Orbital mechanics and formation flying: A digital control perspective

452 Pages·2011·12.242 MB·English

by  Pedro A. Capó-Lugo

1
2
3
4
5
6
Orbital mechanics and 7
8
formation fl ying
9
10
1
2
3
4
5
6
7
8
9
20
1
2
3
4
5
6
7
8
9
30
1
2
3
4
5
6
7
8
9
40
41R
2244330077..iinnddbb ii 1188//0022//1122 11::1155 PPMM
Related titles:
Aerodynamic Measurements: From physical principles to turnkey instrumentation
(ISBN 978-1-84569-992-5)
Aerodynamic Measurements will present to its reader a comprehensive treatment of the
theoretical bases which experimental techniques used in aerodynamics are based on.
Limitations of each method in terms of accuracy, response time and complexity will also
be addressed. This book will serve as a guide in choosing the most pertinent technique for
each type of fl ow fi eld including: 1D, 2D, 3D, steady or unsteady, subsonic, supersonic or
hypersonic. This is currently no book that presents as many techniques as those presented
in this volume, with such a critical review of the various methods offered. Aerodynamic
Measurements will help guide the reader to choose the most appropriate in each case and
for each technique the evolution from old-fashioned mechanical process to the modern
computerized version is reported in order to allow students and practitioners to understand
what is behind the results shown on the coloured screen of their computers.
Leveraging Information Technology for Optimal Aircraft Maintenance, Repair and Overhaul
(ISBN 978-1-84569-982-6)
Aimed at professionals in the aviation industry and students of Aircraft Maintenance, this
book covers the use and management of technology in the Aviation Maintenance, Repair,
and Overhaul (MRO) context. This book will provide a backdrop of current trends in the
industry where Airlines are tending to retain their aircraft longer on the one hand, and
rapidly introducing a new genre of aircraft such as the A380 and B787 into service. This
book aims to provide industry professionals and students of Aviation MRO (at all levels)
with the necessary principles, approaches and tools to respond effectively and effi ciently
to the constant development of new technologies - both in general and within the Aviation
MRO profession. It highlights the unique information requirements for Aviation MRO
and delves into the detailed aspects of information needs from within the industry such
as Engineering and Maintenance Planning, Aircraft/Engine/Component Confi gurations,
Materials Management, Logistics, and Technical Documentation. It will highlight the
difference between on-wing and off-wing maintenance with their unique information
processing needs. This book is designed as a primer on IT services for Aircraft Engineering
professionals and a handbook for IT professionals servicing this niche industry.
Modelling and Simulation of Integrated Systems in Engineering: Issues of methodology,
quality, testing and applications
(ISBN 978-1-85709-078-2)
This book places particular emphasis on issues of model quality and ideas of model testing
and validation. Mathematical and computer-based models provide a foundation for
explaining complex behaviour, for decision-making, for engineering design and for real-time
simulators for research and training. Many engineering design techniques depend on suitable
models. Assessment of the adequacy of a given model for an intended application is therefore
critically important. Generic model structures and dependable libraries of sub-models that
can be applied repeatedly are increasingly important. Applications are drawn from the fi elds
of mechanical, aeronautical and control engineering, and mainly involve non-linear lumped-
parameter models described by ordinary differential equations. Topics considered repeatedly
in the context of these applications include: system identifi cation and parameter estimation;
parameter sensitivity analysis; model optimisation; and inverse simulation.
Details of these and other Woodhead Publishing books can be obtained by:
visiting our web site at www.woodheadpublishing.com
●
contacting Customer Services (e-mail: [email protected]; fax: [phone]
●
832819; tel.: [phone]; address: Woodhead Publishing Limited,
80 High Street, Sawston, Cambridge CB22 3HJ, UK)
If you would like to receive information on forthcoming titles, please send your address
details to Customer Services, at the address above. Please confi rm which subject areas you
are interested in.
2244330077..iinnddbb iiii 1188//0022//1122 11::1155 PPMM
Orbital mechanics and
formation fl ying
A digital control approach
P A. C -L
EDRO APÓ UGO
and
P M. B
ETER AINUM
2244330077..iinnddbb iiiiii 1188//0022//1122 11::1155 PPMM
Published by Woodhead Publishing Limited, 80 High Street, Sawston,
Cambridge CB22 3HJ, UK
www.woodheadpublishing.com
Woodhead Publishing, 1518 Walnut Street, Suite 1100, Philadelphia,
PA 19102-3406, USA
Woodhead Publishing India Private Limited, G-2, Vardaan House, 7/28 Ansari Road,
Daryaganj, New Delhi – 110002, India
www.woodheadpublishingindia.com
First published 2011, Woodhead Publishing Limited
© P. A. Capó-Lugo and P. M. Bainum, 2011
The authors have asserted their moral rights.
This book contains information obtained from authentic and highly regarded sources.
Reprinted material is quoted with permission, and sources are indicated. Reasonable efforts
have been made to publish reliable data and information, but the authors and the publisher
cannot assume responsibility for the validity of all materials. Neither the authors nor the
publishers, nor anyone else associated with this publication, shall be liable for any loss,
damage or liability directly or indirectly caused or alleged to be caused by this book.
