A Multistage Stochastic Programming Approach in Real-Time Process Control

Standard model predictive control for real-time operation of industrial production processes may be inefficient in the presence of substantial uncertainties. To avoid overly conservative disturbance corrections while ensuring safe operation, random influences should be taken into account explicitly. We propose a multistage stochastic programming approach within the model predictive control framework and apply it to a distillation process with a feed tank buffering external sources. A preliminary comparison to a probabilistic constraints approach is given and first computational results for the distillation process are presented.

[1]  Sigurd Skogestad,et al.  Dynamics and control of distillation columns : a critical survey , 1997 .

[2]  Ignacio E. Grossmann,et al.  Design optimization of stochastic flexibility , 1993 .

[3]  Peter Kall,et al.  Stochastic Programming , 1995 .

[4]  A. Genz Numerical Computation of Multivariate Normal Probabilities , 1992 .

[5]  I. Kuban Altinel,et al.  Scheduling of batch processes with operational uncertainties , 1996 .

[6]  J. Dupacová,et al.  Scenario reduction in stochastic programming: An approach using probability metrics , 2000 .

[7]  John R. Birge,et al.  Introduction to Stochastic Programming , 1997 .

[8]  Ana M. Eliceche,et al.  Feasible operating region of natural gas plants under feed perturbations , 1998 .

[9]  Pu Li,et al.  Optimal Control of a Continuous Distillation Process under Probabilistic Constraints , 2001 .

[10]  J. A. Romagnoli,et al.  Advanced controller design for a distillation column , 1994 .

[11]  M. Schervish Multivariate normal probabilities with error bound , 1984 .

[12]  U. Diwekar,et al.  Efficient sampling technique for optimization under uncertainty , 1997 .

[13]  Ignacio E. Grossmann,et al.  An index for operational flexibility in chemical process design. Part I: Formulation and theory , 1985 .

[14]  Efstratios N. Pistikopoulos,et al.  Uncertainty in process design and operations , 1995 .

[15]  Marc C. Steinbach Recursive Direct Algorithms for Multistage Stochastic Programs in Financial Engineering , 1999 .

[16]  Pu Li,et al.  Stochastic Optimization for Operating Chemical Processes under Uncertainty , 2001 .

[17]  S. Uryasev,et al.  Stochastic optimization : Algorithms and Applications , 2001 .

[18]  D. Rippin,et al.  Semi-batch process optimization under uncertainty: Theory and experiments , 1998 .

[19]  Peter Kall,et al.  Operations Research Proceedings 1998 , 1999 .

[20]  István Deák,et al.  Three digit accurate multiple normal probabilities , 1980 .

[21]  Marc C. Steinbach Hierarchical Sparsity in Multistage Convex Stochastic Programs , 2000 .

[22]  R. Schultz,et al.  Multistage Stochastic Integer Programs: An Introduction , 2001 .