| Transport-reaction processes are a class of distributed parameter systems that are characterized by the coupling of chemical reaction with significant convection, diffusion and dispersion phenomena distributed in space and time. Such processes are essential in making many high-value industrial products. Stability analysis and control design of these infinite dimensional systems is typically based on methods developed for finite dimensional systems, which rely on discretization of the PDEs to ODE systems or working with an ODE representative of the PDEs, i.e. Inertial Form. Some shortcomings of these methods prevent them form adequately addressing the system's observability and controllability properties and the analysis relies on the algebraic properties of the resulting equations.; The cornerstone of this work focuses on linking the passivity theory of nonlinear control with inherent dissipative properties of the physical systems to derive stability conditions as well as stabilizing control structures.; Passivity is part of a broader and a general theory of dissipativity. Dissipative systems loose or dissipate energy, and, if a storage function describing the system is a Liapunov-like ‘energy’ function, such systems are guaranteed to be stable at an operating point. Passivity theory exploits the input-output relationship based on energy-related considerations to analyze stability properties, and, if possible, render them passive via passive control structures. A transport-reaction system can be stabilized via passive control at a particular set-point given that the input output pair is passive. The theoretical derivations delineate conditions for passive input output pairs. Uncontrolled dynamics are guaranteed to converge due to the inherent dissipation properties of these systems.; The theoretical results are validated on an industrial case study, the silicon production process, an example of a transport-reaction system. A two-zone process model of the silicon smelting-furnace is developed. The top section is descried by moving bed equations with countercurrent liquid/gas and solid flow equations, while the bottom section is approximated with stirred tank reactor equations.; Process analysis via model simulations reveal that the process exhibits a non-minimum phase behavior, input multiplicity and an inverse response behavior for a traditional set of input output variables, namely, the carbon feed ratio and the silicon production rate. Adapting the passivity-based control approach to select a passive input output pairs, namely, C and SiO2 feed fluxes, and, the reactor total carbon mass and total mass holdups (inventories), render the process insensitive to these behaviors. Via passive controllers, the process can reach a stable operation for a feasible set-point. |
