УДОСКОНАЛЕННЯ АЛГОРИТМУ РОЗРАХУНКУ ТЕМПЕРАТУРИ КВАЗІЛІНІЙНОГО РЕЗИСТИВНОГО СЕНСОРА PT100

Abstract

The paper investigates iterative algorithms for solving the equation according to the Kalendar-Van Dusyn formula, which describes the dependence of the electrical resistance of the Pt100 family sensor on temperature. This family of platinum sensors is considered quasi-linear, but for high-precision measurements the nonlinearity of the sensor cannot be neglected, so it is necessary to solve the nonlinear equation of Pt100. At minus temperatures, the equation according to the Kalendar-Van Dusyn formula reaches the fourth power and has no solution with respect to temperature in an analytical form. The analysis of the previously published iterative algorithm for the approximate solution of the equation reveals a desadvantage of this algorithm. The residual error of the solution is not a monotonic function of the argument, because it contains extrema, moreover, the sign of the error changes to the opposite after each extremum. The purpose of this study was to obtain an algorithm that provides the residual error in the form of a monotonic deterministic function of the argument with the minimization of the maximum error value. The possibility to modify the iterative algorithm-prototype in an elementary way by fixing the number of iterations is shown. The residual error of solving the equation according to the modified algorithm has the form of a monotonic deterministic function of the argument. It is assumed that any iterative calculation algorithm can be improved in this way. At the same time, the minimization of the error values of the modified algorithm is achieved by setting the maximum number of iterations compared to the prototype algorithm. To overcome this desadvantage of the modified algorithm, a new algorithm is proposed, in which, in addition to a fixed number of iterations, the property of the smallness of the components of higher degrees is used. The high efficiency of the new algorithm is shown, which reduces the residual error of the solution to a negligible value in just four iterations. It is claimed that the high efficiency of the new algorithm makes further research in the direction of its improvement unnecessary. The article presents a scheme of the new algorithm and a corresponding program on the VBA platform for Excel, which is suitable for direct use in the software of temperature meters based on Pt100 resistance temperature sensors. References 5, figures 4, tables 3.