Table Of ContentSpace Vehicle Dynamics and Control
Bong Wie
Arizona State University
Tempe, Arizona
EDUCATION SERIES
J. S. Przemieniecki
Series Editor-in-Chief
Air Force Institute of Technology
Wright-Patterson Air Force Base, Ohio
Published by
American Institute of Aeronautics and Astronautics, Inc.
1081 Alexander Bell Drive, Reston, AV 19102
MATLAB is a registered trademark of The MathWorks, Inc.
TM
American Institute of Aeronautics and Astronautics, Inc., Reston, Virginia
345
Library of Congress Cataloging-in-Publication Data
Wie, Bong, 1952-
Space vehicle dynamics and control / Bong Wie.
.p cm.--(AIAA education series)
Includes bibliographical references .p( ) dna index.
ISBN 1-56347-261-9 (alk. paper)
.1 Space vehicles--Dynamics. .2 Space vehicles--Control systems.
I. Series.
TL1050.W52 1998 629.4q--dc21 98-9184
Copyright © 1998 by the American Institute of Aeronautics and Astronautics, Inc. All
rights reserved. Printed in the United States of America. No part of this publication may be
reproduced, distributed, or transmitted, in any form or by any means, or stored in a database
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Data and information appearing in this book are for informational purposes only. AIAA is
not responsible for any injury or damage resulting from use or reliance, nor does AIAA
warrant that use or reliance will be free from privately owned rights.
Foreword
Space Vehicle Dynamics and Control by Bong Wie is a comprehensive textbook
that incorporates the latest methods used for the analysis of spacecraft orbital
dynamics and control, spacecraft attitude dynamics and control, and spacecraft
structural dynamics and control. In addition, the necessary mathematical tools are
provided for modeling, analysis, and control of dynamic systems. The text is a
companion volume to the previously published AIAA Education Series text, An
Introduction to the Mathematics and Methods of Astrodynamics, by Richard H.
Battin. The author's extensive knowledge of the subject and his experience as a
professor while teaching the subject matter at Arizona State University, Tempe,
Arizona, are reflected in this volume.
In this text spacecraft dynamics is treated as a dynamic system with emphasis
on practical applications, typical examples of which are the analysis and redesign
of the pointing control system of the Hubble Space Telescope and the analysis of
an active vibrations control for the COFS (Control of Flexible Structures) Mast
Flight System. The material is organized into four major areas: )1 Dynamic Systems
Modeling, Analysis, and Control, 2) Orbital Dynamics and Control, 3) Attitude
Dynamics and Control, and 4) Structural Dynamics and Control. Thus all the
important aspects of spacecraft control are covered. Another important feature is
the inclusion of exercise problems that form integral parts of the text.
The Education Series of textbooks and monographs, published by the American
Institute of Aeronautics and Astronautics, embraces a broad spectrum of theory
and applications of different disciplines in aeronautics and astronautics, including
aerospace design practice. The series also includes texts on defense science, engine-
ering, and management. The complete list of textbooks published in the series
(over 50 titles) can be found on the end pages of this volume. The series includes
teaching texts as well as reference materials for practicing engineers, scientists,
and managers.
J. S. Przemieniecki
Editor-in-Chief
AIAA Education Series
Preface
This textbook is intended to provide the reader with a coherent and unified flame-
work for mathematical modeling, analysis, and control of space vehicles. Space-
craft dynamics and control problems of practical and/or theoretical interest are
treated from a dynamic systems point of view.
To cover a variety of dynamics and control problems of orbital, rotational, and
structural motions of space vehicles, this textbook is organized into four separate
parts.
Part 1 (Chapters 1 and 2) provides a comprehensive introduction to dynamic
systems modeling, analysis, and control; it provides the necessary background
material for the rest of the text. Chapter 1 is intended as a summary of many of
the useful results in classical mechanics and dynamic systems theory. Chapter 2,
which is somewhat independent of the rest of the text, is concerned with dynamic
systems control. In particular, emphasis is placed on both classical and modern
robust control of uncertain dynamic systems.
