Abstract
Process design is usually approached by considering the steady-state performance of the process based on an economic objective. Only after the process design is determined are the operability aspects of the process considered. This sequential treatment of the process design problem neglects the fact that the dynamic controllability of the process is an inherent property of its design. This work considers a systematic approach where the interaction between the steady-state design and the dynamic controllability is analyzed by simultaneously considering both economic and controllability criteria. This method follows a process synthesis approach where a process superstructure is used to represent the set of structural alternatives. This superstructure is modeled mathematically by a set of differential and algebraic equations which contains both continuous and integer variables. Two objectives representing the steady-state design and dynamic controllability of the process are considered. The problem formulation thus is a multiobjective Mixed Integer Optimal Control Problem (MIOCP). The multiobjective problem is solved using an ∈-constraint method to determine the noninferior solution set which indicates the trade-offs between the design and controllability of the process. The (MIOCP) is transformed to a Mixed Integer Nonlinear Program with Differential and Algebraic Constraints (MINLP/DAE) by applying a control parameterization technique. An algorithm which extends the concepts of MINLP algorithms to handle dynamic systems is presented for the solution of the MINLP/DAE problem. The MINLP/DAE solution algorithm decomposes the problem into a NLP/DAE primal and MILP master problems which provide upper and lower bounds on the solution of the problem. The MINLP/DAE algorithm is implemented in the framework MINOPT which is used as the computational tool for the analysis of the interaction of design and control. The solution of the MINLP/DAE problems is repeated with varying values of ∈ to generated the noninferior solution set. The proposed approach is applied to three design/control examples: a reactor network involving two CSTRs, an ideal binary distillation column, and a reactor/separator/recycle system. The results of these design examples quantitatively illustrate the trade-offs between the steady-state economic and dynamic controllability objectives.
This research was supported by the National Science Foundation and Mobil Corporation.
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References
Bahri, P.A., Bandoni, J.A. and Romagnoli, J.A. (1996), “Effect of dis- turbances in optimizing control: stead-state open-loop backoff problem,” AIChE Journal, Vol. 42, No. 4, 983–994.
Brengel, D.D. and Seider W.D. (1992), “Coordinated design and control optimization of nonlinear processes,” Comp. Chem. Eng., Vol. 16, No. 9, 861–886.
CPLEX Optimization, Inc. (1995), Using the CPLEX callable library.
Douglas, J.M. (1989), Conceptual Design of Chemical Processes. McGraw-Hill, New York.
Duran, M.A. and Grossmann, I.E. (1986), “An outer-approximation algorithm for a class of mixed-integer nonlinear programs,” Math. Prog., Vol. 36, 307–339.
Elliott, T.R. and Luyben, W.L. (1995), “Capacity-based approach for the quantitative assessment of process controllability during the conceptual design stage,” Ind. Eng. Chem. Res., Vol. 34, 3907–3915.
Figueroa, J.L., Bahri, P.A., Bandoni, J.A. and Romagnoli, J.A. (1996), “Economic impact of disturbances and uncertain parameters in chemical processes—a dynamic back-off analysis,” Comp. Chem. Eng., Vol. 20, No. 4, 453–461.
Floudas, C.A., Aggarwal, A., and Ciric, A.R. (1989), “Global optimal search for nonconvex NLP and MINLP problems,” Comp. Chem. Eng., Vol. 13, No. 10, 1117.
Floudas, C.A. (1995), Nonlinear and Mixed Integer Optimization: Fundamentals and Applications. Oxford University Press, Oxford.
Geoffrion, A.M. (1972), “Generalized benders decomposition,” J. Opt. Theory Applic., Vol. 10, No. 4, 237–260.
Gill, P.E., Murray, W., Saunders, M. and Wright, M.H. (1986), User’s Guide for NPSOL (Version 4.0). Systems Optimization Laboratory, Department of Operations Research, Stanford University, Technical Report SOL 86–2.
Jarvis, R.B. and Pantelides, C.C. (1992), DASOLV: A Differential-Algebraic Equation Solver. Center for Process Systems Engineering, Imperial College of Science, Technology, and Medicine, London, Version 1. 2.
Kocis, G.R. and Grossmann, I.E. (1987), “Relaxation strategy for the structural optimization of process flow sheets,” Ind. Eng. Chem. Res., Vol. 26, No. 9, 1869.
Luyben, M.L. and Floudas, C.A. (1994), “Analyzing the interaction of design and control-1. A multiobjective framework and application to binary distillation synthesis,” Comp. Chem. Eng, Vol. 18, No. 10, 933–969.
Luyben, M.L. and Floudas, C.A. (1994), Analyzing the interaction of design and control-2. Reactor-separator-recycle system,“ Comp. Chem. Eng., Vol. 18, No. 10, 971–994.
Mohideen, M.J., Perkins, J.D. and Pistikopoulos, E.N. (1996), “Optimal design of dynamic systems under uncertainty,” AIChE Journal, Vol. 42, No. 8, 2251–2272.
Morari, M and Perkins, J.D. (1994), “Design for operations,” FOCAPD Conference Proceedings.
Murtagh, B.A. and Saunders, M.A (1993), MINOS 5.4 User’s Guide, Systems Optimization Laboratory, Department of Operations Research, Stanford University, Technical Report SOL 83–20R.
Narraway, L.T., Perkins, J.D. and Barton, G.W. (1991), “Interaction between process design and process control: economic analysis of process dynamics,” J. Process Control, Vol. 1, 243–250.
Narraway, L.T. and Perkins, J.D. (1993), “Selection of process control structure based on linear dynamic economics,” Ind. Eng. Chem. Res., Vol. 32, 2681–2692.
Narraway, L.T. and Perkins, J.D. (1993), “Selection of control structure based on economics,” Comp. Chem. Eng., Vol. 18, S511–515.
Schweiger, C.A. and Floudas, C.A. (1996), MINOPT: A Software Package for Mixed-Integer Nonlinear Optimization. Princeton University, Princeton, New Jersey.
Vassiliadis, V.S., Sargent, R.W.H. and Pantelides, C.C. (1994), C.C. (1994), “Solution of a class of multistage dynamic optimization problems. 1. Problems without path constraints,” Ind. Eng. Chem. Res., Vol. 33, 2111 2122.
Viswanathan, J. and Grossmann, I.E. (1990), “A combined penalty function and outer approximation method for MINLP optimization,” Comp. Chem. Eng., Vol. 14, No. 7, 769–782.
Walsh, S. and Perkins, J.D. (1996), “Operability and control in process synthesis and design,” in Advances in Chemical Engineering, John L. Anderson, ed., Vol. 23, Academic Press, New York, 301–402.
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Schweiger, C.A., Floudas, C.A. (1998). Interaction of Design and Control: Optimization with Dynamic Models. In: Optimal Control. Applied Optimization, vol 15. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6095-8_19
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DOI: https://doi.org/10.1007/978-1-4757-6095-8_19
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