On the evaluation of the observability of the temperature field of slabs during heating in methodological furnaces

The problem of estimating the observability of the temperature field of slabs during their heating in continuous furnaces is considered. Its relevance is due to the fact that only the temperature of the metal surface is available for direct measurement; however, to build high-quality control systems, information about the temperature of internal points is also necessary. It is known that for the solution, including this problem, a model of non-stationary heat transfer tuned to the “real process” is needed, which, according to the physics of phenomena, is, in fact, a model with distributed parameters. To estimate the observability, the spatial discretization of the heat conduction equation describing the internal heat transfer of the metal was carried out. Due to this, the mathematical description is transferred to the class of systems with lumped parameters. The temperature field of the workpiece at some point in time can be unambiguously determined from the measurement data of the surface temperature and the temperature of the working space at some subsequent time interval. Specific algorithms for solving the problem are given, and the influence of surface temperature measurement errors on the accuracy of the estimate is also determined. Thus, it has been shown that continuous temperature control during the heating process from the very beginning is not absolutely necessary in principle in order to be able to determine the temperature field of the slab at some critical time points. The results of the work can be used in the construction of automated control systems for methodical heating furnaces of rolling production.