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Design of the European Lunar Penetrator (ELUPE) Descent Module Controller Design of the European Lunar Penetrator (ELUPE) Descent Module Controller W.J. Bouma Master of Science Thesis Design of the European Lunar Penetrator (ELUPE) Descent Module Controller Master of Science Thesis For obtaining the degree of Master of Science in Aerospace Engineering at Delft University of Technology W.J. Bouma To be defended publicly on: August 29, 2019 Front cover background image courtesy: Lunar Reconnaissance Orbiter, NASA Faculty of Aerospace Engineering · Delft University of Technology Copyright c Delft University of Technology All rights reserved. Delft University of Technology Faculty of Aerospace Engineering Department of Space Systems Engineering The undersigned hereby certify that they have read and recommend to the Faculty of Aerospace Engineering for acceptance a thesis entitled Design of the European Lunar Penetra- tor (ELUPE) Descent Module Controller by W.J. Bouma in partial fulfillment of the requirements for the degree of Master of Science. Dated: August 29, 2019 Head of department: prof. dr. E.K.A. Gill Supervisor: dr. ir. R. Fonod Co-supervisor: dr. J. Guo Reader: ir. K.J. Cowan MBA Preface With this thesis, I conclude the master Space Flight at TU Delft's faculty of Aerospace Engi- neering. The thesis was built on an earlier project, completed during my stay at ESA/ESTEC in the last half of 2017, and refined throughout 2018, while fulfilling the remainder of my course requirements. The actual thesis project ran from January to August 2019. In effect, the topic has been keeping me busy for two years { give or take. \It's been uh... It's been... interesting. But I'm glad we have her done." | Jack's Mannequin, MFEO Before moving on to the content, I would like to acknowledge a few people. First off, my daily supervisor, dr. ir. Robert Fonod; thank you for expressing your interest in supervising the project after having presented it to you back in November. Your involvement fuelled the project with some welcome new energy and fresh perspective. Thank you for our fruitful discussions and your invaluable feedback. Also, my co-supervisor, dr. Jian Guo; thank you for all the time you devoted to supervising the project right from the very start at ESTEC, when everything still had to take shape. Outside the academic environment, I would like to thank my parents for endlessly supporting and encouraging me; without you, all of this would not have been possible. I would also like to thank my `parents-in-law' for being sincerely invested in the progress of this project. I would like to thank my close friends; in particular Inger, for regularly checking in, and Syward, for proof-reading part of the content and having to endure my ongoing rambling about control algorithms and simulations. Finally, my gratitude and appreciation goes to my girlfriend, Floor, who has been there through thick and thin, low lows and high highs; thank you for bearing with me all this time { you are the greatest and sweetest. Wouter Bouma Amsterdam, 2019 vii Abstract To obtain unambiguous ground truth of water-ice residing in permanently shaded regions of the Moon and to characterise the local regolith, ESA considers a mission involving an instrumented penetrator implanted there by high-speed impact. Released into lunar orbit, the European Lunar Penetrator (ELUPE) Descent Module will autonomously traverse a controlled trajectory to its designated target. The associated attitude control problem involves highly nonlinear large-angle slew manoeuvres and unstable minor-axis spin manoeuvres. To establish a benchmark, a controller based on classical control techniques was designed, verified and tested in a simulation. Legacy control algorithms were implemented and extended. A thruster management function was developed to translate the control commands into thruster actions. For the simulator, accurate models of the descent module and its environment were created. A Monte Carlo simulation was run to determine the success rate of the ELUPE mission from a descent-and-landing perspective, and to assess the performance of the controller under off-nominal conditions. From the results, it was found that the success rate was 58.5% for a surface slope of 20◦, and 74.2% for a slope of 10◦ or lower. Key factors affecting the success rate were identified to be the centre-of-mass offset and the solid rocket motor thrust misalignment angle. As further constraining these parameters would be unrealistic, it was recommended to modify the thrust curve of the solid rocket motor to improve the success rate. Analysis of the attack angle and the nutation angle just prior to impact, revealed their success criteria were met in 98.7% and 99.8% of all cases, respectively. These successful