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Features of the backstepping method for control of nonlinear objects

Field of Science:Computer ScienceEngineering
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O_TJ.2025.02.3_d38ab09f.pdf

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“TEXTILE JOURNAL OF UZBEKISTAN” Scientific-technical journal

“TEXTILE JOURNAL OF UZBEKISTAN” Scientific-technical journal

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The paper presents a backstepping control method, which is a recursive procedure using the Lyapunov function and a systems approach to design for special forms of nonlinear systems. The proposed multifunctional control method is implemented based on the Lyapunov function theory. A control algorithm is developed with the entire system divided into n cascade subsystems. The results are obtained from the state of the first subsystem, which acts as a control variable for the next subsystem. A virtual control law is calculated that ensures the desired behavior of the first subsystem. Based on the developed algorithm, the calculation is performed sequentially until the last subsystem is reached. A Lyapunov function is developed for the entire system. The MATLAB software package is used as a tool for modeling the proposed method. Numerical examples and computer simulation results illustrate the advantages of the backstepping method for solving problems of synthesizing control laws for a two-dimensional class of nonlinear plants. A standard backstepping control scheme is presented, which shows greater flexibility than the feedback linearization approach, since the backstepping scheme does not require the final I/O dynamics to be linear.

AUTHORS

Д.Хушназарова

"ISLOM KARIMOV NOMIDAGI TOSHKENT DAVLAT TEXNIKA UNIVERSITETI" DAVLAT MUASSASASI

Tags

# asymptotic stability# backstepping# nonlinear system# virtual controller# Lyapunov function

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References

Sundarapandian Vaidyanathan and Ahmad Taher Azar. Backstepping Control of Nonlinear Dynamical Systems. https://doi.org/10.1016/B978-0-12-817582-8.00008-8. Copyright © 2021.

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Siddikov I.H., Khalmatov D.A., Khushnazarova D.R., Khujanazarov U.O. Neural network control of a nonlinear dynamic plant with a predictive model // International Journal of Electrical and Computer Engineering (IJECE) Vol. 14, No. 5, October 2024, pp. 5131~5138 ISSN: 2088-8708, doi: 10.11591/ijece.v14i5.pp5131-5138.

Siddikov I.H., Khalmatov D.A., Khushnazarova D.R., Moydunov T.T., Sarimsakov A.A. Sintez sinergeticheskogo zakonov upravleniya nelineynix dinamicheskix obyektov // Izvestiya OshtU, 2023 № 2, chast 2. Kirgiziy. Str. 37-45. https://elibrary.ru/item.asp?id=54753553.

Siddikov I.H., Khalmatov D.A., Khushnazarova D.R. Modelirovaniye sistemi upravleniya skorosti dvigatelya metodom beksteppinga // О‘zbekiston tо‘qimachilik jurnali, 2023 yil, 2 – son, 37-43 betlar.

Khalmatov D.A., Khushnazarova D.R. Algoritm sinteza upravleniya odnomernix nelineynix obyektov // «Aktualniye zadachi matematicheskoy modelirovaniya i informatsionnix texnologiy» mejdunarodnaya nauchno – prakticheskaya konferensiya, Nukus, 2-3 may, 2023 g., 328-330 str.

Khalmatov D.A., Khushnazarova D.R. Adaptivniy bekstepping konstruirovaniya regulyatorov sistem. II-Mejdunarodnaya nauchnaya konferensiya «Nauchniye osnovi ispolzovaniya informatsionnix texnologiy novogo urovnya i sovremenniye problemi avtomatizatsii» 19-20 may, SBUMIPTK, Tashkent 2023 g., 446-451 str.

Upravleniya dvigatelem postoyannogo toka s pomoshyu metoda adaptivnogo beksteppinga po sostoyaniy. “Texnik jihatdan tartibga solish, metrologiya va standartlashtirishning ishlab chiqarishdagi o‘rni va vazifalari” respublika ilmiy-amaliy anjumani, FarPI, 2024 yil 17-18 may, 413-418 betlar.