٛ‬ى‬ ‫انخصً‪ٛ‬ى ٔيٕاصفبحٓب‪ًَ .‬زصت انطبئشة بخطب‪ٛ‬ق ػًه‪ ٙ‬ػهٗ انطبئشة انخضش‪ٚ‬ب‪ٛ‬ت انخ‪ ٙ‬حى اخخ‪ٛ‬بس انؼًم ػه‪ٓٛ‬ب‬ ‫ْٔ‪ ٙ‬راث األصُغت انزببخت (‪ )Ultrastick-25e‬ابخذاء يٍ حغٕ‪ٚ‬م انًؼبدالث انغ‪ٛ‬ش خط‪ٛ‬ت إنٗ يؼبدالث‬ ‫خط‪ٛ‬ت ‪ًٚ‬كٍ االػخًبد ػه‪ٓٛ‬ب ف‪ ٙ‬حصً‪ٛ‬ى انط‪ٛ‬بس ا‪ٜ‬ن‪ ٙ‬ع‪ٛ‬ذ حى ػًم ًَٕرس س‪ٚ‬بض‪ ٙ‬خط‪ٚ ٙ‬صف انغشكت‬ ‫انطٕن‪ٛ‬ت ًَٕٔرس س‪ٚ‬بض‪ ٙ‬آخش ‪ٚ‬صف انغشكت انؼشض‪ٛ‬ت ببنطش‪ٚ‬قت انخفبضه‪ٛ‬ت انؼبيت ٔاعخخذاو ( ‪Taylor‬‬ ‫‪ )Expansion‬نهغصٕل ػهٗ يصفٕفت صبكٕب‪ ٙ‬انخفبضه‪ٛ‬ت‪ .‬كًب حى حغٕ‪ٚ‬م انًؼبدالث انغ‪ٛ‬ش ًَط‪ٛ‬ت إنٗ‬ ‫يؼبدالث ًَط‪ٛ‬ت حصف انغشكت ببعخخذاو طش‪ٚ‬قت حغه‪ٛ‬ه‪ٛ‬ت صذ‪ٚ‬ذة حؼخًذ ػهٗ صفبث انط‪ٛ‬شاٌ‪ .‬كًب ‪ٚ‬قذو‬ ‫انبغذ حصً‪ٛ‬ى كبيم نهط‪ٛ‬بس ا‪ٜ‬ن‪ ٙ‬يغ ٔعذاث انخغكى انضبَب‪ٛ‬ت ٔانطٕن‪ٛ‬ت ف‪ ٙ‬انغشكت ‪ ,‬حًج يقبسَت َخبئش‬ ‫اخخببس انخصً‪ٛ‬ى يغ حصً‪ٛ‬ى صبيؼت (‪ )Minnesota‬ع‪ٛ‬ذ أكذث َخبئش االخخببس أٌ انط‪ٛ‬بس ا‪ٜ‬ن‪ ٙ‬انًقخشط‬ ‫ْٕ أفضم يٍ ٔعذة حغكى (‪ْ .)Minnesota‬زا انخصً‪ٛ‬ى ‪ٚ‬أخز بؼ‪ ٍٛ‬االػخببس انشٕششة انؼشٕائ‪ٛ‬ت انُبحضت‬ ‫يٍ أصٓضة ٔعغبعبث انطبئشة كًب ‪ٚ‬أخز ف‪ ٙ‬االػخببس االضطشاببث ي‪ٛ‬ش انًخٕقؼت انُبحضت ػٍ‬ ‫االضطشاببث انب‪ٛ‬ئ‪ٛ‬ت‪ .‬كًب ‪ٚ‬قذو انبغذ حُف‪ٛ‬ز ػًه‪ ٙ‬نُظبو انغ‪ٛ‬طشة ا‪ٜ‬ن‪ ٙ‬ػهٗ انط‪ٛ‬شاٌ ػٍ طش‪ٚ‬ق اعخخذاو‬ ‫انًكَٕبث انًخخهفت نهُظبو ْٔ‪ ٙ‬انغبعب انًٕصٕد ػهٗ عطظ انطبئشة ٔأصٓضة االعخشؼبس انصغ‪ٛ‬شة‬ ‫انكٓشٔي‪ٛ‬كبَ‪ٛ‬ك‪ٛ‬ت (‪( )MEMS‬انض‪ٛ‬شٔعكٕببث‪ ,‬أصٓضة ق‪ٛ‬بط انؼضهت‪ ,‬انبٕصهت انكٓشب‪ٛ‬ت‪َٔ ,‬ظى حغذ‪ٚ‬ذ‬ ‫انًٕاقغ انؼبنً‪ .))GPS( ٙ‬اعخخذاو حقُ‪ٛ‬بث حقذ‪ٚ‬ش انغبنت (‪ )state estimation‬يغ ارُ‪ ٍٛ‬يٍ انخقُ‪ٛ‬بث‬ ‫انخ‪ ْٙ ٙ‬انًششغبث انخكً‪ٛ‬ه‪ٛ‬ت (‪ٔ )complementary filter‬يششظ كبنًبٌ (‪.)Kalman Filter‬‬ ‫حصً‪ٛ‬ى َظبو حغذ‪ٚ‬ذ انٕضؼ‪ٛ‬ت (‪ .)AHRS‬حى حصً‪ٛ‬ى يشعهت انًؼبنش انغق‪ٛ‬ق‪ ٙ‬يغ انًُٕرس انًصًى‬ ‫‪ )PIL( Processor In Loop‬ع‪ٛ‬ذ أكذث انُخبئش ػهٗ أفضه‪ٛ‬ت اعخخذاو بشايخشاث انخغكى انًغخُخضت‬ ‫ف‪ ٙ‬انخصً‪ٛ‬ى‪ .‬حى اعخكًبل حصً‪ٛ‬ى َظبو انغ‪ٛ‬طشة ا‪ٜ‬ن‪ ٙ‬ػهٗ انط‪ٛ‬شاٌ بخغق‪ٛ‬ق االحصبل انالعهك‪ ٙ‬ب‪ٍٛ‬‬ ‫انط‪ٛ‬بس ا‪ٜ‬ن‪ٔ ٙ‬بشَبيش إظٓبس عبنت انطبئشة ٔحغق‪ٛ‬ق اعخقببل انًؼهٕيبث يٍ انطبئشة إنٗ انًغطت‬ ‫األسض‪ٛ‬ت‪.‬‬ ‫وتقع الرسالة فً ‪ 041‬صفحة تحتوي على ستة فصول باإلضافة إلى قائمة المراجع التً تحتوي على ‪001‬‬ ‫مرجعا حدٌثا وشامل فً ذاا المجال‪ٔ .‬حى حُظ‪ٛ‬ى ْزا انبغذ ػهٗ انُغٕ انخبن‪:ٙ‬‬ ‫‪-‬‬

