DEGREE PROJECT IN ,SPACE TECHNOLOGY SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2016 Attitude Determination and Control of the CubeSat MIST JIEWEI ZHOU KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING SCIENCES Preface The thesis work presented in this paper has been carried out between January and June 2016 under the scheme of the CubeSat Student Satellite Project MIST at KTH. I did it as a member of the 3rd MIST Student Team under the supervision of Dr. Gunnar Tibert, Associate Professor at the Department of Aeronautical and Vehicle Engineering at KTH, and Dr. Sven Grahn, the former Technical Director of the Swedish Space Corporation and the Project Manager of MIST. I am very thankful to Gunnar and Sven for having offered me this great opportunity to work in a real engineering project and contribute to build a satellite that will be launched in the near future. Many thanks to them also for their valuable guidance during my work, their experience in a large number of real satellite missions definitely helped me learn and make a better thesis. I would like to thank Prof. Yifang Ban for helping me to get in contact with Gunnar and Sven when I was looking for a thesis work at KTH. During my everyday work inside the MIST Student Team I was surrounded by great people that are not only quite professional and skillful in their respective fields but very pleasant persons to deal with as well. Many thanks to all of them for their cooperation to my work, specially to the Team Leader Simon G¨orries,Project Assistant Agnes G˚ardeb¨ack and the rest of members working in attitude control Oscar Bylund and Csaba J´eger. Finally, but certainly not least, I would like to say thanks to my family and friends for supporting me during my work. My very special thanks to Shreyas and Rutvika, who were my most close friends during my Erasmus+ stay in Stockholm. Jiewei Zhou Madrid July, 2016 Abstract The ADCS concept in MIST reflects the limitations of the CubeSat in terms of space, power and on- board computer computational capability. The control is constrained to the use of only magnetic torquers and the determination to magnetometers and Sun sensors in spite of the the under-actuation and under- determination during eclipses. Usually small satellites with a similar ADCS and demanding requirements fail, therefore MIST would be a design reference for this kind of concept in the case it succeeds. The objectives of this thesis work are the feasibility assessment of the concept to meet the nominal requirements in MIST and the consideration of alternatives. Firstly, the importance of gravitational stabilization and different configurations for the inertial properties are analyzed based on the linear stability regions for nadir pointing spacecraft. Besides, extended stability regions are derived for the case when a momentum wheel is used to consider alternative options for passive stabilization in terms of the inertial properties. Then a controller based on the Asymptotic Periodic Linear Quadratic Regulation (AP LQR) theory, the currently most extended and effective for pure magnetic control in small satellites, is assessed. Also a Liner Quadratic Regulator design by means of numerical optimization methods, which has not been used in any real mission, is considered and its performances compared with the AP LQR. Regarding attitude determination a Linear Kalman Filter is designed using the AP LQR theory. Finally, a robustness analysis is conducted via Monte Carlo simulations for those control and determination strategies. Sammanfattning Systemet f¨orattitydstyrning och -best¨amning i nanosatelliten MIST reflekterar sm˚asatelliters begr¨ansningarnai utrymme, elkraft och omborddatorkapacitet. Regleringen ¨arbegr¨ansadtill styrning med magnetspolar som genererar kraftmoment. F¨orattitydbest¨amningenanv¨andsmagnetometrar och solsensorer trots under-man¨ovreringoch -best¨amningvid solf¨orm¨orkelse. Vanligtvis misslyckas sm˚asatel- liter med liknande reglersystem och h¨ogakrav, s˚aom MIST lyckas skulle den bli ett referenskoncept. M˚alenmed detta examensarbete ¨aratt utf¨oraen genomf¨orbarhetsstudieav ett reglerkoncept f¨oratt m¨otade nominella kraven f¨orMIST samt unders¨oka av alternativa reglersystem. Effekten av gravitation- sstabilisering och olika masstr¨oghetskonfigurationer har analyserats med hj¨alpav linj¨ariseradestabilitet- sregioner f¨oren nadirpekande satellit. Stabilitetsregionerna f¨orstorasd˚aett roterande hjul inf¨orsi ett al- ternativt stabiliseringskoncept eftersom det roterande hjulet p˚averkar de effektiva masstr¨oghetsmomentet. Regleringsalgoritmen som utv¨arderatsi detta arbete ¨arbaserad p˚ateorin om Asymptotisk Periodisk Linj¨ar Kvadratisk Regulering (AP LKR), den som ¨armest anv¨andsamt effektiv f¨orren magnetisk