NLGA based Active Control in Aerospace: fault tolerability, disturbance rejection, and parameter estimation

A new control scheme has been presented in this thesis. Based on the NonLinear Geometric Approach, the proposed Active Control System represents a new way to see the reconfigurable controllers for aerospace applications. The presence of the Diagnosis module (providing the estimation of generic signals which, based on the case, can be faults, disturbances or system parameters), mean feature of the depicted Active Control System, is a characteristic shared by three well known control systems: the Active Fault Tolerant Controls, the Indirect Adaptive Controls and the Active Disturbance Rejection Controls. The standard NonLinear Geometric Approach (NLGA) has been accurately investigated and than improved to extend its applicability to more complex models. The standard NLGA procedure has been modified to take account of feasible and estimable sets of unknown signals. Furthermore the application of the Singular Perturbations approximation has led to the solution of Detection and Isolation problems in scenarios too complex to be solved by the standard NLGA. Also the estimation process has been improved, where multiple redundant measuremtent are available, by the introduction of a new algorithm, here called "Least Squares - Sliding Mode". It guarantees optimality, in the sense of the least squares, and finite estimation time, in the sense of the sliding mode. The Active Control System concept has been formalized in two controller: a nonlinear backstepping controller and a nonlinear composite controller. Particularly interesting is the integration, in the controller design, of the estimations coming from the Diagnosis module. Stability proofs are provided for both the control schemes. Finally, different applications in aerospace have been provided to show the applicability and the effectiveness of the proposed NLGA-based Active Control System.

Natural patterns and anthropogenic disturbance in north Adriatic marine benthic assemblages: descriptive and methodological studies

Marine soft bottom systems show a high variability across multiple spatial and temporal scales. Both natural and anthropogenic sources of disturbance act together in affecting benthic sedimentary characteristics and species distribution. The description of such spatial variability is required to understand the ecological processes behind them. However, in order to have a better estimate of spatial patterns, methods that take into account the complexity of the sedimentary system are required. This PhD thesis aims to give a significant contribution both in improving the methodological approaches to the study of biological variability in soft bottom habitats and in increasing the knowledge of the effect that different process (both natural and anthropogenic) could have on the benthic communities of a large area in the North Adriatic Sea. Beta diversity is a measure of the variability in species composition, and Whittaker’s index has become the most widely used measure of beta-diversity. However, application of the Whittaker index to soft bottom assemblages of the Adriatic Sea highlighted its sensitivity to rare species (species recorded in a single sample). This over-weighting of rare species induces biased estimates of the heterogeneity, thus it becomes difficult to compare assemblages containing a high proportion of rare species. In benthic communities, the unusual large number of rare species is frequently attributed to a combination of sampling errors and insufficient sampling effort. In order to reduce the influence of rare species on the measure of beta diversity, I have developed an alternative index based on simple probabilistic considerations. It turns out that this probability index is an ordinary Michaelis-Menten transformation of Whittaker's index but behaves more favourably when species heterogeneity increases. The suggested index therefore seems appropriate when comparing patterns of complexity in marine benthic assemblages. Although the new index makes an important contribution to the study of biodiversity in sedimentary environment, it remains to be seen which processes, and at what scales, influence benthic patterns. The ability to predict the effects of ecological phenomena on benthic fauna highly depends on both spatial and temporal scales of variation. Once defined, implicitly or explicitly, these scales influence the questions asked, the methodological approaches and the interpretation of results. Problem often arise when representative samples are not taken and results are over-generalized, as can happen when results from small-scale experiments are used for resource planning and management. Such issues, although globally recognized, are far from been resolved in the North Adriatic Sea. This area is potentially affected by both natural (e.g. river inflow, eutrophication) and anthropogenic (e.g. gas extraction, fish-trawling) sources of disturbance. Although few studies in this area aimed at understanding which of these processes mainly affect macrobenthos, these have been conducted at a small spatial scale, as they were designated to examine local changes in benthic communities or particular species. However, in order to better describe all the putative processes occurring in the entire area, a high sampling effort performed at a large spatial scale is required. The sedimentary environment of the western part of the Adriatic Sea was extensively studied in this thesis. I have described, in detail, spatial patterns both in terms of sedimentary characteristics and macrobenthic organisms and have suggested putative processes (natural or of human origin) that might affect the benthic environment of the entire area. In particular I have examined the effect of off shore gas platforms on benthic diversity and tested their effect over a background of natural spatial variability. The results obtained suggest that natural processes in the North Adriatic such as river outflow and euthrophication show an inter-annual variability that might have important consequences on benthic assemblages, affecting for example their spatial pattern moving away from the coast and along a North to South gradient. Depth-related factors, such as food supply, light, temperature and salinity play an important role in explaining large scale benthic spatial variability (i.e., affecting both the abundance patterns and beta diversity). Nonetheless, more locally, effects probably related to an organic enrichment or pollution from Po river input has been observed. All these processes, together with few human-induced sources of variability (e.g. fishing disturbance), have a higher effect on macrofauna distribution than any effect related to the presence of gas platforms. The main effect of gas platforms is restricted mainly to small spatial scales and related to a change in habitat complexity due to a natural dislodgement or structure cleaning of mussels that colonize their legs. The accumulation of mussels on the sediment reasonably affects benthic infauna composition. All the components of the study presented in this thesis highlight the need to carefully consider methodological aspects related to the study of sedimentary habitats. With particular regards to the North Adriatic Sea, a multi-scale analysis along natural and anthopogenic gradients was useful for detecting the influence of all the processes affecting the sedimentary environment. In the future, applying a similar approach may lead to an unambiguous assessment of the state of the benthic community in the North Adriatic Sea. Such assessment may be useful in understanding if any anthropogenic source of disturbance has a negative effect on the marine environment, and if so, planning sustainable strategies for a proper management of the affected area.

