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Optimal control of hybrid electric vehicles for real-world driving patternsVagg, Christopher January 2015 (has links)
Optimal control of energy flows in a Hybrid Electric Vehicle (HEV) is crucial to maximising the benefits of hybridisation. The problem is complex because the optimal solution depends on future power demands, which are often unknown. Stochastic Dynamic Programming (SDP) is among the most advanced control optimisation algorithms proposed and incorporates a stochastic representation of the future. The potential of a fully developed SDP controller has not yet been demonstrated on a real vehicle; this work presents what is believed to be the most concerted and complete attempt to do so. In characterising typical driving patterns of the target vehicles this work included the development and trial of an eco-driving driver assistance system; this aims to reduce fuel consumption by encouraging reduced rates of acceleration and efficient use of the gears via visual and audible feedback. Field trials were undertaken using 15 light commercial vehicles over four weeks covering a total of 39,300 km. Average fuel savings of 7.6% and up to 12% were demonstrated. Data from the trials were used to assess the degree to which various legislative test cycles represent the vehicles’ real-world use and the LA92 cycle was found to be the closest statistical match. Various practical considerations in SDP controller development are addressed such as the choice of discount factor and how charge sustaining characteristics of the policy can be examined and adjusted. These contributions are collated into a method for robust implementation of the SDP algorithm. Most reported HEV controllers neglect the significant complications resulting from extensive use of the electrical powertrain at high power, such as increased heat generation and battery stress. In this work a novel cost function incorporates the square of battery C-rate as an indicator of electric powertrain stress, with the aim of lessening the affliction of real-world concerns such as temperatures and battery health. Controllers were tested in simulation and then implemented on a test vehicle; the challenges encountered in doing so are discussed. Testing was performed on a chassis dynamometer using the LA92 test cycle and the novel cost function was found to enable the SDP algorithm to reduce electrical powertrain stress by 13% without sacrificing any fuel savings, which is likely to be beneficial to battery health.
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3D modelling of ship resistance in restricted waterways and application to an inland eco-driving prototype / Modélisation 3D de la résistance à l’avancement en milieu confiné et application à un éco-pilote fluvialLinde, Florian 19 October 2017 (has links)
Les travaux de cette thèse ont pour but de développer un prototype d’éco-pilote, nommé EcoNav, permettant d’optimiser la vitesse d’un bateau afin de réduire sa consommation de carburant. EcoNav est composé de plusieurs modules dont : un modèle hydraulique 2D simulant l’écoulement hydrodynamique (vitesse du courant et hauteur d’eau) le long du trajet du bateau; - un modèle de résistance à l’avancement servant à alimenter un modèle de prédiction de la consommation de carburant; - un algorithme d’optimisation permettant de trouver le profil optimal de vitesse. Afin de pouvoir estimer la consommation de carburant, un modèle numérique de la résistance à l’avancement en milieu confiné a été développé durant la première partie de cette thèse. Ce modèle numérique 3D simule l’écoulement du fluide autour du bateau et permet de calculer les forces agissant sur sa coque. La résolution des équations RANS est couplée avec un algorithme de quasi-Newton afin de trouver la position d’équilibre du bateau et calculer son enfoncement. Cette méthode est validée en comparant les résultats numériques avec des résultats expérimentaux issus d’essais en bassin de traction. L’influence de l’enfoncement sur la résistance à l’avancement et la précision de la méthode est étudiée en comparant les résultats numériques obtenus avec et sans enfoncement. La précision des modèles empiriques de prédiction de la résistance à l’avancement est également comparée à celle du modèle numérique. Enfin, le modèle numérique est utilisé afin de déterminer si le confinement en largeur ou en profondeur ont une influence identique sur l’augmentation de résistance à l’avancement. Les résultats de cette étude permettent d’établir si le confinement de la voie d’eau peut être caractérisé à l’aide d’un paramètre unique (coefficient de blocage par exemple) ou bien deux paramètres permettant de distinguer le confinement latéral et vertical. Dans la seconde partie de cette thèse, les méthodes numériques utilisées pour le modèle d’éco-pilote sont décrites et comparées afin de sélectionner celles qui sont le plus adaptées à chaque module. EcoNav est ensuite utilisé afin de modéliser un cas réel : celui du bateau automoteur Oural navigant sur la Seine entre Chatou et Poses (153 km). La consommation optimisée est comparée à la consommation non optimisée, calculée à partir des vitesses AIS observées sur le tronçon étudié. L’influence de la trajectoire du bateau et de son temps de parcours sur sa consommation sont également étudiés. Les résultats de ces investigations