Abstract
The performance of empirical model based fed-batch process optimal control is strongly affected by the model prediction reliability at the end-point of a batch. An optimal control profile calculated from an empirical model may not give the best performance when applied to the actual process due to model-plant mismatches. To tackle this issue, a new method for improving the reliability of fed-batch process optimal control by incorporating model prediction confidence bounds is proposed. Multiple neural networks (MNN) are used to build an empirical model of fed-batch process based on process operation data. Model prediction confidence bounds are calculated based on predictions of all component networks in an MNN model and the model prediction confidence bound at the end-point of a batch is incorporated into the optimization objective function. The modified objective function penalizes wide prediction confidence bounds in order to obtain a reliable optimal control profile. The non-linear optimization problem based on MNN with augmented objective function is solved by iterative dynamic programming. The proposed control strategy is illustrated on a simulated fed-batch ethanol fermentation process. The results demonstrate that the optimal control profile calculated from the proposed approach is reliable in the sense that its performance degradation is limited when applied to the actual process.
Similar content being viewed by others
References
P. Terwiesch, M. Argarwal, and D.W.T. Rippin, “Batch unit optimization with imperfect modeling: A survey,” Journal of Process Control, vol. 4, pp. 238–258, 1994.
D. Bonvin, “Optimal operation of batch reactors—A personal view,” Journal of Process Control, vol. 8, pp. 355–368, 1998.
C.A. Nascimento, R. Giudici, and R. Guardani, “Neural network based approach for optimisation of industrial chemical processes,” Computers Chem. Engng., vol. 24, pp. 2303–2314, 2000.
G. Cybenko, “Approximation by superpositions of a sigmoidal function,” Math. Control Signal Systems, vol. 2, pp. 303–314, 1989.
J. Sjoberg, Q. Zhang, L. Ljung, A. Benveniste, B. Delyon, P.Y. Glorennec, H. Hjalmarsson, and A. Juditsky, “Nonlinear black-box modeling in system identification: a unified overview,” Automatica, vol. 31, pp. 1691–1724, 1995.
N. Bhat and T. McAvoy, “Use of neural nets for dynamic modeling and control of chemical process systems,” Computers Chem. Engng., vol. 14, pp. 573–583, 1990.
K.J. Hunt, D. Sbarbaro, R. Zbikowski, and P.J. Gawthrop, “Neural networks for control systems—A survey,” Automatica, vol. 28, pp. 1083–1112, 1992.
Y. Tian, J. Zhang, and A.J. Morris, “Optimal control of a batch emulsion copolymerisation reactor based on recurrent neural network models,” Chemical Engineering and Processing, vol. 41, pp. 531–538, 2002.
D.H. Wolpert, “Stacked generalization,” Neural Networks, vol. 5, pp. 241–259, 1992.
D.V. Sridhar, R.C. Seagrave, and E.B. Bartlett, “Process modeling using stacked neural networks,” AIChE J., vol. 42, pp. 2529–2539, 1996
D.V. Sridhar, E.B. Bartlett, and R.C. Seagrave, “An information theoretic approach for combining neural network process models,” Neural Networks, vol. 12, pp. 915–926, 1999.
B. Eikens and M.N. Karim, “Process identification with multiple neural network models,” Int. J. Control, vol. 72, pp. 576–590, 1999.
U. Anders and O. Korn, “Model selection in neural networks,” Neural Networks, vol. 12, pp. 309–323, 1999.
J. Zhang, “Inferential estimation of polymer quality using bootstrap aggregated neural networks,” Neural Networks, vol. 12, pp. 927–938, 1999.
Y. Tian, J. Zhang, and A.J. Morris, “Modeling and optimal control of a batch polymerization reactor using a hybrid stacked recurrent neural network model,” Ind. Eng. Chem. Res., vol. 40, pp. 4525–4535, 2001.
P. Terwiesch, D. Ravemark, B. Schenker, and D.W.T. Rippin, “Semi-batch process optimization under uncertainty: Theory and experiments,” Computers Chem. Engng., vol. 22, pp. 201–213, 1998.
S.A. Russell, P. Kesavan, and J.H. Lee, “Recursive data-based prediction and control of batch product quality,” AIChE J., vol. 44, pp. 2442–2458, 1998.
E. Visser, B. Srinivasan, S. Palanki, and D. Bonvin, “A feedback-based implementation scheme for batch process optimisation,” Journal of Process Control, vol. 10, pp. 399–410, 2000.
R. Luus, “Optimal control by dynamic programming using systematic reduction in grid size,” Int. J. Control, vol. 51, pp. 995–1013, 1990.
R. Luus and S.G. Smith, “Application of dynamic programming to high-dimensional system described by difference equations,” Chem. Eng. Technol., vol. 14, pp. 122–126, 1991.
A. Tholudur and W.F. Ramirez, “Optimization of fed-batch bioreactors using neural network parameter function models,” Biotechnol. Prog., vol. 12, pp. 302–309,1996.
A. Rusnak, M. Fikar, M.A. Latifi, and A. Meszaros, “Receding horizon iterative dynamic programming with discrete time models,” Computers Chem. Engng., vol. 25, pp. 161–167, 2001.
B.Bulsari (ed.), Computer-Aided Chemical Engineering, vol. 6, Neural Networks for Chemical Engineers, Elsevier, 1995.
I.M. Mujtaba and M.A. Hussain, Application of Neural Networks and Other Learning Technologies in Process Engineering, Imperial College Press, 2001.
J.M. Bates and C.W.J. Granger, “The combination of forecasts,” Oper. Res. Q., vol. 20, pp. 451–468, 1969.
J. Zhang, A.J. Morris, E.B. Martin, and C. Kiparissides, “Estimation of impurity and fouling in batch polymerisation reactors through the application of neural networks,” Computers Chem. Engng., vol. 23, pp. 301–314, 1999.
L. Breiman, “Stacked regression,” Machine Learning, vol. 23, pp. 49–64, 1996.
S. Hashem, “Improving model accuracy using optimal linear combinations of trained neural networks,” IEEE Trans. on Neural Networks, vol. 6, pp. 792–794, 1995.
R. Luus and O. Rosen, “Application of dynamic programming to final state constrained optimal control problems,” Ind. Eng. Chem. Res., vol. 30, pp. 1525–1530, 1990.
R. Luus, “Application of dynamic programming to differential—Algebraic process systems,” Computers Chem. Engng., vol. 17, pp. 373–377, 1993.
J. Hong, “Optimal substrate feeding policy for fed batch fermentation with substrate and product inhibition kinetics,” Biotechnol. Bioeng., vol. 27, pp. 1421–1431, 1986.
C.T. Chen and C. Hwang, “Optimal control computation for differential-algebraic process systems with general constraints,” Chem. Engng Commun., vol. 97, pp. 9–26, 1990.
J. Zhang and A. J. Morris, “Recurrent neuro-fuzzy networks for non-linear process modeling,” IEEE Trans. on Neural Networks, vol. 10, pp. 313–326, 1999.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Xiong, Z., Zhang, J. Optimal Control of Fed-Batch Processes Based on Multiple Neural Networks. Appl Intell 22, 149–161 (2005). https://doi.org/10.1007/s10489-005-5603-y
Issue Date:
DOI: https://doi.org/10.1007/s10489-005-5603-y