H∞ Orbital Control of a Space Vehicle on a Low Earth Orbit

A Low Earth Orbit (LEO) is the trajectory of a space vehicle such as a satellite, missile or space shuttle relative to the Earth with an altitude of 1,500 km or less. Keplerian orbits only take in account the gravitational forces between bodies, however, in real life applications there are a lot of perturbations that alter the initial trajectory or the “mathematical ideal orbit” of the space vehicle. The perturbations analyzed in this dissertation were the atmospheric drag and the oblateness of the Earth (J2). It is necessary to control this trajectory in order to adjust the orbital elements so that the space vehicle can operate in the surroundings of the initial orbit and perform its mission adequately. There are many types of controllers for these space vehicles like the Linear-Quadratic Regulator (LQR), the Sliding Mode Control (SMC), the Linear Matrix Inequality (LMI) and the H-infinity (H∞) Controller. It is essential to find the best type of controller for each specific mission. Considering the inherent limitations of the methods mentioned above, the H8 Controller was judged to be the most suitable for this application under certain conditions. The focus of this dissertation is the development of an H8 robust controller that can successfully alter the trajectory of a space vehicle with perturbations, so that it follows a referenced Keplerian trajectory with the same initial conditions.Uma Órbita Terrestre Baixa (LEO) é a trajetória de um veículo espacial tal como um satélite, míssil ou vaivém espacial relativa à Terra com uma altitude de 1500 km ou menos. As órbitas Keplerianas são apenas caracterizadas pelas forças gravitacionais entre corpos, no entanto, em aplicações reais há muitas perturbações que alteram a trajetória inicial ou a “órbita matemática ideal” do veículo espacial. As perturbações analisadas nesta dissertação foram a força de resistência aerodinâmica e a não esfericidade da Terra (J2). É necessário controlar esta trajetória de maneira a ajustar os elementos orbitais para que o veículo espacial possa operar na vizinhança da órbita inicial e executar a sua missão adequadamente. Há vários tipos de controladores para estes veículos espaciais como o Regulador Quadrático Linear (LQR), o Controlo por Modo Deslizante (SMC), Desigualdades Matriciais Lineares (LMI) e o Controlador H-infinito (H∞). É essencial encontrar o melhor tipo de controlador para cada missão específica. Tendo em conta as limitações intrínsecas dos métodos acima mencionados, o Controlador H8 foi julgado o mais adequado neste caso, dentro de certas condições. O principal objetivo desta dissertação é o desenvolvimento de um controlador H8 robusto que consegue alterar a trajetória de um veículo espacial com perturbações, de maneira a fazê-lo seguir uma trajetória Kepleriana com as mesmas condições iniciais

34th Midwest Symposium on Circuits and Systems-Final Program

Organized by the Naval Postgraduate School Monterey California. Cosponsored by the IEEE Circuits and Systems Society. Symposium Organizing Committee: General Chairman-Sherif Michael, Technical Program-Roberto Cristi, Publications-Michael Soderstrand, Special Sessions- Charles W. Therrien, Publicity: Jeffrey Burl, Finance: Ralph Hippenstiel, and Local Arrangements: Barbara Cristi

Nonparametric Identification of nonlinear dynamic Systems

In der vorliegenden Arbeit wird eine nichtparametrische Identifikationsmethode für stark nichtlineare Systeme entwickelt, welche in der Lage ist, die Nichtlinearitäten basierend auf Schwingungsmessungen in Form von allgemeinen dreidimensionalen Rückstellkraft-Flächen zu rekonstruieren ohne Vorkenntnisse über deren funktionale Form. Die Vorgehensweise basiert auf nichtlinearen Kalman Filter Algorithmen, welche durch Ergänzung des Zustandsvektors in Parameterschätzer verwandelt werden können. In dieser Arbeit wird eine Methode beschrieben, die diese bekannte parametrische Lösung zu einem nichtparametrischen Verfahren weiterentwickelt. Dafür wird ein allgemeines Nichtlinearitätsmodell eingeführt, welches die Rückstellkräfte durch zeitvariable Koeffizienten der Zustandsvariablen beschreibt, die als zusätzliche Zustandsgrößen geschätzt werden. Aufgrund der probabilistischen Formulierung der Methode, können trotz signifikantem Messrauschen störfreie Rückstellkraft-Charakteristiken identifiziert werden. Durch den Kalman Filter Algorithmus ist die Beobachtbarkeit der Nichtlinearitäten bereits durch eine Messgröße pro Systemfreiheitsgrad gegeben. Außerdem ermöglicht diese Beschreibung die Durchführung einer vollständigen Identifikation, wobei die restlichen konstanten Parameter des Systems zusätzlich geschätzt werden. Die Leistungsfähigkeit des entwickelten Verfahrens wird anhand von virtuellen und realen Identifikationsbeispielen nichtlinearer mechanischen Systeme mit ein und drei Freiheitsgraden demonstriert

7th International Conference on Nonlinear Vibrations, Localization and Energy Transfer: Extended Abstracts

International audienceThe purpose of our conference is more than ever to promote exchange and discussions between scientists from all around the world about the latest research developments in the area of nonlinear vibrations, with a particular emphasis on the concept of nonlinear normal modes and targeted energytransfer

Applied Dynamics and Geometric Mechanics

This one week workshop was organized around several central subjects in applied dynamics and geometric mechanics. The specific organization with afternoons free for discussion led to intense exchanges of ideas. Bridges were forged between researchers representing different fields. Links were established between pure mathematical ideas and applications. The meeting was not restricted to any particular application area. One of the main goals of the meeting, like most others in this series for the past twenty years, has been to facilitate cross fertilization between various areas of mathematics, physics, and engineering. New collaborative projects emerged due to this meeting. The workshop was well attended with participants from Europe, North America, and Asia. Young researchers (doctoral students, postdocs, junior faculty) formed about 30% of the participants

Mathematical theory of the Goddard trajectory determination system

Basic mathematical formulations depict coordinate and time systems, perturbation models, orbital estimation techniques, observation models, and numerical integration methods

AAS/GSFC 13th International Symposium on Space Flight Dynamics

This conference proceedings preprint includes papers and abstracts presented at the 13th International Symposium on Space Flight Dynamics. Cosponsored by American Astronautical Society and the Guidance, Navigation and Control Center of the Goddard Space Flight Center, this symposium featured technical papers on a wide range of issues related to orbit-attitude prediction, determination, and control; attitude sensor calibration; attitude dynamics; and mission design

Nonparametric identification of nonlinear dynamic systems

A nonparametric identification method for highly nonlinear systems is presented that is able to reconstruct the underlying nonlinearities without a priori knowledge of the describing nonlinear functions. The approach is based on nonlinear Kalman Filter algorithms using the well-known state augmentation technique that turns the filter into a dual state and parameter estimator, of which an extension towards nonparametric identification is proposed in the present work