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研究生：	張家媛 Chong, Chia-Yen
論文名稱：	微衛星姿態估測及判定次系統之設計、實現和驗證 Design, Implementation and Verification of Microsatellite Attitude Determination and Control Subsystem
指導教授：	苗君易 Miau, Jiun-Jih
共同指導教授:	莊智清 Juang, Jyh-Ching
學位類別：	碩士 Master
系所名稱：	工學院 - 航空太空工程學系 Department of Aeronautics & Astronautics
論文出版年：	2011
畢業學年度：	99
語文別：	英文
論文頁數：	120
中文關鍵詞：	CKUTEX微衛星、姿態判定、軟体迴路模擬、程序迴路模擬
外文關鍵詞：	CKUTEX, Microsatellite, Attitude Determination, Software-in-the-loop (SIL), Processor-in-the-loop (PIL)
相關次數：	點閱：89 下載：2
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CKUTEX (Cheng‐Kung University Technology Experimental)衛星係國立成功大學自主發展參拾公斤等級的實驗型微衛星。於衛星姿態判別及控制次系統，主要為提供衛星姿態控制、姿態估測及穩定衛星角速度。
CKUTEX衛星操作模式主要分為三種：初始模式(Initial mode)、減速模式(Detumbling mode)及正常模式(Normal mode)。在初始模式下，此次系統將利用星載感測器擷取早期軌道資訊進而下傳到地面站作後處理分析。在減速模式時，則運用磁力控制法則來降低及穩定衛星角速度。衛星在正常操作模式下，姿態次系統將開啓姿態判別來估測衛星姿態。
在初步設計時，本論文運用軟体迴路模擬(Software-in-the-Loop Simulation)設計及驗證系統的架構及參數。於軟體迴路模擬驗證後，採用程序迴路模擬(Processor-in-the-Loop Simulation)驗證姿態判別及控制次系統星上飛行軟體及演算法。軟体迴路模擬係利用Matlab Simulink實現，而程序迴路模擬主要由即時動態模擬器及姿態判別及控制次系統上嵌入式微控制晶片和整合電路所構成。即時動態模擬器主要用於模擬太空環境、軌道資訊、姿態動態、感測器及控制器；姿態判別及控制次系統上嵌入式微控制晶片和整合電路則用來實現衛星姿態判別及控制演算法。最後，藉由程序迴路模擬來驗證整個衛星姿態判別及控制次系統效能，並提出改進方法。

At NCKU, Taiwan, a 30 kg experimental micro satellite named CKUTEX is being developed. The role of the Attitude Determination and Control Subsystem (ADCS) is to provide attitude control functions, including the detumbling and stabilizing the satellite angular velocity, and as well as estimating the orbit and attitude information during the satellite operation.
For CKUTEX, the operation of the ADCS consists of three modes which are initialization mode, detumbling mode, and normal modes respectively. During the initialization mode, ADCS collects the early-orbit measurement data from various sensors so that the data can be downlinked to the ground station for further analysis. During the detumbling mode, ADCS implements the magnetic control method to decrease the satellite angular velocity. During normal mode, ADCS provides the attitude determination function for the estimation of the satellite state.
During the development stage, Software-in-the-Loop (SIL) simulation is used for designing the architecture and parameters of ADCS. In addition of SIL simulation, a Processor-in-the-Loop (PIL) test platform has been set up for the verification test of the designed ADCS hardware. The SIL simulation is achieved by using Matlab software, while PIL test implement a real-time dynamic simulator and controller, as well as some interfacing circuitry. The real-time dynamic simulator is capable of performing simulation of the space environment, orbit dynamic, attitude dynamic, and sensor/actuator models. The controller/estimator is a realization of the embedded controller for attitude determination and control. The CKUTEX employs three sensors including magnetometer, sun sensor, and IMU for attitude determination. The control actions of the CKUTEX are provided by magnetic torque rods.
At last, the design and performance of ADCS can be verified by the PIL test and some suggestion will be given to improve this subsystem.