‫انفصم األٔل‪ُٚ :‬قغى إنٗ صضئ‪ ٍٛ‬ع‪ٛ‬ذ ‪ٚ‬غخٕ٘ انضضء األٔل ػهٗ دساعت ألَٕاع يخخهفت يٍ انطبئشاث‬ ‫بذٌٔ ط‪ٛ‬بس ٔاعخخذايبحٓب عٕاء انؼغكش‪ٚ‬ت أٔانًذَ‪ٛ‬ت ‪ ,‬أيب انضضء ا‪ٜ‬خش يٍ انفصم ‪ٚ‬غخٕ٘ ػهٗ دساعت‬

‫يهخص انشعبنت‬ ‫نُظى انغ‪ٛ‬طشة ا‪ٜ‬ن‪ ّٛ‬ػهٗ انط‪ٛ‬شاٌ يغ دساعت بؼض إَٔاع انط‪ٛ‬بس ا‪ٜ‬ن‪ٔ ٙ‬يفبْ‪ٛ‬ى انخصً‪ٛ‬ى ٔيٕاصفبحٓب‪.‬‬ ‫ٔحشًم دساعت انط‪ٛ‬بس ا‪ٜ‬ن‪ ٙ‬ػهٗ األَٕاع ا‪ٜ‬ح‪ٛ‬ت ( انخضبس‪ٚ‬ت‪ ,‬يفخٕعت انًصذس‪ٔ ,‬أبغبد انضبيؼبث)‪.‬‬ ‫‪-‬‬

