Energy Storage in Paraffin: A PDE Backstepping Experiment

This article proposes a novel control algorithm of a thermal phase-change process and shows its experimental verification using paraffin as a phase-change material (PCM). The core problem is to design a boundary feedback control for the “Stefan system” that describes the time evolution of the temperature profile in the liquid phase, which is associated with the time evolution of a position of liquid–solid phase interface, for the sake of stabilizing the interface position at a chosen set point. First, we design the continuous-time full-state feedback control law by means of the PDE backstepping method, which, in the absence of a demand for accelerated convergence, can also be arrived at by the energy-shaping method, and rigorously prove the stability of the closed-loop system under sufficiently small heat loss. Next, the control law is refined via observer-based output feedback under sampled-data measurements of the surface temperature and the phase interface position so that the control algorithm is practically implementable. Then, we conducted an experiment under a constant input to calibrate unknown parameters involved with the heat loss. Finally, the proposed model-based boundary feedback control algorithm is implemented in the experiment of melting paraffin. The experiment was successful: the convergence of the phase interface to the set point was achieved.