Part 2 (Chapters 3 and 4) is concerned with orbital dynamics and control of
space vehicles. Chapter 3 deals with the fundamental problems of orbital me-
chanics, such as the two-body and restricted three-body problems. Chapter 4 is
concerned with orbital maneuvering and control problems. The problems of orbital
transfer, rendezvous, and orbit control are treated with special emphasis on a halo
orbit determination and control problem.
Part 3 (Chapters 5-7) deals with attitude dynamics and control of rigid space-
craft. Chapters 5 and 6 are concerned with the rotational kinematics and attitude
dynamics of rigid spacecraft, respectively. Chapter 7 deals with rotational ma-
neuvering and attitude control problems of rigid spacecraft under the influence of
reaction jet firings, internal energy dissipation, or momentum transfer via reaction
wheels or control moment gyros.
Part 4 (Chapters 8-10) is concerned with structural dynamics and control of
flexible spacecraft. Chapter 8 provides basic physical concepts and mathemati-
cal tools necessary for the modeling, analysis, and control of structural dynamic
systems in space. Chapter 9 is mainly concerned with the analysis and design of at-
titude control systems for spacecraft in the presence of structural flexibility and/or
propellant sloshing. Active structural vibration control problems are also treated
in Chapter 9. Chapter 10 deals with robust fuel- and time-optimal maneuvering
control problems of flexible spacecraft and robotic manipulators in the presence
of structural modeling uncertainties.
Because of the limited scope of the book, many other important topics, such
as orbit and attitude determination, stability of multispin satellites, optimal or-
bit transfer, and multiflexible body dynamics, are not treated in detail. However,
such interesting topics are discussed briefly at appropriate places throughout the
text.
xi
iix
This textbook is intended for use in a variety of undergraduate or graduate
courses in dynamics, dynamic systems and control, dynamics and vibration, space-
flight dynamics, astrodynamics, spacecraft dynamics and control, and structural
vibration control, with proper combinations of the material from the book.
For example, Chapters ,1 3, 5, and 6 are suitable for a one-semester course in
dynamics with emphasis on applications of dynamic systems theory. Chapters 1
and 2 contain enough material for a one-semester course in dynamic systems and
control at the senior or graduate level. Chapters 3-7 are suitable for a one-semester
course in spacecraft dynamics and control at the senior or graduate level; however,
control-related topics in these chapters may be omitted for a junior-level course
in spacecraft dynamics. Chapters 7-10 (also Secs. 2.6, 2.7, and 4.7) are intended
mainly for either a graduate level course or self-study by practicing engineers
and researchers who are involved in dynamics and control problems of complex
spacecraft.
Prerequisite to reading this text is a thorough knowledge of vector and matrix
algebra, calculus, ordinary differential equations, linear system dynamics, and en-
gineering mechanics. Chapter 1 provides a summary of such necessary background
material. Some familiarity with structural dynamics and partial differential equa-
tions is presumed for studying Chapter 8 on flexible spacecraft dynamics. The
reader is also presumed to have some acquaintance with feedback control for
studying Chapter 2 on dynamic systems control.
The exercise problems, which appear at appropriate places throughout the text,
form an integral part of the text, and they extend the subject matter covered. Hence,
the problems should be worked out prior to studying the following sections. Certain
problems may require the use of computer software such as MATLAB for the
TM
analysis, control design, and numerical simulation. This book assumes that the
reader has access to computational software such as MATLAB on a personal
computer.
References cited in the text are listed at the end of each chapter. A bibliography
is provided at the end of the book for those readers who wish to pursue further
research in dynamics and control of space vehicles. No attempt was made to
provide a complete bibliography nor to provide the original sources of the subject
matter. The citation of more of my own technical papers, mostly coauthored with
my former graduate students and published in the Journal of ,ecnadiuG ,lortnoC
and ,scimanyD does not indicate any measure of their relative importance to the
subject; they are frequently cited in this book simply because numerous sections
of this book are, in fact, based on those papers.
