A.M. Rulev1

1 St. Petersburg State University of Aerospace Instrumentation (St. Petersburg, Russia)

1 andreyrul84@gmail.com

To solve the problem of synthesizing nonlinear automatic control systems (ACS) using the generalized Galerkin method, it is necessary to approximate the characteristics of the nonlinear elements included in the system. The accuracy of solving the synthesis problem depends on the approximation method used, which leads to the problem of choosing a specific approximation method for each case under consideration. Aim of article to select a method for approximating a nonlinear characteristic of the «dead zone» type, which is included in the mathematical model of a DC electric drive. Various ways of approximating a nonlinear static characteristic are considered using the example of a mathematical description of a DC motor, which includes a non-linearity of the «dead zone» type. It is established that, in relation to the object under consideration, approximation by irrational functions allows achieving a higher quality of approximation compared to other methods under consideration.

The results obtained will improve the accuracy of solving the problem of synthesizing nonlinear ACS using the generalized Galerkin method in relation to a certain class of nonlinear characteristics (in particular, for characteristics such as «dead zone»), which in turn will expand the engineer's toolkit in the field of ACS development.

Rulev A.M. Selection of a method for approximating the nonlinear characteristics of an electric drive with a DC motor. Information-measuring and Control Systems. 2025. V. 23. № 4. P. 19−27. DOI: https://doi.org/10.18127/j20700814-202504-03 (in Russian)

1. Shishlakov V.F. Sintez nelineinykh SAU s razlichnymi vidami modulyatsii. SPb.: GUAP. 1999. (in Russian)
2. Shishlakov V.F., Shishlakov D.V. Parametricheskii sintez mnogosvyaznykh sistem avtomaticheskogo upravleniya obobshchennym metodov Galerkina. Informatsionno-upravlyayushchie sistemy. 2006. № 3. S. 51−62. (in Russian)
3. Feldbaum A.A. Vvedenie v teoriyu nelineinykh tsepei. M.: Energoizdat. 1948. 342 s. (in Russian)
4. DC-Micromotors Series M223U. GS. URL: https://www.faulhaber.com/en/products/series/2233s/ (10.04.2025).
5. Nikitin A.V., Shishlakov V.F. Parametricheskii sintez nelineinykh sistem avtomaticheskogo upravleniya. Pod red. V.F. Shishlakova. SPb.: GUAP. 2003. 358 s. (in Russian)
6. Shishlakov V.F., Reshetnikova N.V., Vataeva E.Yu., Shishlakov D.V. Polinomialnaya approksimatsiya nelineinykh zvenev pri reshenii zadachi sinteza sistem avtomaticheskogo upravleniya. Naukoemkie tekhnologii. 2021. T. 22. № 8. S. 69−74.
7. Shishlakov V.F., Shishlakov F.V., Timofeev S.S. Sintez SAU pri razlichnykh vidakh approksimatsii nelineinykh kharakteristik: teoriya i praktika. Pod red. V.F. Shishlakova. SPb.: GUAP. 2017. 151 s. (in Russian)
8. Rulev A.M., Brunov M.S., Krivolpachuk I.G., Shishlakov V.F. Ispolzovanie irratsionalnykh funktsii dlya approksimatsii tipovykh staticheskikh nelineinostei sistem avtomaticheskogo upravleniya. Sb. dokl. "Zavalishinskie chteniya – 25". SPb.: GUAP. 2025. S. 191−197. (in Russian)
9. Shishlakov V.F., Anisimova E.V., Shishlakov A.V., Shishlakov D.V. Sintez parametrov zakona upravleniya dlya nelineinykh SAU pri razlichnykh vidakh approksimatsii kharakteristik. Izvestiya VUZov. Priborostroenie. 2015. T. 58. № 9. S. 701−706. (in Russian)