Oksana I. The application of balanced approximation by Chebyshev rational splines for modeling of physical quantities sensors

The theoretical bases for finding the balanced approximation of functions by Chebyshev discontinuous splines with links as the rational expressions are developed. The general theory for finding the parameters of these balanced approximations with given error or given number of links and also the algorithm of choice the optimal rational approximating expression with fixed number of parameters on the each spline links are offered. It provides realization of effective methods of approximating representation of transformation functions of sensor of physical quantities. On the basis of developed approximation methods the procedure of optimization of compensational coupling parameters for linearization of characteristics of primary converters of digital measuring devices with nonlinear transformation functions is developed, that provides increase of accuracy of temperature measuring devices. The simplified methods for approximating representation of the graduated characteristics of sensor of physical quantities, which transformation functions are modeled by elementary and special functions, namely exponential, trigonometrical, hyperbolic functions are developed. The packages based on the proposed theory have been realized in computer algebra system Maple. Key words: simulation, transformation function, sensor of physical quantities, the best Chebyshev approximation, balanced approximation, Chebyshev rational spline.