I am indebted to many persons without whose previous work this text would
not have been possible. In particular, special thanks go to my former graduate
students: Wayne Warren, Tobin Anthony, Marcelo Gonzalez, Evan Wedell, Kuk-
Whan Byun, Ravi Sinha, Qiang Liu, David Cielaszyk, and Jianbo Lu for their
hardworking, creative research efforts. Their contributions to numerous sections
of this text are gratefully acknowledged.
I would like to thank many of my professional colleagues, including Carl Ples-
cia, John Lehner, Nobi Furumoto, Peter Barba, Arun Banerjee, and Peter Chu (at
Ford Aerospace and Communications Corporation, Palo Alto, California); Jason
Speyer, David Hull, Roger Broucke, and Heim Weiss (at the University of Texas at
Austin); David Schmidt, Karl Bilimoria, and Rafael Livneh (formerly at Arizona
iiix
State University); Christopher Heiberg and David Bailey (Honeywell Space Sys-
tems, Glendale, Arizona); and Srinivas R. Vadali and John Junkins (Texas A & M
University) for their direct and indirect contributions to this book. In addition, I
would like to thank the many students in my classes at Arizona State University
over the past several years. They have patiently read through many drafts of this
book and have made numerous corrections.
I am also indebted to John Sunkel, David Geller, Kenneth Cox, Frank Bauer,
Harold Frisch, Stanley Carroll, Rudeen Smith-Taylor, and Jerry Newsom at NASA
for their support through various research projects. Certainly, this book would not
have been possible without such support from NASA. Special thanks also go to the
Department of Control Engineering and the Department of Aerospace Engineering
at Seoul National University for providing me an opportunity to use my draft text
in two graduate courses in dynamics and control during my sabbatical leave in
1995. The effort of writing this book has been in part supported by the Korea
Science and Engineering Foundation.
Finally, I wish to thank my parents, my wife Sang, and my two sons Brian and
Chris, for their support and sacrifice. In particular, my sincere thanks go to my
father (Professor Emeritus S.-K. Wie of Aerospace Engineering at Seoul National
University) and Professor Emeritus Arthur E. Bryson, Jr., at Stanford University for
their advice and guidance throughout the course of my education and professional
career. This textbook is therefore dedicated to my parents and family and Arthur
Bryson for their inspiration and support.
gnoB Wie
yaM 8991
Table of
Contents
Preface ................................................ xi
Part .1 Dynamic Systems Modeling, Analysis, and Control
Chapter 1. Dynamic Systems Modeling and Analysis ............ 3
1.1 Matrix and Vector Analysis ............................. 3
1.2 Classical Mechanics ................................. 20
1.3 Dynamic Systems Analysis ............................ 68
Chapter 2. Dynamic Systems Control ..................... 115
2.1 Feedback Control Systems ........................... 115
2.2 Classical Frequency-Domain Methods ................... 117
2.3 Classical Gain-Phase Stabilization ...................... 129
2.4 Digital Control ................................... 145
2.5 Modern State-Space Methods ......................... 153
2.6 Stability Robustness Analysis ......................... 176
2.7 Robust Control of Uncertain Dynamic Systems ............. 195
Part 2. Orbital Dynamics and Control
Chapter 3. Orbital Dynamics ........................... 209
3.1 Two-Body Problem ................................ 209
3.2 Geometry of Conic Sections .......................... 216
3.3 Vis-Viva Equation ................................. 220
3.4 Kepler's Time Equation ............................. 222
3.5 Orbital Position and Velocity .......................... 225
3.6 Orbital Perturbations ............................... 233
3.7 Circular Restricted Three-Body Problem .................. 240
3.8 Elliptic Restricted Three-Body Problem .................. 256
