Abstract |
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Tubular reactors cover a large class of processes in chemical and biochemical engineering. They are typically reactors in which the medium is not homogeneous (like fixed-bed reactors, packed-bed reactors, fluidized-bed
reactors,...) and possibly involve diferent phases (liquid/solid/gas). The dynamics of nonisothermal axial dispersion or plug flow tubular reactors are described by semilinear partial differential equations (PDE's) derived
from mass and energy balances. The main source of nonlinearities in such dynamics is concentrated in the kinetics terms of the
model equations. Like tubular reactors many physical phenomena are modelled by partial differential equations (PDE's). Such systems are called distributed parameter systems. Control problems of these systems can be formulated in
state-space form in a way analogous to those of lumped parameter systems (those described by ordinary differential equations) if one introduces a suitable infinite-dimensional
state-space and suitable operators instead of the usual matrices.
This thesis deals with the synthesis of optimal control laws with a view to regulate the temperature and the reactant concentration
of a nonisothermal plug flow reactor model. Several tools of linear and semilinear infinite-dimensional system theory are extended and/or
developed, and applied to this model. On the one hand, the concept of asymptotic stability is studied for a class of infinite-dimensional
semilinear Banach state- space systems. Asymptotic stability criteria are established, which are based on the concept of strictly m-dissipative operator. This theory is applied to a nonisothermal plug flow reactor.
On the other hand, the concept of optimal Linear-Quadratic (LQ) feedback is studied for class of infinite-dimensional linear systems. This theory
is applied to a linearized plug flow reactor model in order to design an LQ optimal feedback controller. Then the resulting nonlinear closed-loop system performances are analyzed. Finally this control design strategy is extended to a large class of first-order hyperbolic PDE's systems. |