Modeling and Control of A Pico-satellite Attitude Using Fuzzy Logic Controller

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Modeling and Control of A Pico-satellite Attitude Using Fuzzy Logic Controller

By

Zaridah Binti Mat Zain (0630610091)

A thesis submitted

in fulfillment of the requirements for the degree of Master of Science (Mechatronic Engineering)

School of Mechatronic Engineering UNIVERSITI MALAYSIA PERLIS

2009

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4.5 Adaptive Predictive Fuzzy Logic Controller ... 41

4.6 Two Axis and Three Axis Pico-satellite System ... 45

4.7 The Simulation of APFLC using Y-Thompson Spin Rate ... 46

4.8 Implementation of UniMAP ACS on the InnoSAT System ... 50

4.9 Basic Proportional, Integral, Derivative Controller ... 52

5.2 Simulation Results of Basic FLC for One Axis Problem ... 56

5.3 Simulation Results of Predictive Fuzzy Logic Controller for One Axis Problem .. 59

5.4 Simulation Results of Adaptive Predictive Fuzzy Logic Controller for One Axis Problem ... 60

5.5 Simulation Results of Basic FLC for Two Axis Problem ... 66

5.6 Simulation Results of Predictive FLC for Two Axis Problem ... 68

5.7 Simulation Results of Adaptive Predictive FLC for Two Axis Problem ... 69

5.8 Simulation Results of Basic FLC for Three Axis Problem ... 70

5.9 Simulation Results of Predictive FLC for Three Axis Problem ... 72

5.10 Simulation Results of APFLC for Three Axis Problem ... 74

5.11 Simulation Results of APFLC Compared with PID Controller for Three Axis Problem ... 78

5.12 Simulation Results Of Y-Thompson Spin ... 82

6.2 The Genetic Algorithm ... 89

6.3 The optimization of Two Points ... 94

6.4 The optimization of Four Points ... 97

6.5 The optimization of Six Points ... 101

7.1 Summary ... 107

7.2 Future Works ... 110

REFERENCES ... 111

LIST OF PUBLICATIONS ... 116

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DECLARATION OF THESIS

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ACKNOWLEDGEMENT

This dissertation is submitted in partial fulfillment of the requirement of Master Degree of Science at Malaysia Perlis University. This research has been carried out in the period from November 2006 to January 2009 under supervision of Associate Professor Dr. Paulraj M P and Professor Dr. Sazali Bin Yaacob. I am mostly thankful to both of my supervisors for their guidance during the research program.

I would express my sincere thanks to Professor Dr. R Nagarajan for his encouragement and inspiring discussions during my research period. I also greatly acknowledge the Ministry of Science, Technology and Innovation Malaysia, Astronautic Technology (M) Sdn Bhd and School of Mechatronic Engineering, Malaysia Perlis University for scholarship and economical support in my research work.

I am greatly thankful to all InnoSAT team members for all assistance and support. I am greatly indebted to my parents, Mat Zain Bin Yahaya and Samsiah Binti Man and my siblings who always believed that I would succeed in my studies. I would like to express my deepest thanks to my husband Mohd Jum’adi Bin Ab. Shukor for his patience and support during all these years. Last but not least to all my friends at UniMAP Research Cluster for your supports along this research period.

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LIST OF TABLES

Table Page

4.1 Three by Three FAM 38

4.2 Parameters analysis of kp, kd and ki 54

5.1 RMSE Performances of Basic FLC, Predictive FLC and APFLC

66

5.2 System analysis of APFLC and PID controller 79

6.1 Base Points of Two Points Optimization 94

6.2 Selected Base Points of Two Points Optimization 94

6.3 Base Points of Four Points Optimization 98

6.4 Base Points of Six Points Optimization 101

6.5 Summary of APFLC compared to APFLC with optimization using Genetic Algorithm

104

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LIST OF FIGURES

Figure Page

2.1 Inertia Frame 7

2.2 Orbit frame with Respected to Inertial Frame 7

2.3 Attitude control 11

2.4 Control System Architecture 16

3.1 The Discrete Transfer Function Model 28

4.1 Fuzzy Logic Control Block Diagram 33

4.2 Membership Function of Error (e(k)) 34

4.3 Membership Function of Change of Error (Δe(k)) 35

4.4 Membership Function of Actual Signal (m(k)) 36

4.5 Step Response of 3x3 FAM 38

4.6 Block Diagram of Basic FLC 39

4.7 Block Diagram of Predictive FLC 40

4.8 Block Diagram of APFLC with Disturbance, Noise and Nonlinearity

41

4.9 Operation of APFLC 44

4.10 Block Diagram of Two Axis System 45

4.11 Block Diagram of Three Axis Pico-satellite with Off Diagonal Coupling

46

4.12 Y-Thompson Spin for ϕ Axis 48

4.13 Y-Thompson Spin for θ Axis 49

4.14 Y-Thompson Spin for ψ Axis 50

4.15 InnoSAT Operating System of Attitude Control System 51

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4.16 PID Controller Block Diagram 53

