Spacecraft Momentum Control Systems

Transcription

1 Spacecraft Momentum Control Systems

2 SPACE TECHNOLOGY LIBRARY Published jointly by Microcosm Press and Springer The Space Technology Library Editorial Board Managing Editor: James R. Wertz (Microcosm, Inc., El Segundo, CA) Editorial Board: Roland Doré (Professor and Director International Space University, Strasbourg) Tom Logsdon (Senior member of Technical Staff, Space Division, Rockwell International) F. Landis Markley (NASA, Goddard Space Flight Center) Robert G. Melton (Professor of Aerospace Engineering, Pennsylvania State University) Keiken Ninomiya (Professor, Institute of Space & Astronautical Science) Jehangir J. Pocha (Letchworth, Herts.) Rex W. Ridenoure (CEO and Co-founder at Ecliptic Enterprises Corporation) Gael Squibb (Jet Propulsion Laboratory, California Institute of Technology) Martin Sweeting (Professor of Satellite Engineering, University of Surrey) David A. Vallado (Senior Research Astrodynamicist, CSSI/ AGI) Richard Van Allen (Vice President and Director, Space Systems Division, Microcosm, Inc.) More information about this series at

3 Frederick A. Leve Brian J. Hamilton Mason A. Peck Spacecraft Momentum Control Systems 123

4 Frederick A. Leve Space Vehicles Directorate Air Force Research Laboratory Kirtland A.F.B., NM, USA Brian J. Hamilton Honeywell Glendale, AZ, USA Mason A. Peck Cornell University Ithaca, NY, USA Space Technology Library ISBN ISBN (ebook) DOI / Library of Congress Control Number: Springer Cham Heidelberg New York Dordrecht London Springer International Publishing Switzerland 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www. springer.com)

5 Preface It s remarkable how often we, the authors, have had a similar experience. At a conference, or during a break at a technical meeting, someone asks can you recommend a good book about CMGs and reaction wheels? The answer is always about the same: Well, there s this spacecraft dynamics book and that spacecraft design book, and the new edition of that old reference book we all use, but none of them really talk about momentum control in any depth. You probably already know as much as you ll find there. Then there s a pause. Not that those books are bad; I m not saying that. They re a decent start for a certain audience, such as students who have never worked on a flight program. How about academic articles? Sure, there are a few helpful survey papers and some useful older stuff especially from the 70s. For some reason they really seemed to know what they were doing back then. Another awkward pause. I don t really want to go digging into all that. Then, inevitably, maybe you should just write a book. So that s what we did. The reader will find that this book differs from other books on spacecraft dynamics and control. Others provide a broad overview of actuators, sensors, and feedback-control architectures without ever going into these important matters of implementation. And while there exist whole books on propulsive actuators, offering useful depth in the design and operation of rocket engines such as those used for reaction control, there is nothing analogous for momentum actuators. But omitting momentum actuators from a treatment of spacecraft design is like explaining all about automobiles, except for the engine and the transmission. So, finally, there s a book that addresses the crucial matters of what kind and how many momentum devices to implement, how they should be sized, and how to control the array of them. This book is an effort to offer a complete picture of momentum actuators spinning rotors and gimbaled devices for use in attitude control of spacecraft. It s a picture that combines our diverse experience in government space systems (satellites for the Air Force, Navy, and NASA) as well as in the commercial space industry and academia. The scope of this book extends from electromechanical v

6 vi Preface details of individual actuators to space-system architecture issues of interest in spacecraft concept development. We discuss the foundational rigid- and flexiblebody dynamics, the subtle mathematics of steering multiple devices within an array, and the applications of these technologies. These momentum actuators are at the heart of contemporary spacecraft that perform Earth imaging. The rapid growth of commercial success in this application area since the beginning of the twenty-first century is ultimately due to the technological capabilities that these actuators offer. In the decades to come, our industry is likely to see new applications: asteroid mining, in-orbit servicing and repair of satellites, and new human-space missions, all of which will require high torque and momentum storage. Small spacecraft, now the most commonly launched type of satellite, are only just beginning to incorporate sophisticated momentum control, thanks to entrepreneurial investment and a new generation of passionate spacecraft technologists. The momentum devices described in this book enable contemporary spacecraft and will make the future possible. The authors hope that the breadth of information offered here, most of which has never been collected in one place, will serve the needs of this new generation of spacecraft engineers. And, at least as important, we ll have an answer to that perennial question, can you recommend a book about this stuff? Kirtland A.F.B., NM, USA Glendale, AZ, USA Ithaca, NY, USA Frederick A. Leve Brian J. Hamilton Mason A. Peck

