隨著太空產業的蓬勃發展，立方衛星成為近幾年衛星發展的重點
之一。這種小型衛星的形狀通常是由邊長 10 公分的立方體組成，具
有體積小、重量輕和成本低等優勢。由於小尺寸和簡化的設計使其成
本相對較低，使大專院校以及更多的機構和團隊能夠參與太空探索和
研究。然而台灣也乗上了這股潮流，目前正在進行第三期太空科技長
程發展計畫 （2019-2028）[1]，包括先導型光學遙測衛星星系和超高
解析度光學遙測衛星等，遙測衛星的姿態控制至關重要。姿態控制是
確保這些衛星能夠正確定位、指向和捕捉所需的地球或太空目標。本
研究提出了一種新穎的反作用輪設計，用作衛星的姿態控制器，並透
過數值有限元素法進行研究。利用磁流變液能夠在磁化作用下從液體
轉變為半固體的特性，使用磁流變液封裝圓柱型磁鐵生成角動量。透
過有限元素法參數研究，找到了線圈的最佳放置位置。模擬結果顯示
線圈同心排列將能在管道內產生均勻磁場，並依次安排在反作用輪的
圓形管周圍。透過這種設計，不只大幅度降低製作成本及重量也解決
了原先反作用輪軸棒、軸承運動部件的接觸和摩擦問題。
關鍵字：立方衛星、遙測衛星、反作用輪、姿態控制器、磁流變流
體

With the rapid development of the space industry, CubeSats have become a key
focus in satellite development in recent years. These small satellites are typically
composed of 10-centimeter cubes, offering advantages such as small size, lightweight,
and low cost, yet they possess many vital applications. Their small size and simplified
design reduce costs, enabling universities and various institutions to participate in space
exploration and research. Taiwan has also joined this trend and is implementing the
third phase of the Long-Term Space Technology Development Program （2019-2028）
[1], which includes the development of pioneering optical remote sensing satellite
constellations and ultra-high-resolution optical remote sensing satellites. Attitude
control is crucial for these remote sensing satellites to ensure accurate positioning,
pointing, and capturing of the desired Earth or space targets. This study proposes a
novel reaction wheel design for satellite attitude control, investigated through
numerical finite element analysis. Utilizing the property of Magnetorheological fluid
（MRF）, which can change from liquid to solid under magnetization, magnetic spheres
encapsulated in MRF generate angular momentum. Parametric studies using the finite
element method identified the optimal placement of the coils. Simulation results
showed that a concentric arrangement of the coils creates a uniform magnetic field
within the conduit, sequentially arranged around the circular tube of the reaction wheel.
This design significantly reduces production costs and weight and addresses the issues
of contact and friction in the reaction wheel's axle and bearing components.
Keywords: CubeSat, Reaction wheel, Attitude controller, Magnetorheological fluid

[1] 國家科學及技術委員會. "行政院正式核定我國第三期國家太空
科技發展長程計畫." (accessed.
[2] https://www.nanosats.eu/, https://www.nanosats.eu/ ed.
[3] 維基百科. (accessed.
[4] R. A. Deepak and R. J. Twiggs, "Thinking out of the box: Space
science beyond the CubeSat," Journal of Small Satellites, vol. 1, no.
1, pp. 3-7, 2012.
[5] T.-Y. Shao, S.-L. Kao, and C.-M. Su, "Taiwan AIS CubeSat tracking
system for marine safety," in 2019 international conference on
intelligent computing and its emerging applications (ICEA), 2019:
IEEE, pp. 70-73.
[6] Y. Duann et al., "IDEASSat: A 3U CubeSat mission for ionospheric
science," Advances in Space Research, vol. 66, no. 1, pp. 116-134,
2020.
[7] Y.-K. Chen, Y.-C. Lai, W.-C. Lu, and A. Lin, "Design and
implementation of high reliability electrical power system for 2U
NutSat," IEEE Transactions on Aerospace and Electronic Systems,
vol. 57, no. 1, pp. 614-622, 2020.
