Reduced model of boundary value dynamics of 1D diffusion - application to heat conduction

Boundary value of a quantity, e.g. the surface temperature of a slab, has to be modeled in some cases, because it affects a process of interest. However, the boundary value is also affected back by the process on one side, and by the internal diffusion on the other side. Therefore, in this paper, the whole diffusion model has to be taken into account to handle the dynamics. Unfortunately, the diffusion model is quite computationally expensive, which is an issue especially for model based control. Model order reduction, namely balanced truncation, has been applied to the time-continuous system of numerical representation of diffusion to keep just the necessary essence. This numerical representation has been modified in such a way to derive a state-space system with certain beneficial properties, such as system's symmetry, which allow a simpler procedure of the reduction. The one-dimensional diffusion has been manifested by heat conduction, where the internal temperature is affected just through the one (of two) boundary point by general time-pvarying heat flux. The concepts have been introduced in a practical way and followed by application examples.