139. BOUNDARY CONTROL AND ESTIMATION OF A SOLID-LIQUID INTERFACE IN A MELTING MATERIAL
Name: Shumon Koga
Grad Year: 2019
Solid-liquid phase transition is a phenomenon which appears in various kinds of science and engineering process. Representative applications include sea-ice melting and freezing, continuous casting of steel, crystal or dissolution-growth processes, freeze-drying of foodstuffs, and thermal energy storage system. The description of the physical problem is that, as a material composed of liquid and solid (e.g. water and ice) is melting or freezing, the interface between the two phase is moving due to its phase transition. Such a problem is formulated by the one-phase Stefan problem, which refers to a thermal diffusion PDE defined on a time varying spatial domain whose dynamics is described by an ODE actuated by the heat flux at the interface. The control objective is to drive the interface to a desired setpoint by manipulating heat flux at one boundary. The full-state boundary feedback result was obtained by introducing a backsteppping transformation for moving boundary. The state feedback controller ensures the exponential stability of the moving intereface and H1-norm of temperature profile with keeping physical constraints under an initial condition. In the case where only the position of the moving interface is measured without any information about its temperature profile, the output boundary feedback result was obtained by constructing an estimator of both of temperature profile and the interface position and introducing a backstepping transformation for moving boundary as in the full-state case. The output feedback controller ensures the exponential stability of the moving interface, H1-norm of the temperature profile, and their estimation errors with keeping physical constraints under some initial conditions. As a future work, an estimator design with a measurement of a temperature at one boundary is investigated, aiming an application to the estimation of the dynamics of ice-sheet in Antarctica through the measurement of sea temperature on its surface under melting or freezing.
Industry Application Area(s)
Control Systems | Energy/Clean technology | Materials