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20190619_BV_Manuscrit_final.pdf
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Authors
Supervisors
Denis, Dochain
 ;
Laurent, Lefèvre
Abstract
Dynamical systems described by partial differential equations - more precisely by conservation laws interconnected through nonlinear transport coefficients and nonlinear couplings - are defined as multi-physics systems. Structured formulations of dynamical systems aim at distinguishing conservative and dissipative phenomena in the state equations governing the dynamics of the considered system. The thesis is devoted to the development of structured-based techniques for modelling and analysis of this class of multi-physics systems. Two applications are identified: the control of burning plasma profiles in Tokamaks; and, the rejection of thermo-acoustic instabilities in a Rijke's tube. For the first application, we consider the control model associated to the interconnection of electromagnetic, heat, and mass transport equations. The second application illustrates an unstable thermo-acoustic phenomenon arising experimentally under specific geometry and heating conditions within a vertical tube. The control model associated to this system is two wave equations interconnected with a finite-dimensional system. The port-Hamiltonian and GENERIC formalisms are considered and compared throughout the thesis. Key contributions include structured modelling from first-principle equations, structure-preserving geometric reduction and discretization, as well as passivity and stability analysis for multi-physics systems based on total irreversible entropy production.
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Vincent, B. (2019). Modelling and analysis of multi–physics control systems. https://hdl.handle.net/2078.5/63256