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

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

A robust asymptotic observer for systems that converge to unobservable states. A batch reactor case study

International audienceIn this paper we propose an observer for a dynam-ical system for which the states on the frontier of its domain are not observable, and all trajectories converge to the frontier. The proposed case study, a bioreactor in batch operating conditions with a single microbial reaction and gas production, is standard and largely encountered in practical situations. We show also how to extend this observer to obtain an observer in higher dimension that is robust with respect to unbiased noise

Dynamical Modelling of a Wastewater Treatment Process of the Metallurgical Industry

In this paper we consider the dynamical modelling and parameter identification of a biological wastewater treatment process from the galvanisation industry used to remove a mixture of organic matter and surface-active agents. In the present study we have considered mainly the measurements of dissolved oxygen and COD (Chemical Oxygen Demand) collected on laboratory and pilot-scale processes. From the identification study, we can conclude that the degradation is characterized by two reactions: one part of the easily biodegradable effluent is degraded with fast kinetics while the remaining part of the effluent is degraded via a slower reaction. This has been modelled by considering two different classes of substrates that indeed correspond to real components of the mixture

Capturing persistence of delayed complex balanced chemical reaction systems via decomposition of semilocking sets

With the increasing complexity of time-delayed systems, the diversification of boundary types of chemical reaction systems poses a challenge for persistence analysis. This paper focuses on delayed complex balanced mass action systems (DeCBMAS) and derives that some boundaries of a DeCBMAS can not contain an $\omega$-limit point of some trajectory with positive initial point by using the method of semilocking set decomposition and the property of the facet, further expanding the range of persistence of delayed complex balanced systems. These findings demonstrate the effectiveness of semilocking set decomposition to address the complex boundaries and offer insights into the persistence analysis of delayed chemical reaction network systems

Convex optimization of bioprocesses

We optimize a general model of bioprocesses, which is nonconvex due to the microbial growth in the biochemical reactors. We formulate a convex relaxation and give conditions guaranteeing its exactness in both the transient and steady state cases. When the growth kinetics are modeled by the Monod function under constant biomass or the Contois function, the relaxation is a second-order cone program, which can be solved efficiently at large scales. We implement the model on a numerical example based on a wastewater treatment system

Accurate control to run and stop chemical reactions via relaxation oscillators

Regulation of multiple reaction modules is quite common in molecular computation and deep learning networks construction through chemical reactions, as is always a headache for that sequential execution of modules goes against the intrinsically parallel nature of chemical reactions. Precisely switching multiple reaction modules both on and off acts as the core role in programming chemical reaction systems. Unlike setting up physical compartments or adding human intervention signals, we adopt the idea of chemical oscillators based on relaxation oscillation, and assign corresponding clock signal components into the modules that need to be regulated. This paper mainly demonstrates the design process of oscillators under the regulation task of three modules, and provides a suitable approach for automatic termination of the modules cycle. We provide the simulation results at the level of ordinary differential equation and ensure that equations can be translated into corresponding chemical reaction networks