On the steady state optimization of the biogas production in a two-stage anaerobic digestion model

Bayen, Térence; Gajardo, Pedro

doi:10.1007/s00285-018-1301-3

Cited by 19 publications

(37 citation statements)

References 17 publications

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“…In Section 2, we recall some properties of the AM2-model that are useful to transform (1.1) into a two-dimensional affine system with a drift and one input. We also recall a result of [2] (see Proposition 2.1) which shows that the target point maximizing the biogas production at steady state necessarily belongs to the collinearity curve of the system. This property appears to be an essential key point in this study.…”

Section: Introductionmentioning

confidence: 92%

“…In this section, we briefly recall the modeling of a two-step fermentor that will be useful to state the optimal control problem. Following [2], the model (1.1) proposed in [6], can be written as the following equivalent dynamical system…”

Section: Statement Of the Problem 21 Preliminaries On The Modeling Omentioning

confidence: 99%

“…Here, u max > 0 is the maximum value for the dilution rate (it depends on the characteristics of the fermentor). Since this static optimization problem problem was recently studied in [2], we shall only recall one optimality result that will be useful to state the optimal control problem.…”

Section: Statement Of the Problem 21 Preliminaries On The Modeling Omentioning

confidence: 99%

“…the quantityμ 2 (S 2 )X 2 among constant dilution rates. Following [2], this procedure allows us to obtain steady states of (1.1) maximizing the biogas production.…”

Section: Introductionmentioning

confidence: 99%

“…Our aim in this work is to address essentially the second point using the theory of optimal control (the first point which consists in maximizing (1.2) among steady states of (1.1) was recently addressed in [2]). From a practical point of view, a reactor cannot be initiated at the optimal point due to uncertainties and to the initial conditions inside a fermentor.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of an Optimal Control Problem Related to the Anaerobic Digestion Process

Bayen

Cots

Gajardo

2018

J Optim Theory Appl

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Our aim in this work is to synthesize optimal feeding strategies maximizing over a time period the biogas production in a continuously filled bioreactor controlled by its dilution rate. Following [6], such an anaerobic process is described by the so-called AM2 model which is a four-dimensional dynamical system. Instead of modeling the optimization of the biogas production as an optimal control problem of Lagrange type, we propose in this paper a slightly different optimal control approach : we study the minimal time control problem to reach a target point which is chosen in such a way that it maximizes the biogas production in the AM2 model at steady state. Thanks to the Pontryagin Maximum Principle and to geometric control theory, we provide an optimal feedback control for the minimal time control problem when initial conditions are taken on the invariant and attractive manifold of the system. The optimal synthesis exhibits turnpike and anti-turnpike singular arcs and a cut-locus.

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Section: Introductionmentioning

confidence: 92%

Section: Statement Of the Problem 21 Preliminaries On The Modeling Omentioning

confidence: 99%

Section: Statement Of the Problem 21 Preliminaries On The Modeling Omentioning

confidence: 99%

“…the quantityμ 2 (S 2 )X 2 among constant dilution rates. Following [2], this procedure allows us to obtain steady states of (1.1) maximizing the biogas production.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Analysis of an Optimal Control Problem Related to the Anaerobic Digestion Process

Bayen

Cots

Gajardo

2018

J Optim Theory Appl

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A minimum time control problem for aerobic degradation processes in biocell composting plants

Martalò

Bianchi

Buonomo

et al. 2020

Optim Control Appl Methods

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We introduce a mathematical model for the composting process in biocells. The model includes several phenomena, like the aerobic biodegradation of the soluble substrate by means of a bacterial population, the hydrolysis of insoluble substrate, and the biomass decay. We investigate the best strategies to reduce substrate components in minimal time by controlling the effects of cell oxygen concentration on the degradation phenomenon. It is shown that singular controls are not optimal for this model and the optimal control time profiles are of bang or bang‐bang type. The occurrence of switching curves is discussed. In the case of a bang‐bang control we prove that optimal control profiles have a unique switching time and the corresponding switching curve is determined.

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Stabilization of the chemostat system with mutations and application to microbial production

Bayen

Coville

Mairet

2023

Optim Control Appl Methods

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In this article, we consider the chemostat system with species, one limiting substrate, and mutations between species. Our objective is to globally stabilize the corresponding dynamical system around a desired equilibrium point. Doing so, we introduce auxostat feedback controls which are controllers allowing the regulation of the substrate concentration. We prove that such feedback controls globally stabilize the resulting closed‐loop system near the desired equilibrium point. This result is obtained by combining the theory of asymptotically autonomous systems and an explicit computation of solutions to the limit system. The performance of such controllers is illustrated on an optimal control problem of Lagrange type which consists in maximizing the production of species over a given time period w.r.t. the dilution rate chosen as control variable.

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On the steady state optimization of the biogas production in a two-stage anaerobic digestion model

Cited by 19 publications

References 17 publications

Analysis of an Optimal Control Problem Related to the Anaerobic Digestion Process

Analysis of an Optimal Control Problem Related to the Anaerobic Digestion Process

A minimum time control problem for aerobic degradation processes in biocell composting plants

Stabilization of the chemostat system with mutations and application to microbial production

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