‫انفصم انزبَ‪ٓٚ :ٙ‬ذف انفصم انزبَ‪ ٙ‬إنٗ إ‪ٚ‬ضبد ًَٕرس س‪ٚ‬بض‪ٚ ٙ‬صف عشكت انطبئشة ػٍ طش‪ٚ‬ق يشاصؼت‬ ‫انقٕٖ ٔانؼضٔو انًؤرشة ػهٗ عشكت انطبئشة يغ األخز ف‪ ٙ‬اإلػخببس االضطشاببث انضٕ‪ٚ‬ت ٔانب‪ٛ‬ئ‪ٛ‬ت‪ .‬كزنك‬ ‫يؼب‪ُٚ‬ت طش‪ٚ‬قت ق‪ٛ‬بع‪ٛ‬ت نهغصٕل ػهٗ يؼبدالث انغشكت ي‪ٛ‬ش انخط‪ٛ‬ت نهطبئشة بذٌٔ ط‪ٛ‬بس راث األصُغت‬ ‫انزببخت‪.‬‬

‫‪-‬‬

‫انفصم انزبنذ‪ :‬اعخكًبل ًَزصت انطبئشة بخطب‪ٛ‬ق ػًه‪ ٙ‬ػهٗ انطبئشة انخضش‪ٚ‬ب‪ٛ‬ت انخ‪ ٙ‬حى اخخ‪ٛ‬بس انؼًم ػه‪ٓٛ‬ب‬ ‫ْٔ‪ ٙ‬راث األصُغت انزببخت (‪ )Ultrastick-25e‬ابخذاء يٍ حغٕ‪ٚ‬م انًؼبدالث انغ‪ٛ‬ش خط‪ٛ‬ت إنٗ يؼبدالث‬ ‫خط‪ٛ‬ت ‪ًٚ‬كٍ االػخًبد ػه‪ٓٛ‬ب ف‪ ٙ‬حصً‪ٛ‬ى انط‪ٛ‬بس ا‪ٜ‬ن‪ .ٙ‬كزنك حى ػًم ًَٕرس س‪ٚ‬بض‪ ٙ‬خط‪ٚ ٙ‬صف انغشكت‬ ‫انطٕن‪ٛ‬ت ًَٕٔرس س‪ٚ‬بض‪ ٙ‬آخش ‪ٚ‬صف انغشكت انؼشض‪ٛ‬ت ػٍ طش‪ٚ‬ق حًُ‪ٛ‬ظ انًؼبدالث ببنطش‪ٚ‬قت انخفبضه‪ٛ‬ت‬ ‫انؼبيت ٔاعخخذاو (‪ )Taylor Expansion‬نهغصٕل ػهٗ يصفٕفت صبكٕب‪ ٙ‬انخفبضه‪ٛ‬ت‪ .‬حى حغٕ‪ٚ‬م‬ ‫انًؼبدالث انغ‪ٛ‬ش ًَط‪ٛ‬ت إنٗ يؼبدالث ًَط‪ٛ‬ت حصف انغشكت ببعخخذاو طش‪ٚ‬قت حغه‪ٛ‬ه‪ٛ‬ت صذ‪ٚ‬ذة حؼخًذ ػهٗ‬ ‫صفبث انط‪ٛ‬شاٌ‪ٔ .‬ف‪َٓ ٙ‬ب‪ٚ‬ت ْزا انفصم حى حق‪ٛٛ‬ى انًُبرس انش‪ٚ‬بض‪ٛ‬ت انًغخُخضت ٔيقبسَخٓب ببنًُبرس‬ ‫انش‪ٚ‬بض‪ٛ‬ت انغ‪ٛ‬ش خط‪ٛ‬ت نًؼشفت يذٖ قذسة ْزِ انًُبرس انخط‪ٛ‬ت انًغخُخضت ف‪ ٙ‬حٕص‪ٛ‬ف عشكت انطبئشة عخٗ‬ ‫حغبػذَب ف‪ ٙ‬حصً‪ٛ‬ى انط‪ٛ‬بس ا‪ٜ‬ن‪ ٙ‬نهطبئشة بذقت‪.‬‬

