Modeling, simulation and optimization of process chains

在优先项目第二阶段的子项目C5的第一个资助期内，对时间依赖控制的过程链进行了敏感性分析。这包括必要的数学存在的扩展。唯一性和规律性理论。过程链用非线性非局部偏微分方程进行数学描述。基于导数优化的理论结果可用于具有筛选和磨铣反馈的喷雾造粒过程的示例性实现。拟资助期的重点在于工艺链综合优化的三个方面：首先，扩展了工艺链基础方程的数学理论；将已经分析的色散性质的非局域性推广到方程中的时间非局域源项。这些术语出现在具有延迟反馈的流程链中，因此在优先级程序中是相关的。此外，将考虑积分核的非线性控制，例如在过程链的反馈回路中控制铣削速度的重要作用。与理论工作并行，DYSSOL框架内的优化模块将被实现。因此，分析灵敏度可用于计算给定流程的最优控制。特定工艺链的优化将在优先项目的协作（Z、A3、A8、C3、C4）中实现。在这里，必须对特定问题的目标函数进行建模，以得出其相对于所需控制变量的灵敏度。此外，在优化过程中，还必须定义底层模型的有效范围，以保证这些模型的预测特性。因此，在资助期结束时，DYSSOL框架内基于灵敏度的优化算法将可用，可用于优化各种工艺链。

The sensitivity analysis of process chains with respect to time dependent controls was performed within the first funding period of sub-project C5 in the second period of the priority program. This included an extension of the necessary mathematical existence-. uniqueness-, and regularity-theory. Process chains are described mathematically by non-linear non-local partial differential equations. The theoretical results for the derivative based optimization were exemplary implemented for the spray granulation process with screened and milled feedback. The focus of the proposed funding period lies on three aspects of the comprehensive optimization of process chains:First the mathematical theory for the underlying equations of process chains is extended. The already analyzed non-locality in the dispersive properties is extended to temporally non-local source terms within the equations. These terms occur in process chains with delayed feedback and are thus relevant within the priority program. Moreover non-linear controls of integral kernels will be considered which play for example an important role for controlling the milling velocity within a feedback loop in a process chain. Parallel to the theoretical work an optimization module within the DYSSOL framework will be implemented. Thus the analytical sensitivities can be used to compute optimal controls for given flowsheets.The optimization of specific process chains will be realized in collaborations (Z,A3,A8,C3,C4) within the priority program. Here a problem specific objective functional has to be modeled to derive its sensitivities with respect to desired control variables. Furthermore the range of validity of the underlying models has to be defined to ensure the predictive character of these models during optimization. Hence at the end of the funding period a sensitivity based optimization algorithm within the DYSSOL framework will be available which can be applied for optimizing various process chains.