[8] J.-H. Huang, T.-Y. Lin, C.-M. Liu, and J.-C. Juang, "Design and
evaluation of the attitude control system of the PHOENIX CubeSat,"
in 2013 CACS International Automatic Control Conference (CACS),
2013: IEEE, pp. 47-51.
[9] A. B. M. CIFUENTES, J.-C. JUANG, J.-J. MIAU, Y.-P. TSAI, and
Y.-R. YANG, "LESSON LEARNED ON IN-ORBIT OPERATION
OF THE IRIS-A ATTITUDE DETERMINATION AND CONTROL
SUBSYSTEM."
[10] A. Scholz, J.-J. Miau, and J.-C. Juang, "PACE-Taiwan’s First
Nanosatellite for Evaluation of Momentum-Biased Attitude Control,"
in 7th IAA Symposium on Small Satellites for Earth Observation,
Berlin, Germany, 2009.
[11] T.-C. Lin and T.-C. Hsueh, "A modular structural design for payload
replaceable cubesat," in AIAA Scitech 2021 Forum, 2021, p. 1257.
[12] Q. Young, R. Burt, M. Watson, and L. Zollinger, "PEARL CubeSat
bus building toward operational missions," in Small Satellites
Conference from AIAA/Utah State University, Logan, Utah, 2009.
[13] A. Nucera, "Development of an attitude estimator for the PEARL
Cubesat," ed, 2009.
[14] N. Popp et al., "Multi-shaft reaction wheel design for a 2U Cubesat,"
ed: Progress in Canadian Mechanical Engineering, 2021.
[15] Y. Zhe, T. Chunxia, W. Yanxuan, and W. Zhengjie, "Characteristic
modeling and attitude control for small satellite via variable inertial
reaction wheel," in Proceedings of the 32nd Chinese Control
Conference, 26-28 July 2013 2013, pp. 5373-5378.
[16] M. F. Mehrjardi, H. Sanusi, and M. A. M. Ali, "Developing a
proposed satellite reaction wheel model with current mode control,"
in 2015 International Conference on Space Science and
Communication (IconSpace), 2015: IEEE, pp. 410-413.
[17] D.-C. Hsiao and M.-F. Hsieh, "Integrated Design and Analysis of
Reaction Wheel Motor Applied to Satellite Attitude Control," in 2021
24th International Conference on Electrical Machines and Systems
(ICEMS), 2021: IEEE, pp. 1090-1094.
[18] B. Zandbergen, "Micropropulsion systems for Cubesats," CubeSat
Technology and Applications, pp. 1-36, 2013.
[19] M. Pasand, A. Hassani, and M. Ghorbani, "A study of spacecraft
reaction thruster configurations for attitude control system," IEEE
Aerospace and Electronic Systems Magazine, vol. 32, no. 7, pp. 22-
39, 2017.
[20] M. J. Turner, Rocket and spacecraft propulsion: principles, practice
and new developments. Springer Science & Business Media, 2008.
[21] A. El Fatimi, A. Addaim, and Z. Guennoun, "Design and analysis of
a nanosatellite attitude control system using processor-in-the-loop
approach," AEU-International Journal of Electronics and
Communications, vol. 171, p. 154880, 2023.
[22] J. Li, M. Post, T. Wright, and R. Lee, "Design of attitude control
systems for CubeSat-class nanosatellite," Journal of Control Science
and Engineering, vol. 2013, pp. 4-4, 2013.
[23] M.-C. Chou, C.-M. Liaw, S.-B. Chien, F.-H. Shieh, J.-R. Tsai, and H.-
C. Chang, "Robust current and torque controls for PMSM driven
satellite reaction wheel," IEEE Transactions on Aerospace and
Electronic Systems, vol. 47, no. 1, pp. 58-74, 2011.
[24] M.-C. Chou and C.-M. Liaw, "PMSM-driven satellite reaction wheel
system with adjustable DC-link voltage," IEEE Transactions on
Aerospace and Electronic Systems, vol. 50, no. 2, pp. 1359-1373,
2014.