摘要…………………………………………………………………………………I
Abstract…………………………………………………………………………………………………………………………………III
Acknowledgement……………………………………………………………………………………………………………………V
Contents…………………………………………………………………………………………………………………………………VII
List of Tables………………………………………………………………………………………………………………………X
List of Figures…………………………………………………………………………………………………………………XI
Chapter 1 Introduction…………………………………………………………………………………………………1
1.1 Overview……………………………………………………………………………………………………………………………1
1.2 Background………………………………………………………………………………………………………………………1
1.3 Attitude Determination and Control Subsystem……………………………6
1.3.1 ADCS Sensors……………………………………………………………………………………………………………8
1.3.2 ADCS Actuator………………………………………………………………………………………………………10
1.3.3 ADCS Processor……………………………………………………………………………………………………11
1.3.4 ADCS Design and Verification Tools………………………………………………12
1.3.5 Organization…………………………………………………………………………………………………………13
Chapter 2 Satellite & Environment Model…………………………………………………15
2.1 Attitude definitions and conventions………………………………………………15
2.1.1 Direction Cosine Matrix……………………………………………………………………………15
2.1.2 Euler Angles…………………………………………………………………………………………………………18
2.1.3 Quaternion………………………………………………………………………………………………………………19
2.2 Equation of Motions……………………………………………………………………………………………21
2.2.1 Dynamic Equations……………………………………………………………………………………………21
2.2.2 Kinematic Equations………………………………………………………………………………………22
2.2.3 Satellite Rotational Model……………………………………………………………………23
2.3 Coordinate Frames…………………………………………………………………………………………………24
2.3.1 Celestial Coordinate System…………………………………………………………………24
2.3.2 Earth centered inertial frame (ECI)……………………………………………26
2.3.3 Earth centered earth fixed frame……………………………………………………27
2.3.4 Orbit frame……………………………………………………………………………………………………………27
2.3.5 Body frame………………………………………………………………………………………………………………28
2.4 Coordinate Frame Transformation……………………………………………………………29
2.4.1 ECI and ECEF frame transformation…………………………………………………29
2.4.2 ECI and orbit frame transformation………………………………………………31
2.4.3 ECI and body frame transformation…………………………………………………31
2.4.4 Orbit and body frame transformation……………………………………………32
2.5 Keplerian Orbit………………………………………………………………………………………………………32
2.5.1 Orbital elements………………………………………………………………………………………………33
2.5.2 Time system……………………………………………………………………………………………………………35
2.5.3 Position and velocity as a function of time………………………36
2.6 Orbit Perturbations……………………………………………………………………………………………38
2.6.1 Perturbations due to Non-spherical Earth………………………………38
2.6.2 Perturbations due to third body interaction………………………39
2.7 Space Environment Model…………………………………………………………………………………41
2.7.1 Magnetic Field Model (IGRF Model)…………………………………………………42
2.7.1.1 Calculation of Earth Magnetic Field Intensity……………44
2.7.2 The Earth’s Upper Atmosphere Model………………………………………………49
2.7.3 Sun Position Model…………………………………………………………………………………………49
2.8 Disturbance torques……………………………………………………………………………………………52
2.8.1 Gravity-gradient torque……………………………………………………………………………53
2.8.2 Aerodynamic Torque…………………………………………………………………………………………54
2.8.3 Magnetic Disturbance……………………………………………………………………………………56
2.9 Sensor and Actuator Models…………………………………………………………………………57
2.9.1 Gyro………………………………………………………………………………………………………………………………57
2.9.1.1 Gyro Error Model…………………………………………………………………………………………58
2.9.2 Sun Sensor………………………………………………………………………………………………………………61
2.9.3 Magnetometer…………………………………………………………………………………………………………63
2.9.4 Magnetic Torque Rod………………………………………………………………………………………64
Chapter 3 ADCS Design…………………………………………………………………………………………………66
3.1 Attitude Control……………………………………………………………………………………………………66
3.1.1 Magnetic Attitude Control………………………………………………………………………67
3.1.2 B dot Control Law……………………………………………………………………………………………68
3.1.3 Periodic Measurement and Actuation………………………………………………71
