This report presents the bending modes study conducted on a heavy launcher. The controller of the launcher takes as inputs the attitude and attitude rate measurements given by the Inertial Measurement Unit (IMU). Since the bending modes generate measurement errors at the IMU location, the study of deformations due to these bending modes is critical to assess the stability of the launcher during the atmospheric flight phase. The goal of this master thesis project is to detect and then select the most excitable bending modes among the large number of modes provided by a detailed structural analysis of the launcher. Only these relevant modes will be later used to generate reduced dynamical models of the launcher in order to efficiently design an appropriate controller. Indeed, considering all the bending modes will dramatically increase the calculation time and will not significantly improve the representativeness of the model at the control law frequency range of interest. To reach this objective, an extended excitability (the maximum of the module of the transfer function between the effective deflection and the considered mode generalized coordinate transported at the IMU location) is defined and computed for each mode. A criterion has been implemented to choose only the relevant modes. The sensitivity study conducted during this master thesis project has shown that with around 20 modes over 200, one can reproduce the dynamic behavior of the complete system. / Denna rapport presenterar studien för böjningslägen som utförts på en bärraket. Eftersom böjningslägen genererar mätfel vid IMU-platsen är studien av deformationer på grund av dessa böjningslägen avgörande för att bedöma stabiliteten under den atmosfäriska flygfasen. Målet med detta examensarbete är att upptäcka och sedan välja de mest spännande böjningslägena bland det stora antalet lägen som tillhandahålls av en detaljerad strukturanalys av bärraketen. Endast dessa relevanta lägen kommer senare att användas för att generera reducerade dynamiska modeller av bärraketen för att effektivt utforma en lämplig styrenhet. Faktum är att övervägande av alla böjningslägen dramatiskt ökar beräkningstiden och kommer inte att förbättra modellens representativitet väsentligt. För att uppnå detta mål definieras och beräknas en utvidgad excitabilitet (det maximala för överföringsfunktionens modul mellan effektiv avböjning och den övervägda modaliserade koordinaten som transporteras på IMU-platsen) för varje läge. Ett kriterium har implementerats för att bara välja de relevanta lägena. Känslighetsstudien som genomfördes under detta examensarbete har visat att med cirka 20 lägen över 200 kan man återge det dynamiska beteendet hos hela systemet.

