APPROXIMATION OF THE (1 – W(р)) FUNCTION USING A REAL DIFFERENTIATING TRANSFER FUNCTION AND A SECOND-ORDER APERIODIC TRANSFER FUNCTION

UDC 681.51

 

Karpovich Dzmitry Semenovich – PhD (Engineering), Associate Professor, Head of the Department of Automation of Production Processes and Electrical Engineering. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: d.karpovich@belstu.by

Fokin Timophej Pavlovich – teacher trainee, the Department of Automation of Production Processes and Electrical Engineering. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: fokin@belstu.by

 

DOI: https://doi.org/ 10.52065/2520-6141-2024-284-8.

Key words: approximation, transfer function, approximation error, second-order delayed transfer function with delay.

For citation: Karpovich D. S., Fokin T. P. Approximation of the (1 – W(р)) function using a real differentiating transfer function and a second-order aperiodic transfer function. Proceedings of BSTU, issue. 3, Physics and Mathematics. Informatics, 2024, no. 2 (284), pp. 53–57 (In Russian). DOI: 10.52065/2520-6141-2024-284-8.

Abstract

This paper considers the representation of the function (1 – W(р)) with delay in the form of a real differentiating link and serial connection with the second-order link. The article shows the influence of changing the value of the delay and time constant of the object on the accuracy of approximation. The peculiarity of the implementation of this method is a large delay of the function W(p), which makes the control and prediction of the behaviour of such functions a difficult task. The feasibility and sufficient accuracy of this approximation are analysed. The implementation features required to match the original and approximated functions are presented. Functions are created to analyse the influence of transfer function parameters on the approximation error. A model comparing the behaviour of the function (1 – W(р)) with its representation in the form of a real differentiating transfer function and a second-order transfer function at different parameters of the original function and the dependence of the approximation error on the delay and time constant of this function is also given. The optimal parameters of the original function, at which the approximation most accurately repeats the behaviour of the original function, are determined as the equation of dependence between the time constant and delay of the function. The plane of propagation of the approximation error with respect to the parameters of the original function is constructed.

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16.05.2024