styrning av sm˚asatelliter. En utformning av ett koncept baserat p˚aLinj¨arKvadratisk Reglering med numerisk opti- mering, vilket inte tidigare verkar anv¨ants f¨orett riktigt rymduppdrag, har unders¨oktsoch j¨amf¨ortsmed AP LKR-regleringen. N¨ardet g¨allerattitydbest¨amningens˚ahar ett linj¨artKalmanfilter utformats f¨or AP LKR-regleringen. Slutligen s˚ahar en robusthetsanalys gjorts genom Monte Carlo-simuleringar f¨or styrnings- och best¨amningsstrategierna. Resumen El concepto para el ADCS en MIST refleja las limitaciones de los CubeSats en cuanto a espacio, potencia y capacidad computacional del ordenador a bordo. El control est´arestringido al uso de s´olo magnetopares y la determinaci´ona magnet´ometrosy sensores de Sol a pesar de la imposibilidad de actuaci´onseg´untodos los ejes y el conocimiento incompleto en actitud durante eclipses. Normalmente peque~nossat´elitescon un ADCS similar y exigentes requisitos fallan, por la tanto MIST ser´ıauna referencia de dise~nopara este tipo de concepto en el caso de que tenga ´exito. Los objetivos de este trabajo fin de m´asterson la evaluaci´onde la viabilidad del concepto para cumplir los requisitos nominales en MIST y la consideraci´onde alternativas. Primero, la importancia de la estabilizaci´ongravitacional y diferentes configuraciones para las propiedades m´asicasson analizadas en base a las regiones de estabilidad lineales para veh´ıculos espaciales apuntando seg´unnadir. Adem´as, regiones de estabilidad extendidas son deducidas para el caso en el que una rueda de momento es usada con el fin de considerar opciones alternativas de estabilizaci´onpasiva en t´erminosde las propiedades m´asicas. Despu´esun controlador basado en la teor´ıa del Asymptotic Periodic Linear Quadratic Regulation, el actualmente m´asextendido y efectivo para control magn´eticopuro en peque~nossat´elites,es evaluado. Tambi´enun dise~node LQR por medio de m´etodos de optimizaci´onnum´erica,el cual no ha sido usado en ninguna misi´onreal, es considerado y sus prestaciones comparadas con el AP LQR. En relaci´ona la determinaci´onde actitud un Linear Kalman Filter es dise~nadousando la teor´ıadel AP LQR. Finalmente, un an´alisisde robustez es llevado a cabo a trav´esde simulaciones de Monte Carlo para esas estrategias de control y determinaci´on. Contents 1 Introduction 1 1.1 Background..............................................1 1.2 Problem Statement..........................................1 1.3 Previous Work............................................2 2 Literature Study 2 3 Modeling 3 3.1 Generalities..............................................3 3.2 Spacecraft...............................................5 3.3 Disturbances.............................................6 3.4 Actuators...............................................7 3.5 Sensors................................................7 4 ADCS Algorithms 8 4.1 Attitude Control...........................................8 4.2 Attitude Determination.......................................8 5 Disturbances Analysis 9 5.1 Aerodynamic Torque.........................................9 5.2 Residual Dipole............................................ 10 6 Passive Stabilization 10 6.1 Gravity Gradient........................................... 10 6.2 Momentum Bias........................................... 12 6.3 Pitch-Orbital Resonance....................................... 13 7 ADCS Design 14 7.1 Asymptotic Periodic LQR...................................... 14 7.2 LQR via Numerical Optimization.................................. 15 7.3 Asymptotic Periodic LQE...................................... 20 8 Conclusions and Discussions 21 References 22 1 Introduction There is also a prototype of a propulsion module that will be tested in MIST from one of the experi- 1.1 Background ments. However, these thrusters will not be used for active attitude control. Their only mission related to CubeSats were invented in 1999 as an educational pointing is to divert the CubeSat from the nominal tool. They were conceived to be small and simple attitude (described in Sec. 1.2). enough for university students, and with standard In the case of attitude determination the gyro- sizes to accommodate them in the rockets. Launches scopes in the on-board computer could be used to of CubeSats increased significantly in 2013. The deal with the under-determination during eclipses. number of deployments that year was nearly half of However, this proposal has been ruled out to reduce the total until then. Currently not only universi- power consumption and simplify the on-board data ties are investing in them but the governments and handling. private companies as well. This interest is due to its low cost, the availability of standardized parts, To sum up, the ADCS concept in MIST is quite the