Thermodynamic approach for the control of a nonlinear system of infinite dimension: application to tubular reactors

Etudiant : Weijun Zhou

Ecole doctorale :Array

Directeur ou Directrice : F. Couenne, B. Hamroun

Financement :allocation ministère

Date de la soutenance :15/09/2014

This thesis will deal on Port Hamiltonian modeling, reduction and control of infinite dimensional thermodynamical system. In first time, the work will consist on the Port-Hamiltonian formulation of a benchmark tubular reactor. Then the stabilization will be proposed by using the passivity based approach and Thermodynamics issued Lyapunov functions.


  • Boussad Hamroun
  • Francoise Couenne
  • Denis Dochain
  • Bernhard Maschke
  • Laurent Lefevre
  • Didier Georges
  • Yann Le Gorrec

The main objective of this thesis consists to investigate the problem of modelling and control of a nonlinear parameter distributed thermodynamic system: the tubular reactor. We address the control problem of this nonlinear system relying on the
thermodynamic properties of the process. This approach requires using the classical extensive variables as the state variables. We use the thermodynamic availability as well as the reduced thermodynamic availability (this function is formed from some terms of the thermodynamic availability) as Lyapunov functions in order to asymptotically stabilize the tubular reactor around a steady profile. The distributed temperature of the jacket is the control variable. Some simulations illustrate these results as well as the efficiency of the control in presence of perturbations.

Next we study the Port Hamiltonian representation of irreversible infinite dimensional systems. We propose a Stokes-Dirac structure of a reaction- diffusion system by means of the extension of the vectors of the flux and effort variables. We illustrate this approach on the example of the reaction diffusion system. For this latter we use the internal energy as well as the opposite of the entropy to obtain Stokes-Dirac structures. We propose also a pseudo-Hamiltonian representation for the two Hamiltonians. Finally we tackle the boundary control problem. The objective is to study the existence of solutions associated to a linearized model of the tubular reactor controlled to the boundary.

Keywords :
Infinite-dimensional systems, Tubular reactors, Irreversible Thermodynamics, Lyapunov function, Distributed control, Port Hamiltonian system