Skip to main content
Log in

Development of nonsingular optimization algorithm and its application to chemical engineering systems

  • Published:
Korean Journal of Chemical Engineering Aims and scope Submit manuscript

Abstract

A nonsingular transformation algorithm which converts a singular control problem to nonsingular one was developed to calculate optimal control profiles. Several chemical engineering problems for applying a nonsingular transformation algorithm were presented and optimal profiles were calculated in this paper. The singular control algorithm and nonsingular transformation algorithm were compared. The efficiency of the transformation algorithm was displayed in this article. The switching points from bang-bang to singular control were calculated by imposed initial conditions and control variable constraints.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Chen, B.J., Hirt, W., Lim, H.C. and Tsao, G.T., “Growth Characteristics of a New Methylomonad”,Applied and Environmental Microbiology,Feb., 269 (1977).

    Google Scholar 

  • Dibiasio, D., Lim, H.C. and Weigand, W.A., “An Experimental Investigation of Stability and Multiplicity of Steady States in a Biological Reactor”,AIChE Journal,27, 284 (1981).

    Article  CAS  Google Scholar 

  • Douglas, J. M. and Derm, M. M., “Optimal Design and Control by Variational Methods”Industrial and Engineering Chemistry,57(11), 18 (1965).

    Article  CAS  Google Scholar 

  • Fraser-Andrews, G., “Numerical Methods for Singular Optimal Control,”,Journal of Optimization Theory and Applications,61(3), 377 (1989).

    Article  Google Scholar 

  • Goh, B. S., “Necessary Conditions for Singular Extremals Involving Multiple Conrol Variables”,J. SIAM Control,4, 716 (1966).

    Article  Google Scholar 

  • Kelley, H. J., Kopp, R. E. and Moyer, A. G., “Topics in Optimization”, ed. Leitman, G., Academic Press, New York (1966).

    Google Scholar 

  • Ko, D. Y. C. and Stevens, W. F., “Studies of Singular Solution in Dynamic Optimization: I. Theoretical Aspects and Methods of Solution”,AIChE Journal,17, 160 (1971).

    Article  Google Scholar 

  • Ko, D. Y. C. and Stevens, W. F., “Studies of Singular Solution in Dynamic Optimization: H. Optimal Singular Design”,AIChE Journal,17, 160 (1971).

    Article  Google Scholar 

  • Maurer, H., “Numerical Solution of Singular Control Problems Using Multiple Shooting Techniques”,Journal of Optimization Theory and Applications,18, 235 (1976).

    Article  Google Scholar 

  • Modak, J. M., Bonte, P. and Lim, H. G, “An Improved Computational Algorithm for Singular Control Problems in Chemical Reaction Engineering”,Chem. Eng. Comm.,86, 165 (1989).

    Article  CAS  Google Scholar 

  • Oberle, H. J., “Numerical Computation of Singular Control Problems with Application to Optimal Heating and Cooling by Solar Energy”,Appl. Math. Optim.,5, 297 (1979).

    Article  Google Scholar 

  • Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R.V. and Mischenks, E. F., “The Mathematical Theory of Optimal Processes”, Wiley, New York (1962).

    Google Scholar 

  • Seinfeld, J. H. and Lapidus, L., “Singular Solutions in the Optimal Control of Lumped-and Distributed Parameter Systems”,Chem. Eng. Sci.,23(12), 1485 (1968).

    Article  CAS  Google Scholar 

  • Siebenthal, C. D. and Aris, R., “Studies in Optimization VI. The Application of Pontryagin’s Method to the Control of a Stirred Reactor”,Chem. Eng. Sci.,19, 729 (1964).

    Article  CAS  Google Scholar 

  • Soliman, M. A. and Ray, W. H., “A Computational Technique for Optimal Control Problems Having Singular Arcs”,International Journal of Control,16, 261 (1972).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jung Heon Lee.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lee, J.H., Lim, H.C. Development of nonsingular optimization algorithm and its application to chemical engineering systems. Korean J. Chem. Eng. 16, 118–127 (1999). https://doi.org/10.1007/BF02699014

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02699014

Key words

Navigation