Dynamics and control issues of multi-rotor platforms

This thesis deals with the analytic study of dynamics of Multi--Rotor Unmanned Aerial Vehicles. It is conceived to give a set of mathematical instruments apt to the theoretical study and design of these flying machines. The entire work is organized in analogy with classical academic texts about airplane flight dynamics. First, the non--linear equations of motion are defined and all the external actions are modeled, with particular attention to rotors aerodynamics. All the equations are provided in a form, and with personal expedients, to be directly exploitable in a simulation environment. This has requited an answer to questions like the trim of such mathematical systems. All the treatment is developed aiming at the description of different multi--rotor configurations. Then, the linearized equations of motion are derived. The computation of the stability and control derivatives of the linear model is carried out. The study of static and dynamic stability characteristics is, thus, addressed, showing the influence of the various geometric and aerodynamic parameters of the machine and in particular of the rotors. All the theoretic results are finally utilized in two interesting cases. One concerns the design of control systems for attitude stabilization. The linear model permits the tuning of linear controllers gains and the non--linear model allows the numerical testing. The other case is the study of the performances of an innovative configuration of quad--rotor aircraft. With the non--linear model the feasibility of maneuvers impossible for a traditional quad--rotor is assessed. The linear model is applied to the controllability analysis of such an aircraft in case of actuator block.

Statistical mechanics formalism and methods for the analysis of real networks

This thesis provides a thoroughly theoretical background in network theory and shows novel applications to real problems and data. In the first chapter a general introduction to network ensembles is given, and the relations with “standard” equilibrium statistical mechanics are described. Moreover, an entropy measure is considered to analyze statistical properties of the integrated PPI-signalling-mRNA expression networks in different cases. In the second chapter multilayer networks are introduced to evaluate and quantify the correlations between real interdependent networks. Multiplex networks describing citation-collaboration interactions and patterns in colorectal cancer are presented. The last chapter is completely dedicated to control theory and its relation with network theory. We characterise how the structural controllability of a network is affected by the fraction of low in-degree and low out-degree nodes. Finally, we present a novel approach to the controllability of multiplex networks

Analysis of the main phenomena affecting solid rocket motors internal ballistics

In solid rocket motors, the absence of combustion controllability and the large amount of financial resources involved in full-scale firing tests, increase the importance of numerical simulations in order to asses stringent mission thrust requirements and evaluate the influence of thrust chamber phenomena affecting the grain combustion. Among those phenomena, grain local defects (propellant casting inclusions and debondings), combustion heat accumulation involving pressure peaks (Friedman Curl effect), and case-insulating thermal protection material ablation affect thrust prediction in terms of not negligible deviations with respect to the nominal expected trace. Most of the recent models have proposed a simplified treatment to the problem using empirical corrective functions, with the disadvantages of not fully understanding the physical dynamics and thus of not obtaining predictive results for different configurations of solid rocket motors in a boundary conditions-varied scenario. This work is aimed to introduce different mathematical approaches to model, analyze, and predict the abovementioned phenomena, presenting a detailed physical interpretation based on existing SRMs configurations. Internal ballistics predictions are obtained with an in-house simulation software, where the adoption of a dynamic three-dimensional triangular mesh together with advanced computer graphics methods, allows the previous target to be reached. Numerical procedures are explained in detail. Simulation results are carried out and discussed based on experimental data.