‫‪-‬‬

‫انفصم انشابغ‪ٚ :‬قذو حصً‪ٛ‬ى كبيم نهط‪ٛ‬بس ا‪ٜ‬ن‪ ٙ‬يغ ٔعذاث انخغكى انضبَب‪ٛ‬ت ٔانطٕن‪ٛ‬ت ف‪ ٙ‬انغشكت ‪ ,‬حخى‬ ‫يقبسَت َخبئش اخخببس انخصً‪ٛ‬ى يغ حصً‪ٛ‬ى صبيؼت (‪ .)Minnesota‬أكذث َخبئش االخخببس أٌ انط‪ٛ‬بس ا‪ٜ‬ن‪ٙ‬‬ ‫انًقخشط ْٕ أفضم يٍ ٔعذة حغكى (‪ٚ .)Minnesota‬ؼخبش انًُٕرس انًصًى ببشَبيش‬ ‫(‪ًَٕ ) MATLAB SIMULINK‬رس يغخغذد يغخقم ٔيغبًْت كب‪ٛ‬شة يغخخشصت يٍ ْزِ انشعبنت‬ ‫ع‪ٛ‬ذ أَّ ‪ٚ‬ؼبش ػٍ ٔعذة حغكى انغشكت انضبَب‪ٛ‬ت ٔٔعذة حغكى انغشكت انطٕن‪ٛ‬ت‪ْ .‬زا انخصً‪ٛ‬ى ‪ٚ‬أخز بؼ‪ٍٛ‬‬ ‫االػخببس انشٕششة انؼشٕائ‪ٛ‬ت انُبحضت يٍ أصٓضة ٔعغبعبث انطبئشة كًب ‪ٚ‬أخز ف‪ ٙ‬االػخببس االضطشاببث‬ ‫ي‪ٛ‬ش انًخٕقؼت انُبحضت ػٍ االضطشاببث انب‪ٛ‬ئ‪ٛ‬ت‪.‬‬

‫‪-‬‬

‫انفصم انخبيظ‪ٚ :‬قذو حُف‪ٛ‬ز ػًه‪ ٙ‬نُظبو انغ‪ٛ‬طشة ا‪ٜ‬ن‪ ٙ‬ػهٗ انط‪ٛ‬شاٌ ػٍ طش‪ٚ‬ق اعخخذاو انًكَٕبث‬ ‫انًخخهفت نهُظبو ْٔ‪ ٙ‬انغبعب انًٕصٕد ػهٗ عطظ انطبئشة ٔأصٓضة االعخشؼبس انصغ‪ٛ‬شة انكٓشٔي‪ٛ‬كبَ‪ٛ‬ك‪ٛ‬ت‬ ‫(‪( )MEMS‬انض‪ٛ‬شٔعكٕببث‪ ,‬أصٓضة ق‪ٛ‬بط انؼضهت‪ ,‬انبٕصهت انكٓشب‪ٛ‬ت‪َٔ ,‬ظى حغذ‪ٚ‬ذ انًٕاقغ انؼبنً‪ٙ‬‬ ‫(‪ .))GPS‬اعخخذاو حقُ‪ٛ‬بث حقذ‪ٚ‬ش انغبنت (‪ )state estimation‬يغ ارُ‪ ٍٛ‬يٍ انخقُ‪ٛ‬بث انخ‪ْٙ ٙ‬‬ ‫انًششغبث انخكً‪ٛ‬ه‪ٛ‬ت (‪ٔ )complementary filter‬يششظ كبنًبٌ (‪ .)Kalman Filter‬صً‪ٛ‬غ‬ ‫انًكَٕبث انغببقت شكهج حصً‪ٛ‬ى َظبو حغذ‪ٚ‬ذ انٕضؼ‪ٛ‬ت (‪ )AHRS‬نخؼ‪ ٍٛٛ‬ق‪ٛ‬ى دق‪ٛ‬قت نغبنت انطبئشاث يًزهّ‬ ‫ف‪ ٙ‬انضٔا‪ٚ‬ب انقطب‪ٛ‬ت (‪ .)ψ ,θ ,φ‬أيب انضضء األخ‪ٛ‬ش يٍ ْزِ انشعبنت ْٕ يشعهت (‪ )PIL‬انز٘ حى اعخخذايّ‬ ‫كًشعهت َٓبئ‪ٛ‬ت نخق‪ٛٛ‬ى انط‪ٛ‬بس ا‪ٜ‬ن‪ ٙ‬انًصًى ػٍ طش‪ٚ‬ق انخغكى انًغخُخش نًُٕرس انطبئشة‬ ‫(‪ٔ )Ultrastick-25e‬انز٘ حى يغبكبحّ ببشَبيش (‪ .)MATLAB‬قذ أكذث َخبئش حق‪ٛٛ‬ى ‪ PIL‬ػهٗ‬ ‫أفضه‪ٛ‬ت اعخخذاو بشايخشاث انخغكى انًغخُخضت ف‪ ٙ‬انخصً‪ٛ‬ى‪ٔ .‬بغهٕل انًشعهت األخ‪ٛ‬شة يٍ ْزِ انشعبنت حى‬

