Application of Intelligent Algorithms to Aerospace Problems

186 Pages·2011·1.1 MB·English

Universidad Nacional de Educación a Distancia
(UNED)
E.T.S. Ingeniería Informática
Dpto. Informática y Automática

TESIS DOCTORAL

INGENIERÍA DE SISTEMAS Y AUTOMÁTICA

Application of Intelligent
Algorithms to Aerospace
Problems

Fernando Alonso Zotes
Ingeniero Industrial

2011
Universidad Nacional de Educación a Distancia
(UNED)
E.T.S. Ingeniería Informática
Dpto. Informática y Automática

TESIS DOCTORAL

INGENIERÍA DE SISTEMAS Y AUTOMÁTICA

Application of Intelligent
Algorithms to Aerospace
Problems
Author:
Fernando Alonso Zotes
Ingeniero Industrial (esp. Electrónica y Automática)
Universidad Carlos III de Madrid

Supervisor:
Matilde Santos Peñas
Dpto. Arquitectura de Computadores y Automática
Facultad de Informática, Universidad Complutense de Madrid

2011
Es mi deseo agradecer el apoyo prestado por mi familia durante el tiempo que han
durado mis estudios.

Asimismo, quiero agradecer a mi directora Matilde Santos su ayuda desde que
inicié mis estudios de doctorado, ya hace unos cuantos años, por compartir su interés
por la inteligencia artificial y la automática, sus buenos consejos y sin quien los
artículos llevados a congresos o publicados en revistas no habrían visto la luz.

También quiero agradecer al Dpto de Informática y Automática de la UNED el
haberme brindado la oportunidad de haber realizado mis estudios de doctorado,
compaginándolo con mis obligaciones laborales en Reino Unido y Alemania.

Table of Figures 5 of 186
TABLE OF CONTENTS

LIST OF FIGURES ........................................................................................................ 9
LIST OF TABLES ........................................................................................................ 13
ACRONYMS ................................................................................................................. 15

CHAPTER 1 INTRODUCTION ................................................................................. 17
1.1 MOTIVATION ................................................................................................... 18
1.2 OBJECTIVES ..................................................................................................... 19
1.3 STRUCTURE OF THIS DOCUMENT ..................................................................... 19
1.4 LIST OF PUBLICATIONS .................................................................................... 20
1.4.1 Articles in Journals ..................................................................................... 20
1.4.2 Book Chapters ............................................................................................ 21
1.4.3 Conferences ................................................................................................ 22
1.5 PHD ON SYSTEMS ENGINEERING AND AUTOMATICS ....................................... 24
CHAPTER 2 INTRODUCTION TO AEROSPACE PROBLEMS ......................... 27
2.1 OVERVIEW OF RELATED WORKS AND STATE OF THE ART ............................... 28
2.1.1 Fuzzy Logic, Lagrange Points and Satellite Control ................................. 28
2.1.2 Genetic Algorithms and Launchers ............................................................ 29
2.1.3 Genetic Algorithms, Particle Swarm Optimisation and Interplanetary
Trajectories ............................................................................................................. 30
2.2 FUNDAMENTAL AEROSPACE CONCEPTS .......................................................... 32
2.2.1 Gravity field ................................................................................................ 32
2.2.2 Orbital Trajectories in an Isolated System ................................................. 35
2.2.3 Orbital Energy ............................................................................................ 36
2.2.4 Orbital Elements ......................................................................................... 39
2.2.5 Lagrange Points ......................................................................................... 41
2.2.6 The Gauss’ Problem and Orbit Transfers .................................................. 46
2.2.7 Fly-by or Gravitational Assistance around Planets ................................... 50
2.2.8 Propulsion Systems ..................................................................................... 52
2.2.9 Gravity Turn ............................................................................................... 53
2.2.10 Air Drag ...................................................................................................... 54
Table of Figures 6 of 186
2.3 ARTIFICIAL INTELLIGENCE AND INTELLIGENT STRATEGIES ............................. 55
2.3.1 Fuzzy Logic ................................................................................................. 56
2.3.2 Evolutionary Strategies .............................................................................. 57

CHAPTER 3 MODELLING, SIMULATION AND FUZZY CONTROL OF
SATELLITES IN LAGRANGE POINTS .................................................................. 65
3.1 INTRODUCTION ................................................................................................ 66
3.2 DESCRIPTION OF THE MODEL .......................................................................... 67
3.3 CONTROL RESULTS .......................................................................................... 73
3.3.1 Conventional P and PD Controllers .......................................................... 74
3.3.2 Intelligent Fuzzy P and PD Controllers ..................................................... 76
3.4 CONCLUSIONS ................................................................................................. 80