Neither this book nor any part may be reproduced or transmitted in any form or by any
means, electronic or mechanical, including photocopying, microfi lming and recording, or by
any information storage or retrieval system, without permission in writing from Woodhead
Publishing Limited.
The consent of Woodhead Publishing Limited does not extend to copying for general
distribution, for promotion, for creating new works, or for resale. Specifi c permission must
be obtained in writing from Woodhead Publishing Limited for such copying.
Trademark notice: Product or corporate names may be trademarks or registered trademarks,
and are used only for identifi cation and explanation, without intent to infringe.
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library.
Library of Congress Control Number: 2011919191
Woodhead Publishing ISBN: 978-0-85709-054-6 (print)
ISBN: 978-0-85709-387-5 (online)
Typeset by Refi neCatch Ltd, Bungay, Suffolk
Printed in the UK and USA
2244330077..iinnddbb iivv 1188//0022//1122 11::1155 PPMM
1
2
3
4
5
6
7
To my wife, my newborn son, and my family, thanks for their patience
8
and support.
9
Pedro A. Capó-Lugo
10
1
To my wife, my son, and his wife for their support and understanding. 2
Peter M. Bainum 3
4
5
6
7
8
9
20
1
2
3
4
5
6
7
8
9
30
1
2
3
4
5
6
7
8
9
40
41R
2244330077..iinnddbb vv 1188//0022//1122 11::1155 PPMM
2244330077..iinnddbb vvii 1188//0022//1122 11::1155 PPMM
Contents
List of fi gures xi
List of tables xvii
List of symbols xix
Acknowledgements xxix
Preface xxxi
About the authors xxxiii
1 Introduction 1
1.1 Introduction to the book 1
1.2 Book division 2
1.3 References 4
2 Two body orbital motion 7
2.1 Introduction to orbital motion 7
2.2 Constraints and generalized coordinates 8
2.3 Lagrange’s equation 10
2.4 System of particles 11
2.5 Two body orbital motion problem 13
2.6 Orbital equations of motion 15
2.7 Energy and velocity of orbiting bodies 21
2.8 Escape velocity 24
2.9 Earth coordinate inertial (ECI) system 25
2.10 Period of an orbit 27
2.11 Development of Kepler’s equation 29
2.12 Suggested problems 31
2.13 References 34
vii
2244330077..iinnddbb vviiii 1188//0022//1122 11::1155 PPMM
Orbital mechanics and formation fl ying
3 Orbital perturbations in the two body motion 37
3.1 Introduction to disturbance effects 37
3.2 Lagrange planetary equations 38
3.3 Perturbation due to the earth oblateness 41
3.4 The near-Earth atmosphere effects 52
3.5 Solar radiation pressure force 58
3.6 Other disturbance effects 67
3.7 Suggested problems 69
3.8 References 71
4 Frame rotations and quaternions 75
4.1 Introduction to rotations and quaternions 75
4.2 Two-dimensional frame rotations 76
4.3 Three-dimensional frame rotations 78
4.4 Example of frame rotations 80
4.5 Quaternion defi nition and rotations 85
4.6 Quaternion to Euler angle relations 88
4.7 Suggested problems 90
4.8 References 90
5 Rigid body motion 93
5.1 Introduction to attitude dynamics 93
5.2 Rate of change of a vector 95
5.3 Moment of inertia 97
5.4 Principal moments of inertia 101
5.5 Energy formulation 102
5.6 Rate of change of a quaternion 108
5.7 Ares V equations of motion 109
5.8 Suggested problems 117
5.9 References 119
viii
2244330077..iinnddbb vviiiiii 1188//0022//1122 11::1155 PPMM
Contents
6 Environmental and actuator torques 121
6.1 Introduction to torque formulation 121
6.2 Environmental torques 122
6.3 Actuator (or control) torques 134
6.4 Suggested problems 151
6.5 References 152
7 Continuous and digital control systems 155
7.1 Introduction to methods of designing continuous and
discrete control systems 155
7.2 Ares V equations of motion for fi rst stage fl ight 157
7.3 Continuous control formulation 158
7.4 Discrete control formulation 213
7.5 Adaptive and intelligent controls 233
7.6 Suggested problems 238
7.7 References 243
8 Example 247
8.1 Introduction to examples in spacecraft attitude dynamics
and control 247
8.2 Nanosatellite problem defi nition 248
8.3 B-dot controller for fast corrections 253
8.4 Linear quadratic regulator for attitude correction 255
8.5 Linear quadratic regulator control weight design 262
8.6 Suggested problems 270
8.7 References 273
9 Formation fl ying 277
9.1 Introduction to formation fl ying 277
9.2 Tschauner–Hempel formulation 278
9.3 Clohessy–Wiltshire formulation 286
ix
2244330077..iinnddbb iixx 1188//0022//1122 11::1155 PPMM
Orbital mechanics and formation fl ying
9.4 Earth oblateness and solar effects in formation fl ying 286
9.5 Lawden solution 293
9.6 Discrete optimal control problem for formation fl ying 294
9.7 Formation fl ying controller implementation 301
9.8 Suggested problems 316
9.9 References 318
10 Deployment procedure for a constellation 321
10.1 Introductory comments 321
10.2 Desired conditions of the satellites in the proposed
tetrahedron constellation 322
10.3 Transfer from a circular orbit to the elliptical orbit (stage 1) 323
10.4 Station-keeping procedure (stage 2) 328
10.5 Deployment procedure for the tetrahedron constellation 329
10.6 Remarks 335
10.7 Suggested problems 335
10.8 References 336
11 Reconfi guration procedure for a constellation 339
11.1 Introduction to the reconfi guration process of a
constellation 339
11.2 Data mining process of the Lagrange Planetary equations 341
11.3 Fuzzy logic controller 344
11.4 Phase I to II in-plane motion fuzzy logic control system 348
11.5 Phase II to III in-plane motion fuzzy logic controller 351
11.6 Out-of-plane motion correction 353
11.7 Some solutions for the reconfi guration procedures 356
11.8 Implementation of the fuzzy logic controller 365
11.9 Adaptive control scheme for reconfi guration procedure 365
11.10 Remarks 372
11.11 Suggested problems 373
11.12 References 375
x
2244330077..iinnddbb xx 1188//0022//1122 11::1155 PPMM