5.1 Step Response of a Single Axis System with Basic FLC 57

5.2 Square Wave Reference Input 57

5.3 Output Response of One Axis system with Basic FLC for Square Wave Reference

58

5.4 Output Response of One Axis system with PFLC for Step Input Reference

59

5.5 Output Response of One Axis system with PFLC for Square Wave Reference

60

5.6 Output Response of One Axis System with APFLC for Step Input Reference

61

5.7 Output Response of One Axis System with APFLC for Square Wave Reference

62

5.8 Output Response of One Axis Model Reference System for Square Wave Reference

62

5.9 Gain Adaptation of One Axis Model Reference System with APFLC for Square Wave Reference

63

5.10 Output Response of One Axis APFLC for Square Wave Reference with Added Noise, External Disturbance and Nonlinearity

64

5.11 Output Response of One Axis Model Reference System for Square Wave Reference with Added Noise, External Disturbance and Nonlinearity

64

5.12 Gain Adaptation of One Axis Model Reference System for Square Wave Reference with Added Noise, External Disturbance and Nonlinearity

65

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5.13 Roll Axis Output Response of Two Axis System with Basic FLC 67 5.14 Pitch Axis Output Response of Two Axis System with Basic FLC 67 5.15 Roll Axis Output Response of Two Axis System with PFLC 68 5.16 Pitch Axis Output Response of Two Axis System with PFLC 68 5.17 Roll Axis Output Response of Two Axis System with APFLC 69 5.18 Pitch Axis Output Response of Two Axis System with APFLC 70 5.19 Roll Axis Output Response of Three Axis System with Basic FLC 71 5.20 Pitch Axis Output Response of Three Axis System with Basic

FLC

71

5.21 Yaw Axis Output Response of Three Axis System with Basic FLC 72 5.22 Roll Axis Output Response of Three Axis System with PFLC 73 5.23 Pitch Axis Output Response of Three Axis System with PFLC 73 5.24 Yaw Axis Output Response of Three Axis System with PFLC 74 5.25 Roll Axis Output Response of Three Axis System with APFLC 75 5.26 Pitch Axis Output Response of Three Axis System with APFLC 75 5.27 Yaw Axis Output Response of Two Axis System with APFLC 76 5.28 Roll Axis Output Response of Three Axis System with FLC and

Added Noise, Disturbance and Nonlinearity

77

5.29 Pitch Axis Output Response of Three Axis System with APFLC and Added Noise, Disturbance and Nonlinearity

77

5.30 Yaw Axis Output Response of Three Axis System with Basic FLC and Added Noise, Disturbance and Nonlinearity

78

5.31 Output Response of System with APFLC and PID Controller with Step Input

79

5.32 Output response of Satellite System with APFLC and PID 80

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5.33 Output response of Satellite System with APFLC and PID controller and Pseudorandom Noise

81

5.34 Output response of Satellite System with APFLC and PID controller and Added Pseudorandom Noise and Disturbance

82

5.35 Output Response of Roll Axis with Y-Thompson Spin 83 5.36 Disturbance Effect of Roll Axis with Y-Thompson Spin 83 5.37 Output Response of Pitch Axis with Y-Thompson Spin 84 5.38 Disturbance Effect of Pitch Axis with Y-Thompson Spin 84 5.39 Output Response of Yaw Axis with Y-Thompson Spin 85 5.40 Disturbance Effect of Yaw Axis with Y-Thompson Spin 86 6.1 Triangle Points Selected for Optimization Using GA 90 6.2 Flowchart of base points fuzzy membership function optimization

using GA

91

6.3 Triangle Points Selected for Two Points Optimization 94 6.4 Membership Function of Error for Two Points Optimization 95 6.5 Membership Function of Change of Error for Two Points

