Development of simplified mathematical model of glass melting furnace
DOI:
https://doi.org/10.15587/1729-4061.2015.40563Keywords:
glass melting furnace, Fourier method, orthogonal decomposition, system identification, state spaceAbstract
A simplified mathematical model of the glass melting furnace, constructed based on the method of separation of variables (Fourier method) was proposed in the paper. This method allows to simplify the computational procedures and evaluate the approximation error. To construct a simplified model, basis vectors and Fourier coefficients were determined. The optimal basis vectors are determined from the minimization condition of - norm of the corresponding error vector from all orthonormal bases of the n-th order. norm of the error vector is minimized by maximizing the limited vector of Fourier coefficients. Determination of Fourier coefficients was performed by system identification. In order to study the quality of a simplified mathematical model of glass melting furnace, the simulation was carried out. As input variables, fuel feeds to 3 burners were used. The values of input variables were formed as a sequence of pseudo-random binary signals. Analysis of the results indicates a high enough accuracy of the simplified mathematical model. The largest model errors occur at relatively high rates of temperature change.
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Copyright (c) 2015 Анатолій Іванович Жученко, Виталій Степанович Цапар
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