不確かさをもつ非線形システムにおける適応ロバスト制御理論とその環境システムへの応用に関する研究

博甲第30号生命システム科学博士県立広島大

Hybrid and Intelligent Energy Storage Systems in Standalone Photovoltaic Applications.

Remote systems such as communication relays or irrigation control installations cannot usually be powered by the electrical grid. One of the alternatives is to power these systems through solar panels, in what is known as standalone photovoltaic applications.Most of these systems need a continuous operation, but a standalone photovoltaic installation cannot be powered during the night. For this reason, they use batteries to store excess energy during the day. These storage systems have been traditionally based on Valve Regulated Lead Acid (VRLA) batteries, but some effects can alter their performance in terms of reliability, operation cost and maintenance. One of the key issues that alter the energy behavior of the photovoltaic off-grid systems is the Partial State of Charge (PSoC) effect: Batteries cannot be completely charged as manufacturers indicate due to the day-night cycle. This gets the battery into an intermediate state of charge that effectively reduces its capacity, even halving it in some cases. To mitigate the impact of these effects on the installation, batteries tend to be oversized with some security margins. These oversizing factors can be incredibly high and have a huge impact on the deployment and maintenance cost of the facility.The first part of this thesis highlights some of these key concepts, analyzing which of them are critical in specific design cases, modeling them into a simulation tool, and as an outcome, establishing optimal sizing regions for the installations. After the analysis, different ways of improving the performance of the installations are proposed. One idea to mitigate PSoC is to combine different storage technologies in a Hybrid Energy Storage Systems (HESS). HESSs have traditionally combined high energy density elements as batteries with high power density elements as ultracapacitors. An iteration of this idea is carried out throughout this thesis, where different types of batteries are combined. Each of them is best fitted to different power patterns in the application, such as daily cycles or emergency periods. It is possible to further increase the performance by using intelligent algorithms to improve the functionalities of the Battery Management Systems embedded in these applications. To this end, failure prediction and health estimation algorithms are proposed as contributions of this work. These new algorithms endow the HESS with tools to predict possible energy disruption events and to anticipate aging, and thus, act accordingly.<br /

Foliated Lie systems: Theory and applications

A $\mathcal{F}$- foliated Lie system is a first-order system of ordinary differential equations whose particular solutions are contained in the leaves of the foliation $\mathcal{F}$ and all particular solutions within any leaf can be written as a certain function, a so-called foliated superposition rule, of a family of particular solutions of the system within the same leaf and several parameters. We analyse the properties of such systems and we illustrate our results by studying Lax pairs and a class of $t$-dependent Hamiltonian systems. We finally study foliated Lie systems through Poisson structures and $r$-matrices.Comment: 24 page

Lie systems: theory, generalisations, and applications

Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of mapping: the so-called superposition rule. Apart from this fundamental property, Lie systems enjoy many other geometrical features and they appear in multiple branches of Mathematics and Physics, which strongly motivates their study. These facts, together with the authors' recent findings in the theory of Lie systems, led to the redaction of this essay, which aims to describe such new achievements within a self-contained guide to the whole theory of Lie systems, their generalisations, and applications.Comment: 161 pages, 2 figure