Optimization

95

6.6 Membership Function of Actual Signal for Two Points Optimization

96

6.7 Output Response of the Best Fitness Value of Two Points Optimization

96

6.8 Output Response of Non-optimize APFLC 97

6.9 Triangle Points Selected for Four Points Optimization 98

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6.10 Membership Function of Error for Four Points Optimization 99 6.11 Membership Function of Change of Error for Four Points

Optimization

99

6.12 Membership Function of Actual Signal for Four Points Optimization

100

6.13 Output Response of the Best Fitness Value of Four Points Optimization Using GA

100

6.14 Triangle Points Selected for Two Points Optimization 101 6.15 Membership Function of Error for Six Points Optimization 102 6.16 Membership Function of Change of Error for Six Points

Optimization

102

6.17 Membership Function of Actual Signal for Six Points Optimization

103

6.18 Output Response of APFLC for the Optimization Technique of Six Points Using GA

103

6.19 Output Response of APFLC for the Optimization Technique of Six Points Using GA with Added Disturbance

104

6.20 Output Response of APFLC for the Optimization Technique of Six Points Using GA with Pseudorandom Noise

105

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ABBREVIATIONS

InnoSAT Innovation Satellite

UniMAP Universiti Malaysia Perlis

ADCS Attitude Determination and Control System

OBC On-Board Computer

ACS Attitude Control System

ANGKASA Malaysia National Space Agency

FLC Fuzzy Logic Controller

PFLC Predictive FLC

APFLC Adaptive Predictive Fuzzy Logic Controller

PID Proportional Integral Derivative

GA Genetic algorithm

ADS Attitude Determination System

AI Artificial Intelligent

ZOH Zero Order Hold

SISO Single Input Single Output

MIMO Multi Input Multi Output

MISO Multi Input Single Output

NE Negative

ZE Zero

PO Positive

LO Low

NO Normal

HI High

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U Universe of Discourse

FIS Fuzzy Inference System

FAM Fuzzy associate memory

MF Membership Function

RMSE Root Mean Square Error

EA Evolutionary Algorithms

L Lower point

H Upper point

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NOMENCLATURES

𝐹 Force

a Acceleration

ms Mass

𝑇𝑜 Time per orbit

𝑔 Gravitational attraction at Earth’s surface

𝑅 Radius of Earth

𝑟 Radius of the orbit

𝑣 Velocity

T Torque

I Moment of inertia

^ Angular acceleration

 Angular velocity

Tc Control moments

Td Disturbance moments

T_gg Gravity gradient torque

h Angular momentum

hb Momentum of the rigid body hw Momentum of exchange devices

bi Velocity vector of the body frame relative to the inertial frame

br Angular velocity vector of the body frame relative to the reference frame

rib Angular velocity vector of the reference frame relative to the

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p, q & r Body angular rates

 Roll Angle

 Pitch Angle

 Yaw Angle

( )

m s Controller Input in S-Domain ( )s

 Attitude angle in S-Domain

m(k) Controller Output θ(k) Satellite Output

Ts Sampling time

e(k) Error Input

Δe(k) Change of error Input r(k) Reference Input

ep Predictor error

Δep Predictor change of error θm Output of Reference Model a₁, a₀, b₁ & b₀ Model Reference parameters

Q Adaptation gain

μ(k) Convergence factor α , δ Positive constant

kp Proportional gain

ki Integral gain

k_d Derivative gain

K Coupling Factor

T_p Peak time

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T_s Settling time

Tr Rise Time

%OS Percent overshoot 𝜃_𝑟𝑒𝑓 Measured Attitude

𝑕 Momentum of the satellite in the body frame

𝜔₀ Orbital rate

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ABSTRACT

Modeling and Control of A Pico-satellite Attitude Using Fuzzy Logic Controller Fuzzy logic concept was first conceived by Lotfi Zadeh in 1965 by incorporating rule based approach to solve control problems. The advantage of Fuzzy Logic Controller (FLC) is that the control process can be controlled without knowing much knowledge of their dynamics. FLC is applied as the controller to most of commercial mercantile products in past 25 years. Since that, many applications of the FLC in controlling the Pico-satellite’s attitude have been proposed successfully. In this regards, a new method of Pico-satellite attitude control using Mamdani Fuzzy Logic Principles is introduced.