[25] M.-C. Chou and C.-M. Liaw, "Development of robust current 2-DOF
controllers for a permanent magnet synchronous motor drive with
reaction wheel load," IEEE Transactions on Power Electronics, vol.
24, no. 5, pp. 1304-1320, 2009.
[26] R. Wiśniewski and M. Blanke, "Fully magnetic attitude control for
spacecraft subject to gravity gradient," Automatica, vol. 35, no. 7, pp.1201-1214, 1999.
[27] P. Wang and Y. B. Shtessel, "Satellite attitude control using only
magnetorquers," in Proceedings of the 1998 American Control
Conference. ACC (IEEE Cat. No. 98CH36207), 1998, vol. 1: IEEE,
pp. 222-226.
[28] M. Ovchinnikov and D. Roldugin, "A survey on active magnetic
attitude control algorithms for small satellites," Progress in
Aerospace Sciences, vol. 109, 06/01 2019.
[29] KONGSBERG. (accessed.
[30] R. FISCHELL and F. MOBLEY, "A system for passive gravitygradient stabilization of earth satellites," in Guidance and Control
Conference, 1964, p. 326.
[31] S. Exploration. (accessed.
[32] M. Choi and C. J. Damaren, "Structural dynamics and attitude control
of a solar sail using tip vanes," Journal of Spacecraft and Rockets, vol.
52, no. 6, pp. 1665-1679, 2015.
[33] S. Hassanpour and C. J. Damaren, "Collocated attitude and vibrations
control for square solar sails with tip vanes," Acta Astronautica, vol.
166, pp. 482-492, 2020.
[34] I. Medina, L. Santiago, J. Hernández-Gómez, R. Castillo, and C.
Couder-Castañeda, "Speed PID controller simulation of a reaction
wheel for CubeSat orientation applications," in Journal of Physics:
Conference Series, 2021, vol. 1723, no. 1: IOP Publishing, p. 012013.
[35] K. Lemmer, "Propulsion for cubesats," Acta Astronautica, vol. 134,
pp. 231-243, 2017.
[36] M. Kciuk and R. Turczyn, "Properties and application of
magnetorheological fluids," Journal of achievements in materials and
manufacturing engineering, vol. 18, no. 1-2, pp. 127-130, 2006.
[37] J. E. Kim and H. J. Choi, "Magnetic carbonyl iron particle dispersed
in viscoelastic fluid and its magnetorheological property," IEEE
transactions on magnetics, vol. 47, no. 10, pp. 3173-3176, 2011.
[38] A.-G. Olabi and A. Grunwald, "Design and application of magnetorheological fluid," Materials & design, vol. 28, no. 10, pp. 2658-2664,
2007.
[39] J. D. Carlson, "What makes a good MR fluid?," Journal of intelligent
material systems and structures, vol. 13, no. 7-8, pp. 431-435, 2002.
[40] H.-S. Chen, K.-Y. Peng, K.-Y. Ho, and J.-Y. Chang, "Design of a
Reaction Wheel with MRF-encapsulated Magnetic Ball," in 2023
IEEE International Magnetic Conference-Short Papers (INTERMAG
Short Papers), 2023: IEEE, pp. 1-2.
[41] M. Ehresmann, G. H. Herdrich, and S. Fasoulas, "Device for
generating a variable angular momentum, in particular for spacecraft
attitude control," ed: Google Patents, 2021.
[42] T. INSTRUMENTS. "DRV5053-Q1 Automotive Analog-Bipolar
Hall Effect Sensor." (accessed.
[43] D. T. Greenwood, Principles of dynamics (no. 6). Prentice-Hall
Englewood Cliffs, NJ, 1988.
[44] S. S. Nudehi, U. Farooq, A. Alasty, and J. Issa, "Satellite attitude
control using three reaction wheels," in 2008 American Control
Conference, 2008: IEEE, pp. 4850-4855.
[45] ROCKETLAB. "https://www.rocketlabusa.com/." (accessed 2006).