Minimal time control of fed-batch processes with growth functions having several maxima

TL;DR

This paper develops a numerical method for minimal time optimal control of fed-batch reactors with complex, non-monotonic growth kinetics characterized by multiple maxima, including singular arcs.

Contribution

It introduces a numerical approximation approach to determine globally optimal trajectories in fed-batch processes with complex growth functions.

Findings

Successfully computes optimal control trajectories with multiple singular arcs.

Demonstrates effectiveness on models with combined Haldane kinetics.

Provides a framework for handling complex non-monotonic growth in process control.

Abstract

We address the issue of minimal time optimal control of fedbatch reactor in presence of complex non monotonic kinetics, that can be typically characterized by the combination of two Haldane models. The optimal synthesis may present several singular arcs. Global optimal trajectory results are provided on the basis of a numerical approach that considers an approximation method with smooth control inputs.