Flatness based open loop control for a parabolic partial differential equation with a moving boundary

The present paper deals with the flatness based open loop boundary control of a solidification process. A model to describe solidification is well-known as the Stefan problem. Depending on the mathematical model of the phase between solidus and liquidus one can differentiate between the one phase and the two phases Stefan problem. The paper presents a method for both cases to show that this moving boundary value problem described by a parabolic partial differential equation is flat and the boundary control can be easily calculated from the flat output. The results achieved using a Taylor series expansion will be compared with numerical solutions. The solution is facilitated by coordinate transformations.