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Acceptedvp~O 1 Jaime Peraire A Predictor-Corrector Guidance Algorithm Design for a Low L/D Autonomous Re-entry Vehicle by Carla Haroz B.S. Aerospace Engineering B.A. Russian Language and Literature The University of Texas at Austin, 1996 Submitted to the Department of Aeronautics and Astronautics in partial fulfillment of the requirements for the degree of Master of Science in Aeronautics and Astronautics at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY S 11~SACHUSETTSINSTITUTE r - OFTECHNOLOGY December 1998 1AY 1 71999 BAg- oopkPubkd rr oC'.crnd 1 Ctihes <lttit'v-. p~rsons, mu~j J © 1998 Carla Haroz, Ail Rights Reserved. -1 , i;nAj!n whoae .-tr In pAt. LIBRARIES Author .................. Department of Aeronautics and Astronics (!IY, VES Approvedbye. Nx........ December 1998 Peter Neirinckx Charles Stark Draper Laboratory, Inc. Technical Supervisor C ertified by ..................................... .......................... ..................................... Richard H. Battin Professor of Aeronautics and Astronautics Thesis Supervisor Accepted by ..... ... .... ... .. .. AcceptedVP~o.. 1........... ............. JaimePeraire Associate Professor of Aeronautics and Astronautics Chairman, Department Graduate Committee 0. 2 A Predictor-Corrector Guidance Algorithm Design for a Low L/D Autonomous Re-entry Vehicle by Carla Haroz Submitted to the Department of Aeronautics and Astronautics on December 18, 1998, in Partial Fulfillment of the Requirements for the Degree of Master of Science in Aeronautics and Astronautics Abstract The Precision Landing Reusable Launch Vehicle (PL-RLV) is a low L/D, 2-stage craft with a mission plan that calls for low cost, speedy retrieval, and quick turn-around-times for successive flights. A guidance scheme that best adheres to these goals and captures the vehicle's capability is desired. During re-entry, the PL-RLV's second stage, the Precision Landing Vehicle 2 (PLV-2), will perform a reversal maneuver. This thesis concentrates on a possible re-entry guidance scheme for the PLV-2 during the terminal phase, the time from the completion of the reversal until the landing system parachutes are deployed. A simple bank-to-steer algorithm is suggested. The angle of attack is trimmed, and the bank angle (or bank rate) remains as the only means for control. The algorithm controls the time history of the vehicle's bank angle and tunes the bank angle history to meet land- ing and fuel requirements. This versatile guidance approach employs predictor-corrector methods. The guidance scheme presented generates a possibility of bankrate profiles within limitations that could be used for target acquisition. Selection of a robust target location and the nominal bankrate profile which will yield a minimum target miss are investigated. Testing shows the trade-offs between fuel cost and landing capability. Dis- persion testing with winds and density are also performed. The predictor-corrector combination can yield target miss distances on the order of hun- dreds of feet or less. Open-loop and closed-loop results display the guidance system's ability to capture the PLV-2's capability in the presence of dispersions while still meeting system requirements. Thesis Supervisor: Dr. Richard H. Battin Title: Professor of Aeronautics and Astronautics Technical Supervisor: Peter J. Neirinckx Title: Member Technical Staff, The Charles Stark Draper Laboratory, Inc. 4 Acknowledgements There are many people that I would like to thank that have made my experience at MIT and Draper Labs educationally broadening, challenging, and enriching. Thank you to Tim Brand, who gave me the opportunity to work at Draper, and to Peter Neir- inckx for supervising during the thesis process. Thank you also to Lee Norris, Doug Fuhry, and George Schmidt for their guidance and advice. I have been honored to be in the classrooms of two of the greatest minds in Orbital Mechan- ics, Dr. Richard Battin and Dr. Victor Szebehely. A special thanks to both of them for presenting the beauty of planetary motion to me and for bringing the history of US Space Exploration alive. A big thanks to my professors at the University of Texas who encouraged me to attend MIT and who are always there for advice and support: Dr. Hans Mark, Dr. Wallace Fowler, and Dr. Robert Bishop. Thank you to all my friends at Draper Labs - Gregg "TMG" Barton for all the encouragement and cookies!, Chris D'Souza for checking up on me to make sure I was still alive in my cubicle, Chris "Sparkster" Stoll for constantly battling the gremlins in my computer, Jenn "KB" Hamelin for the chats, Ed Bachelder for the tete-e-tete's and love of Trader Joe's Chocolate, and to all my Draper fellow friends with whom I made it through classes, work, and fun with - Christina, Atif, Nate "Shenckenstein", Geoff, Pat, Chisolm, and my favorite softball team, the Draper Monkeys!! Also, a thank you smile to my encouraging friends at the DLR German Space Center - Manfred, M. Klimke, M. Reichart, and Dr. Seiboldt; to Shaun, Carolyn, Benno, Tobias, Jonathan, Santiago, and my NASA buds, Terry, Greg, and Andy. Thank you to Nick Nuzzo, for all the love and support, thesis empathy, late night Draper din- ners, Swing dancing in the halls, and our thesis getaway island adventure in Greece. S'agapo. The biggest thank you goes to my family: Mom, Dad, Lezlie, Tammy, and Kim. To my older sisters, you can officially stop calling me your "LITTLE" sister now. Mom and Dad, you have always encouraged me to follow my dreams and shoot for the stars. I continue my journey on the road less traveled knowing that you are always there for me. I love you. 5 This thesis was prepared at the Charles Stark Draper Laboratory, Inc. Publication of this thesis does not constitute approval by the Draper Laboratory or the sponsoring agency of the findings or conclusions contained herein. It is published for the exchange and stim- ulation of ideas. Permission is hereby granted by the Charles Stark Draper Laboratory, Inc. to the Massachusetts Institute of Technology to reproduce any or all of this thesis. I= Carla " S. Haro z Carla S. Haroz a 6 Table of Contents 1 Introduction .......................................... 15 1.1 Problem Definition........................................... 16 1.2 Autonomous Bank-to-Steer Guidance Challenges ..........................................18 1.3 Thesis O verview ............................................................................................. 19 1.4 Chapter Breakdown .........................................................................................19 2 Mission Overview and Requirements ....................................... 21 2.1 Flight Profile ....................................... 21 2.2 PLV-2 Aerodynamic and Mass Properties ....................................... 22 2.3 Coordinate Frames ........................................ 25 3 Simulation Code Structure.................................... 31 3.1 Simulation Environments ........................................................................... 31 3.2 General Design Features of the Re-entry Guidance ....................................... 31 3.3 PLV-2 Entry Guidance Code Definition..........................................................33 3.4 Functions of the Initial Subphases ........................................ 34 3.5 Terminal Subphase .................................. 38 3.6 Landing System Phase ........................................ 38 3.7 Atmospheric Models ................................... 40 3.8 Vehicle Uncertainty and Environment Dispersion Sources .............................42 4 Guidance Design .................................................. 45 4.1 Guidance Scheme Definitions.................................................. 45 4.2 Trajectory Control.................................................. 49 4.3 Predictor..........................................................................................................50 4.4 Corrector ........................................ 57 5 Nominal Bank Rate Profile Selection ........................................ 65 5.1 Profile Generation ............................................................................................66 5.2 Bank Rate Bin Definition.................................................................................67 5.3 Example Profiles ........................................ 69 5.4 Nominal Profile Selection .......................................... 72 6 Robustness Testing ....................................... 77 6.1 Range Capability . ...................................... 77 6.2 Nominal Target Robustness Results ........... ................................. 82 6.3 Footprint Range ........................................ 85 7 Guidance Performance..................................... 91 7.1 Predictor and Corrector Performance ........................................ 91 7.2 Fuel Cost vs. Landing Performance....................................... 99 7.3 Corrector Performance On Nominal Profile .................................................. 112 7.4 Bin Number Selection ................................................................................ 113 7.5 Effects of Atmospheric Dispersions ........................................ 118 8 C onclusions ...................................................................................................... 127 Appendix A Analytical Study of the PL-RLV Re-entry Guidance .............................129 Appendix B Acceleration Model for Bank Maneuvers . .............................. 157 Appendix C Nominal Profile
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