‫يهخص انشعبنت‬ ‫اعخكًبل حصً‪ٛ‬ى َظبو انغ‪ٛ‬طشة ا‪ٜ‬ن‪ ٙ‬ػهٗ انط‪ٛ‬شاٌ بخغق‪ٛ‬ق االحصبل انالعهك‪ ٙ‬ب‪ ٍٛ‬انط‪ٛ‬بس ا‪ٜ‬ن‪ٙ‬‬ ‫ٔبشَبيش إظٓبس عبنت انطبئشة ٔحغق‪ٛ‬ق اعخقببل انًؼهٕيبث يٍ انطبئشة إنٗ انًغطت األسض‪ٛ‬ت‪.‬‬ ‫‪-‬‬

‫ٔ أخ‪ٛ‬شا ‪ٚ‬خخخى الفصل السادس انشعبنت بخهخ‪ٛ‬ص يب صبء بٓب ٔ ‪ٚ‬ؼط‪ ٙ‬بؼض انًقخشعبث انًغخقبه‪ٛ‬ت نهبغذ‬ ‫ف‪ْ ٙ‬زا انًضبل‪.‬‬

‫(وما أُوتِيتُم مِّن ا ْل ِعْلمِ‬ ‫ََ‬ ‫َ‬ ‫ِ‬ ‫إِاَّل قَليال)‬ ‫س ورة اإلس راء ‪ :‬اَّلي ة ‪58‬‬

‫جاهعت بٌها‬ ‫كليت الهٌذست بشبرا‬ ‫قسن الهٌذست الكهربيت‬ ‫القبىل الٌهائي للرسالت‬ ‫عٌىاى الرسالت‪:‬‬

‫تصوين ًظام السيطر ِة اآللي علي الطيراى (طيار آلي) باستخذام‬ ‫األًظوت الوذهجت هتٌاهيت الصغر‬ ‫لجٌت الحكن والوٌاقشت‬ ‫أ‪ .‬د‪ .‬سعيــــــــــــــــذ عــــبـــــــــذ الـوـٌــعــــــــــن و ـــــــــــ‬

‫التىقيع‪......................................:‬‬

‫أستـــــــــــــــو لكــــــــــتـــ ا لكــــتــــاىــــــــــــــ وث لك ـــــــــــــــــ‬ ‫معهــــــــــــــــــــــل ـــــــــــــــــــــ ـ لاكــــتــــاىــ ــــــــــــــــــــــــــوث‬