Optimal orbital trajectories are obtained through the solution of highly nonlinear large scale problems. In the case of low-thrust propulsion applications, the spacecraft benefits from high specific impulses and, hence, greater payload mass. However, these missions require a high count of orbital revolutions and, therefore, display augmented sensitivity to many disturbances. Solutions to such problems can be tackled via a discrete approach, using optimal feedback control laws. Historically, differential dynamic programming (DDP) has shown outstanding results in tackling these problems. A state of the art software that implements a variation of DDP has been developed by Whiffen and it is used by NASA’s DAWN mission [Mystic: Implementation of the Static Dynamic Optimal Control Algorithm for High-Fidelity, Low-Thrust Trajectory Design" , AAS/AIAA Astrodynamics Specialist Conference, (Keystone, Colorado), American Institute of Aeronautics and Astronautics, Aug. 21, 2006]. One of the latest techniques implemented to deal with these discrete constrained optimizations is the Hybrid Differential Dynamic Programming (HDDP) algorithm, introduced by Lantoine and Russell in [A Hybrid Differential Dynamic Programming Algorithm for Constrained Optimal Control Problems. Part 1: Theory", Journal of Optimization Theory and Applications, vol. 154, pp. 382-417, issue 2, Aug. 1, 2012]. This method complements the reliability and efficiency of classic nonlinear programming techniques with the robustness to poor initial guesses and the reduced computational effort of DDP. The key feature of the algorithm is the exploitation of a second order state transition matrix procedure to propagate the needed partials, decoupling the dynamics from the optimization. In doing so, it renders the integration of dynamical equations suitable for parallelization. Together with the possibility to treat constrained problems, this represents the greatest improvement of classic DDP. Nevertheless, the major limitation of this approach is the high computational cost to evaluate the required state transition matrices. Analytical derivatives, when available, have shown a significant reduction in the computational cost and time for HDDP application. This work applies differential algebra to HDDP to cope with this limitation. In particular, differential algebra is introduced to obtain state transition matrices as polynomial maps. These maps come directly from the integration of the dynamics of the system, removing the dedicated algorithmic step and reducing its computational cost. Moreover, by operating on polynomial maps, all the solutions of local optimization problems are treated through differential algebraic techniques. This approach allows us to deal with higher order expansions of the cost, without modifying the algorithm. The leading assumption of this work is that, treating higher than second order expansions, grants larger radii of convergence for the algorithm, improved robustness to initial guesses, hence faster rates of convergence. Examples are presented in this thesis to assess the performance of the newly constructed algorithm and to test the assumptions.​ / Optimala omloppsbanor erhålls genom lösningen av mycket storskaliga olinjära problem. I fallet med låg framdrivningskraft så drar farkosten nytta av hög specifik impuls och därmed större slutlig farkostmassa. Dock så kräver dessa rymduppdrag flera omloppsvarv och uppvisar därför ökad känslighet för olika störningskrafter. Lösningar på dessa problem kan hanteras via ett diskret tillvägagångssätt med hjälp av optimal reglering. Historiskt har differentialdynamisk programmering (DDP) visat enastående resultat för att hantera dessa problem. En toppmodern programvara som implementerar en variation av DDP har utvecklats av Whiffen i ["Mystic: Implementation of the Static Dynamic Optimal Control Algorithm for High-Fidelity, Low-Thrust Trajectory Design" , AAS/AIAA Astrodynamics Specialist Conference, (Keystone, Colorado), American Institute of Aeronautics and Astronautics, Aug. 21, 2006] och används av NASA:s rymduppdrag Dawn. En av de senaste teknikerna som implementerats för att hantera dessa diskreta och begränsade optimeringar är en hybrid differentialdynamisk programmeringsalgoritm (HDDP) som introducerades av Lantoine och Russell i ["A Hybrid Differential Dynamic Programming Algorithm for Constrained Optimal Control Problems. Part 1: Theory", Journal of Optimization Theory and Applications, vol. 154, pp. 382-417, issue 2, Aug. 1, 2012]. Denna metod kompletterar pålitligheten och effektiviteten hos klassiska olinjära programmeringstekniker med robusthet mot dåliga initiala gissningar och den reducerade beräkningskostnaden för DDP. Nyckelegenskapen hos algoritmen är utnyttjandet av en procedur för andra ordningens övergångsmatris för propagering av de erforderliga partiella derivatorna. Denna procedur frikopplar också dynamiken från optimeringen. Genom att göra så blir integration av de dynamiska ekvationerna lämpliga för parallellisering. Tillsammans med förmågan att ta itu med begränsade problem representerar detta den största förbättringen av klassisk DDP. Ändå är den stora begränsningen av detta tillvägagångssätt den höga kostnaden för beräkningar som krävs för att utvärdera tillståndsövergångsmatriserna. När de är tillgängliga, har analytiska derivatorer visat en signifikant minskning av beräkningskostnaden och tiden för HDDP-tillämpningar. Detta arbete tillämpar differentialalgebra på HDDP för att klara av denna begränsning. I synnerhet införs differentialalgebra för att erhålla tillståndsövergångsmatriser som polynomavbildningar. Dessa avbildningar kommer direkt från integrationen av systemets dynamik och därför är det möjligt att ta bort det dedikerade algoritmiska steget och minska beräkningskostnaden. Vidare behandlas alla lösningar av lokala optimeringsproblem genom olika algebraiska tekniker genom att använda polynomkartor. Detta tillvägagångssätt tillåter oss att hantera högre ordningens expansionstermer av kostnadsfunktionen utan att ändra algoritmen. Det främsta antagandet i detta arbete är att behandling av högre än andra ordningens expansionstermer ger större konvergensradier för algoritmen, förbättrad robusthet mot sämre initiala gissningar och följaktligen snabbare konvergensnivåer. Exempel presenteras i denna examensarbete för att bedöma prestandan hos den nybyggda algoritmen och för att testa antagandena.

Designing a flight control system for an aircraft is a multifaceted task which has to take many requirements and constrints into account. Being able to quickly evaluate the feasibility of achieving design targets in terms of – for example – maneuvering capability and stability mar-gins is valuable when faced with the task of designing a flight control system for a new aircraft or aircraft configuration. This thesis presents methods to quickly assess the maneuverability capability of an aircraft with certain dynamics and control servo constraints by inverting the aircraft dynamics. Limitations related to the achievable robustness properties are also de-scribed with an emphasis on unstable aircraft configurations. The influence from variations of key flight mechanical parameters such as Cmα is investigated and the results are exempli-fied for a linearized model of the Admire aircraft.