Chapter 4. Orbital Maneuvers and Control ................. 261
4.1 Launch Vehicle Trajectories ........................... 261
4.2 Orbit Injection .................................... 267
4.3 Single-Impulse Maneuvers ........................... 270
4.4 Hohmann Transfer ................................. 271
4.5 Interplanetary Flight ................................ 274
iiv
iiiv
4.6 Orbital Rendezvous ................................ 282
4.7 Halo Orbit Determination and Control .................... 286
Part 3. Attitude Dynamics and Control
Chapter 5. Rotational Kinematics ........................ 307
5.1 Direction Cosine Matrix ............................. 307
5.2 Euler Angles ..................................... 310
5.3 Euler's Eigenaxis Rotation ........................... 312
5.4 Quaternions ..................................... 318
5.5 Kinematic Differential Equations ....................... 322
Chapter 6. Rigid-Body Dynamics ........................ 331
6.1 Angular Momentum of a Rigid Body .................... 331
6.2 Inertia Matrix and Inertia Dyadic ....................... 332
6.3 Principal Axes .................................... 337
6.4 Euler's Rotational Equations of Motion ................... 340
6.5 Torque-Free Motion of an Axisymmetric Rigid Body ......... 343
6.6 General Torque-Free Motion .......................... 347
6.7 Stability of Torque-Free Motion About Principal Axes ......... 350
6.8 Spinning Axisymmetric Body with Constant Body-Fixed Torque . 352
6.9 Asymmetric Rigid Body with Constant Body-Fixed Torques .... 355
6.10 Rigid Body in a Circular Orbit ......................... 365
6.11 Gyrostat in a Circular Orbit ........................... 374
6.12 Dual-Spinner with a Platform Damper .................... 376
Chapter 7. Rotational Maneuvers and Attitude Control ........ 381
7.1 Control of Spinning Spacecraft ........................ 381
7.2 Time-Optimal Reorientation Maneuvers .................. 392
7.3 Quaternion-Feedback Reorientation Maneuvers ............. 402
7.4 Attitude Control and Momentum Management .............. 419
7.5 Steering Logic for Control Moment Gyros ................. 435
7.6 Optimal Jet Selection Logic ........................... 445
7.7 Pulse-Modulated Attitude Control ...................... 451
Part 4. Structural Dynamics and Control
Chapter 8. Structural Dynamics ......................... 463
8.1 Introduction ..................................... 463
8.2 Uniform Bars .................................... 463
8.3 Uniform Beams ................................... 472
8.4 Rigid Body with Beamlike Appendages ................... 481
8.5 Rigid/Flexible Frame with a Pretensioned Membrane ......... 485
8.6 Flexible Toroidal Structures ........................... 491
8.7 Summary ....................................... 501
Chapter 9. Attitude and Structural Control ................. 503
9.1 Thrust Vector Control Design for a Spacecraft
with Propellant Sloshing ............................ 503
9.2 Attitude Control Design for a Bias-Momentum
Stabilized Spacecraft .............................. 514
9.3 Stationkeeping Attitude Control of a Flexible Spacecraft ....... 526
9.4 Nonlinear Pulse-Modulated Control Analysis and Design ....... 534
9.5 Attitude Control Redesign for the Hubble Space Telescope ...... 547
9.6 Active Structural Vibration Control ...................... 557
9.7 Summary ....................................... 580
Chapter 10. Robust Optimal Maneuvers ................... 585
10.1 Time-Optimal Control .............................. 585
10.2 Robust Time-Optimal Control ......................... 595
10.3 Robust Time-Optimal Control Using One-Sided Control Inputs... 602
10.4 Robust Fuel- and Time-Optimal Control .................. 607
10.5 Robustified Feedforward and Feedback Control ............. 623
Bibliography .......................................... 635
Index ............................................... 653
Part 1
Dynamic Systems Modeling,
Analysis, and Control