‫أ‪ .‬د‪.‬‬

‫ســـــــام الذيـــــــــي سيـــــــي أ وـــــــــــــــــــــذ‬

‫التىقيع‪......................................:‬‬

‫أســـتــــــــو هنلست لإلكـتـاى وث اشبـــــوث لاتـصــــــــــواث‬ ‫عم ـــــــل كل ـــــــت لكهنلســـــــت لإلكـتـاى ـــــــت ـمنـــــــ ـ سوـ ــــــــــــــو‬ ‫كل ـــــــت لكهنلســـــــت لإلكـتـاى ـــــــت ـمنـــــــ ـ جومعـــــــت لكمن ـــــــت‪.‬‬

‫أ‪ .‬د‪.‬‬

‫هـــــــــــــــالت هحوـــــــذ عبـــــذ القـــــادر هٌصـــــىر‬

‫التىقيع‪......................................:‬‬

‫أستــــــــــــــــــــــــــو تـــــل ــــــــــــــــــــــــ لاشـــــــــــــــــــــــــــــــــــو لث‬ ‫كل ــــــــــــت لكهنلســــــــــــت ــــبــــــــــــــل جومــــــــــــــــعت ــنــــــــــــــــــهو‪.‬‬

‫أ‪ .‬م‪ .‬د‪ .‬عـــذلـــــــــــــي تـــــحاث تــــــــــاـ الـــــذيــــــــــي‬

‫التىقيع‪......................................:‬‬

‫أســـتو مســـوعل ـــ هنلســـت لإلكـتـاى ــــــــــــــــــــــــــــــــــــوث‬ ‫(شــــــــــــــــــــــــــــــــــــــــــــــــــــبـوث لإلتصــــــــــــــــــــــــــــــــــــــــــــــــــــواث‬ ‫كل ـــــــــت لكهنلســـــــــت ــبـــــــــــــــــل – جومعـــــــــت ـنـهــــــــــــــــــــــو‪.‬‬

‫لك وهـة – جمه يت مصـ لكعــ ت‬ ‫‪6102‬‬

‫جاهعت بٌها‬ ‫كليت الهٌذست بشبرا‬ ‫قسن الهٌذست الكهربيت‬

‫حصوين ًظام السيطر ِة اآللي علي الطيراى (طيار آلي) باسخخذام‬ ‫األًظوت الوذهجت هخٌاهيت الصغر‬ ‫رسانت مقدمت إنى كهيت انهندست بشبرا كجزء من متطهباث انحصىل عهي درجت دكتىراة انفهسفت في‬ ‫(هٌذست اإللكخروًياث)‬

‫إعــذاد‬

‫الوهٌذس‪ /‬أحوذ السيذ أحوذ علي البٌا‬

‫ححج إشــراف‪:‬‬ ‫أ‪.‬د ‪ /‬حسام الذيي حسيي أحوذ‬

‫أ‪.‬د ‪ /‬هالت هحوذ عبذ القادر‬

‫أستاذ هندست اإلنكترونياث وشبكاث االتصاالث‪,‬‬ ‫عميد كهيت انهندست اإلنكترونيت بمنىف سابقا‪ ,‬كهيت انهندست‬ ‫اإلنكترونيت بمنىف‪ ,‬جامعت انمنىفيت‪.‬‬ ‫[‬ ‫]‬

‫أستاذ تحهيم اإلشاراث‪,‬‬ ‫كهيت انهندست بشبرا‪,‬‬ ‫جامعت بنها‪.‬‬ ‫[‬ ‫]‬

‫د ‪ /‬أشـــرف هحوــذ حــافظ‬

‫د ‪ /‬أحوذ ًصر الذيي ابراهين‬

‫قســم انهندســت انكهربيــــت‪,‬‬ ‫كهيت انهندست بشبرا‪,‬‬ ‫جامعت بنها‪.‬‬ ‫[‬ ‫]‬

‫قســم انهندســت انكهربيــــت‪,‬‬ ‫انكهيت انفنيــــــت انعسكريت‪.‬‬ ‫]‬

‫القاهرة ‪ -‬جمهورية مصر العربية‬ ‫‪6102‬‬

‫[‬