Analysis of Lead-Acid batteries with a third-order dynamical model

Electrical energy storage is a really important issue nowadays. As electricity is not easy to be directly stored, it can be stored in other forms and converted back to electricity when needed. As a consequence, storage technologies for electricity can be classified by the form of storage, and in particular we focus on electrochemical energy storage systems, better known as electrochemical batteries. Largely the more widespread batteries are the Lead-Acid ones, in the two main types known as flooded and valve-regulated. Batteries need to be present in many important applications such as in renewable energy systems and in motor vehicles. Consequently, in order to simulate these complex electrical systems, reliable battery models are needed. Although there exist some models developed by experts of chemistry, they are too complex and not expressed in terms of electrical networks. Thus, they are not convenient for a practical use by electrical engineers, who need to interface these models with other electrical systems models, usually described by means of electrical circuits. There are many techniques available in literature by which a battery can be modeled. Starting from the Thevenin based electrical model, it can be adapted to be more reliable for Lead-Acid battery type, with the addition of a parasitic reaction branch and a parallel network. The third-order formulation of this model can be chosen, being a trustworthy general-purpose model, characterized by a good ratio between accuracy and complexity. Considering the equivalent circuit network, all the useful equations describing the battery model are discussed, and then implemented one by one in Matlab/Simulink. The model has been finally validated, and then used to simulate the battery behaviour in different typical conditions.

A Comparative Analysis of Dynamical Models for Tidal Dissipation in Natural Satellite Ephemerides

The study of the tides of a celestial bodies can unveil important information about their interior as well as their orbital evolution. The most important tidal parameter is the Love number, which defines the deformation of the gravity field due to an external perturbing body. Tidal dissipation is very important because it drives the secular orbital evolution of the natural satellites, which is even more important in the case of the the Jupiter system, where three of the Galilean moons, Io, Europa and Ganymede, are locked in an orbital resonance where the ratio of their mean motions is 4:2:1. This is called Laplace resonance. Tidal dissipation is described by the dissipation ratio k2/Q, where Q is the quality factor and it describes the dampening of a system. The goal of this thesis is to analyze and compare the two main tidal dynamical models, Mignard's model and gravity field variation model, to understand the differences between each model with a main focus on the single-moon case with Io, which can help also understanding better the differences between the two models without over complicating the dynamical model. In this work we have verified and validated both models, we have compared them and pinpointed the main differences and features that characterize each model. Mignard's model treats the tides directly as a force, while the gravity field variation model describes the tides with a change of the spherical harmonic coefficients. Finally, we have also briefly analyzed the difference between the single-moon case and the two-moon case, and we have confirmed that the governing equations that describe the change of semi-major axis and eccentricity are not good anymore when more moons are present.

Estimation of the satellite ephemerides of Saturn using optical navigation pictures of Cassini

The goal of this dissertation thesis is the estimation of the Saturnian satellites ephemerides using optical data of Cassini. In the first part we describe the software employed for the reduction of the images showing its main features and the accuracy that can be achieved comparing the results with published astrometry. Afterwards we describe the orbit determination problem (ODP) with particular focus on the weights selection for the estimation process. The third chapter describes the dynamical model used and the sources of potential errors in the residuals. The model have been validated trying to replicate JPL's published ephemerides SAT365, SAT375, SAT389 and SAT409. The final part investigates the residuals and the estimated ephemerides with particular focus on the giant moon Titan, the only in the solar system with an atmosphere other than the Earth. No astrometry have been retrieved in literature of Titan using optical observables, thus this represents one of the first investigations of the giant.

An optimal control tool for trajectory generation of autonomous drones

In the recent years, autonomous aerial vehicles gained large popularity in a variety of applications in the field of automation. To accomplish various and challenging tasks the capability of generating trajectories has assumed a key role. As higher performances are sought, traditional, flatness-based trajectory generation schemes present their limitations. In these approaches the highly nonlinear dynamics of the quadrotor is, indeed, neglected. Therefore, strategies based on optimal control principles turn out to be beneficial, since in the trajectory generation process they allow the control unit to best exploit the actual dynamics, and enable the drone to perform quite aggressive maneuvers. This dissertation is then concerned with the development of an optimal control technique to generate trajectories for autonomous drones. The algorithm adopted to this end is a second-order iterative method working directly in continuous-time, which, under proper initialization, guarantees quadratic convergence to a locally optimal trajectory. At each iteration a quadratic approximation of the cost functional is minimized and a decreasing direction is then obtained as a linear-affine control law, after solving a differential Riccati equation. The algorithm has been implemented and its effectiveness has been tested on the vectored-thrust dynamical model of a quadrotor in a realistic simulative setup.

