Optimal periodic control of nonlinear chemical reactions with a time‐varying flow rate

Abstract

This paper deals with a mathematical model of a non-isothermal chemical reaction described by nonlinear ordinary differential equations with two-dimensional control. The control variables correspond to the possibility of manipulating the concentration of the input reactant and the total flow rate. We consider the task of maximizing the reactor performance as an isoperimetric optimal control problem with periodic boundary conditions. Necessary optimality conditions are derived by the Pontryagin maximum principle with Lagrange multipliers corresponding to the isoperimetric constraints.

Analysis of Switching Strategies for the Optimization of Periodic Chemical Reactions with Controlled Flow-Rate

“…Consider a nonlinear control system describing non-isothermal chemical reactions of the type "A → Product" and order n [8,16]:…”

“…System (1) can be transformed to the control-affine form with respect to the inputs u 1 = v 1 v 2 and u 2 = v 2 as follows [16]:…”

“…Note that the above papers deal with reaction models with a constant flow-rate, while the periodic flow-rate modulation is shown to be an important ingredient for improving the reaction performance [8]. The corresponding isoperimetric optimal control problem is rigorously formulated in [16] for a non-isothermal mathematical model with two independent inputs: the inlet concentration and the flow-rate. As in the case of constant flow-rate, it is shown in [16] that the optimal controls are piecewise constant, and their switching times are defined in terms of zeros of certain auxiliary functions.…”

“…The corresponding isoperimetric optimal control problem is rigorously formulated in [16] for a non-isothermal mathematical model with two independent inputs: the inlet concentration and the flow-rate. As in the case of constant flow-rate, it is shown in [16] that the optimal controls are piecewise constant, and their switching times are defined in terms of zeros of certain auxiliary functions. However, the structure of switching controllers has not been analyzed so far.…”

“…However, the structure of switching controllers has not been analyzed so far. This paper aims at developing an efficient approach for computing periodic bang-bang controls and evaluating the cost for the isoperimetric optimal control problem introduced in [16].…”