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Parafoil Control for STRAPLEX

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FACULDADE DE ENGENHARIA DA UNIVERSIDADE DO PORTO Parafoil Control for STRAPLEX João Luís Granja da Costa FOR JURY EVALUATION Mestrado Integrado em Engenharia Eletrotécnica e de Computadores Supervisor: Sérgio Reis Cunha June 25, 2013 c João Luís Granja da Costa, 2013 Resumo Esta dissertação está inserida no projeto STRAPLEX (STRAtospheric PLatform EXperiment), que é um programa da Faculdade da Engenharia da Universidade do Porto em parceria com a Agencia Espacial Europeia (ESA). Este projeto é constituído por uma plataforma que permite à comunidade científica enviar experiências para a estratosfera recorrendo a balões de hélio. Devido às condições extremas presentes na estratosfera, o balão rebenta e a plataforma inicia a sua fase de descida estabilizada por um pára-quedas circular. Uma vez que este pára-quedas não permite qualquer tipo de controlo, nesta dissertação sugere-se que seja utilizado um parapente no lugar deste. O objetivo principal desta dissertação é implementar um fiável algoritmo de controlo para este sistema. Este trabalho dá continuidade a uma dissertação desenvolvida anteriormente, que propôs uma estrutura mecânica e de hardware que possibilita a implementação do algoritmo de controlo para a descida da plataforma. O movimento descendente da plataforma é descrito por um fiável modelo matemático, que inclui os vários movimentos relativos entre os diferentes objetos da plataforma. Este modelo tam- bém engloba os distintos tipos de controlo existentes no sistema, possibilitando a implementação de um algoritmo de controlo. Este algoritmo foi concebido para permitir a aterragem da plataforma no local desejado, sob certas condições atmosféricas. Como suporte ao sistema de controlo, é efetuada uma análise do modelo quanto à sua esta- bilidade, controlabilidade e observabilidade. No fim, é realizada uma optimização de ganhos de controlo recorrendo à técnica da teoria de controlo pole placement. Durante o desenvolvimento do trabalho são ilustrados alguns resultados de simulação que foram obtidos recorrendo ao programa MATLAB. i ii Abstract This thesis is part of the project STRAPLEX (STRAtospheric PLatform EXperiment), which re- sults from a partnership between the Faculty of Engineering of the University of Porto and the European Spatial Agency (ESA). This project is constituted by a platform that allows the scien- tific community to send experiments for educational purpose into the stratosphere, using balloons filled with helium. Due to the extreme conditions in the stratosphere, the balloon bursts and the platform begins to fall back into the atmosphere. This fall is stabilized by a round parachute. Since this type of parachute does not allow any kind of control, in this thesis is suggested the usage of a parafoil, instead of the round parachute. The main goal of this thesis is implementing a reliable control algorithm for this system. This work gives continuity to another one developed before, in which a mechanical structure for the control of the parafoil is proposed. This structure includes some suitable hardware that allows the implementation of the control algorithm. The downward movement of the platform is described by a reliable mathematical model which includes the various relative movements between each of the elements of the platform. This model also comprises the distinct types of control of the system, allowing the implementation of a control algorithm. Such algorithm was designed to allow the landing of the platform in the desired place, under some constrained atmospheric conditions. As a support to the control system, an analysis of the stability, controllability and observability of the mathematical model is made. At the end, an optimization of the control gains is developed by using the pole placement technique. Along the thesis, some simulation results are shown, which were obtained with the software MATLAB. iii iv Agradecimentos Ao meu orientador, Professor Sérgio Reis Cunha, pela sua constante motivação, ajuda e dedicação que sempre demonstrou ao longo de todo este trabalho. Aos meus amigos por todos os momentos, aprendizagens e experiências que me propor- cionaram. Em especial aos meus amigos de sempre porque sem dúvida contribuíram para a pessoa que sou hoje. Estou extremamente grato aos meus colegas e amigos Diogo Pernes, Hugo Cruz e Luís Pires pelo companheirismo e amizade ao longo do meu percurso académico. À minha família por serem sempre um pilar na minha vida. Em especial aos meus pais e irmãos pelo amor e incansável apoio que sempre demonstraram. À minha namorada, Joana, pelo acompanhamento, paciência e amor prestado durante estes últimos 5 anos. João Luís Granja da Costa v vi “The true sign of intelligence is not knowledge but imagination” Albert Einstein vii viii Contents 1 Introduction1 1.1 Motivation . .1 1.2 Objectives . .1 1.3 Thesis Outline . .2 1.4 Website . .2 2 STRAPLEX3 2.1 STRAPLEX project . .3 2.2 Actual status . .5 2.3 The STRAPLEX project’s next step . .7 2.4 State of the art . .8 3 System Overview 13 3.1 System Components . 13 3.2 Parafoil . 14 3.2.1 Dimensions . 15 3.2.2 Features . 16 3.3 Drone . 18 3.3.1 Dimensions . 18 3.3.2 Features . 19 3.4 Capsule . 19 3.4.1 Dimensions . 20 3.4.2 Features . 21 3.5 Transponder . 21 3.6 Control Input . 22 3.6.1 Main Lines Control . 22 3.7 Flight Stages . 24 4 Mathematical Model 25 4.1 Model Description . 25 4.1.1 Vector Notation and Frames . 29 4.1.2 Rotation Matrices . 30 4.2 Position Points and Vectors . 33 4.2.1 Position Points . 33 4.2.2 Position Vectors . 34 4.3 System Kinematics . 35 4.3.1 Rotation Kinematics . 35 4.3.2 Position Kinematics . 41 ix x CONTENTS 4.4 System Dynamics . 45 4.4.1 Forces . 46 4.4.2 Moments . 52 4.5 Equations of Motion . 56 4.6 Simulation Results . 58 5 Control Algorithm 67 5.1 Horizontal Control . 67 5.1.1 Heading . 67 5.1.2 Course . 68 5.1.3 One Point Localizer and Course or Two Points Localizer . 69 5.2 Vertical Control . 71 5.3 Spiral Mode . 72 6 Stability Analysis 77 6.1 Linear Model . 77 6.1.1 Lyapunov’s Linearization Method . 78 6.2 Stability Analysis . 79 6.2.1 Stability . 79 6.2.2 Controllability . 79 6.2.3 Observability . 80 6.3 Pole Placement . 80 6.4 Graphic User Interface . 80 7 Final Remarks 83 7.1 Conclusions . 83 7.2 Future Work . 84 A Appendix 85 A.1 Equation of Coriolis . 85 A.2 Poisson’s Kinematical Equation . 85 A.3 Derivative of a Vector . 86 A.4 Drone Rotation Kinematics . 88 A.5 Capsule Rotation Kinematics . 89 A.6 Transponder Rotation Kinematics . 89 A.7 Drone Position Kinematics . 90 A.8 Capsule Position Kinematics . 93 A.9 Transponder Position Kinematics . 95 A.10 Apparent Force . 96 A.11 Matrix M and B . 97 A.11.1 Matrix M . 97 A.11.2 Matrix N . 98 A.12 Matrix A and B . 99 References 101 List of Figures 2.1 Launch of STRAPLEX . .4 2.2 STX center . .7 3.1 STRAPLEX components . 14 3.2 Parafoil . 14 3.3 Aerodynamic angles (a and b) for an Airplane [1]................ 17 3.4 View of the Drone . 18 3.5 Capsule . 20 3.6 Transponder . 21 3.7 Drone displacement . 23 3.8 Flight Stages . 24 4.1 Platform front view . 26 4.2 Roll, Pitch and Yaw Directions for an Airplane ..
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