Optimal spatial temperature control of a steady-state exothermic plug flow reactor. Part II: Singular control

This paper is the second in a series of two dealing with the spatial optimization of the heat exchanger temperature profiles of exothermic tubular reactors under the assumption of steady-state and plug flow characteristics. The minimum principle of Pontryagin (optimal control theory) is applied in a straightforward, analytical sense. To enable a trade-off between process performance and global heat loss a weighted cost criterion is defined. In Part I of this series, it is demonstrated that (weighted combinations of) terminal costs give rise to control inputs of bang-bang type. In this Part II, the terminal cost criterion is extended with an integral term which accounts for the global heat loss during the process. Analysis of the extremal control sequence reveals that integral cost terms generically induce control of bang-singular-bang type. The singular arc is carefully analyzed. Furthermore it is illustrated that a practically more feasible bang-bang profile exhibits near optimal performance.