ont montré qu’optimiser la vitesse du bateau permet d’obtenir une réduction de la consommation de carburant de l’ordre de 8 % et qu’optimiser la trajectoire du bateau ainsi que prendre en compte des informations en temps réel (disponibilité des écluses, trafic sur le fleuve) peuvent permettre de réaliser des économies de carburant supplémentaires. / An eco-driving prototype, named EcoNav, is developed with the aim of optimizing a vessel speed in order to reduce fuel consumption for a given itinerary. EcoNav is organized in several modules : - a 2D hydraulic model simulating the flow conditions (current speed and water depth) along the itinerary; - a ship resistance model calculating the thrust necessary to counteract the hydrodynamic forces ; - a fuel consumption model calculating the fuel consumption corresponding to the thrust input; - a non linear optimization algorithm calculating the optimal speed profile. In order to evaluate the fuel consumption of an inland vessel, a ship resistance numerical model is developed in the first part of this PhD. This 3D numerical model simulates the flow around an inland self-propelled vessel and evaluates the hydrodynamic forces acting on the hull. A RANS solver is coupled with a quasi-Newton approach to find the equilibrium position and calculate ship sinkage. This method is validated by comparing the results of numerical simulations to towing tank tests. The numerical results with and without sinkage are also compared to study the influence of sinkage on ship resistance and on the accuracy of the method. Additionally, some empirical models are investigated and compared with the accuracy of the numerical method. Finally, the numerical model is used to determine if channel with and water depth restriction contribute to the same amount of ship resistance increase for the same level of restriction. The results of that investigation give insight to whether channel restriction can be characterized by a unique parameter (for instance the blockage ratio) or two parameters to distinguish water depth and channel with effects. In the second part of this PhD, the numerical methods used in the speed optimization model are described and validated. The speed optimization model is then used to simulate a real case: the itinerary of the self-propelled ship Oural on river Seine, between Chatou and Poses (153 km). The optimized fuel consumption is compared with the non-optimized fuel consumption, based on AIS speed profile retrieved on this itinerary. The effects of the ship trajectory and travel duration on fuel consumption are also investigated. The results of those investigations showed that optimizing the ship speed lead to an average fuel saving of 8 % and that using an optimal track and including real time information such as lock availability and river traffic can lead to additional fuel savings.
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Desenvolvimento e aplicação de um modelo para o Pollution Routing Problem. / Developing and implementing a model for a Pollution Routing Problem.Anderson Oliveira de Ornelas Paschoal 27 April 2015 (has links)
O transporte rodoviário é uma das atividades econômicas do homem que mais contribuem para a emissão de Gases de Efeito Estufa (GEE) na atmosfera. Sabe-se que a emissão de CO2 está diretamente vinculada ao consumo de combustível. Por isso, é possível encontrar uma série de trabalhos que objetivam diminuir as emissões por meio da redução do consumo de combustível dos veículos. A otimização de rotas é uma importante ferramenta para essa redução e, consequentemente, possibilita minimizar as emissões dos veículos. Esta pesquisa tem como objetivo aplicar em uma empresa líder na distribuição de revistas no país o PRP, que é um modelo de minimização do consumo de combustível/emissão de GEE por meio de ajustes das variáveis como velocidade média, quantidade de carga transportada, distância percorrida e inclinações das vias. Como a maioria das metodologias de estimativa de combustível existentes na literatura não considera a inclinação das vias nos seus cálculos, neste trabalho foi necessário desenvolver uma metodologia para incluí-la no modelo. Testes foram efetuados com variações nas janelas de tempo, e o modelo mostrou-se sensível a cada uma das variáveis analisadas, gerando economias em 100% das rotas estudadas. / Road transport is one of the biggest contributors of Greenhouse Gases emissions of all humans economic activities. It is known that CO2 emissions are directly related to fuel consumption, so that is why it is possible to find a series of studies that aims to reduce emissions by reducing vehicles fuel consumption. Route optimization is an important tool for reducing fuel consumption and hence emissions. This research aims to implement the PRP model in a leading company in the country, which is a model that minimizes fuel consumption/GHG emissions through adjustments of variables such as average speed, pay load, distance traveled and slopes of the road. Most existing fuel estimation methodologies found in the literature does not consider the slope of the roads in their calculations. So in this research it was necessary to develop a methodology to include it in the model. Tests were performed with variations in the time windows and the model was sensitive to each of the variables analyzed, generating savings on 100% of the studied routes.