3.1.4 Pulse Width Modulation (PWM)………………………………………………………………72
3.2 Attitude Determination……………………………………………………………………………………73
3.2.1 Attitude Determination Algorithm……………………………………………………74
3.2.2 EKF Model…………………………………………………………………………………………………………………75
3.2.3 EKF Implementation…………………………………………………………………………………………79
3.2.4 Filter Tuning………………………………………………………………………………………………………82
3.2.5 Attitude Error Representation……………………………………………………………83
Chapter 4 Verification of ADCS…………………………………………………………………………85
4.1 Verification Tests………………………………………………………………………………………………85
4.1.1 Software-in-the-Loop Testing ……………………………………………………………89
4.1.2 Processor-in-the-Loop Testing……………………………………………………………91
4.1.2.1 Data Monitoring Center…………………………………………………………………………95
4.1.2.2 Space Environment Simulation…………………………………………………………97
4.1.2.3 ADCS Module……………………………………………………………………………………………………100
Chapter 5 Simulation Result………………………………………………………………………………103
5.1 The Simulation of Attitude Determination in SIL and PIL………………………………………………………………………………103
5.1.1 SIL Simulation…………………………………………………………………………………………………105
5.1.2 PIL Test…………………………………………………………………………………………………………………109
5.2 Discussion of the SIL and PIL Results…………………………………………113
Chapter 6 Conclusions………………………………………………………………………………………………115
6.1 Future Research……………………………………………………………………………………………………115
Reference………………………………………………………………………………………………………………………………117

List of Tables
Table 2.1: IGRF coefficients for epoch 2010 to 2015…………………45
Table 2.2: Random Noise coefficients…………………………………………………………60
Table 3.1 Summary of EKF Algorithm………………………………………………………………78
Table 5.1 Orbit Elements in SIL and PIL Tests………………………………103
Table 5.2: Satellite model Parameters……………………………………………………104
Table 5.3: Initial Conditions of CKUTEX………………………………………………104
Table 5.4: Initial Conditions of EKF………………………………………………………104
Table 5.5: The Mean and Standard Deviation of the Estimation Error in SIL Test…………………………………………………………………………………………………………109
Table 5.6: The Mean and Standard Deviation of the Estimation Error in PIL Test…………………………………………………………………………………………………………113


List of Figures
Figure 1.1: CKUTEX satellite structure and components………………3
Figure 1.2: System Architecture of CKUTEX………………………………………………5
Figure 1.3: ADCS Architecture………………………………………………………………………………6
Figure 1.4: ADCS State Transition……………………………………………………………………8
Figure 1.5: MEMS gyroscope, Magnetometer and sun sensor………10
Figure 1.6: Magnetic torque rod………………………………………………………………………11
Figure 1.7: PIC microcontroller………………………………………………………………………11
Figure 1.8: NI PXI-1042……………………………………………………………………………………………13
Figure 2.1: Satellite Rotational Model in Simulink……………………24
Figure 2.2: The Celestial Coordinate System………………………………………25
Figure 2.3: Definition of ECI Frame……………………………………………………………26
Figure 2.4: Definition of ECEF Frame…………………………………………………………27
Figure 2.5: Definition of Orbit Frame………………………………………………………28
Figure 2.6: Definition of Body Frame…………………………………………………………29
Figure 2.7: Relationship between ECI and ECEF Frame…………………30
Figure 2.8: Keplerian Orbit Elements…………………………………………………………35
Figure 2.9: Elliptical Orbit………………………………………………………………………………35
Figure 2.10: Elliptical orbit and Circumscribed Circle…………38
Figure 2.11: Satellite Position in ECI Frame for 1 Orbital Period…………………………………………………………………………………………………………………………………………41
Figure 2.12: Satellite Velocity in ECI Frame for 1 Orbital Period…………………………………………………………………………………………………………………………………………41
Figure 2.13: Contour maps of total intensity (nT) at 2010.0…………………………………………………………………………………………………………………………………………43
Figure 2.14: Secular variation of total intensity (nT/year) for 2010.0-2015.0……………………………………………………………………………………………………………43
Figure 2.15: Mean Density of Atmosphere as Function of Altitude……………………………………………………………………………………………………………………………………49
