Periodic optimal control of a plug flow reactor model with an isoperimetric constraint

TL;DR

This paper develops an optimal control framework for a plug flow reactor modeled by nonlinear hyperbolic PDEs, aiming to maximize product yield through periodic boundary control strategies.

Contribution

It introduces an isoperimetric optimal control formulation with periodic constraints for PFRs and proves bang-bang optimality for single-input control.

Findings

Bang-bang control strategy is optimal for the single-input system.

Method of characteristics is used to analyze flow rate control.

A case study demonstrates the effectiveness of different control strategies.

Abstract

We study a class of nonlinear hyperbolic partial differential equations with boundary control. This class describes chemical reactions of the type ``$A \to$ product'' carried out in a plug flow reactor (PFR) in the presence of an inert component. An isoperimetric optimal control problem with periodic boundary conditions and input constraints is formulated for the considered mathematical model in order to maximize the mean amount of product over the period. For the single-input system, the optimality of a bang-bang control strategy is proved in the class of bounded measurable inputs. The case of controlled flow rate input is also analyzed by exploiting the method of characteristics. A case study is performed to illustrate the performance of the reaction model under different control strategies.