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Système actif d'aide à une conduite Eco avec prise en compte de l'interaction conducteur-véhicule-usage / Active Eco driving support system with consideration of driver-vehicle-road interactionJavanmardi, Setareh 28 November 2017 (has links)
L’éco-conduite a été identifié comme l’un des moyens efficaces pour l’économie d’énergie dans le domaine des véhicules terrestres. Le gain potentiel en consommation ainsi que sa facilité de mise en œuvre, rendent cette solution très recherchée dans le milieu industriel pour à la fois améliorer la consommation des véhicules mais aussi satisfaire les utilisateurs. Cette thèse contribue au développement d’un système actif d’aide à l’éco-conduite pour assister le conducteur dans son économie d’énergie. Ce système s’appuie sur une optimisation énergétique et tient compte de l’interaction du conducteur avec le véhicule et son usage (la route). Nous avons tout d’abord développé un modèle multi-variable de style de conduite pour représenter le conducteur humain par un modèle virtuel. L’identification des paramètres de ce modèle a permis de caractériser trois styles de conduite sur plusieurs cas d’usage et de reproduire de manière assez fidèle les trois niveaux de consommation de carburant. Considérant les cas d’usage péri-urbains et autoroutiers, le problème d’optimisation de la trajectoire sur des critères énergétiques a été reformulé afin de déterminer un profil de vitesse constant par morceaux minimisant la consommation d’énergie, tout en respectant la durée de trajet désirée et les limitations de vitesse. Le profil de vitesse optimal fournit des vitesses cibles, informations du premier ordre pour réduire la consommation. Plusieurs extensions ont été ensuite introduites dans la trajectoire optimale afin d’y intégrer l’anticipation des phases de décélération et les phases d’accélération. L’originalité principale de cette approche est le temps de calcul extrêmement faible, tout en obtenant des résultats très proches des résultats optimaux issus de méthodes classiques d’optimisation (ex. programmation dynamique). Afin d’aller encore plus loin dans l’éco-conduite, nous avons étudié la possibilité de réduire la consommation d’énergie en intégrant des stratégies de conduite telle que le ''swaying'' qui consiste en une oscillation de la vitesse du véhicule autour d’une vitesse moyenne. Nous avons alors pu montrer que, « en théorie », il existe bien des paramètres permettant de réduire la consommation de cette manière. Le système actif d’aide à l’éco-conduite a donc été développé en conjuguant les deux aspects précédents. Il se base sur le partage de la commande moteur entre le conducteur humain et un contrôleur optimal. Des niveaux de partage variables ont été établis afin de représenter différents niveaux d’économie d’énergie et d’intervention sur la conduite du conducteur. Enfin, ce système d’aide actif a été testé expérimentalement sur un simulateur de conduite. / Eco-driving has been identified as one of the most effective ways to save energy in the field of ground vehicles. The potential gain in fuel consumption reduction as well as its easy implementation, make this solution very sought after in the industrial environment for improving both the fuel consumption of vehicles and the user satisfaction. This thesis contributes to the development of an active eco-driving support system for assisting the driver to improve his fuel economy. This system is based on energy optimization and takes into account the driver's interaction with the vehicle and its use (the road). For this purpose, first of all a multi-variable driving style model is developed to represent the human driver by a virtual model. The identification of the parameters of this model made it possible to characterize three driving styles in several use cases and to reproduce the three levels of fuel consumption fairly accurately. Considering the suburban and motorway use cases, the trajectory optimization problem based on energy criteria has been reformulated in order to determine a piecewise constant velocity profile minimizing energy consumption, while respecting constraints on trip duration and velocity limitations. The optimal velocity profile provides target cruising velocity, which is the first order information to reduce fuel consumption. Several extensions were then introduced in the optimal trajectory in order to incorporate the anticipation of the deceleration phases and the acceleration phases. The main originality of this approach is the extremely low computation time, while obtaining results very close to the optimal solution, achieved by classical optimization methods (e.g. dynamic programming). In order to investigate even further in eco-driving, we have studied the possibility of reducing energy consumption by integrating driving strategies such as ''swaying'', which consists of an oscillation of the vehicle's speed around an average speed. We were then able to show that, "theoretically", this problem can be parametrized so that the energy consumption is reduced. The active eco-driving support system was therefore developed by combining the two previous aspects. It is based on the shared control of the engine between the human driver and an optimal controller. Variable sharing laws have been established to represent different levels of optimal controller intervention on human driver driving, which results to different levels of fuel economy. Finally, this active support system has been tested experimentally on a driving simulator.
