Zeta and L-functions of elliptic curves

In questa tesi si studiano alcune proprietà fondamentali delle funzioni Zeta e L associate ad una curva ellittica. In particolare, si dimostra la razionalità della funzione Zeta e l'ipotesi di Riemann per due famiglie specifiche di curve ellittiche. Si studia poi il problema dell'esistenza di un prolungamento analitico al piano complesso della funzione L di una curva ellittica con moltiplicazione complessa, attraverso l'analisi diretta di due casi particolari.

Feedback linearization of antagonistically actuated variable stiffness joints with twisted string actuators

The work of this thesis is on the implementation of a variable stiffness joint antagonistically actuated by a couple of twisted-string actuator (TSA). This type of joint is possible to be applied in the field of robotics, like UB Hand IV (the anthropomorphic robotic hand developed by University of Bologna). The purposes of the activities are to build the joint dynamic model and simultaneously control the position and stiffness. Three different control approaches (Feedback linearization, PID, PID+Feedforward) are proposed and validated in simulation. To improve the properties of joint stiffness, a joint with elastic element is taken into account and discussed. To the end, the experimental setup that has been developed for the experimental validation of the proposed control approaches.

Development of a state-variable filter for a motion control application.

In collaboration with G.D. SpA I attended an internship with the purpose of developing a filter for the position control of industrial machines during testing and maintenance operations. The filter elaborates a signal in position provided by an electonic handwheel, in order to enable the application to be controlled with a signal in velocity with arbitrarily dynamics chosen during the design phase. Limiting the dynamics of the filter provide a more stable and less demanding reference trajectory which reduce the vibrations and tracking errors of the motor controlled by it. It also prevents misusages of the handwheel from the technician which could end up in harmful interferences between the mechanical parts moved by the handwheel.

Models for the assessment of resilience in water distribution networks

The following thesis work focuses on the use and implementation of advanced models for measuring the resilience of water distribution networks. In particular, the functions implemented in GRA Tool, a software developed by the University of Exeter (UK), and the functions of the Toolkit of Epanet 2.2 were investigated. The study of the resilience and failure, obtained through GRA Tool and the development of the methodology based on the combined use of EPANET 2.2 and MATLAB software, was tested in a first phase, on a small-sized literature water distribution network, so that the variability of the results could be perceived more clearly and with greater immediacy, and then, on a more complex network, that of Modena. In the specific, it has been decided to go to recreate a mode of failure deferred in time, one proposed by the software GRA Tool, that is failure to the pipes, to make a comparison between the two methodologies. The analysis of hydraulic efficiency was conducted using a synthetic and global network performance index, i.e., Resilience index, introduced by Todini in the years 2000-2016. In fact, this index, being one of the parameters with which to evaluate the overall state of "hydraulic well-being" of a network, has the advantage of being able to act as a criterion for selecting any improvements to be made on the network itself. Furthermore, during these analyzes, was shown the analytical development undergone over time by the formula of the Resilience Index. The final intent of this thesis work was to understand by what means to improve the resilience of the system in question, as the introduction of the scenario linked to the rupture of the pipelines was designed to be able to identify the most problematic branches, i.e., those that in the event of a failure it would entail greater damage to the network, including lowering the Resilience Index.