Systems of Systems (SoS) represent a view where individual, independent systems named Constituent System (CS) collaborate to achieve overarching capabilities not attainable by a single CS alone. In cyberphysical systems, CS can be engineered entities like boats or aircraft, when they collaborate in an environment it can be viewed as an SoS. There is a large interest in modeling and simulation of phenomena present at different scales of SoS, which requires choosing appropriate model fidelity and resolution for the study. This thesis delves into the intricacies of modeling and simulation of mission scenarios within SoS, with a keen focus on engineered CS operating in physical environments. At the heart of the thesis lies the concept of model fidelity, examined through philosophical, scientific, and engineering perspectives. A maritime search and rescue scenario by airborne search assets serves as case study, using Agent Based Simulation (ABS) to explore the Measures of Effectiveness (MoE) of the mission. Through a hierarchical viewpoint it is studied how the model fidelity on Sub-System (SS) level affects its performance and how it aggregates up to performance on the CS level and at last the MoE on SoS level. In the scenarios, manned assets utilize traditional search patterns that is used in present search and rescue operations. Concurrently, autonomous assets employ a belief map search strategy where the map is based on probability density functions underpinned by a Bayesian modeling approach to new observations as the search progresses. The study shows that increasing the model fidelity at the SS level, particularly by refining the representation of the search sensor, can impact the MoE of the mission at the SoS level. However, this influence shows to be notably scenario-dependent, emphasizing the intricate relationship between model fidelity and system performance. The findings indicate that the relevance of model fidelity is tied to how measures of performance at lower levels aggregate to influence overarching mission outcomes. The thesis concludes by discussing validation and verification of the case study and ties encountered modeling difficulties to resolution and model fidelity aspects. Future work is suggested to be a deeper dive into mission engineering, where the mission itself is viewed as the system of interest, and how it could be combined with modeling and simulation in product development.

Climate change and greenhouse gas emissions are arguably some of the most pressing threats that today's society has to face. Emissions from the transport sector, including air traffic, play an important role in the pursuit of reducing climate impact. One way to reduce emissions from air traffic can be to fly more fuel efficient through route planning. However, to do this, a sufficiently accurate aircraft performance model is required. A first principle, equation-based, aircraft performance model for an Airbus A320 is developed for the purpose of route planning. The model is based on equations found in literature in combination with a large set of tabulated aircraft performance data. Numerical methods are used to estimate aircraft performance parameters and quantify model accuracy. Three kinds of comparisons are carried out. Firstly, a comparison between the model and tabulated reference data. Secondly, a comparison with flight data registered by aircraft, model and tabulated reference data. Lastly, a comparison of trajectory simulations with model and reference data. The results show that the equation-based model is sufficiently accurate for the purpose of estimating fuel consumption for route planning. / Klimatförändring och utsläpp av växthusgaser är utan tvekan några av de största hoten som dagens samhälle måste hantera. Utsläpp från transportsektorn, flygtrafik inkluderat, har en stor påverkan på klimatförändringarna. Ett sätt att minska utsläpp från flygtrafik är att flyga mer bränsleeffektivt genom ruttplanering. För att genomföra detta krävs en modell för flygplansprestanda som reflekterar verklig prestanda. En ekvationsbaserad modell för flygplansprestanda för en Airbus A320 utvecklas med syfte att användas för ruttplanering. Modellen baseras på ekvationer från tillgänglig litteratur i kombination med ett stort dataset med tabulerad flygplansprestanda. Numeriska metoder används för att uppskatta parametrar för flygplansprestanda och kvantifiera träffsäkerhet. Tre sorters jämförelser genomförs. Först genomförs en jämförelse mellan modell och tabulerad referensdata. Sedan jämförs flygdata som registrerads av flygplan, modell och tabulerad referensdata. Sist jämförs flygruttsoptimering med modell och referensdata. Resultaten visar att den ekvationsbaserade modellen producerar tillräckligt goda resultat för syftet att uppskatta bränsleförbrukning för ruttplanering.

Satellite constellations intended for communications services are becoming increasingly relevant with multiple companies such as Starlink and OneWeb launching constellations consisting of hundreds or thousands of satellites. This thesis investigated how such a constellation can be designed for a small user terminal with a diameter of approximately 15 cm. Four constellations, two at 8 500 km altitude and two at 1 200 km altitude, were proposed. Methods for systematic placement of satellites in orbital planes, aspects going into the link budget, and relevant regulations on the international level were investigated. It was found that the most favourable constellation was a medium Earth orbit constellation with a minimum elevation of 30°. The primary reason for this choice was the limited budget which did not allow for a large number of satellites being launched. Finally, the concept of a hybrid constellation with both geostationary satellites and non-geostationary satellites was considered. / Satellitkonstellationer inriktade på satellitkommunikation har ökat i relevans i och med att ett flertal företag, i synnerhet Starlink och OneWeb, skjutit upp konstellationer bestående av hundratals eller tusentals satelliter. Det här examensarbetet undersökte hur sådana konstellationer kan designas för en liten markterminal med en diameter på omkring 15 cm. Fyra konstellationer, två med banhöjd 8 500 km och två med banhöjd 1 200 km föreslogs. Metoder för en systematisk placering av satelliter i banplan, aspekter i länkbudgeten, samt relevanta föreskrifter på ett internationellt plan undersöktes. En konstellation med en banhöjd på 8 500 km och minsta elevation 30° var den mest fördelaktiga konstellationen. Den primära anledningen till detta var att budgeten för konstellationen tillät endast att en liten mängd satelliter skjuts upp. Slutligen undersöktes konceptet av en hybrid konstellation som består av både geostationära och icke-geostationära satelliter.