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Road Freight Transport : Transport Purchasing and Environmental ImpactsArmstrong, Amrith January 2014 (has links)
This paper on the environmental impacts of transport purchasing in road freight is to highlight how the adaptive capability of transport chains are affected through collaboration and the aim for sustainability through political regulations and societal demands.This paper is divided into a theoretical framework and an empirical study, followed by the analysis, conclusions and discussions based on the framework and empirical study.The theoretical framework will discuss the different aspects of road freight transport which impact the environment and show the interdependencies of each aspect.The analysis will highlight the empirical chapter with a comparison of the theoretical framework in order to make substantial conclusions.Conclusions among others are that standardization is needed although flexibility and agility is also needed. By standardizing processes, routine measures can be implemented and it creates a sense of certainty within the company. Agility and flexibility can be achieved by adding modular processes which can be implemented if the need for customization arises.Governmental involvement is necessary for the development of infrastructure to minimize traffic congestion and improve the infrastructure for increased reliability, accessibility, and flexibility. By developing the rail infrastructure, a larger share of goods can be transferred via railway and thus reduce the environmental impacts of road freight through intermodal transportation. / Program: Industrial Engineering – Logistics Management
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Simulation studies of the effects of lean operation, turbocharging and heat transfer on spark ignition enginesWatts, Paula A January 1979 (has links)
Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1979. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / by Paula A. Watts. / M.S.
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Desempenho de conjunto motor-gerador utilizando biocombustíveis sob cargas variadas / Performance of engine-generator set using biofuels under varied loadsRigotte, Marcio Roberto 14 February 2014 (has links)
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Previous issue date: 2014-02-14 / The rising demand for energy, coupled with its high cost and the search for sustainability propitiated in recent years an increase in demand for renewable biofuels, including biodiesel. Although Brazil, and specifically Paraná, present agricultural vocation, with diversity of raw materials for biodiesel production, it remains tied to demand compulsory. This work aimed to evaluate the energetic performance of an engine-generator set using diesel oil and biodiesel of different feedstocks. The experiment was conducted in the Experimental Nucleus for Agricultural Engineering (NEEA), State University of West Paraná (UNIOESTE), located in Cascavel - Paraná, using entirely randomized design. The treatments were diesel oil, and three different types of biodiesel (crambe, soybean and waste frying oil) being used pure biodiesel (B100) and the binary blends B10, B20 and B50. The resistive loads used were 1, 2, 3, 4 and 5 kW for each type of fuel, a total of five replications. Among other observations, we evaluated the heating value, specific fuel consumption (CE) and energy efficiency (EE). The best CE was diesel with 0,349 Kg KW h-1 in the load 5 KW, followed by BC20-2 with 0,524 Kg kW h-1 and BC50-3 with 0,433 Kg kW h-1. Biodiesel has the CE nearest of the diesel with increasing resistive load, indicating that its use in operation closest the rated capacity is more efficient. Among the types of biodiesel, the crambe oil showed lower CE, with some values without significant differences (Tukey 5%) of the diesel CE, as BC20-4 with 0,383 Kg kW h-1 and BC10-5 with 0,367 Kg KW h-1. The best EE were DI-5 25,6%, BC100-5 25,5%, BC50-5 25,0%, BS100-5 24,8% and BORF100-5 24,6%. Pure biodiesel (B100) tends to show best EE that the binary blends used. The BC100 showed EE of 9,9 17,8, 21,8, 24,3 and 25,5% respectively for resistive load of 1, 2, 3, 4 and 50 KW. In the range of biodiesel evaluated, crambe oil obtained EE closer to diesel, and the BC100 exceeded diesel EE to the loads 2, 3 and 4 / A crescente demanda por energia, associada a seus elevados custos e