This study investigates the application of a recently developed construct, the uniform trigonometrization method (UTM), to the singular control problems in chemical engineering. The UTM involves minimal modifications to the original problem, thereby generating near-singular control solutions that can be used for conceptual design and serve as an alternate to direct techniques like nested and simultaneous approaches. Eight classical singular control problems with known analytical solutions and three complex singular control problems from chemical engineering domain are solved in this study. The results obtained using the UTM for these problems are found to match well with the literature and are of higher resolution as compared to the results obtained using a direct pseudospectral-based solver. The ability of the UTM to handle complex chemical engineering problems with both singular controls and state path constraints has also been demonstrated in this study.

中文翻译：

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用均匀三角法求解奇异控制问题

这项研究调查了最近开发的构造，即均匀三角法（UTM）在化学工程中的奇异控制问题中的应用。UTM只需对原始问题进行最少的修改，即可生成可用于概念设计的近似奇异的控制解决方案，并可以替代诸如嵌套和同时方法之类的直接技术。本研究解决了八个具有已知解析解的经典奇异控制问题和三个来自化工领域的复杂奇异控制问题。与使用直接基于伪谱的求解器获得的结果相比，使用UTM获得的解决这些问题的结果与文献非常吻合，并且具有更高的分辨率。