Abstract Reduced models enable real-time optimization of large-scale processes. We propose a reduced model of distillation columns based on multicomponent nonlinear wave propagation (Kienle 2000). We use a nonlinear wave equation in dynamic mass and energy balances. We thus combine the ideas of compartment modeling and wave propagation. In contrast to existing reduced column models based on nonlinear wave propagation, our model deploys a hydraulic correlation. This enables the column holdup to change as load varies. The model parameters can be estimated solely based on steady-state data. The new transient wave propagation model can be used as a controller model for flexible process operation including load changes. To demonstrate this, we implement full-order and reduced dynamic models of an air separation process and multi-component distillation column in Modelica. We use the open-source framework DyOS for the dynamic optimizations and an Extended Kalman Filter for state estimation. We apply the reduced model in-silico in open-loop forward simulations as well as in several open- and closed-loop optimization and control case studies, and analyze the resulting computational speed-up compared to using full-order stage-by-stage column models. The first case study deals with tracking control of a single air separation distillation column, whereas the second one addresses economic model predictive control of an entire air separation process. The reduced model is able to adequately capture the transient column behavior. Compared to the full-order model, the reduced model achieves highly accurate profiles for the manipulated variables, while the optimizations with the reduced model are significantly faster, achieving more than 95% CPU time reduction in the closed-loop simulation and more than 96% in the open-loop optimizations. This enables the real-time capability of the reduced model in process optimization and control.

中文翻译：

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一种用于蒸馏塔简化动态建模的波传播方法：优化和控制

摘要 简化模型能够实时优化大规模流程。我们提出了一种基于多分量非线性波传播的蒸馏塔简化模型 (Kienle 2000)。我们在动态质量和能量平衡中使用非线性波动方程。因此，我们结合了隔室建模和波传播的思想。与现有的基于非线性波传播的简化柱模型相比，我们的模型采用了水力相关性。这使得色谱柱滞留量随负载变化而变化。模型参数可以仅基于稳态数据进行估计。新的瞬态波传播模型可用作包括负载变化在内的灵活过程操作的控制器模型。为了证明这一点，我们在 Modelica 中实现了空气分离过程和多组分蒸馏塔的全阶和简化动态模型。我们使用开源框架 DyOS 进行动态优化，使用扩展卡尔曼滤波器进行状态估计。我们在开环前向仿真以及几个开环和闭环优化和控制案例研究中应用了简化的硅片模型，并分析了与使用全阶分阶段相比所产生的计算速度列模型。第一个案例研究涉及单个空气分离蒸馏塔的跟踪控制，而第二个案例研究涉及整个空气分离过程的经济模型预测控制。简化模型能够充分捕捉瞬态柱行为。与全阶模型相比，简化模型实现了操纵变量的高度准确的配置文件，而简化模型的优化速度明显更快，在闭环仿真中实现了 95% 以上的 CPU 时间减少，在开环优化中实现了 96% 以上的 CPU 时间减少。这使得简化模型在过程优化和控制中的实时能力成为可能。