UC San Diego

The dissertation presents results on control and state estimation for a physics-based ``Stefan" model of phase change. Design procedures, theoretical analysis, applications to industrial processes, and experimental validation are addressed. The Stefan model describes a time-evolution of a material's temperature profile during melting/solidification phenomena along with the dynamics of the liquid-solid interface position. The mathematical description comprises a parabolic Partial Differential Equation (PDE), defined on a time-varying spatial domain, whose boundary position dynamics are governed by an Ordinary Differential Equation (ODE) driven by the PDE's state. None of the existing systematic and theoretical control are applicable to this problem due to the system's geometric nonlinearity as well as the infinite dimensionality. We design a boundary heat control to promote the melting so that the liquid-solid interface position is driven to a desired setpoint position. Our design is an extension of the ``PDE backstepping" method to the Stefan system. The closed-loop stability is proven by Lyapunov analysis. The constraints of the temperature state and the heat input are guaranteed by virtue of the maximum principle. Analogous results for the state estimation are also developed to estimate the entire temperature profile from available measurements of the surface temperature and the liquid-solid interface position.

The latter half of the dissertation is devoted to the application of the designed method to several practical problems. First, we introduce a Stefan model of ``sea ice", which has been studied intensively due to the recent rapid melting of sea ice. We verify the desired robust performance of the designed estimator in a numerical simulation, which incorporates further complexity in the model and uncertainties. Second, we focus on ``lithium-ion batteries", which have become ubiquitous in electronic devices, such as laptops and smartphones, and in electric vehicles. The model is described by a Stefan system of the lithium-ion concentration due to a solid-solid phase change in the electrodes during the charging and discharging cycles. Our estimator achieves accurate State-of-Charge estimation in simulation. Third, we apply the designed control method to ``polymer 3D-printing" via screw extrusion for the sake of stabilizing the filament production under a fast printing, by extending the design to deal with the convection and heat loss. Fourth, we focus on ``metal 3D-printing" which has a high impact on products and supply chains in industries. The proposed control method is applied for generating the desired shape of the melt pool, which shows the robust performance with respect to a radiation effect and sensor noise in numerical study. Finally, we conduct experiments of melting paraffin wax as an energy storage material, which shows the successful performance of our PDE-based control algorithm.