非线性色谱的非平衡热力学理论Ⅰ.非线性-非理想-平衡色谱过程的局域Lagrangian方法  

Non-Equilibrium Thermodynamic Separation Theory of Nonlinear Chromatograph Ⅰ.Local Lagrangian Approach for Nonlinear Equilibrium-Dispersive Processes

作　　者：梁恒[1] 

机构地区：[1]西安交通大学分离科学研究所生物医学信息工程教育部重点实验室,陕西西安710049

出　　处：《色谱》2007年第5期664-680,共17页Chinese Journal of Chromatography

基　　金：国家自然科学基金资助项目(批准号20299030;20175015;29775017)

摘　　要：提出非线性-非理想-平衡色谱过程的局域Lagrangian(LLA)方法的矩阵形式。基于Lagrangian描述、局域平衡假设和热力学状态函数等基本物理原理,设计了局域热力学路径(LTP),采用LTP获得了完全热力学状态递推方程的矩阵形式。该递推方程具有Markov特性。对基于LTP的LLA方法的收敛性、相容性和稳定性进行了理论分析和数值实验,给出LLA的稳定性条件。以矢量形式表示了该LLA计算机程序,并模拟了空间分布、轴向扩散和进样量等因素对洗脱曲线的影响。在遍历空间中,建立了离散时间形式的溶质带演化轨线和离散时间控制矢量之间的对应关系。按Bellman动态规划思想,给出对于非线性-非理想-平衡色谱进行优化控制的多段决策问题的简明算法,以此可获得状态矢量和控制矢量的优化轨线。该LLA的矩阵形式消除了制备色谱理论和Markov决策过程或其他基于离散时间状态的现代控制方法之间的鸿沟。The matrix forms of local Lagrangian .approach （LLA） are developed based on Lagrangian description for single-component in nonlinear, non-ideal chromatography. A local thermodynamic path （LTP） is designed based on essential physical principles, such as the Lagrangian description, the local equilibrium assumption and the thermodynamic state functions. With the LTP, the iteration equations of fully thermodynamic states on time sequence in the matrix forms are obtained with the Markov character. And the convergence, compatibility and stability of the LLA based on the LTP are discussed with some theoretical analysis and numerical experiments, and the stability condition of the LLA is given. The algorithm of the LLA in the vector form is shown as the computer program to simulate the elution profiles affected by a few of factors, space-distribution, axial diffusions, injection samples, etc. According to the LLA, the corresponding relationships are established between the trajectories of discrete time state and discrete time control vectors in the ergodic space. And a compendium algorithm of multi- stage decision problems concerning the optimal control of nonlinear, non-idea chromatography is given with Bellman＇s dynamic programming to find the optimal trajectories of state vector and control vector. The matrix forms of the LLA remove the gap between preparative chromatography theories and Markov decision processes or optimal control approaches based on discrete time states.

关 键 词：非线性色谱 Lagrangian描述 非线性控制系统 

分 类 号：O658[理学—分析化学]