a busca por sustentabilidade propiciaram nos últimos anos um aumento na procura por biocombustíveis renováveis, dentre eles o biodiesel. Apesar do Brasil, e especificamente o Paraná, apresentarem vocação agrícola, com diversidade de matérias-primas para obtenção de biodiesel, esta permanece atrelada a demanda compulsória. Este trabalho buscou avaliar o desempenho energético de um conjunto motor-gerador utilizando diesel de petróleo e biodiesel de diferentes matérias primas. O experimento foi conduzido no Núcleo Experimental em Engenharia Agrícola (NEEA), da Universidade Estadual do Oeste do Paraná (UNIOESTE), Cascavel Paraná, utilizando delineamento experimental inteiramente casualizado. Os tratamentos utilizados foram o diesel de petróleo, e três diferentes tipos de biodiesel (crambe, soja e óleo residual de fritura), sendo o biodiesel utilizado puro (B100) e nas misturas binárias B10, B20 e B50. As cargas resistivas utilizadas foram de 1, 2, 3, 4 e 5 KW para cada tipo de combustível, com total de cinco repetições. Entre outras observações, foi avaliado o poder calorífico, o consumo específico (CE) e a eficiência energética (EE). O melhor CE foi o diesel com 0,349 Kg KW h-1 na carga 5 KW, seguido por BC20-2 com 0,524 Kg KW h-1 e o BC50-3 com 0,433 Kg KW h-1. O biodiesel apresenta CE mais próximo do diesel com o aumento da carga resistiva, indicando que sua utilização em operações mais próxima da capacidade nominal é mais eficiente. Dentre os tipos de biodiesel, o de óleo de crambe apresentou menor CE, com alguns valores sem diferenças significativas (Tukey 5%) do CE do diesel, como o BC20-4 com 0,383 Kg KW h-1 e o BC10-5 com 0,367 Kg KW h-1. As melhores EE foram DI-5 25,6%, BC100-5 25,5%, BC50-5 25,0%, BS100-5 24,8% e BORF100-5 24,6%. O biodiesel puro (B100) tende a apresentar melhor EE que as misturas binárias utilizadas. O BC100 apresentou EE de 9,9 17,8 21,8 24,3 e 25,5% respectivamente para as cargas resistivas de 1, 2, 3, 4 e 5 KW. Na gama de biocombustíveis avaliados, o de óleo de crambe obteve EE mais próxima ao do diesel, sendo que BC100 superou EE do diesel nas cargas 2, 3 e 4.
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Hybrid Controls Development and Optimization of a Fuel Cell Hybrid PowertrainKoch, Alexander Karl January 2012 (has links)
The University of Waterloo Alternative Fuels Team’s participation in EcoCAR: The Next Challenge provided an unparalleled opportunity to execute advanced vehicle technology research with hands on learning and industry leading mentoring from practicing engineers in the automotive industry. This thesis investigates the optimization of the hybrid operating strategy on board the EcoCAR development vehicle. This investigation provides the framework to investigate the pros and cons of different hybrid control strategies, develop the model based design process for controls development in a student team environment and take the learning of this research and apply them to a mule development vehicle.
A primary controls development model was created to simulate software controls before releasing to the vehicle level and served as a tool to evaluate and compare control strategies. The optimization routine was not directly compatible with this model and so a compromise was made to develop a simplified vehicle model in the MATLAB environment that would be useful for observing trends but realizing that the accuracy of the results may not be totally consistent with the real world vehicle. These optimization results were then used to create a new control strategy that was simulated in the original vehicle development model. This new control strategy exhibited a 15% gain in fuel economy over the best case from the literature during an Urban Dynamometer Driving Schedule (UDDS) drive cycle.
Recommendations for future work include adding charge depletion operation to the simulation test cases and improving the accuracy of the optimization model by removing the simplifications that contributed to faster simulation time. This research has also illustrated the wide variability of drive cycles from the mildly aggressive UDDS cycle having 5 kilowatts average propulsion power to the very aggressive US06 cycle having 19 kilowatts average propulsion power and their impact on the efficiency of a particular control strategy. Understanding how to adapt or tune software for particular drive cycle or driver behaviour may lead to an interesting area of research.
