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.
参考文献
| [1] | Rathore A S,Velayudhan A.Scale-Up and Optimization in Preparative Chromatography,Principles and Biopharmaceutical Applications.New York:Marcel Dekker,2003:1 |
| [2] | Guiochon G,Lin B C.Modeling for Preparative Chromatography.Amsterdam:Academic Press,2003:1 |
| [3] | Guiochon G,Shirazi S G,Katti A M.Fundamentals of Preparative and Nonlinear Chromatography.Boston:Academic Press,1994:1 |
| [4] | Wilson J N.J Am Chem Soc,1940,62:1 583 |
| [5] | Cazes J,Scott P P W.Chromatography Theory.New York:Marcel Dekker,2002:3 |
| [6] | Giddings J C.Unified Separation Science.New York:Wiley-Interscience,1991:1 |
| [7] | Wiener N.Cybernetics,or Control and Communication in the Animal and Machine.New York:John Wiley and Sons,1948 |
| [8] | Martin A J P,Synge R L M.Biochem J,1941,35:1 358 |
| [9] | Van Deemter J J,Zuiderweg F J,Klinkenberg A.Chem Eng Sci,1956,5:271 |
| [10] | Sniedovich M.Dynamic Programing.New York:Marcel Dekker,1992:1 |
| [11] | Vincent T L,Grantham W J.Nonlinear and Optimal Control Systems.New York:John Wiley and Sons,1997:1 |
| [12] | Thoms J W.Numerical Partial Differential Equations:Finite Difference Methods.New York:Springer-Verlag,1995:14,23,128,141,232 |
| [13] | Meyn S P,Tweedie R L.Markov Chains and Stochastic Stability.3rd ed.London:Springer-Verlag,1996:1 |
| [14] | Howard R.Dynamic Programming and Markov Decision Processes.Cambridge:MIT Press,1960 |
| [15] | Currie I G.Fundamental Mechanics of Fluids.3rd ed.New York:Marcel Dekker,2003:1 |
| [16] | Hans S.Lagrangian Fluid Description with Simple Applications in Compressible Plasma and Gas Dynamics//Physics Reports.Germany:Physikalisches Institut,2004,392:279 |
| [17] | Prigogine I.Introduction to Thermodynamics of Irreversible Processes.3rd ed.New York:Jone Wiley and Sons,1967:1 |
| [18] | Kreuzer H J.Non-Equilibrium Thermodynamics and Its Statistical Foundations.Oxford:Clarendon Press,1981:1 |
| [19] | Liang H,Lin B C.J Chromatogr A,1998,828:3 |
| [20] | Liang H,Wang Z G,Lin B C,Xu C G,Fu R N.J Chromatogr A,1997,763:237 |
| [21] | Liang H,Lin B C.J Chromatogr A,1999,841:133 |
| [22] | Liang H,Liu Y.J Chromatogr A,2004,1 040:19 |
| [23] | Liang H,Liu X L.Science in China Series B:Chemistry,2004,6:443 |
| [24] | Heath M T,Heath M.Scientific Computing:An Introductory Survey.2nd ed.New York:McGraw-Hill Companies,2002:1 |
| [25] | Watkins D S.Fundamentals of Matrix Computations.New York:John Wiley and Sons,2002:1 |
| [26] | Wagner D H.J Differential Equations,1987,68:118 |
| [27] | Shu C W,Oshert S.J Comput Phys,1989,83:32 |
| [28] | Hui W H,Li P Y,Li Z W.J Comput Phys,1999,153:596 |
| [29] | Lin X B.J Differential Equations,2000,168:321 |
| [30] | Malcevic I,Ghattas O.Finite Elem Anal Des,2002,38:965 |
| [31] | Hirt C W,Cook J L,Butler T D.J Comput Phys,1970,5:103 |
| [32] | Loh C Y,Liou M S.J Comput Phys,1994,113:224 |
| [33] | Hui W H,He Y.SIAM J Appl Math,1997,57:893 |
| [34] | Karlsen K H,Lie K A,Natvig J R,Nordhaug H F,Dahle H K.J Comput Phys,2001,173:636 |
| [35] | Espedal M S,Karlsen K H.Numerical Solution of Reservoir Flow Models Based on Large Time Step Operator Splitting Algorithms.Berlin:Springer-Verlag,2000,1 734:9 |
| [36] | Karlsen K H,Risebro N H.J Numer Anal,2000,37:980 |
| [37] | Grigoryev Yu N,Vshivkov V A,Fedoruk M P.Numerical "Particle-in-Cell" Methods-Theory and Applications.Utrecht:VSP BV,2000:1 |
| [38] | Bellman R.Dynamic Programming.Princeton:Princeton University Press,1957:83 |
| [39] | Lee H G.Chemical Thermodynamics for Metals and Materials.London:Imperial College Press,1999 |
| [40] | Ferziger J H,Peric M.Computational Methods for Fluid Dynamics.3rd ed.Berlin:Springer-Verlag,2002:1 |
上一张
下一张
上一张
下一张
计量
- 下载量()
- 访问量()
文章评分
- 您的评分：
-
10%
-
20%
-
30%
-
40%
-
50%