Thermal structure and dynamical modeling of a Mediterranean tropical-like cyclone

In the present work, a detailed analysis of a Mediterranean TLC occurred in January 2014 has been conducted. The author is not aware of other studies regarding this particular event at the publication of this thesis. In order to outline the cyclone evolution, observational data, including weather-stations data, satellite data, radar data and photographic evidence, were collected at first. After having identified the cyclone path and its general features, the GLOBO, BOLAM and MOLOCH NWP models, developed at ISAC-CNR (Bologna), were used to simulate the phenomenon. Particular attention was paid on the Mediterranean phase as well as on the Atlantic phase, since the cyclone showed a well defined precursor up to 3 days before the minimum formation in the Alboran Sea. The Mediterranean phase has been studied using different combinations of GLOBO, BOLAM and MOLOCH models, so as to evaluate the best model chain to simulate this kind of phenomena. The BOLAM and MOLOCH models showed the best performance, by adjusting the path erroneously deviated in the National Centre for Environmental Prediction (NCEP) and ECMWF operational models. The analysis of the cyclone thermal phase shown the presence of a deep-warm core structure in many cases, thus confirming the tropical-like nature of the system. Furthermore, the results showed high sensitivity to initial conditions in the whole lifetime of the cyclone, while the Sea Surface Temperature (SST) modification leads only to small changes in the Adriatic phase. The Atlantic phase has been studied using GLOBO and BOLAM model and with the aid of the same methodology already developed. After tracing the precursor, in the form of a low-pressure system, from the American East Coast to Spain, the thermal phase analysis was conducted. The parameters obtained showed evidence of a deep-cold core asymmetric structure during the whole Atlantic phase, while the first contact with the Mediterranean Sea caused a sudden transition to a shallow-warm core structure. The examination of Potential Vorticity (PV) 3-dimensional structure revealed the presence of a PV streamer that individually formed over Greenland and eventually interacted with the low-pressure system over the Spanish coast, favouring the first phase of the cyclone baroclinic intensification. Finally, the development of an automated system that tracks and studies the thermal phase of Mediterranean cyclones has been encouraged. This could lead to the forecast of potential tropical transition, against with a minimum computational investment.

Dynamical models in neuroscience: the delay FitzHugh-Nagumo equation

Il primo modello matematico in grado di descrivere il prototipo di un sistema eccitabile assimilabile ad un neurone fu sviluppato da R. FitzHugh e J. Nagumo nel 1961. Tale modello, per quanto schematico, rappresenta un importante punto di partenza per la ricerca nell'ambito neuroscientifico delle dinamiche neuronali, ed è infatti capostipite di una serie di lavori che hanno puntato a migliorare l’accuratezza e la predicibilità dei modelli matematici per le scienze. L’elevato grado di complessità nello studio dei neuroni e delle dinamiche inter-neuronali comporta, tuttavia, che molte delle caratteristiche e delle potenzialità dell’ambito non siano ancora state comprese appieno. In questo lavoro verrà approfondito un modello ispirato al lavoro originale di FitzHugh e Nagumo. Tale modello presenta l’introduzione di un termine di self-coupling con ritardo temporale nel sistema di equazioni differenziali, diventa dunque rappresentativo di modelli di campo medio in grado di descrivere gli stati macroscopici di un ensemble di neuroni. L'introduzione del ritardo è funzionale ad una descrizione più realistica dei sistemi neuronali, e produce una dinamica più ricca e complessa rispetto a quella presente nella versione originale del modello. Sarà mostrata l'esistenza di una soluzione a ciclo limite nel modello che comprende il termine di ritardo temporale, ove tale soluzione non può essere interpretata nell’ambito delle biforcazioni di Hopf. Allo scopo di esplorare alcune delle caratteristiche basilari della modellizzazione del neurone, verrà principalmente utilizzata l’impostazione della teoria dei sistemi dinamici, integrando dove necessario con alcune nozioni provenienti dall’ambito fisiologico. In conclusione sarà riportata una sezione di approfondimento sulla integrazione numerica delle equazioni differenziali con ritardo.