Algoritmo de otimização de sistemas modelados por equações diferenciais ordinárias aplicado a processos de fermentação em batelada alimentada

Abstract

Mathematical models allow the simulation of sundry processes, within distinct shapes, providing estimation of their results, before being experimentally executed. In this sense, the processes modeled by ordinary differential equations are of great importance for several knowledge areas. There are countless situations in which it is want to optimize such processes, in order to minimize costs and maximize performance. In this scenario, the absence of comprehensive methodologies capable of optimizing these processes leads to the creation of numberless different methodologies aimed at optimizing only one particular case of these processes. Such methodologies commonly employ the use of different tools that operate together through an integration algorithms, factors that cause slowness in the optimization process. The processes of fermentation are found in this context, which have considerable relevance for the industrial and academic environments. For this reason, there is great interest in optimizing such processes, in order to make them cheaper and more productive. In this work, an algorithm for optimization of processes modeled by ordinary differential equations was proposed, which allows the modeling of single and multiobjective optimization problems on this type of process and its solution by different methods of optimization, interpolation and for ODEs. In addition to the proposition of the algorithm, a software library was developed that implements it, built entirely on a single programming platform, avoiding the computational and time costs present in methodologies that involve the integration between more than one tool, in addition to have a series of optimization, interpolation and ODE methods available to the user. This thesis also proposed to carry out two case studies involving optimization of fed-batch fermentation processes, which employ the algorithm and tool developed therein. The first case study involved the optimization of an L-lysine generation process by solving problems proposed in another work, whose results were analyzed, discussed and compared to those achieved in the latter. The results of this study showed that solutions that have higher productivity show lower performance and shorter operating time; and vice versa, in addition to showing the reliability of the algorithm, since the results obtained here are similar to those obtained in the work that proposed the problems. The second case study involved the optimization of an alcoholic production process in a real industrial plant through the proposition and resolution of problems relevant to the process in question, from which the results obtained were analyzed and discussed. The results of this study showed that solutions that generate more ethanol preserve less yeast and vice versa, in addition to presenting solutions that provide significant gain in time and yeast preservation without prejudice to ethanol generation, when compared to the solution in use in the plant.