7 Contents 1 Introduction Spacecraft Design, Commercial Space, and Angular Momentum Momentum Control Devices and Attitude Control Systems A Brief History of Spin The Proliferation of Momentum Control About This Book References Applications Spacecraft Applications GEO Communications Spacecraft Agile Spacecraft Missions and ConOps Space Stations Small Spacecraft Satellite Servicing Asteroid Grappling Space Robotics Terrestrial Applications Brennan s Monorail Wolseley s Two-Wheeled Wonder Car Lit Motors Nautical Roll and Pitch Stabilization Chapter Summary References Requirements Development for Momentum Control Systems Quantifying Agility Requirements Slew Angle vs. Time Performance Ratios: Vehicle Performance Ratios: Momentum System Vehicle Velocity Summary vii

8 viii Contents 3.2 Momentum Device Technology Torque, Momentum, and De-mystifying Precession The Reaction Wheel The Double-Gimbal Control Moment Gyroscope (DGCMG) The Single-Gimbal Control Moment Gyroscope (SGCMG) Vehicle Rate and the SGCMG Gimbal Torquer Torque-Amplification Revisited Momentum Device Technology Tradeoffs Momentum and Torque Power Vibration Torque Accuracy Array Control Guidelines for Selecting Momentum Device Technology Chapter Summary References Dynamics of Momentum-Control Systems Notation Spacecraft Attitude and Momentum-Device Kinematics Equations of Motion for a Gyrostat with Balanced Rotors Relative Equilibria and Stability of Gyrostats RWA Spacecraft CMG Spacecraft Large-Angle Slews Control-Moment Gyroscopes Actuator Jacobians Rotor and Gimbal Structural Dynamics Effects of Scaling CMG Actuators Torque Amplification Degradation with Scaling Chapter Summary References Singularities of Control Moment Gyroscopes Singular Values Coordinate Singularities Versus Geometric Singularities Coordinate Singularities Singularities Associated with Geometric Constraints Control Moment Gyroscope Singularities The Concept of CMG Singularity Double-Gimbal Control Moment Gyroscope Singularities DGCMG Gimbal Lock Single-Gimbal Control Moment Gyroscope Singularities SGCMG Gimbal Lock

9 Contents ix 5.6 Classification of Singularities Singularity Conditions Defined Mathematically Determination of Singularity Degeneracy Hyperbolic Singularities Non-degenerate Hyperbolic Singularities Degenerate Hyperbolic Singularities Elliptic Singularities External Elliptic Singularities Internal Elliptic singularities Passability and Impassability of Singular Points Impassable Singular Points Passable Singular Points Singular Surfaces for SGCMG Characteristics of Singular Surfaces Numerical Sensitivity in the Vicinity of a Singularity Variable-Speed Control Moment Gyroscope Singularities Zero-Momentum Spin Up RWA Zero-Momentum Spin-Up Four-CMG Roof Zero-Momentum Spin-Up Four CMG Pyramid Zero-Momentum Spin-Up Chapter Summary References Momentum-Control System Array Architectures The Nature of Momentum Devices Momentum and Torque Capability of an Array of RWAs Momentum and Torque Capability of an Array of CMGs Double-Gimbal CMG Arrays Single-Gimbal CMG Arrays Scissored Pairs of CMGs Collinear (Multiple-Type) Arrays /4 (3 of 4) Box Array Pyramid Arrays Dynamic Arrays Blended Arrays and Other Designs Double-Gimbal/Single-Gimbal Scissored Pairs Langley Six-Pac Single-Gimbal Six GAMS (Six-CMG Pyramid Array) Scissored Pair with High-Torque Reaction Wheels Variable-Speed CMG Arrays Energy Storage Optimization and Arbitrary Array Configurations Chapter Summary References

10 x Contents 7 Steering Algorithms CMG Steering Algorithms Origin of Pseudoinverse Methods Blended Inverse Moore Penrose Inverse Singularity-Escape Algorithms (Torque-Error Algorithms) Singularity Robust Inverse Singularity Direction Avoidance Pseudoinverse Generalized Singularity Robust Inverse Singularity Avoidance Algorithms Generalized Inverse Steering Law Local Gradient (LG) Methods Constrained Gimbal Angle or Angular Momentum Methods Limited Angular Momentum Methods Singularity Avoidance and Escape Algorithms Hybrid Steering Logic Angular Momentum Artificial Potential Steering Feedback Steering Law Optimal CMG Attitude Control Variable Speed Control Moment Gyroscopes Chapter Summary References Inner-Loop Control of Momentum Devices Spin-Speed Control CMG Spin-Speed Loops RWA Spin Speed Gimbal Rate Loops Errors Mitigated by Gimbal Rate Loops Impact on Vehicle Structure Bandwidth Considerations Friction and ACS Limit Cycling Chapter Summary Motors in Space Motor Technology Sizing a DC Motor Sizing a Brushless DC Motor Electrical Numerical Example Chapter Summary

