This thesis deals with the analysis of water management in a network of canals, focusing on the Cavallino di Venezia drainage network. In particular, it is proposed an improvement for the water distribution of this site. Aiming to find a feasible solution to this issue, it is derived a nonautonomous difference-equation-based model that considers the constraints imposed on a general water network. The presented approach primarily leverages graph-theoretical tools and, by means of a modified version of the distributed consensus protocol accounting for the physical restrictions within the network, the water exchange among nodes is regulated at a common level given by the average of the initial heights. The main contribution of this thesis is thus devoted to the adaptation of the classic consensus protocol to this specific framework, by introducting a time-variant adjustment to cope with different water regimes occurring at each canal loading or draining. In addition, the proposed solution is shown to have general application properties, namely it is designed to be suitable for many frameworks in which the consensus protocol needs to take into account restricted capacity of information exchange. This aspect is explored through a theoretical study on the convergence of the developed distributed algorithm towards the state agreement and, consequently, an analytical metric for the convergence rate is suggested. Finally, to support the obtained theoretical results, numerical simulations using MATLAB are also reported and the devised distributed algorithm is applied to the Cavallino di Venezia drainage network in order to show its performances in a real scenario.
Questa tesi si occupa della gestione dell’acqua facente parte di un sistema di canali e, in dettaglio, viene preso in considerazione il sistema di canali della città di Cavallino di Venezia. In particolare, viene proposto un miglioramento nella redistribuzione delle acque di questo sito. Con l’obbiettivo di trovare una soluzione per questo tipo di problema, è proposto un modello non autonomo di equazioni alle differenze in grado di considerare i limiti fisici di un generico sistema di canali. L’ approccio descritto fa leva sulla teoria dei grafi, e mediante una versione modificata del già noto protocollo di consensus distribuito, viene tenuto conto delle restrizioni fisiche del sistema, e l’ altezza dell’acqua nei vari nodi del sistema viene portata verso la media delle altezze iniziali. Il contributo principale di questa tesi è l’adattamento del protocollo del consensus a questo campo specifico. Ciò viene raggiunto introducendo parametri tempo varianti calcolati in base alla capacità del sistema di caricare e scaricare acqua da un canale all’altro. Inoltre, la soluzione trovata presenta applicabilità generica per tutti i sistemi riconducibili a grafi che risentono di ridotte capacità di trasmissione tra i propri nodi. Questo aspetto è approfondito tramite uno studio teorico sulla convergenza dell’ algoritmo distribuito proposto e, conseguentemente, viene descritta una metrica analitica per la velocità di convergenza dello stesso. Infine, a supporto dei risultati teorici ottenuti, vengono effettuate delle simulazioni numeriche in ambiente MATLAB testando l’algoritmo proposto per gestire le acque della rete di canali di Cavallino di Venezia in modo da valu- tarne le prestazioni in uno scenario reale.
"Water distribution network control via adaptive consensus"
BELLINAZZI, MARCO DAVIDE
2021/2022
Abstract
This thesis deals with the analysis of water management in a network of canals, focusing on the Cavallino di Venezia drainage network. In particular, it is proposed an improvement for the water distribution of this site. Aiming to find a feasible solution to this issue, it is derived a nonautonomous difference-equation-based model that considers the constraints imposed on a general water network. The presented approach primarily leverages graph-theoretical tools and, by means of a modified version of the distributed consensus protocol accounting for the physical restrictions within the network, the water exchange among nodes is regulated at a common level given by the average of the initial heights. The main contribution of this thesis is thus devoted to the adaptation of the classic consensus protocol to this specific framework, by introducting a time-variant adjustment to cope with different water regimes occurring at each canal loading or draining. In addition, the proposed solution is shown to have general application properties, namely it is designed to be suitable for many frameworks in which the consensus protocol needs to take into account restricted capacity of information exchange. This aspect is explored through a theoretical study on the convergence of the developed distributed algorithm towards the state agreement and, consequently, an analytical metric for the convergence rate is suggested. Finally, to support the obtained theoretical results, numerical simulations using MATLAB are also reported and the devised distributed algorithm is applied to the Cavallino di Venezia drainage network in order to show its performances in a real scenario.File | Dimensione | Formato | |
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https://hdl.handle.net/20.500.12608/31492