The design of the APFLC is initially started with the designation of Basic FLC with two input and single output system. Then, a Predictive FLC is designed to compensate the effects of delay time which occurs in the Pico-satellite control system. The predictor is a one step-ahead predictor which estimates the required control at the next sampling time and applies to the system at current sampling time. Finally the adaptive portion of FLC is applied in order to compensate the effect of unknown parameter variations in the Pico-satellite system by using an adaptable gain which is connected in the forward path of the FLC. The response of the Pico-satellite is compared with a model reference adaptive system, derived on the basis of deviation in the responses and updates the adaptive gain. The adaptation continues until the Pico-satellite attitude reaches the set- reference attitude. The design schemes of modeling adaptive and predictive FLC (APFLC) is described as follow: Basic FLC, Predictive FLC (PFLC) and APFLC. The APFLC is compared with a conventional Proportional Integral Derivative (PID) controller. The simulation results are presented and the output responses indicate that this approach of FLC is acceptable even in the case of a Pico-satellite subjected to input noise, measurement noises, intermittent disturbances and also with sensor nonlinearity. It is observed that the APFLC showed convincing performance over the entire simulation of the Pico-satellite. Genetic Algorithm (GA) is a computational model inspired by evaluation. This algorithm encode a potential solution to a specific problem on a simple chromosome like data structure and apply recombination operators to this structure to preserve critical information. The contribution of this work is to optimize the base of Fuzzy membership function of the APFLC by using GA technique. The optimization technique involved from two points to four points and end with six points. The performances obtained show that the optimized APFLC is better than the non-optimize APFLC in terms of RMSE and the settling time.

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BSTRAK

Pembangunan dan Kawalan Sikap Sebuah Piko Satelit Menggunakan Pengawal Logik Kabur

Konsep logik kabur adalah pertama yang difikirkan oleh Lotfi Zadeh pada 1965 dengan menggabungkan undang-undang berpangkalan pendekatan untuk menyelesaikan masalah kawalan. Kelebihan bagi Pengawal Logik Kabur adalah proses kawalan itu boleh dikawal tanpa mengetahui banyak pengetahuan tentang dinamik mereka. FLC Pengawal Logik Kabur diaplikasikan sebagai pengawal kepada kebanyakan produk dagangan di dalam lebih 25 tahun. Sejak itu, banyak permohonan Pengawal Logik Kabur di dalam kawalan sikap sebuah Piko Satelit telah dicadangkan dengan jayanya.

Di dalam anggapan ini, satu kaedah baru bagi kawalan sikap sebuah Piko Satelit dengan menggunakan Pengawal Logik Kabur Mamdani diperkenalkan. Reka bentuk Pengawal Ramalan Logik Kabur Mudah Suai adalah dimulakan daripada Asas Pengawal Logik Kabur dengan dua masukan dan satu keluaran. Kemudian, satu Ramalan Pengawal Logik Kabur adalah direkabentuk untuk memampas kesan masa mati yang berlaku di dalam sistem kawalan Piko Satelit tersebut. Peramal adalah satu langkah meramal masa hadapan yang menganggarkan keperluan kawalan pada masa pensampelan yang akan datang dan digunakan ke atas sistem pada masa pensampelan semasa. Akhirnya bahagian Pengawal Logik Kabur Mudahsuai diaplikasikan dengan tujuan memampas kesan variasi parameter yang tidak diketahui di dalam sistem Piko Satelit tersebut dengan menggunakan satu keuntungan yang boleh disesuaikan dan dikaitkan di dalam laluan yang di hadapan Pengawal Logik Kabur. Sambutan Piko Satelit tersebut dibandingkan dengan satu sistem mudah suai rujukan yang contohnya perolehan tentang asas sisihan di dalam jawapan-jawapan dan kemaskini keuntungan ubah suai.