11 Contents xi 10 Modeling Simulation and Test Beds Math Modeling and Computer Simulation First Principles What Is the Question? Modularity Choices of States Polarities Body Models Attachment Models Integration Hardware-in-the-Loop Test Beds Precision Rotational Air-Bearing Systems Anisoelasticity Active Mass Balancing Controlling the Mass-Balancing System Chapter Summary References A Extended Equations of Motion for Spacecraft with CMGs A.1 It Begins with A Particle A.2 Components A.3 Reference Frames for Spacecraft n-cmg System A.4 Spacecraft n-cmg Array Kinematic and Kinetic Equations of Motion A.4.1 Spacecraft Angular Momentum A.4.2 CMG Gimbal Angular Momentum A.4.3 CMG Rotor Angular Momentum A.4.4 Spacecraft and Actuator Equations of Motion A.5 Summary B Stability Analysis of Momentum-Based Attitude Control Systems B.1 Lyapunov Analysis B.2 Rest-to-Rest Attitude Control B.3 Attitude and Angular Velocity Tracking Control B.4 Steering Algorithm Effects on Attitude Regulation and Tracking. 240 B.5 Summary Index

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13 Author Biographies Frederick A. Leve, Research Aerospace Engineer at the Air Force Research Laboratory, Space Vehicles Directorate, received his Ph.D. in Aerospace Engineering from the University of Florida in While at the University of Florida, he received the IAF Silver Hermann Oberth Medal and the AIAA Abe Zarem Award for Astronautics. Currently, he is the technical advisor to the Guidance, Navigation, and Controls Group and has published many papers in the area of attitude dynamics and control, specifically with respect to momentum control systems and also performs research in under-actuated control, fault tolerant control, control allocation, analytical mechanics, and system identification. Dr. Leve is a recipient of the 2014 AFRL Early Career Award. Brian J. Hamilton, Engineering Fellow at Honeywell Aerospace, received a BSEE with Honors from the University of Illinois, Mr. Hamilton has nearly 40 years of experience at Honeywell (formerly, Sperry) and has participated in the development of CMG technology since its infancy. In recent years, his research focus has been on CMG array control and steering, and the general application of momentum systems to agile spacecraft attitude control. Other areas of specialty include nonlinear modeling, controls design, system optimization, and active magnetic suspension. Mr. Hamilton holds 12 patents. Mason A. Peck, Associate Professor at Cornell University in Mechanical and Aerospace Engineering, received his Ph.D. in Aerospace Engineering from the University of California, Los Angeles, in He has worked as an aerospace engineer since 1994 and has been on the faculty at Cornell since From late 2011 through early 2014, he was NASA s Chief Technologist. In that role, he served as the agency s chief strategist for technology investment and prioritization and advocate for innovation in aeronautics and space technology. His research lab xiii

14 xiv Author Biographies focuses on fundamental research in space technology that can be advanced through flight experiments. Examples include Violet, a nanosatellite for demonstrating CMG steering laws, and KickSat, the world s first crowdfunded spacecraft. Dr. Peck holds 19 patents in the USA and the E.U. and has over 100 academic publications. He received the NASA Distinguished Public Service Medal in 2014.

15 Acronyms CMG DGCMG IGA IV LOS MBS MCS rms rpm RWA SGCMG VSCMG Control moment gyroscope Double-gimbal control moment gyroscope Inner gimbal assembly Induced vibration Line-of-sight Mass balancing system Momentum control system Root mean square Revolutions per minute Reaction wheel assembly Single-gimbal control moment gyroscope Variable-speed control moment gyroscope xv

