Modeling, simulation and optimization of process chains

在优先计划第二阶段的子项目C5的第一个供资期内，对工艺链进行了与时间相关的控制的敏感性分析。这包括必要的数学存在的延伸。唯一性和正则性理论。过程链在数学上由非线性非局部偏微分方程描述。基于导数的优化的理论结果被示例性地实施用于具有筛选和研磨反馈的喷雾造粒过程。建议资助期的重点在于三个方面的综合优化的过程链：第一，数学理论的基础方程的过程链进行了扩展。已经分析的色散特性的非局部性扩展到时间上的非局部源项内的方程。这些术语出现在具有延迟反馈的过程链中，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，其例如在控制过程链中的反馈回路内的铣削速度方面发挥重要作用。平行的理论工作的DYSSOL框架内的优化模块将实施。因此，分析灵敏度可以用于计算给定流程的最优控制。特定过程链的优化将在优先级程序内的协作（Z，A3，A8，C3，C4）中实现。在这里，一个问题的具体目标功能必须建模，以获得其灵敏度相对于所需的控制变量。此外，必须定义基础模型的有效性范围，以确保这些模型在优化过程中的预测特性。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.