Boundary Control of Coupled Nonlinear - Villeurbanne, France - LAGEPP

Description

Réf
-
ABG-112443

• Sujet de Thèse 23/03/2023
• Contrat doctoral
• LAGEPP
• Lieu de travail
• VILLEURBANNE
• Auvergne-RhôneAlpes
• France
• Intitulé du sujet
• Champs scientifiques
• Mathématiques
• Numérique

• Mots clés

• Boundary control, Stabilisation, EDO-EDP model, 2x2 inhomogeneous hyperbolic PDEs, Numerical schemes for simulation, Bioreactor coupled to a Clarifier, wastewater treatment
  Description du sujet:

Scientific field and context:

The heart of a wastewater treatment system is composed of a biological aeration tank in which adapted bacteria will degrade the different types of pollutants (nitrites, nitrates, carbons, ammonia,...) coupled with a clarifier which allows the settling of the biomass (solid particles) contained in the sludge to be pumped back into the biological aeration tank and the discharge of the clarified water into the environment by overflow.

The aim of such a system is to ensure that the amount of pollutants included in the clarified water meets environmental standards regardless of the quality and quantity of wastewater entering the treatment plant.

The biological aeration tank behaves like a perfectly stirred reactor and its operation is described by a system of non-linear EDOs whereas the clarifier is a non-linear hyperbolic non-homogeneous distributed parameter system [7, 8].

The operation of these 2 coupled equipments is described by an EDO-EDP model whose particularity is linked to the non-linear source terms [9].

The action variables are for example the recirculation and sludge extraction flows.

This thesis topic is part of the research activities of the DYCOP (Dynamics, Control and Observation of Processes) team of LAGEPP on the modelling and control of systems described by PDEs.

It is part of the work carried out in the framework of the C-StaRRE 4.

0 project of the AURA region "From Wastewater Collection to Water Resource Recovery Plant:
New digital tools for decision support".

It is also at the heart of the interests of the GDR MACS community, particularly the "EDP control" action coordinated by Swann MARX.

Original contributions expected:

The use of approaches based on Lyapunov functions [1,3,5] will play a key role in the approach.


Research programme and scientific approach divided into three parts:

• To understand the coupled behaviour of the settling tank and the biological aeration tank and their respective dynamic models. The settling tank is a two-phase liquid/solid system whose model is based on mass and momentum balances. The aeration tank model is based on mass balances and a kinetic model of the biological reactions involved [2,7,8,9].
• To carry out a more complete bibliography on the boundary control of this class of systems [2,3,4,5,6] in parallel with the mathematical formulation of the coupled system of interest, if necessary in a linearised form and/or with approximations. Handling of the mathematical tools necessary for the achievement of the thesis [2,3,4,5,6,7,8].
• To propose one or more methods of synthesising the boundary control adapted to this coupled "biological aeration reactor clarifier" system and to complete the numerical schemes already developed [7,8] to simulate the behaviour of the closed loop system under several relevant operating conditions.

Valorisation of the research work:

The research work will be promoted through publications in conferences and journals in the field of Automatic Control and digital sciences.

It will also be presented within competitive clusters such as AXELERA and scientific and technical associations of water professionals such as ASTEE and the MACS research group.

Skills to be developed during the PhD:
The PhD student will have acquired solid skills in non-linear Automatic and in mathematics for infinite dimensional systems.

He will have applied the theorems developed to the closed loop control of the core of a wastewater treatment plant.

He will have learned to situate his work among those of the same field in the international community, to present it English (or in French when appropriate) to different types of audience orally and to write scientific papers in English for conferences and journals.

Professional opportunities after the doctorate:

The skills acquired will enable the doctor to pursue a career in Higher Education as well as in research organisations such as the CNRS and in private companies with activities in Automatic Control or Digital Sciences


References:

[1] G. Bastin, J.M. Coron, 2016, Stability and Boundary Stabilization of 1-D Hyperbolic Systems, Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 88), Birkhauser Verlag AG.

[2] S. Diehl, & Farås, S., 2013, Control of an ideal activated sludge process in wastewater treatment via an ODE-PDE model. Journal of Process Control, 23(3),

[3] F. Di Meglio, F. Bribiesca Argomedo, L. Hu, and M. Krstic, 2018, Stabilization