This work shows a comparative assessment of open-loop and closed-loop processes to select, among a set of alternatives, the best distillation scheme regarding its controllability. A new point of view to assess the controllability using the information from the singular value decomposition (SVD) technique is proposed. In the research, the techniques for comparing the open-loop analysis and closed-loop analysis were standardized. The open-loop controllability index was calculated from the minimum singular value and the condition number of the certain areas in the frequency domain and a simplified index for measuring the singularity in SVD results. The derived controllability index then was compared with the normalized value of the Integral Absolute Error (IAE) of a proportional–integral (PI) controller obtained under closed-loop operation. Several different frequency areas were investigated to calculate the SVD and were used to compare the open-loop and closed-loop behaviors. The selected best distillation scheme was the same despite the chosen approach. Through the simulation study, it is verified that the newly proposed controllability index based on the condition number derived from open-loop responses can be useful to predict the best performance under closed-loop operation. This prediction is suitable to use in an optimization algorithm, because of the structure of the proposed controllability index.

中文翻译：

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通过开环分析对强化分离过程进行闭环控制的动态行为的展望

这项工作显示了对开环和闭环过程的比较评估，以从一组替代方案中选择关于其可控制性的最佳蒸馏方案。提出了一种使用奇异值分解（SVD）技术的信息来评估可控性的新观点。在研究中，用于比较开环分析和闭环分析的技术已经标准化。开环可控性指标是根据频域中某些区域的最小奇异值和条件数以及用于测量SVD结果中奇异性的简化指标来计算的。然后将导出的可控性指标与在闭环操作下获得的比例积分（PI）控制器的积分绝对误差（IAE）的标准化值进行比较。研究了几个不同的频率区域以计算SVD，并用于比较开环和闭环行为。尽管选择了方法，但选择的最佳蒸馏方案是相同的。通过仿真研究，验证了基于从开环响应得出的条件数的新提出的可控性指标可用于预测闭环运行下的最佳性能。由于所提出的可控性指标的结构，该预测适合在优化算法中使用。验证了基于从开环响应得出的条件数新提出的可控性指标可用于预测闭环操作下的最佳性能。由于所提出的可控性指标的结构，该预测适合在优化算法中使用。验证了基于从开环响应得出的条件数新提出的可控性指标可用于预测闭环操作下的最佳性能。由于所提出的可控性指标的结构，该预测适合在优化算法中使用。