Elsevier

Applied Mathematical Modelling

Volume 50, October 2017, Pages 257-278
Applied Mathematical Modelling

Time-optimal control of concentration changes in the chemostat with one single species

https://doi.org/10.1016/j.apm.2017.05.037Get rights and content
Under an Elsevier user license
open archive

Highlights

  • Control of bioprocesses with applications in wastewater treatment.

  • Modeling of a chemostat system including a recirculation parameter for the biomass.

  • Synthetize optimal feedback control laws based on singular strategies.

  • Singular strategies represent a trade-off in comparison with bang-bang trajectories.

  • Characterize robust control laws that can be implemented easily for a practitioner.

Abstract

We consider the problem of driving in minimal time a system describing a chemostat model to a target point. This problem finds applications typically in the case where the input substrate concentration changes yielding in a new steady state. One essential feature is that the system takes into account a recirculation of biomass effect. We depict an optimal synthesis and provide an optimal feedback control of the problem by using Pontryagin’s Principle and geometric control theory for a large class of kinetics.

Keywords

Chemostat model
Optimal feedback
Pontryagin maximum principle
Singular control

Cited by (0)

A preliminary version of this paper appeared at the 2014 European Control Conference [1].