results confirmed the attitude control problem could be satisfactorily solved by a `classical' controller. However, despite its good global performance, the proposed controller was found to also exhibit some serious shortcomings. For this reason, it was recommended to explore the possibilities for a different controller. To the best of the author's knowledge, this thesis represented the first known attempt at de- signing a comprehensive controller for a fully actuated, thruster-controlled penetrator mission targeted for an airless body. In addition, it was the first known study to provide insight into the feasibility and success rate of such a mission from a descent-and-landing perspective. ix Table of Contents Preface vi Abstract viii List of Figures xvii List of Tables xx Nomenclature xxi 1 Introduction 1 1-1 Background and Motivation . 1 1-2 The ELUPE Mission . 3 1-2-1 Mission Goals, Objectives and Outcomes . 3 1-2-2 Spacecraft . 4 1-2-3 Descent Scenario . 5 1-3 Problem Statement . 7 1-4 Literature Review . 9 1-4-1 Planetary Penetrators . 9 1-4-2 Control Techniques . 10 1-5 Research Question . 11 1-6 Contributions . 12 1-7 Report Structure . 12 xi xii Table of Contents 2 Spacecraft Modelling 15 2-1 Preliminaries . 15 2-2 Attitude and Orbit Control System . 16 2-2-1 Reaction Control System . 16 2-2-2 De-Orbit Motor . 23 2-3 Inertial Parameters . 24 2-4 Torque Capabilities . 25 3 Spacecraft Motion and Disturbance Modelling 31 3-1 Reference Frames . 31 3-2 State Representation . 32 3-3 Attitude Kinematics . 34 3-4 Attitude Dynamics . 35 3-4-1 Equations of Motion . 35 3-4-2 Disturbance Torques . 38 4 Controller Design 45 4-1 Introduction . 45 4-2 Large-Angle Slew Manoeuvres . 46 4-2-1 Control Law . 46 4-2-2 Gain Selection . 47 4-2-3 Verification . 50 4-3 Minor-Axis Spin Manoeuvres . 54 4-3-1 Spin-Up and Spin-Down Manoeuvres . 54 4-3-2 Denutation Manoeuvres . 54 5 Mission Manager Logic 69 5-1 Control Phases and Control Modes . 69 5-2 Target States and Control Setpoints . 70 5-2-1 Target Spin Rates . 72 5-2-2 Target Orientations . 84 5-2-3 Overview of Target States . 86 W.J. Bouma Master of Science Thesis Table of Contents xiii 6 Simulation Study 87 6-1 Simulator Elements . 87 6-1-1 Thruster Management Function . 87 6-1-2 Navigation System . 95 6-2 Simulator Architecture . 97 6-3 Simulation Set-Up . 99 6-3-1 Simulation Input . 99 6-3-2 Integrator . 99 6-3-3 Monte Carlo Simulations . 103 6-3-4 Simulation Output . 104 6-4 Simulation Results . 105 6-4-1 Nominal Case . 106 6-4-2 Off-Nominal Cases . 114 7 Conclusions and Recommendations 127 A Penetrator Descent Module 131 A-1 Penetrator . 131 A-2 Penetrator Delivery System . 133 A-3 Mass Budget . 133 B Mission Requirements 135 B-1 Penetration . 135 B-2 Fly-Away Manoeuvre . 138 C Propellant Slugs 139 C-1 Solid Propellant Slug . 139 C-2 Liquid Propellant Slug . 150 D State Variable Transformations 155 D-1 Euler Angles to Unit Quaternions . 155 D-2 Unit Quaternions to Euler Angles . 155 E Frame Transformations 157 Master of Science Thesis W.J. Bouma xiv Table of Contents F Translational Equations of Motion 159 G Hardware Specifications 161 Bibliography 163 W.J. Bouma Master of Science Thesis List of Figures 1-1 Spacecraft: CATIA render . 4 1-2 Descent scenario: schematic of the descent trajectory . 5 1-3 Descent scenario: schematic of the second phase of the descent . 8 2-1 Preliminaries: schematic of spacecraft configuration . 16 2-2 Reaction control system: schematic of thruster configuration . 17 2-3 Reaction control system: performance diagram of thrusters . 18 2-4 Reaction control system: schematic of propellant tank . 20 2-5 Reaction control system: average output thrust capabilities of thrusters . 22 2-6 De-orbit motor: performance diagrams . 23 2-7 Inertial parameters: schematic of propellant slugs . 25 2-8 Torque capabilities: schematic indicating force components and moment arms . 27 3-1 Reference frames: definitions of reference frames considered . 32 3-2 Viscous friction torque: example spin-axis transition manoeuvre . 43 3-3 Viscous friction torque: reproduction of Figure 3-2 . 43 4-1 Large-angle slew manoeuvres: relative difference settling times . 50 4-2 Large-angle slew manoeuvres: reevaluation of Figure 4-1 . 51 4-3 Large-angle slew manoeuvres: example time histories of quaternions . 52 4-4 Large-angle slew manoeuvres: reproduction of Figure 4-3 . 52 xv xvi List of Figures 4-5 Large-angle slew manoeuvres: example time histories of body rates and eigenangle 53 4-6 Large-angle slew manoeuvres: reproduction of Figure 4-5 . 53 4-7 Spin-up and spin-down manoeuvres: example results . 55 4-8 Denutation manoeuvres: definition of angular momentum vector . 56 4-9 Denutation manoeuvres: visualisation of thruster pulse timing strategy . 57 4-10 Denutation manoeuvres: control logic .
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