© 2010 Andrzej Pukniel. THE DYNAMICS AND CONTROL OF THE CUBESAIL MISSION—A SOLAR SAILING DEMONSTRATION BY ANDRZEJ PUKNIEL DISSERTATION Submitted in partial fulfillment of the requirements for the degree of Doctor in Philosophy in Aerospace Engineering in the Graduate College of the University of Illinois at Urbana-Champaign, 2010 Urbana, Illinois Doctoral Committee: Professor Victoria Coverstone, Chair Professor John Prussing Professor Rodney Burton Professor Gary Swenson ABSTRACT The proposed study addresses two issues related to the slow emergence of solar sailing as a viable space propulsion method. The low technology readiness level and complications related to stowage, deployment, and support of the sail structure are both addressed by combining the CU Aerospace and University of Illinois-developed UltraSail and CubeSat expertise to design a small-scale solar sail deployment and propulsion experiment in low Earth orbit. The study analyzes multiple aspects of the problem from initial sizing and packaging of the solar sail film into two CubeSat-class spacecraft, through on-orbit deployment dynamics, attitude control of large and flexible space structure, and predictions of performance and orbital maneuvering capability. ii ACKNOWLEDGEMENTS The following work would have not been possible without the continuous support and encouragement of my advisor, Professor Coverstone. Her patience, scientific insight, and enthusiasm are a rare combination that fosters a unique research environment. It allows the students to develop both as highly competent engineers as well as young individuals. Few advisors sincerely care for their students’ personal development as much as Professor Coverstone and I consider myself privileged to be part of her research group. I would also like to thank Professors Rod Burton and Gary Swenson as well as Dr. David Carroll for excellent advice and insightful discussions. Their questions and experience often steered my research and increased my understanding of the problem at hand. Professor Prussing has been an inspiration starting with my early undergraduate years, and is largely responsible for my interest in astrodynamics. It is a privilege to have him serve on my committee. CubeSail team members Alex Ghosh and Julia Laystrom-Woodard were essential throughout the project and performed majority of the hardware development, modeling, and testing. I wish them the best of luck as they continue to support this and future solar sailing efforts. Lastly, I would like to acknowledge NASA Marshall Space Flight Center and specifically Les Johnson for his continuous support of the solar sailing endeavors at the University of Illinois. iii TABLE OF CONTENTS CHAPTER 1 ................................................................................................................................................................1 INTRODUCTION.........................................................................................................................................................1 1.1 HISTORY OF SOLAR SAILING .....................................................................................................................1 1.2 SOLAR SAIL DESIGN CHALLENGES...........................................................................................................8 1.3 ULTRASAIL HERITAGE DESIGN ...............................................................................................................11 1.4 CUBESAT PROGRAM ...............................................................................................................................12 1.5 CUBESAIL MISSION..................................................................................................................................14 1.6 RESEARCH OBJECTIVES..........................................................................................................................17 CHAPTER 2 ..............................................................................................................................................................20 ATTITUDE DETERMINATION AND CONTROL PRIOR TO FILM DEPLOYMENT .....................................20 2.1 CUBESAIL MISSION SEQUENCE ..............................................................................................................20 2.2 ATTITUDE DETERMINATION......................................................................................................................22 2.3 ATTITUDE CONTROL ................................................................................................................................23 2.3.1 Torque Coil Theory and Design ..................................................................................................24 2.3.2 Earth Magnetic Field Model..........................................................................................................26 2.4 LINEAR QUADRATIC REGULATOR ...........................................................................................................29 2.4.1 Asymptotic Periodic Linear Quadratic Regulator ..................................................................30 2.4.2 CubeSail’s Asymptotic Periodic LQR Design..........................................................................31 2.5 ATTITUDE CONTROL SIMULATOR ............................................................................................................32 2.5.1 Q and R Matrix Computation with Genetic Algorithm...........................................................36 2.5.2 Robust Results of Initial Detumbling and Stabilization of CubeSail Assembly .............39 2.5.3 Energy Usage During Initial Detumbling and Stabilization of CubeSail Assembly.......42 CHAPTER 3 ..............................................................................................................................................................47 DEPLOYMENT METHODS AND SELECTION...................................................................................................47 3.1 PRELIMINARY ANALYSIS OF DEPLOYMENT STRATEGIES........................................................................47 3.1.1 Preliminary Analysis of Spin Induced Deployment ...............................................................48 3.1.2 Preliminary Analysis of Gravity Gradient Induced Deployment.........................................57 3.2 SELECTION OF DEPLOYMENT METHOD FOR THE FIRST CUBESAIL DEMONSTRATION ..........................61 3.2.1 Deployment Method Selection using Force Field Diagrams ...............................................61 3.2.2 Deployment Method Selection using Matrix Diagrams.........................................................66 3.3 PRELIMINARY ORBIT MANEUVERING ANALYSIS .....................................................................................68 3.4 PRELIMINARY ORBIT SELECTION.............................................................................................................71 3.4.1 Spacecraft Orbital Lifetime Analysis .........................................................................................71 3.4.2 Spacecraft Orbital Lighting Analysis.........................................................................................74 CHAPTER 4 ..............................................................................................................................................................78 DETAILED ANALYSIS OF GRAVITY GRADIENT DEPLOYMENT ................................................................78 4.1 SEPARATION RELEASE UNIT DESIGN......................................................................................................78 4.1.1 Impact of SRU Operations on Satellite Dynamics..................................................................79 4.1.2 Spring Selection for Initial Spacecraft Separation.................................................................82 4.2 CUBESAIL REFERENCE FRAMES.............................................................................................................84 4.2.1 Earth Centered Inertial Reference Frame .................................................................................84 4.2.2 Earth Centered Fixed Reference Frame....................................................................................85 4.2.3 Orbital Reference Frame ...............................................................................................................85 4.2.4 SatL and SatU Reference Frames...............................................................................................86 4.2.5 ‘Sail’ Reference Frame...................................................................................................................87 4.2.6 Transformation between ECI and ECF Reference Frames...................................................89 4.2.7 Transformation between ECI and Orbital Reference Frames..............................................91 iv 4.2.8 Transformation between Orbital and SatL and SatU reference frames............................92 4.2.9 Transformation between Satellite and Sail reference frames .............................................93 4.3 MODELING OF FORCES AND TORQUES ON THE SPACECRAFT ...............................................................95 4.3.1 Aerodynamic Drag..........................................................................................................................95 4.3.2 Comparison of Coefficient of Drag Models for a Flat Plate ...............................................109