Geometric and Combinatorial Aspects of NonEquilibrium Statistical Mechanics

Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.

Fluidodinamica biomedica computazionale del flusso sanguigno in presenza di affezioni strumentali e/o patologiche

La tesi di Dottorato studia il flusso sanguigno tramite un codice agli elementi finiti (COMSOL Multiphysics). Nell’arteria è presente un catetere Doppler (in posizione concentrica o decentrata rispetto all’asse di simmetria) o di stenosi di varia forma ed estensione. Le arterie sono solidi cilindrici rigidi, elastici o iperelastici. Le arterie hanno diametri di 6 mm, 5 mm, 4 mm e 2 mm. Il flusso ematico è in regime laminare stazionario e transitorio, ed il sangue è un fluido non-Newtoniano di Casson, modificato secondo la formulazione di Gonzales & Moraga. Le analisi numeriche sono realizzate in domini tridimensionali e bidimensionali, in quest’ultimo caso analizzando l’interazione fluido-strutturale. Nei casi tridimensionali, le arterie (simulazioni fluidodinamiche) sono infinitamente rigide: ricavato il campo di pressione si procede quindi all’analisi strutturale, per determinare le variazioni di sezione e la permanenza del disturbo sul flusso. La portata sanguigna è determinata nei casi tridimensionali con catetere individuando tre valori (massimo, minimo e medio); mentre per i casi 2D e tridimensionali con arterie stenotiche la legge di pressione riproduce l’impulso ematico. La mesh è triangolare (2D) o tetraedrica (3D), infittita alla parete ed a valle dell’ostacolo, per catturare le ricircolazioni. Alla tesi sono allegate due appendici, che studiano con codici CFD la trasmissione del calore in microcanali e l’ evaporazione di gocce d’acqua in sistemi non confinati. La fluidodinamica nei microcanali è analoga all’emodinamica nei capillari. Il metodo Euleriano-Lagrangiano (simulazioni dell’evaporazione) schematizza la natura mista del sangue. La parte inerente ai microcanali analizza il transitorio a seguito dell’applicazione di un flusso termico variabile nel tempo, variando velocità in ingresso e dimensioni del microcanale. L’indagine sull’evaporazione di gocce è un’analisi parametrica in 3D, che esamina il peso del singolo parametro (temperatura esterna, diametro iniziale, umidità relativa, velocità iniziale, coefficiente di diffusione) per individuare quello che influenza maggiormente il fenomeno.

Fault detection, diagnosis and active fault tolerant control for a satellite attitude control system

Modern control systems are becoming more and more complex and control algorithms more and more sophisticated. Consequently, Fault Detection and Diagnosis (FDD) and Fault Tolerant Control (FTC) have gained central importance over the past decades, due to the increasing requirements of availability, cost efficiency, reliability and operating safety. This thesis deals with the FDD and FTC problems in a spacecraft Attitude Determination and Control System (ADCS). Firstly, the detailed nonlinear models of the spacecraft attitude dynamics and kinematics are described, along with the dynamic models of the actuators and main external disturbance sources. The considered ADCS is composed of an array of four redundant reaction wheels. A set of sensors provides satellite angular velocity, attitude and flywheel spin rate information. Then, general overviews of the Fault Detection and Isolation (FDI), Fault Estimation (FE) and Fault Tolerant Control (FTC) problems are presented, and the design and implementation of a novel diagnosis system is described. The system consists of a FDI module composed of properly organized model-based residual filters, exploiting the available input and output information for the detection and localization of an occurred fault. A proper fault mapping procedure and the nonlinear geometric approach are exploited to design residual filters explicitly decoupled from the external aerodynamic disturbance and sensitive to specific sets of faults. The subsequent use of suitable adaptive FE algorithms, based on the exploitation of radial basis function neural networks, allows to obtain accurate fault estimations. Finally, this estimation is actively exploited in a FTC scheme to achieve a suitable fault accommodation and guarantee the desired control performances. A standard sliding mode controller is implemented for attitude stabilization and control. Several simulation results are given to highlight the performances of the overall designed system in case of different types of faults affecting the ADCS actuators and sensors.