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Bewertung von alternativen Antriebskonzepten in Fahrzeugen mit unterschiedlichen Einsatzcharakteristiken / Evaluation of alternative propulsion concepts of vehicles with different characteristicsAhmed, Mohamed 20 November 2004 (has links) (PDF)
Der weltweit steigende Mobilitätsbedarf führt in der Zukunft zur weiteren Zunahme des Primärenergiebedarfs. Die Rohstoffvorräte unserer Erde sind begrenzt. Rohstoffe, die heute verbraucht werden, stehen zukünftigen Generationen nicht mehr zur Verfügung. Die sparsame und effiziente Nutzung der Ressourcen stellt deshalb den Schlüssel zu einer nachhaltigen Entwicklung dar. Im Mittelpunkt steht dabei der Energieverbrauch. Vor allem die Industrieländer stehen vor der Herausforderung, ihren Verbrauch an begrenzten Energierohstoffen Schritt für Schritt zurückzufahren. Der Wirtschaftsbereich der Europäischen Union kann dabei eine positive Bilanz vorweisen. Eingeschlossen in diese Bilanz ist der Verkehrsbereich. Die modernen Fahrzeugflotten konnten durch die ständige Weiterentwicklung den Streckenkraftstoffverbrauch und die Abgasemissionen erheblich absenken. Eine Entwicklung, die noch nicht am Ende ist. Trotz dieser positiven Tendenz gerät die globale Bilanz durch eine dramatische Zunahme der Fahrzeugflotten, besonders in den Entwicklungsländern, kontinuierlich in eine Schieflage. Die Energieverbräuche steigen und die Ressourcen der Energieträger Öl, Gas und Kohle nehmen ab. Es ist bekannt, dass weltweit besonders in hochentwickelten Industrieländern dieser Entwicklung durch Alternativ-Konzepte entgegengesteuert wird. Im Verkehrsbereich sind dies unter anderem veränderte Fahrzeugkonzepte (z. B. Hybridfahrzeuge) sowie die mittel- und längerfristige Substitution der konventionellen, mineralölstämmigen Kraftstoffe durch Erdgaskraftstoffe (SynFuel, nach der Shell-Mittel-Destillat-Synthese, SMDS, hergestellt) oder Kraftstoffe (Sun Fuel) aus regenerativen Energieträgern wie Restholz, Energiepflanzen oder Biomüll. Diese Entwicklungen werden durch eine permanente Reduzierung der Abgasemissionen von verbrennungsmotorisch angetriebenen Fahrzeugen begleitet. Insbesondere sind dies einerseits die limitierten Schadstoffe, welche in den einzelnen Ländern gesetzlich verankert sind, und andererseits die CO2-Emission, die z. B. noch auf einer freiwilligen Selbstverpflichtung der Automobilindustrie (in Deutschland 140 g/km CO2 – Ausstoß) basieren. Kapitel 1: Einführung 2 Alle diese Entwicklungen gilt es im Voraus abzuschätzen bzw. mit fundierten Betrachtungen in den Entwicklungsprozess einzuordnen. Dies gilt besonders für solche Länder, z. B. Ägypten, die den Technikfortschritt aus ökonomischer und ökologischer Betrachtung in sehr kurzer Zeit einzuführen haben. Die Simulationswerkzeuge aller Art werden bekannterweise dazu genutzt, um Fehlentwicklungen zu vermeiden. Je nach Aufgabe und Zielstellung sind diese Werkzeuge fachgerecht anzupassen und zu verifizieren. Im Speziellen werden konventionelle und alternative Antriebskonzepte für Fahrzeuge der verschiedensten Einsatzbedingungen mit einem Simulationswerkzeug bewertet. 1.1 Aufgabenstellung und Zielstellung
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An investigation of fuel optimal terminal descentRea, Jeremy Ryan 16 October 2012 (has links)
Current renewed interest in exploration of the moon, Mars, and other planetary objects is driving technology development in many fields of space system design. In particular, there is a desire to land both robotic and human missions on the moon and elsewhere. The core of a successful landing is a robust guidance, navigation, and control system (GN&C). In particular, the landing guidance system must be able to deliver the vehicle from an orbit above the planet to a desired soft landing, while meeting several constraints necessary for the safety of the vehicle. In addition, due to the performance limitations of current launch vehicles, it is desired to minimize the amount of propellant used during the landing. To make matters even more complicated, the landing site may change in real-time in order to avoid previously undetected hazards which become apparent during the landing maneuver. The Apollo program relied heavily on the eyes of the astronauts to avoid such hazards through manual control. However, for missions to the lunar polar regions, poor lighting conditions will make this much more difficult; for robotic missions, this is not an option. It is desired to find a solution to the landing problem such that the fuel used is minimized while meeting constraints on the initial state, final state, bounded thrust acceleration magnitude, and bounded pitch attitude. With the assumptions of constant gravity and negligible atmosphere, the form of the optimal steering law is found, and the equations of motion are integrated analytically, resulting in a system of five equations in five unknowns. When the pitch over constraint is ignored, it is shown that this system of equations can be reduced analytically to two equations in two unknowns. In addition, when an assumption of a constant thrust acceleration magnitude is made, this system can be reduced further to one equation in one unknown. It is shown that these unknowns can be bounded analytically. An algorithm is developed to quickly and reliably solve the resulting one-dimensional bounded search. The algorithm is used as a real-time guidance and is applied to lunar and Mars landing test cases. / text
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