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Attitude Dynamics and Control of a Spacecraft Using Shifting Mass Distribution

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Attitude Dynamics and Control of a Spacecraft Using Shifting Mass Distribution The Pennsylvania State University The Graduate School College of Engineering ATTITUDE DYNAMICS AND CONTROL OF A SPACECRAFT USING SHIFTING MASS DISTRIBUTION A Dissertation in Aerospace Engineering by Young Tae Ahn 2012 Young Tae Ahn Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy December 2012 The thesis of Young Tae Ahn was reviewed and approved* by the following: David B. Spencer Professor of Aerospace Engineering Thesis Advisor Chair of Committee Robert G. Melton Professor of Aerospace Engineering Sven G. Bilén Associate Professor of Engineering Design, Electrical Engineering, and Aerospace Engineering Christopher D. Rahn Professor of Mechanical Engineering George A. Lesieutre Professor of Aerospace Engineering Head of the Department of Aerospace Engineering *Signatures are on file in the Graduate School iii ABSTRACT Spacecraft need specific attitude control methods that depend on the mission type or special tasks. The dynamics and the attitude control of a spacecraft with a shifting mass distribution within the system are examined. The behavior and use of conventional attitude control actuators are widely developed and performing at the present time. However, the advantage of a shifting mass distribution concept can complement spacecraft attitude control, save mass, and extend a satellite’s life. This can be adopted in practice by moving mass from one tank to another, similar to what an airplane does to balance weight. Using this shifting mass distribution concept, in conjunction with other attitude control devices, can augment the three-axis attitude control process. Shifting mass involves changing the center-of-mass of the system, and/or changing the moments of inertia of the system, which then ultimately can change the attitude behavior of the system. This dissertation consists of two parts. First, the equations of motion for the shifting mass concept (also known as morphing) are developed. They are tested for their effects on attitude control by showing how shifting the mass changes the spacecraft’s attitude behavior. Second, a method for optimal mass redistribution is shown using a combinatorial optimization theory under constraints. It closes with a simple example demonstrating an optimal reconfiguration. The procedure of optimal reconfiguration from one mass distribution to another to accomplish attitude control has been demonstrated for several simple examples. Mass shifting could work as an attitude controller for fine-tuning attitude behavior in small iv satellites. Various constraints can be applied for different situations, such as no mass shift between two tanks connected by a failed pipe or total amount of shifted mass per pipe being set for the time optimum solution. Euler angle changes influenced by the mass reconfiguration are accomplished while stability conditions are satisfied. In order to increase the accuracy, generally, more than two control systems are installed in a satellite. Combination with another actuator will be examined to fulfill the full attitude control maneuver. Future work can also include more realistic spacecraft design and operational considerations on the behavior of this type of control system. v TABLE OF CONTENTS LIST OF FIGURES ................................................................................................................. vii LIST OF TABLES ................................................................................................................... ix NOMENCLATURE ................................................................................................................ xi Chapter 1 INTRODUCTION ................................................................................................... 1 Chapter 2 BACKGROUND ..................................................................................................... 5 2.1 Literature Review ....................................................................................................... 5 2.2 Coordinate System ..................................................................................................... 10 2.2.1 The Inertial Coordinate System ....................................................................... 11 2.2.2 The Earth-Centered Fixed Coordinate System ................................................ 12 2.2.3 The Body-Fixed Coordinate System ............................................................... 13 2.2.4 The Orbital Reference Coordinate System ...................................................... 14 2.3 Attitude Representations ............................................................................................ 15 2.3.1 Direction Cosine Matrix .................................................................................. 16 2.3.2 Euler Angles .................................................................................................... 17 2.4 Basic Representations in Angular Motion and Rotational Dynamics ........................ 19 2.4.1 Moment of Inertia ............................................................................................ 19 2.4.2 Parallel Axis Theorem ..................................................................................... 20 2.4.3 Angular Momentum ........................................................................................ 21 2.5 Sensors and Controllers for Satellite Attitude Dynamics ........................................... 24 2.5.1 Gravity Gradient .............................................................................................. 25 2.6 Controllability and Observability ............................................................................... 34 2.7 Ground Track / Ground Coverage .............................................................................. 37 Chapter 3 ANALYSIS ............................................................................................................. 41 3.1 Governing Equations of Motion for a Satellite with Movable Mass ......................... 41 3.2 Mass Shifting Method ................................................................................................ 44 3.3 Mass Distribution System Design .............................................................................. 48 3.4 Developing Dynamic and Control Equations............................................................. 51 3.5 Finding the Moments of Inertia Changes from Stage 1 to Stage 2 ............................ 67 3.6 Optimization Process ................................................................................................. 71 3.6.1 Optimal Mass Distribution .............................................................................. 71 3.6.2 Combinatorial Optimization ............................................................................ 72 3.6.3 Optimization Solver ........................................................................................ 79 Chapter 4 SIMULATION RESULTS ...................................................................................... 81 Chapter 5 SUMMARY, CONCLUSIONS and FUTURE WORK .......................................... 127 References ................................................................................................................................ 131 Appendix A Conversions between Coordinate Systems ................................................. 137 vi Appendix B Useful Properties of Direction Cosine Matrices ......................................... 140 Appendix C Euler Angle Rotation .................................................................................. 143 Appendix D Conversions Between Attitude Mapping Computations ............................ 148 Appendix E Modified Equations of Motion of the Satellite with a Movable Mass ........ 150 Appendix F Derivation of Steady State Equation for Gravity Gradient Stabilization .... 151 Appendix G Derivation of Steady State Equation for Gravity Gradient Stabilized Satellite with Products of Inertia Elements .............................................................. 154 Appendix H Equations of Motion for the Masses Attached Satellite with Other Actuators .................................................................................................................. 157 vii LIST OF FIGURES Figure 2.1: Diagram of Spacecraft Attitude Dynamics and Control ........................................ 5 Figure 2.2: The Inertial Coordinate System ............................................................................. 12 Figure 2.3: The Eatrh-Centered Fixed Coordinate System ...................................................... 13 Figure 2.4: The Body Fixed Coordinate System ...................................................................... 14 Figure 2.5: The Orbital Reference Coordinate System. ........................................................... 15 Figure 2.6: Rigid Body diagram .............................................................................................. 22 Figure 2.7: Orbital Reference Coordinate System in a Circular Orbit ..................................... 27 Figure 2.8: Diagram of Roll, Pitch and Yaw Angles ............................................................... 27 Figure 2.9: Diagram of Geodetic and Geocentric System. ...................................................... 37 Figure 2.10: Diagram of Trace of Ground Coverage Due to the Satellite Attitude Motion .... 39 Figure 3.1: Diagram of a Vehicle with a Movable Mass ........................................................
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