Identification of a mathematical model of slabs heating in a regular mode

Introduction. In the conditions of increasing requirements for the quality and efficiency of the metal heating process in continuous furnaces, the task of creating and improving the algorithmic support of their control systems, in particular, the feedback loop for the temperature state of the heated billets, is quite relevant. Purpose of the study. To consider the features of solving the problem of parametric identification of the heating model under regular thermal conditions occurring in the soaking zones of continuous furnaces. Materials and methods. The mathematical description of the slab heating process in a regular mode is analyzed. A linearizing transformation of the equation describing the change in time of the surface temperature of the heated billet accessible for instrumental control is applied. This made it possible, including using the least squares method, to find explicit analytical solutions to the identification problem under consideration. Results. Algorithms for identifying external heat exchange models of metal under the condition of the onset of a regular thermal regime are obtained, while cases of symmetrical, one-sided, and asymmetrical heating are considered. It is shown that the accuracy of estimating the desired parameters depends on the error in establishing a regular thermal regime. The influence of systematic and random errors in measuring the surface temperature on the accuracy of determining the heat exchange parameters has been investigated. It has been established that random measurement errors have virtually no noticeable effect on the accuracy of estimating the heat exchange parameters if algorithms obtained on the basis of the point or integral least squares method are used for this. The systematic measurement error is not significant only if its value does not exceed 20 degrees, the error in calculating the metal temperature field using a model adjusted to the real process will not exceed 25 degrees, which is generally acceptable for practice. In this case, the greatest temperature difference across the metal cross-section will be determined with the same error. It has been shown that if accurate data on surface temperatures are used to identify heat exchange parameters, and measurement with an error is allowed for subsequent control of the greatest temperature difference, this error should not exceed 25 degrees. In this case, the error in estimating the entire temperature field of the slab will also not exceed 25 degrees, but the error in determining the largest difference will be only 20 degrees. Conclusion. The results of the work can be used in the development and improvement of algorithmic support for automated process control systems (APCS) of continuous furnaces.