Abstract
This study shows how the optimal control theory for distributed parameter systems can be implemented for a problem of tubular reactor with axial dispersion described by partial differential equations. Two methods are implemented. One is based on differential equation approach and the other is based on integral equation approach. It was found that the approach with partial differential equations is preferable to the one with integral equations for the type of problems treated in this study. Computation algorithms and programs for both cases are developed.
Similar content being viewed by others
References
Bansal, J. G. and Chang, K. S., “Optimal Control of Dispersion Type Distributed-Parameter Systems with Time-delay in Interacting Two-point Boundary Conditions”,Int. J. Control,16, 481 (1972).
Butkovskiy, A. G., “Theory of Optimal Control by Systems with Distributed Parameters”, American Elsevier, 1969.
Chang, K. S., Chap. 6 in “Distributed Parameter Systems”, Marcel Dekker, 1978.
Derzko, N. A., Sethi, S. P. and Thompson, G. L., “Necessary and Sufficient Conditions for Optimal Control for Quasilinear Partial Differential Systems”,J. of Optim. Theo, and Appli. 43, 89 (1984).
Fucik, S. and Kufner, A., “Nonlinear Differential Equations”, Elsevier, Amsterdam, 1980.
Schiesser, W. E., “Manual No. 5 of DSS/2-Differential Systems Simulator Version 2”. Lehigh Univ., Pennsylvania, 1985.
Schiesser, W. E., “The Numerical Method of Lines”, Academic Press, 1991.
Wang, F. Y., “Optimal Control Theory for Distributed Parameter Processes Based on Integral Equation Representations”, Ph.D. Thesis, Univ. of Waterloo, Ontario, 1985.
Zone, G., “Second-order Optimal Control Algorithms for Lumped- and Distributed-Parameter Processes”, Ph.D. Thesis, Univ. of Waterloo, Ontario, 1973.
Zone, G. and Chang, K. S., “A Successive Approximation Method for Non-linear Distributed-Parameter Control Systems”.Int. J. Control,15, 255 (1972).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Choe, YS., Chang, K.S. Comparison of two methods of optimal control synthesis: Partial differential equation approach and integral equation approach. Korean J. Chem. Eng. 12, 198–206 (1995). https://doi.org/10.1007/BF02705647
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02705647