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Spectroscopic Tools for Quantitative Studies of DNA Structure And INSTITUTO POLITÉCNICO NACIONAL Escuela Superior de Ingeniería Mecánica y Eléctrica Unidad Profesional Ticomán Modelado y Control de un Vehículo Aéreo sin Tripulación de Cuatro Rotores Tesina que para oprobar el Seminario de Actualización con opción a Titulación “Sistemas de Aviónica” Daniel Alvarado García Consejeros académicos: Jorge Sandoval1, Raymundo Hernández2 & J. Cesar Jiménez 3 1,2Departamento de Control 3Departamento de Electrónica Ingeniería Aeronáutica Sistemas de Aviónica Ciudad de México Comité de evaluación: M. en C. José Javier Roch Soto Escuela Superior de Ingeniería Mecánica y Eléctrica, Director. M. en I. Raymundo Hernández Barcenas Sistemas de Aviónica, Coordinador. M. en C. Juan Jesús Navarro Parada Escuela Superior de Ingeniería Mecánica y Eléctrica, Departmento de Titulación. MÉXICO Modelado y control de un Vehícu- lo Aéreo sin Tripulación de Cua- tro Rotores Resumen corto: Helicópteros de cuatro rotores o Quad-Rotor helicopters, han emergido como una plataforma popular de investigación de los Vehículos Aéreos sin tripulación, UAV’s, gracias a la facilidad de su construcción y man- tenimiento, su habilidad de hover y su capacidad de aterrizar y despe- gar verticalmente, VTOL. En el presente documento presentaremos las principales características del helicópero de cuatro rotores así como el modelo dinámico del mismo utilizando una aproximación Lagrangiana. Palabras clave: UAV’s, VTOL. Lista de Documentos I A. Y. Elruby, M. M. El-khatib, N.H. El-Amary and A. I. Hashad Dynamic Modeling and Control of Quadrotor Vehicle Arab Academy for Science and Technology, Egypt (2012), 13 II Paul Pounds, Robert Mahony and Peter Corke Modelling and Control of a Quad-Rotor Robot CSIRO ICT Centre, Brisbane, Australia (2010), 10 III Nitin Sydney, Brendan Smyth and Derek A. Paley Dynamic Control of Autonomous Quadrotor Flight in an Estimated Wind Field Department of Control (2012) IV Moses Bangura and Robert Mahony Nonlinear Dynamic Modeling for High Performance Control of a Quadrotor Australian National University, Canberra, Australia. (2012), 3-5 V Gabriel M. Hoffmann, Haomiao Huang, Steven L. Waslander and Claire J. Tomlin Quadrotor Helicopter Flight Dynamics and Control: Theory and Experiment American Institute of Aeronautics and Astronautics (2010), 1-10 VI Samir Bouabdallah and Roland Siegwart Full Control of a Quadrotor Swiss Federal Institute of Technology, ETHZ, Zürich, Switzerland (2012), 3-10 VII P. Castillo, A. Dzul and R. Lozano REAL-TIME STABILIZATION AND TRACKING OF A FOUR ROTOR MINI-ROTORCRAFT Heudiasyc- UTC UMR 6599 VIII Alejandro Sámano, Rafael Castro and Sergio Salazar Modelling and stabilization of a multi-rotor helicopter Informe de la Contribución Documentos I, II, III y V son la base principal del presente documento. Documentos excluidos en la tesis: Nitin Sydney, Brendan Smyth and Derek A. Paley Dynamic Control of Autonomous Quadrotor Flight in an Estimated Wind Field Department of Control (2012) Programas Informáticos utilizados en la tesis: MatLab R2012_b: Análisis y simulación de sistemas. Maple 16: Análisis y simulación de sistemas. Prefacio Una teoría es los más impresionante, lo más simple son sus premisas, lo más distinguible son las cosas que conecta, y lo más amplio es su rango de aplicabilidad. Albert Einstein. Quadrotor helicópteros se están convirtiendo en una plataforma popular para el vehículo aéreo no tripulado (UAV) de investigación, debido a la simplicidad de su construcción y mantenimiento, su capacidad de hover, su despegue vertical y aterrizaje (VTOL). Los diseños actuales a menudo han considerado sólo las condiciones nominales de funcionamiento para el diseño de control del vehículo. Este trabajo trata de abordar los problemas que surgen cuando se desvíen significativamente del régimen de vuelo a punto fijo. La oportunidades de aplicar los principios y métodos de control para aviones miniatura aparecen a principios del siglo XXI. Modelos no lineales y la teoría moderna de control no lineal juegan un papel importante en el logro del vuelo autónomo de alto rendimiento para los nuevos mini y micro-máquinas de volar. El rápido desarrollo también se debe a los avances de la computación, la comunicación y la percepción que cada vez son más accesibles y omnipresentes. Esto hará posible el desarrollo de nuevos y pequeños UAV’s con sofisticadas configuraciones aerodiná micas. El uso de la teoría de control automático permite mini-aviones ser mas eficientes y rentables con un grado de inteligencia y receptividad que ampliará enormemente su campo de aplicación. Objetivos de la Tesis La presente tesis presenta un estudio sistemático de modelado y control no lineal de vehículos aéreos que toman en cuenta ausencias de linealidad físicas y de fuerzas aerodinámicas, las