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17 Symbols F N F Gi F Ri A p i C B C Gi C Ri r B=A r pi =A r Gi =p i r Ri =p i Ob i Os i Oo i Og i m B m G;i m R;i m G;pi m R;pi J s J t J J B J B A Inertial reference frame ith CMG gimbal reference frame ith CMG rotor reference frame Arbitrary point in spacecraft reference frame CMG nominal center of mass reference point at the intersection of the gimbal and rotor axes assumed fixed in the spacecraft body reference frame Spacecraft body center of mass point ith CMG gimbal center of mass point ith CMG rotor center of mass point Differential mass vector position from center of mass of a component Vector from point A to spacecraft body center of mass, C B Vector from point A to point p i Vector from point p i to CMG gimbal center of mass point Vector from point p i to CMG rotor center of mass point Spacecraft body coordinate axis i ith CMG spin coordinate axis ith CMG output torque coordinate axis ith CMG gimbal coordinate axis Spacecraft bus mass ith CMG gimbal mass ith CMG rotor mass ith CMG gimbal particle imbalance mass ith CMG rotor particle imbalance mass Spacecraft rigid body inertia dyadic Rotor transverse inertia Spacecraft inertia dyadic for the spacecraft s mass center, including the spacecraft as a rigid body and all momentum-control devices Inertia dyadic of spacecraft about its own center of mass Inertia dyadic of spacecraft about point A xvii

18 xviii Symbols J G i G i J G i A J R i R i J R i A J r;i J gr;i J g;i J g;eff J g;eff h B A h B B h G i p i h G i G i h R i p i h R i R i h r h Inertia dyadic of ith CMG gimbal about its own center of mass Inertia dyadic of ith CMG gimbal about point A Inertia dyadic of ith CMG rotor about its own center of mass Inertia dyadic of ith CMG rotor inertia about point A Scalar inertia component of ith CMG rotor about its spin axis Scalar inertia component of ith CMG gimbal-wheel assembly about its gimbal axis IGA inertia dyadic, i.e. everything that contributes to the IGA rigid-body inertia in all axes Effective scalar IGA inertia. This inertia includes everything rigid that the gimbal must accelerate along with the output-axis stiffness (K OA ) effect: J g;eff D J g C h2 K OA Effective IGA inertia dyadic. This inertia includes everything that contributes to the IGA rigid-body inertia in all axes, along with the output-axis stiffness effect along the gimbal axis direction. Angular momentum of spacecraft bus about point A Angular momentum of spacecraft bus about its own center of mass Angular momentum of ith CMG gimbal about p i Angular momentum of ith CMG gimbal about its own center of mass Angular momentum of ith CMG rotor about p i Angular momentum of ith CMG rotor about its own center of mass Angular momentum vector of a single CMG rotor P Angular momentum vector for a momentum system such that h D n id1 h r i h h s gf ;i rf ;i r;i g;i d o Angular momentum body coordinate matrix representation for an array of CMG or RWA Superspin Internal friction torque of ith CMG gimbal Internal friction torque of ith CMG rotor ith scalar rotor torque for a single-gimbal CMG (for a perfectly aligned and rigid rotor) ith scalar gimbal torque for a single-gimbal CMG (for a perfectly aligned and rigid IGA and gimbal) Scalar drag torque Vector output torque for a single-gimbal CMG (for a perfectly aligned and rigid IGA and gimbal). This torque acts on the spacecraft and is therefore is equal in magnitude but opposite in direction to the torque that acts on the CMG. B! B=N Angular acceleration vector of a spacecraft-fixed reference frame B relative to an inertial frame N. The overdot associated with a scalar derivative has been replaced with the letter B to indicate that the derivative has been taken relative to the B reference frame

19 Symbols xix! B=N Angular velocity vector of spacecraft body with respect to the inertial reference frame! G i=b Angular velocity vector of ith CMG gimbal with respect to the spacecraft body reference frame! R i=g i Angular velocity vector of ith CMG rotor with respect to the ith CMG gimbal reference frame! Scalar spacecraft angular rate or body coordinates matrix representation of spacecraft angular velocity (context sensitive) v A Translational inertial velocity of point A r;i ith scalar CMG rotor rate r ; P r Matrices of CMG rotor spin rates and accelerations ; P ; R Matrices of CMG gimbal angles, rates, and accelerations ı i ; ı P i ; ı R i ith CMG gimbal angle, rate, and acceleration ˇ CMG array skew angle CMG array clocking angle K OA Output axis stiffness K a Performance ratio (maximum rate over maximum acceleration) K c Performance ratio (maximum acceleration over maximum jerk) K T Motor torque constant (torque per unit current) K MD Motor K M density (ft-lb/sqrt(w) per lb) i Index for a single CMG within a multiple-cmg array n Number of CMGs in a multiple-cmg array m Singularity measure Singularity parameter and scalar angular acceleration (context sensitive) j Scalar angular jerk (context sensitive) B Q A Direction-cosine matrix that relates the representation of a vector v in B coordinates ( B v) to its representation in A coordinates ( A v)