CHAPTER 4 GENETIC ALGORITHMS APPLIED TO LAUNCHERS
OPTIMISATION .......................................................................................................... 83
4.1 FUEL OPTIMISATION OF A TWO-STAGE LAUNCHER FOLLOWING A VERTICAL
TRAJECTORY ............................................................................................................... 84
4.1.1 Introduction ................................................................................................ 84
4.1.2 Implementation of the GA for Momentum Optimisation ............................ 85
4.1.3 Description of the Optimisation Problem ................................................... 87
4.1.4 GA Optimisation Results ............................................................................ 90
4.2 DESIGN OF ASCENT TRAJECTORY TO A FINAL STABLE CIRCULAR ORBIT ........ 92
4.2.1 Introduction ................................................................................................ 92
4.2.2 Implementation of GA for Height Optimisation ......................................... 94
4.2.3 Description of the Optimisation Problem ................................................... 95
4.2.4 GA Optimisation Results ............................................................................ 98
4.3 DESIGN OF A HYPERBOLICAL TRAJECTORY FOR AN ASCENT VEHICLE .......... 105
4.3.1 Introduction .............................................................................................. 105
4.3.2 Implementation of GA for Speed Optimisation ........................................ 107
4.3.3 Description of the Optimisation Problem ................................................. 109
4.3.4 GA Optimisation Results .......................................................................... 110
4.4 CONCLUSIONS ............................................................................................... 114
Table of Figures 7 of 186

CHAPTER 5 OPTIMISATION OF INTERPLANETARY TRAJECTORIES ... 115

5.1 GA APPLIED TO OPTIMISATION OF INTERPLANETARY TRAJECTORIES WITH
GRAVITATIONAL ASSISTANCE ................................................................................... 116
5.1.1 Introduction .............................................................................................. 116
5.1.2 Implementation of the GA for Interplanetary Trajectory Optimisation ... 118
5.1.3 Description of the Optimisation Problem ................................................. 120
5.1.4 GA Optimisation Results for the Trajectory to Jupiter ............................ 126
5.1.5 GA Optimisation Results for the Trajectory to Saturn ............................. 129
5.2 SWARM ALGORITHMS APPLIED TO OPTIMISATION OF A TRAJECTORY FROM
EARTH TO JUPITER (EMJ) .......................................................................................... 131
5.2.1 Introduction .............................................................................................. 131
5.2.2 Implementation of PSO algorithm for Interplanetary Trajectory
Optimisation ......................................................................................................... 132
5.2.3 Implementation of MOPSO algorithm for Interplanetary Trajectory
Optimisation ......................................................................................................... 135
5.2.4 Description of the Optimisation Problem ................................................. 138
5.2.5 PSO and MOPSO Results for Interplanetary Trajectory ......................... 140
5.3 SWARM ALGORITHMS APPLIED TO OPTIMISATION OF A TRAJECTORY FROM
EARTH TO SATURN (EMVVJS) ................................................................................. 146
5.3.1 Introduction .............................................................................................. 146
5.3.2 PSO and MOPSO Results for Interplanetary Trajectory to Saturn ......... 147
5.4 MOPSO APPLIED TO OPTIMISATION OF INTERPLANETARY TRAJECTORIES WITH
LOW THRUST ............................................................................................................. 154
5.4.1 Introduction .............................................................................................. 154
5.4.2 Implementation of MOPSO for Interplanetary Trajectory Optimisation with
Low Thrust ............................................................................................................ 156
5.4.3 Description of the Optimisation Problem ................................................. 159
5.4.4 MOPSO Results for Interplanetary Trajectory with Low Thrust ............. 163
5.5 CONCLUSIONS ............................................................................................... 166
Table of Figures 8 of 186

CHAPTER 6 CONCLUSIONS AND FUTURE WORK ........................................ 171
6.1 CONCLUSIONS ............................................................................................... 172
6.1.1 Control of satellites in Lagrange points ................................................... 172
6.1.2 Genetic Algorithms and Launchers Trajectory Optimisation .................. 173
6.1.3 Optimisation of Interplanetary Trajectories............................................. 175
6.2 FUTURE WORK .............................................................................................. 177

REFERENCES ........................................................................................................... 179
Table of Figures 9 of 186