Penyesuaian diteruskan sehingga sikap Piko Satelit tersebut sampai ke set rujukan sikap. Skim-skim reka bentuk peragaan Ramalan Pengawal Logik Kabur Mudahsuai disifatkan seperti berikut: Asas Pengawal Logik Kabur, Ramalan Pengawal Logik Kabur dan Ramalan Pengawal Logik Kabur Mudahsuai. Ramalan Pengawal Logik Kabur Mudah Suai dibandingkan dengan satu konvensional pengawal Terbitan Kamiran Berkadar. Hasil simulasi dibentangkan dan hasil keluaran menunjukkan pendekatan bagi pengawal logic kabur adalah diterima juga di dalam kes seperti sebuah Piko Satelit dengan menakluki hingar masukan, bising ukuran, gangguan-gangguan terputus-putus dan juga dengan penderia ketaklelurusan. Ianya diperhatikan bahawa Ramalan Pengawal Logik Kabur Mudahsuai menunjukkan prestasi yang meyakinkan kepada hasil simulasi seluruh Piko satellite. Algoritma Genetik adalah satu model pengiraan cemerlang oleh penilaian. Algoritma ini membina kod penyelesaian yang berpotensi untuk satu masalah yang khusus sedang satu selapis kromosom seperti struktur data dan memohon gabungan semula pengendali-pengendali untuk struktur ini untuk mengekalkan maklumat kritikal. Sumbangan kerja ini adalah bagi mengoptimumkan asas bagi keanggotaan logic kabur fungsi Ramalan Pengawal Logik Kabur Mudahsuai dengan menggunakan teknik Algoritma Genetik. Teknik pengoptimuman terlibat daripada dua mata ke empat mata dan diakhiri dengan enam mata. Persembahan keputusan menunjukkan yang Ramalam Pengawal Logik Kabur Mudahsuai adalah lebih baik daripada Ramalan Pengawal Logik Kabur Mudah Suai yang tidak dioptimumkan di dalam soal ralat min punca kuasa dua dan masa penyelesaian.

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CHAPTER 1 INTRODUCTION

1.1 Background of the Study

Aerospace is a branch of engineering that includes design and construction of a spacecraft or aircraft. Aerospace refers to a flight within the atmosphere and applying the principles of science and technology to highly sophisticated products such as space satellites (Wallace, 2002). Space satellite is defined as an object orbiting another object.

Satellites can be celestial such as the moon orbiting a planet in the solar system or a man-made satellite which is typically launched into outer space from the Earth to collect data or images. A man-made satellite is an extremely complicated piece of equipment that includes propulsion system, power system, telemetry and command system, thermal control, superstructure, attitude control system and communication subsystem (Kim, 2007).

In view of a limited research attention in the area of satellite system in Malaysia, Malaysia National Space Agency (ANGKASA) and Astronautic Technology (M) Sdn.

Bhd. organized a research collaboration with Universiti Malaysia Perlis (UniMAP) concerned with the development of a Pico-satellite called the InnoSAT Project. The purpose of this program is to provide an opportunity for UniMAP to design a control algorithm for the Attitude Controller System (ACS) of the InnoSAT payload. The controller is designed by the School of Mechatronic Engineering, Universiti Malaysia Perlis (UniMAP) known as UniMAP ACS. UniMAP ACS is basically an embedded control algorithm firmware that produces necessary control parameters to the three

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magnetorquers based on the measured signals of three axis magnetometer to maintain the satellite in a fixed orientation with respect to the Earth. The firmware of UniMAP ACS is simulated using MATLAB program and embedded to RCM3400 Rabbit-Core Microcontroller Board using C language. The effectiveness of the control methodology is thoroughly and exhaustively tested by simulation studies with a satellite model before being implemented to the InnoSAT system.

1.2 Problem Statements

Immediately after launched and placed in its Low Earth Orbit (LEO), the Pico- satellite can be tumbling at an undefined angular rate. At this time the satellite needs to reduce the roll and yaw angular rates and align to the normal orbit. The proposed controller need to maintain a certain attitude while orbiting to allow accurate orientation towards the Earth. In addition, the proposed controller is necessary to maintain the satellite’s stability even if the satellite is affected with interferences such as magnetic fields, solar wind, disturbance torque reduce the tumbling rate. These phenomena tends to disturb the satellite's attitude, so it is necessary to control the attitude and keep the satellite stable even in addition of noise and disturbances. Although several control laws have been used to design the attitude control of a Pico-satellite (Tisa & Vergez, 2006), a new approach is expected to be more robust and can be efficiently used in real-time control. To handle these difficulties, a study of designing an Adaptive Predictive Fuzzy Logic Controller (APFLC) for the application of attitude control for a Pico-satellite is carried out. Fuzzy logic is selected as the controller suited for situations where the plant is too complex to model. A Predictive controller is introduced to compensate the effects

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of time delay and the adaptive portion is applied in order to compensate the effect of unknown parameter variations in the satellite system.

