Modeling, simulation and optimization of process chains

在优先方案第二阶段的子项目C5的第一个资助期内，进行了流程链相对于时间依赖控制的敏感性分析。这包括必要的数学存在的延伸--。唯一性理论和规律性理论。过程链可用非线性非局部偏微分方程组进行数学描述。将基于导数的优化理论结果应用于具有筛分和球磨反馈的喷雾造粒过程。拟议资金期的重点在于工艺链综合优化的三个方面：第一，扩大了工艺链基本方程的数学理论。已分析的色散性质中的非局域性被推广到方程中的时间非局域源项。这些术语出现在反馈延迟的过程链中，因此与优先计划相关。此外，还将考虑积分核的非线性控制，它例如在过程链中的反馈回路中起着控制铣削速度的重要作用。在开展理论工作的同时，还将在DYSSOL框架内实施一个优化模块。因此，分析灵敏度可用于计算给定流程图的最优控制。特定过程链的优化将在优先计划内的协作(Z、A3、A8、C3、C4)中实现。这里，必须对特定问题的目标泛函进行建模，以推导出其对所需控制变量的灵敏度。此外，必须确定基本模型的有效性范围，以确保这些模型在优化过程中的预测性。因此，在供资期间结束时，将在DYSSOL框架内提供一种基于敏感性的优化算法，可用于优化各种流程链。

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.