2020-01-012024-05-17https://scholars.lib.ntu.edu.tw/handle/123456789/672409摘要：為延續本團隊近期針對加入晶種之批次結晶製程之最適化研究，吾人將套用最佳控制理論中之龐特里亞金最小化原理(Pontryagin’s minimum principle)於一簡單批次結晶製程模型以探討製程最適化問題。套用最佳控制理論所需之計算耗時甚短，且可得到動態最佳化問題之近似解析解。 本計畫預計研究的三個問題包含： (1)根據多組文獻中提及之晶體成長與成核速率動力式，推導相對應之最佳過飽和度以及溫度控制軌跡。 (2)考慮二維結晶系統產物之幾何形狀並將其列為動態最適化問題之限制條件，以探討產物幾何形狀與常見目標函數之關聯。 (3)探討不同晶種平均粒徑及添加重量對於一維以及二維結晶系統最適化結果之影響，並使用常態粒數法(ordinary method of moments)計算升-降溫循環操作後之結晶產物粒徑分布。 分析上述問題將使吾人了解如何在一維以及二維批次結晶系統常見之各個目標函數間取得較佳之平衡。批次結晶製程以及其他牽涉固體操作之製程對於化工及相關產業具高度重要性，完成本計畫除可增進吾人對於固體操作製程之了解，亦可使學生習得固體操作製程之相關知識以及模擬方法。 <br> Abstract: Following on recent work by our group in the field of optimization of seeded batch crystallization, we propose to study three problems by application of optimal control theory (Pontryagin`s minimum principle) to a simple model of a seeded batch crystallizer. The method is computationally efficient and permits nearly-analytical results to be derived. The first problem we propose to consider is the determination of optimal control inputs for a large set of nucleation kinetics for a variety of chemical compounds that was compiled previously. The second problem that we propose to consider is the optimization two-dimensional crystallization systems with constraints on the crystal shape. The third problem that we propose to consider is the effect of seed properties on optimal control results for both one-dimensional and two-dimensional crystal systems and the determination of crystal size distributions after thermocycling using the ordinary method of moments. The solution of these problems will provide understanding of the inherent tradeoffs that are encountered in single-objective and multi-objective optimization of batch crystallization processes. Batch crystallization and more generally all solids processing unit operations are vital to the chemical and related industries, and the completion of the proposed project will also result in the training of students to model and understand these operations.批次結晶製程最適化龐特里亞金最小化原理Batch crystallizationOptimizationPontryagin’s minimum principle