No description available.

This thesis work aims to get an insight into how the organisation at GKN Aerospace Sweden takes on multidisciplinary design and, in particular, how they work with manufacturing aspects in early phases. In addition, the work investigates an approach and explores how this approach can be improved. Firstly, an interview study was conducted to gain more understanding on how the product design processes in the organisation look like today and what challenges the engineers experience. Then a case study was performed to test a method for multidisciplinary robustness evaluation.  In the interview study, 11 engineers from various disciplines at GKN were asked about their opinions, ideas and problems with different components of multidisciplinary work, such as automation, robust design and manufacturability evaluation.  The case study focused on analysing the robustness of a Turbine Rear Structure (TRS) design. A TRS is linked to many different engineering disciplines and must withstand high thermal and structural loads as well as fulfil requirements regarding aerodynamic performance and weight. If these requirements change during the product development process it can in some cases lead to a costly redesign loop in order to meet the updated requirements. In this use case the variation of thermal loads and the impact on stresses and life cycle fatigue is investigated. Based on experience from previous product development programs, the temperatures are often subject to changes during the later phases of the design process. Traditionally, thermal loads are applied on different zones of the structure as certain values, and if the design is optimised only for the nominal values, there is a risk that the component will not meet the life cycle fatigue requirements when the temperature loads change. This is why a robustness evaluation is needed.  The interview study results show that there are challenges related to each of the themes explored when it comes to the multidisciplinary design approach at GKN. From the challenges identified, the ones deemed most important were problems with evaluating and defining robustness, the lack of quantitative tools for considering manufacturability in the early design stage, and the lack of communication and knowledge sharing between disciplines. Overall, a conclusion drawn from the findings is that there is a need for more systematic MD approaches. The case study in turn resulted in an outline of a method for early robustness evaluation using the software platform OptiSLang.

This thesis discusses the solar wind interaction with the Moon and the formation of the lunar plasma wake from a kinetic perspective. The Moon is essentially a non-conducting body which has a tenuous atmosphere and no global magnetic fields. The solar wind plasma impacts directly the lunar day-side and is absorbed by the lunar surface. This creates a plasma void and forms a wake at the night side of the Moon.We study the properties and structure of the lunar wake for typical solar wind conditions using a three-dimensional hybrid plasma solver. Also, we study the solar wind proton velocity space distribution functions at close distances to the Moon in the lunar wake and investigate the effects of lunar surface plasma absorption and non-isothermal solar wind velocity space distribution functions on the solar wind protons there.Finally, we compare the simulation results with the observations and show that a hybrid model of plasma can explain the kinetic aspects of the lunar wake and we investigate the effects of the lunar surface plasma absorption and non-isothermal solar wind velocity distribution on the solar wind proton properties there.

This thesis concerns the microphysical properties of clouds made up of ice particles, called ice clouds. Ice clouds are strong modulators of the outgoing longwave radiation and incoming shortwave radiation, yet our knowledge on several key ice cloud properties, which govern the magnitude and sign of the net contribution to the Earth’s atmospheric radiation budget, is inadequate. For instance, currently climate models are far from consensus on the magnitude and spatial distribution of ice water path (IWP), a vital radiative property of ice clouds, and the main property of concern in this thesis. The large spread amongst the models in terms of IWP is mostly due to the lack of constraints from observations on ice cloud properties. The lacking constraints reflect the major difficulties faced in observing global ice cloud properties.In-situ measurements provide useful sources of information on ice clouds, but are far from adequate due to the sparseness of measurements. Cloud ice observations from satellites provides a global view and is the most useful source of information. However, measurements from satellites also carry large uncertainties and are notoriously difficult to use for model evaluation, due to a mismatch on how IWP is defined in the models compared to what is actually observed. Not one satellite instrument can measure ice particle information from the entire ice cloud column, as desired from the model point of view. Satellite observations of IWP depend for the most part on the wavelength spectrum the instrument measures in, hence the instruments measure related, but different information on clouds.A study addressing the satellite observed and modeled IWP is presented in the first appended article: Eliasson et al. [2011]. Large differences between climate models are observations, especially in areas with frequent deep convection, were reported and discussed. The second appended article is a first evaluation study of cloud parameters, such as IWP, in the EC-Earth climate model using satellite A-Train observations. The model captures large-scale features for the most part but has problems related to ice water content and cloud fraction. This is strongly linked to the treatment of precipitation.The thesis contains introductory chapters on ice clouds; their formation, radiative importance, and representation in climate models. This is followed by a more in depth chapter on the observational data. The different satellite techniques are then discussed following a radiation physics and radiative transfer background section.