本論文探討重力梯度衛星姿態控制系統之設計與模擬。根據衛星設計的需求，軌道高度定在500公里，傾斜角為25度。利用重力梯度杆與三軸磁力線圈來穩定及控制衛星的姿態。重力梯度杆提供被動的控制，三軸磁力線圈則提供主動的控制。在理論分析上，首先將衛星的動態方程式線性化，在考慮地磁的影響下，利用最佳化控制理論中的線性二次調整(LQR)理論來設計控制器。隨後此控制器被使用在非線性的衛星動態方程式作模擬，並函蓋了外來干擾力矩的影響。數值模擬分成三個層面，首先是模擬衛星剛脫離火箭後，使用主動磁控制力矩的減速模式，之後模擬展開重力梯度杆與太陽能板後衛星受到被動控制的一般模式。此外，也模擬了衛星的安全模式，即衛星在一般模式中遇到干擾而失去地球指向精度時，可啟動主動磁控制力矩恢復衛星的地球指向精度。由本文模擬結果顯示，所設計的衛星姿態控制器效果良好。

In this thesis﹐the design and simulation of the attitude control system of the gravity gradient satellite are presented﹐The designed satellite requirement is to use the gravity gradient boom and the magnetic coils controlling the attitude of a satellite at 500 km altitude﹐25 degree inclination orbit. The satellite attitude controller is designed by the theory of Linear Quadratic Regulator (LQR) and then applied to the control of the nonlinear dynamics of the satellite under the influence of the earth's magnetic field and the external disturbing torques﹐The simulation is divided into three modes. The first mode is the despin mode﹐which is to reduce the angular rates to very low values, especially the spin rate﹐right after the satellite is separated from the launcher for erecting a comparatively weak extendible boom. The second mode is the normal mode, in which the satellite is controlled by its gravity gradient boom. The third mode is the detumbling mode﹐in which the earth pointing accuracy of the satellite can be restored by use of active magnetic control torque. The simulation shows satisfactory results.

[1] http://www.space.t.u-tokyo.ac.jp/cubesat/index-e.html
[2] Yang Xu, Sun Zhaowei, Yang Di, “The Study of Active Magnetic Control System for Gravity Gradient Small Satellite”, Flight Dynamics, Vol. 16, No. 1,pp. 90-95, Mar. 1998.
[3] Geng Yunhai, Cui Hutao, Sun Zhaowei and Yang di, “Attitude Control System Design for Small Satellite Earth Acquisition with Active Magnetic Control”, Acta Aeronautica Et Astronautica Sinica,Vol. 21, No. 2, pp. 142-145, Mar. 2000.
[4] Rafał Wi´sniewski, “Satellite Attitude Control Using Only Electromagnetic Actuation”, Department of Control Engineering Aalborg University,1996.
[5] B. S. Leonard, “NPSAT1 Magnetic Attitude Control System”,AIAA Conference on Small Satellites, SSC02-V-7, 2002.
[6] Eli Jerpseth Øverby, “Attitude control for the Norwegian student satellite nCube”, Department of Engineering Cybernetics, Norwegian University of Science and Technology, 2004.
[7] Kristian Svartveit, “Attitude determination of the NCUBE satellite,Department of Engineering Cybernetics”, Norwegian University of Science and Technology, 2003.
[8] Huang Weidong and Zhang Yulin, “An Optimal Control Algorithm Of a Gravity Gradient Stabilized Small Satellite with Momentum Wheel and Magnetic Torque”, Aerospace Control, Vol. 23, No. 4,pp. 27-31, Aug. 2005.
[9] 林詠翔, “微衛星姿態控制次系統設計與模擬”, 國立成功大學航空太空工程學系碩士論文,2000.
[10] 李愷倫,”皮米衛星姿態判定與控制次系統之設計與測試”, 國立成功大學航空太空工程學系碩士論文,2004.
[11] Artur Scholz, “奈米級衛星進階姿態判別與控制技術之實現”, 國立成功大學航空太空工程學系碩士論文,2008.
[12] 吳世驊, “皮米級衛星姿態控制次系統之設計與實現”, 國立成功大學電機工程學系碩士論文, 2006.
[13] 孫煜明, “微微衛星姿態控制次系統之設計與模擬”, 國立成功大學電機工程學系碩士論文, 2003.
[14] 陳明豐,” 低軌道衛星姿態估測演算法”, 國立台灣大學電機工程學系碩士論文, 2002.
[15] 楊士徹, “應用卡爾曼濾波理論於系統之估算與控制”, 逢甲大學航太與系統工程學系, 2006.
[16] Lin Laixing, “Gravity Gradient Control of Small Satellites”, Beijing Institute of Control Engineering
[17] Stian Søndersrød Ose, “Attitude determination for the Norwegian student satellite nCube”, Department of Engineering Cybernetics, Norwegian University of Science and Technology, 2004.
[18] Thomas Røbekk Krogstad, “Attitude Control of Satellites in Clusters”, Department of Engineering Cybernetics, Norwegian University of Science and Technology, 2005.
[19] Guan Yu, “Research on Satellite Attitude Control System Based on Robust Fault-Tolerant Control”, Harbin Institute of Technology, 2006.
[20] P. C. Hughes, Spacecraft Attitude Dynamics, John Wiely & Sons,Inc.,1986.
[21] M. J. Sidi, Spacecraft Dynamics and Control, Cambridge University Press, 1997.
[22] J. R. Wertz, Spacecraft Attitude Determination and Control, Kluwer Academic Publishers, 1978.
[23] 莊智清,苗君易,”地球ELF/ULF觀測微衛星之研究”,國家太
空中心專題研究計畫結案報告,2008.
[24] http://www.nspo.gov.tw
[25] http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html
[26] http://www.cubesat.auc.dk/
[27] http://ssdl.stanford.edu/ssdl/images/stories/AA236/
A06Fall/Lectures/lecture-16.pdf