在制备色谱的优化设计和控制过程中,若试图把基于偏微分方程(PDE)-Eulerian描述的Wilson色谱理论框架和基于离散时间状态的优化控制方法(如Markov决策过程(MDP)和模型预测控制(MPC)等)衔接在一起时,就会出现明显的障碍.本文提出基于Lagrangian-Eulerian描述(L-ED)的非线性传质色谱(NTC)的0-1模型来克服这些障碍.该模型把一个溶质微元单元划分为在流动相中并以其线速度移动的流动相溶质微元(SCm)和在固定相中其移动速度为0的固定相溶质微元(SCs).引入由溶质微元的序号集合、溶质微元的位置矢量、固定相溶质浓度矢量和流动相溶质浓度矢量组成的热力学状态矢量Sk,并用其来描述色谱过程的局域热力学路径(LTP)和宏观热力学路径(MTP).在非线性-理想-传质色谱的理论分析和数值实验中,0-1模型的数值解表现出很好的一致性、稳定性、守恒性及精确性等.该模型能很好地与控制论中的Markov决策过程或其他基于离散时间状态的优化控制方法相衔接.
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