Figure 2.16: Celestial Coordinate…………………………………………………………………50
Figure 2.17: Geocentric (ECI) Coordinates……………………………………………52
Figure 2.18: Eclipse Geometry……………………………………………………………………………52
Figure 2.19: Gravity Gradient Disturbance Torque in one Orbital Period……………………………………………………………………………………………………………………54
Figure 2.20: Aerodynamic Disturbance Torque in one Orbital Period…………………………………………………………………………………………………………………………………………55
Figure 2.21: Magnetic Disturbance Torque in one Orbital Period…………………………………………………………………………………………………………………………………………56
Figure 2.22: Allan Deviation Analysis for MEMS Gyro…………………59
Figure 2.23: Angle Random Walk Model…………………………………………………………60
Figure 2.24: Rate Random Walk Model……………………………………………………………61
Figure 2.25: Gyro Error Model……………………………………………………………………………61
Figure 2.26: Sun Sensor Model……………………………………………………………………………63
Figure 2.27: Magnetometer Model………………………………………………………………………64
Figure 2.28: Magnetic Torque Rod Model……………………………………………………65
Figure 3.1: B dot Control Model………………………………………………………………………70
Figure 3.2: Periodic B dot Control Cycle………………………………………………71
Figure 3.3: PWM Signal Generation in Simulink…………………………………72
Figure 3.4: Block Diagram of the system…………………………………………………76
Figure 3.5: Simulation of Attitude Determination of CKUTEX in Simulink……………………………………………………………………………………………………………………………82
Figure 3.6: Attitude Error Representation in Simulink……………84
Figure 4.1: Flowchart of ADCS Design…………………………………………………………88
Figure 4.2: ADCS in SIL Test………………………………………………………………………………89
Figure 4.3: The Architecture of PIL Test………………………………………………92
Figure 4.4: The Platform of PIL Test…………………………………………………………94
Figure 4.5: The Hardware in PIL Test…………………………………………………………95
Figure 4.6: The Simulation Management of PIL Test………………………96
Figure 4.7: Data and Graphs displayed in LabVIEW front panel……………………………………………………………………………………………………………………………………………97
Figure 4.8: System Architecture of PXI-8106 ……………………………………98
Figure 4.9: ADCS Model in LabVIEW…………………………………………………………………99
Figure 4.10: ADCS Circuit board and ADCS Module…………………………100
Figure 4.11: The Coding Structure in PIC32 microcontroller………………………………………………………………………………………………………………101
Figure 5.1: The Real and Estimated Quaternion in SIL test……………………………………………………………………………………………………………………………………………106
Figure 5.2: The Error of the estimated Quaternion in SIL test……………………………………………………………………………………………………………………………………………106
Figure 5.3: The Estimation Error of Euler Angle in SIL test ………………………………………………………………………………………………………………………………………………………107
Figure 5.4: The Estimation Error of Euler Angle in SIL test (zoomed in)…………………………………………………………………………………………………………………………107
Figure 5.5: The Sun Vector in ECI Frame………………………………………………108
Figure 5.6: The Real and Estimated Angular Rates in SIL test……………………………………………………………………………………………………………………………………………108
Figure 5.7: The Error of the Estimated Angular Rates in SIL test……………………………………………………………………………………………………………………………………………109
Figure 5.8: The Real and Estimated Quaternion in PIL test……………………………………………………………………………………………………………………………………………110
Figure 5.9: The Error of the estimated Quaternion in PIL test……………………………………………………………………………………………………………………………………………111
Figure 5.10: The Error of the estimated Euler Angle in PIL test……………………………………………………………………………………………………………………………………………111
Figure 5.11: The Estimation Error of Euler Angle in PIL test (zoomed in)…………112
Figure 5.12: The Real and Estimated Angular Rates in PIL test……………………………………………………………………………………………………………………………………………112
Figure 5.13: The Error of the Estimated Angular Rates in PIL test……………………………………………………………………………………………………………………………………………113

                                    

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