limitaciones de los sensores y los actuadores y los efectos de los retrasos debido al tiempo de cáculo. El objetivo es obtener leyes de control que se cumplen satisfactoriamente incluso en la presencia de disturbios encontrados comúnmente en aplicaciones reales. Esta tesis se centra particularmente en los vehículos aéreos capaces de realizar hover, como es el caso del helicóptemos, así como la realización de vuelo hacia adelante como los aviones normales. Se estudiará la siguiente máquina: Un helicóptero de Cuatro Rotores. Esquema de la Tesis El Cap´titulo 1 presenta una breve historia de la aeronáutica y se centra espe- cialmente en la evolución del helicóptero multi-rotor. El éxito de los vehículos aéreos de hoy ciertamente no sería posible sin las incesantes intentos realizados en el siglo pasado por muchos pioneros valientes del dominio aeroespacial. El modelo de la aeronave de despegue y aterrizaje vertical planar representa una simplificación del modelo de un verdadero avión de despegue vertical. También representa el modelo longitudinal de un helicópero. La comunidad de control ha mostrado un gran interés en el problema del PVTOL porque es un problema teórico interesante y desafiante de los sistemas no lineales que esta claramente motivado por una aplicación. Diseño de controladores no lineales apropiados basados en el modelo PVTOL se pueden utilizar para mejorar el rendimiento y los márgenes de estabilidad del sistema en lazo cerrado para el despegue en vertical y aterrizaje de aeronaves. El Cap´titulo 2 presenta una estrategia de control no lineal para la estabi- lización del PVTOL utilizando el enfoque de saturaciones anidadas. Hemos desarrollado una plataforma experimental para probar los algoritmos de control que hemos propuesto. El helicóptero de cuatro rotores puede ser visto como una generalización del PVTOL en el espacio tridimensional. También puede ser visto como una alternativa a los helicópteros estándar que no tienen plato oscilante. Helicópteros de cuatro rotores tienen menos partes mecánicas que los mini-helicópteros convencionales. Esto se traduce en una reducción de tiempo empleado en mantenimiento. Dado que las cuchillas giran en direcciones opues- tas, los fenómenos giroscópicos debido a las cuchillas son menos importantes en los helicópteros de cuatro rotores de lo que es para los helicópteros estándar. Co- mo consecuencia el helicóptero de cuatro rotores tiene mayor maniobrabilidad pero esto significa también que tienden a ser mas inestables. En el Cap´tulo 3 presentaremos una estrategia de control no lineal para estabilizar el helicóptero de cuatro rotores. La ley de control propuesta ha sido probada en experimentos en tiempo real. Índice general Índice de figuras IX Índice de cuadros XI 1. Introducción y Motivación1 1.1. Introducción y Antecedentes Históricos..............2 1.1.1. Definiciones.........................2 1.1.2. Primeros conceptos de la Aeronave VTOL........4 1.1.3. Vehículo Aéreo sin Tripulación.............. 12 1.1.4. Primeros experimentos, UAV’s.............. 14 1.1.5. Clasificación de los UAV’s................. 21 1.1.6. Restricciones........................ 24 1.1.7. Configuración del Rotorcraft............... 25 1.1.8. Primeros conceptos del Quad-Rotor Helicóptero..... 26 1.2. El Helicóptero de Cuatro Rotores................. 30 1.2.1. Requerimientos....................... 31 2. Modelo Dinámico 33 2.1. Características del Quad-rotor helicóptero............ 35 2.1.1. Descripción del Sistema.................. 37 3. Control no lineal del Quad-Rotor 43 3.1. Descripción del modelo....................... 44 3.2. Dinámica del Quad-Rotor...................... 45 3.3. Representación en Espacio de Estados............... 46 3.3.1. Vector de estados y Vector de control........... 47 3.4. Punto de equilibrio......................... 47 3.5. Linealización............................. 48 3.5.1. Forma Compa{n...................... 48 3.5.2. Controlabilidad....................... 49 3.5.3. Matriz de Controlabilidad................. 50 3.6. Control Yaw............................. 52 3.7. Control Roll............................. 54 3.8. Técnica de FCL del PVTOL.................... 58 3.8.1. Código............................ 60 4. Conclusiones 63 5. Agradecimientos 65 Índice de figuras 1.1. Principales componentes del Helicóptero..............3 1.2. Diagrama del Quadcopter “XAircraft X650 Flight Style”.Plus Style, motores distribuidos delantero (M1), Izquierda (M2), Trasero (M3), Derecho (M4)....................4 1.3. El primer concepto de ala rotatoria de la aviación........5 1.4. El tornillo aéreo. Créditos - Hiller Aviation Museum [16].....6 1.5. Aerial carriage. Credits - Hiller Aviation Museum [16]......6 1.6. Gustave Ponton d’Amecourt’s helicopters. Credits - Hiller Avia- tion Museum [16]...........................8
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