Method first approximation stability analysis of electrical control systems

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription or Fee Access

Abstract

This article is devoted to the research and analysis of automated control systems and control of electrical equipment of technological processes of agricultural production. The first approximation method is used for evaluation the stability of the operation of electric drive control systems. Methods for assessing the stability zone of electric drive control systems, determining critical gain coefficients, and optimizing the parameters of electrical circuits included systems, in order to increase the efficiency and reliability of production chains are proposed. To solve the problem of controlling the electric drives of automated systems for harvesting and sorting agricultural crops, the method was tested, a critical gain value of 3.2 was obtained, which allows us to talk about optimizing such systems in terms of speed and load.

Full Text

Restricted Access

About the authors

Viktor S. Artemyev

Plekhanov Russian University of Economics

Author for correspondence.
Email: electricequipment@yandex.ru
ORCID iD: 0000-0002-0860-6328
SPIN-code: 8912-5825
Scopus Author ID: 58002154300

senior lecturer, Department of Computer Science

Russian Federation, Moscow

Nataliуa V. Mokrova

National Research Technological University “MISiS”

Email: natali_vm@mail.ru
ORCID iD: 0000-0002-8444-2935
SPIN-code: 5157-9790
Scopus Author ID: 41762121300

Dr. Sci. (Eng.), professor, Department of Info-communication Technologies

Russian Federation, Moscow

References

  1. Chan M., Ricketts D., Lerner S., Malecha G. Formal verification of stability properties of cyber-physical systems. 2016. URL veridrone.ucsd.edu/papers/coqpl2016.pdf
  2. Osinenko P., Devadze G., Streif S. Constructive analysis of control system stability. IFAC-PapersOnLine, 2017. Vol. 50. Issue 1. Pp. 7467–7474. ISSN: 2405-8963. doi: 10.1016/j.ifacol.2017.08.1520.
  3. Andonov P., Savchenko A., Rumschinski P. et al. Controller verification and parametrization subject to quantitative and qualitative requirements. In: 9th IFAC Symp. Advanced Control Chemical Processes (ADCHEM). 2015. Pp. 1174–1179.
  4. Leonov G.A. On stability in the first approximation. Journal of Applied Mathematics and Mechanics. 1998. Vol. 62. Issue 4. Pp. 511–517. ISSN: 0021-8928. doi: 10.1016/S0021-8928(98)00067-7.
  5. Magnússon S., Fischione C., Na Li. Voltage control using limited communication. This work was supported by the VR Chromos Project and NSF 1608509 and NSF CAREER 1553407. IFAC-PapersOnLine. 2017. Vol. 50. Issue 1. Pp. 1–6. ISSN: 2405-8963. doi: 10.1016/j.ifacol.2017.08.001.
  6. Arocas-Pérez J., Griño R. A local stability condition for dc grids with constant power loads. This work was partially supported by the Government of Spain through the Ministerio de Economía y Competitividad under Project DPI2013-41224-P and by the Generalitat de Catalunya under Project 2014 SGR 267. IFAC-PapersOnLine. 2017. Vol. 50. Issue 1. Pp. 7–12. ISSN: 2405-8963. doi: 10.1016/j.ifacol.2017.08.002.
  7. Hastir A., Muolo R. A generalized Routh–Hurwitz criterion for the stability analysis of polynomials with complex coefficients: Application to the PI-control of vibrating structures. IFAC Journal of Systems and Control. 2023. Vol. 26. P. 100235. ISSN: 2468-6018. doi: 10.1016/j.ifacsc.2023.100235.
  8. Ming-Jian Ding, Bao-Xuan Zhu. Some results related to Hurwitz stability of combinatorial polynomials. Advances in Applied Mathematics. 2024. Vol. 152. P. 102591. ISSN: 0196-8858. doi: 10.1016/j.aam.2023.102591.
  9. Bourafa S., Abdelouahab M-S., Moussaoui A. On some extended Routh–Hurwitz conditions for fractional-order autonomous systems of order α ϵ (0, 2) and their applications to some population dynamic models. Chaos, Solitons & Fractals. 2020. Vol. 133. P. 109623. ISSN: 0960-0779. doi: 10.1016/j.chaos.2020.109623.
  10. Araiza-Illan D., Eder K., Richards A. Verification of control systems implemented in simulink with assertion checks and theorem proving: A case study. In: Proc. 2015 European Control Conf. (ECC). 2015. Pp. 2670–2675.
  11. Barkovsky Y., Tyaglov M. Hurwitz rational functions. Linear Algebra and its Applications. 2011. Vol. 435. Issue 8. Pp. 1845–1856. ISSN: 0024-3795. doi: 10.1016/j.laa.2011.03.062.
  12. Soliman M., Ali M.N. Parameterization of robust multi-objective PID-based automatic voltage regulators: Generalized Hurwitz approach. International Journal of Electrical Power & Energy Systems. 2021. Vol. 133. Pp. 107216. ISSN: 0142-0615. doi: 10.1016/j.ijepes.2021.107216.
  13. Xuzhou Zhan, Dyachenko A. On generalization of classical Hurwitz stability criteria for matrix polynomials. Journal of Computational and Applied Mathematics. 2021. Vol. 383. P. 113113. ISSN: 0377-0427. doi: 10.1016/j.cam.2020.113113.
  14. Dyachenko A. Hurwitz matrices of doubly infinite series. Linear Algebra and its Applications. 2017. Vol. 530. Pp. 266–287. ISSN: 0024-3795. doi: 10.1016/j.laa.2017.05.012.
  15. Artemyev V.S., Mokrova N.V. Automated methods of analysis and forecasting of auto-vibrations in agricultural systems. Waste and Resources. 2024. Vol. 11. No. 1. doi: 10.15862/19INOR124.

Supplementary files

Supplementary Files
Action
1. JATS XML
2. Fig. 1. Graph of dependence

Download (198KB)