1.3 Research Methodology

In this study, three schemes of Fuzzy Logic Controller (FLC) are design to complete the APFLC in a package. The design of the APFLC is initially started with the designation of Basic FLC with two inputs and single output system. After that, a Predictive FLC is designed to compensate the effects of time delay which occurs in the satellite system. The predictor is a one step-ahead predictor which estimates the required control at the next sampling time and applies to the system at current sampling time. Later, the adaptive portion of FLC is applied in order to compensate the effect of unknown parameter variations in the Pico-satellite system by using an adaptable gain which is connected in the forward path of the FLC. The measured attitude is compared with a reference model derived on the basis of deviation in the responses and the adaptive algorithm updated the adaptable gain to correct the orientation. By referring to the complex Euler’s equation, a simplified but effective model to represent a Pico- satellite system is introduced. This model is considered to represent the tumbling behavior of a Pico-satellite in space after deployment and used to study the performances of Pico-satellite behavior under various conditions throughout this thesis.

The simulations carried out for several reference input such as step input, square wave input reference and Y-Thompson spin. As it is necessary to control the attitude and keep the satellite stable even in addition of noise and disturbances, the simulations are carried out with presence of Pseudorandom noise and short pulse disturbances. Finally, the APFLC is compared with a conventional Proportional-Integral-Derivative (PID)

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Controller and Genetic algorithm (GA) is presented to optimize the performances of the triangle base of Fuzzy membership function of the APFLC.

1.4 Research Objectives

This research attempts to examine the application of fuzzy logic principle in the development of attitude control of a Pico-satellite. More specifically the objectives of this study are given as follows:

 To design APFLC which consists of a controller using Fuzzy Logic principle named FLC, a Predictive controller to compensate the effects of delay time which occurs in the Pico-satellite system and apply Adaptive algorithm to reduce the effect of variations in unknown parameters due to various environmental phenomena in a single package.

 To develop a satellite model incorporating the APFLC and simulate the Pico- satellite system against disturbances, noises, nonlinearity and cross-coupling effect.

 To compare the APFLC with other conventional controller.

 To optimize the base membership points of APFLC using GA.

1.5 Thesis Outline

The research works carried out are presented in seven chapters in this thesis. In this First Chapter, a brief introduction is given for the proposed controller.

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The Second Chapter briefly reports the review of the literature that necessitate the scope of the present work.

The Third Chapter presents the dynamics modeling of a Pico-satellite using Euler’s method. The dynamics model has been simplified and discretized to form a discrete transfer function model and used throughout all simulation studies.

The Fourth Chapter describes the theoretical background for designing the FLC.

The three different variants of FLC namely Basic FLC, Predictive FLC (PFLC) the APFLC are discussed. All the three methods are simulated with one, two and three axis satellite system. The APFLC being compared with a conventional controller, PID.

The Fifth Chapter presents the simulation results of basic FLC, PFLC, APFLC and conventional PID controller. The advantages of applying APFLC for the attitude control are also discussed in this chapter. The performances of the designed controllers with off diagonal cross-coupling effect are also simulated with noise and disturbances.

The Sixth Chapter proposes an optimization technique of Fuzzy membership function of APFLC using GA. Several potential solutions are obtained and simulations have been carried out for analyzing the performance of APFLC. hence

The Seventh Chapter provides the conclusion of the study and offers some suggestion for further research.

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CHAPTER 2 LITERATURE REVIEW

2.1 Introduction to Satellite Attitude Control

A satellite’s life commences with a specific booster transferring it to an initial orbit called a transfer orbit. The satellite begins to circle the earth in its orbit and it has to be maneuvered to reach the precise final orbit in which the satellite is designed to fulfill its mission. This is achieved by the hardware and software embedded in the satellite system which continuously calibrate its instrumentation and optimizing its control performance in space (Sidi, 2000). The standard size (Cal poly standard) of a Pico-satellite (CubeSAT) is a single CubeSAT should be a 10-cm cube and have a total mass of not more than 1 kg (Nugent, et al., 2008). Though the Pico-satellite is very small, it exhibits virtually all the complex characteristics of a conventional larger one but in a microcosm which requires more manageable infrastructure (Said, et al., 2004) .

The orientation of a Pico-satellite body coordinate with respect to a defined frame is called attitude. This attitude is represent by the relationship between axis (ϕ, θ and ψ) and reference frame. Reference system is the attitude coordinate system and has its origin at the center of the Earth. There are two defined frame in the reference system namely inertia frame and orbit frame. The inertial frame is shown in Figure 2.1.

Modeling and Control of A Pico-satellite Attitude Using Fuzzy Logic Controller