LIST OF FIGURES

Figure 1: An elliptic orbit ............................................................................................... 37
Figure 2: Representation of the Lagrange points in a binary system ............................. 42
Figure 3: Relation between vectors L, L* and L* ..................................................... 45
Figure 4: Fly-by in a planet P ......................................................................................... 51
Figure 5: Local horizon rotating frame for gravity turn modelling ................................ 54
Figure 6: Air density evolution in altitude in Earth’s atmosphere (U.S. Standard
Atmosphere 1976) .................................................................................................. 55
Figure 7: Example of individual in GAs ........................................................................ 58
Figure 8: Representation of the cross-over and mutation operators in GA .................... 60
Figure 9: Control loop for satellites in the Lagrange points ........................................... 69
Figure 10: Initial time of the simulation of the satellites in the Earth-Moon Lagrange
points ...................................................................................................................... 71
Figure 11: Position errors of a satellite in free drift near L1 .......................................... 71
Figure 12: Position errors of a satellite in free drift near L2 .......................................... 72
Figure 13: Position errors of a satellite in free drift near L3 .......................................... 72
Figure 14: Position errors of a satellite in free drift near L4 .......................................... 73
Figure 15: Position errors of a satellite in free drift near L5 .......................................... 73
Figure 16: Position errors of a satellite in L1 (P controller) ........................................... 74
Figure 17: Position errors of a satellite in L4 (P controller) ........................................... 75
Figure 18: Position errors of a satellite in L3 (PD controller) ........................................ 75
Figure 19: Position errors of a satellite in L5 (PD controller) ........................................ 76
Figure 20: Fuzzy sets of the fuzzy P and PD controllers ............................................... 77
Figure 21: Position errors of a satellite in L3 (fuzzy P controller) ................................. 78
Figure 22: Position errors of a satellite in L4 (fuzzy P controller) ................................. 78
Figure 23: Position errors of a satellite in L3 (fuzzy PD controller) .............................. 79
Figure 24: Position errors of a satellite in L4 (fuzzy PD controller) .............................. 80
Figure 25: Evolution of individuals (GA applied to vertical launch) ............................. 90
Figure 26: Height (GA applied to vertical launch) ......................................................... 91
Figure 27: Speed (GA applied to vertical launch) .......................................................... 91
Figure 28: Acceleration (GA applied to vertical launch) ............................................... 92
Table of Figures 10 of 186
Figure 29: Evolution of performance indexes for every individual in the population
along the generations (GA applied to launch trajectory optimisation, final circular
orbit) ..................................................................................................................... 100
Figure 30: Launcher altitude evolution profile (GA applied to launch trajectory
optimisation, final circular orbit) .......................................................................... 101
Figure 31: Launcher altitude evolution in time (GA applied to launch trajectory
optimisation, final circular orbit) .......................................................................... 102
Figure 32: Launcher speed evolution in time (GA applied to launch trajectory
optimisation, final circular orbit) .......................................................................... 102
Figure 33: Launcher acceleration evolution in time (GA applied to launch trajectory
optimisation, final circular orbit) .......................................................................... 103
Figure 34: Launcher flight path angle evolution (GA applied to launch trajectory
optimisation, final circular orbit) .......................................................................... 104
Figure 35: Launcher mass evolution (GA applied to launch trajectory optimisation, final
circular orbit) ........................................................................................................ 104
Figure 36: Performance indexes for every individual in the population (GA applied to
launch trajectory optimisation, hyperbolical trajectory) ...................................... 111
Figure 37: Launcher altitude evolution profile (GA applied to launch trajectory
optimisation, hyperbolical trajectory) .................................................................. 112
Figure 38: Launcher altitude evolution in time (GA applied to launch trajectory
optimisation, hyperbolical trajectory) .................................................................. 112
Figure 39: Launcher speed evolution in time (GA applied to launch trajectory
optimisation, hyperbolical trajectory) .................................................................. 113
Figure 40: Launcher and satellite flight angle evolution in time (GA applied to launch
trajectory optimisation, hyperbolical trajectory) .................................................. 113
Figure 41: Evolution of the best delta-V during the execution (GA applied to Earth-
Jupiter trajectory optimisation) ............................................................................. 127
Figure 42: Trajectory from Earth to Jupiter with fly-by in Mars (GA applied to Earth-
Jupiter trajectory optimisation) ............................................................................. 127
Figure 43: Evolution of the best delta-V during the execution (GA applied to Earth-
Saturn trajectory optimisation) ............................................................................. 129
Figure 44: Trajectory from Earth to Saturn with fly-by in Mars (GA applied to Earth-
Saturn trajectory optimisation) ............................................................................. 130