Parametric synthesis of a low-power potentiometric tracking system

Аuthors

Vataeva E. Y.

Saint Petersburg State University of Aerospace Instrumentation, 67, Bolshaya Morskaya str., Saint Petersburg, 190000, Russia

e-mail: lizon94-06@mail.ru

Abstract

Currently, the most rapidly developing areas of research in the theory of automatic control are nonlinear and stochastic analyses. This interest is justified by the fact that most physical processes in nature and systems in the real world are nonlinear and are also subject to random disturbances, i.e. stochastic. In modern automatic control theory there are a large number of methods and studies devoted to the synthesis of nonlinear automatic control systems, but no unified approach has been developed that would allow the synthesis of nonlinear automatic control systems of any complexity. Also, difficulties in solving the problem of synthesizing nonlinear automatic control systems also arise when constructing an adequate mathematical model, since this issue is related to the idealization of the properties of both the elements of the control system and the automatic control system as a whole. It is known that when constructing a mathematical model, all the basic and most essential features and properties of the synthesized ACS must be preserved; in the presence of nonlinear elements in the ACS, this situation is associated with the choice of the correct choice of approximation [1-10]. As is known, there are various types of approximations of the characteristics of nonlinear elements, for example, analytical, power, piecewise linear, approximation by irrational functions. However, for accurate implementation of a nonlinear characteristic with piecewise linear approximation, it is necessary to increase the number of piecewise linear sections, which leads to complication and an increase in the synthesis time of such a system. With analytical approximation, it is quite difficult to instantly obtain the correct analytical expression. In this work, it is proposed to use polynomial approximation. As a mathematical apparatus it is proposed to use the generalized Galerkin method.

Keywords:

tracking system, nonlinear systems, polynomial approximation, impulse systems, generalized Galerkin method

References

1. Wang J., Aranovskiy S.V., Bobtsov A.A., Pyrkin A.A., Kolyubin S.A. A Method to Provide Conditions for Sustained Excitation, Automation and Remote Control, 2018, vol. 79, no. 2, pp. 258-264. DOI: 10.1134/S0005117918020054

2. Pyrkin A., Bobtsov A., Kolyubin S., Faronov M. Output Controller for Uncertain Nonlinear Systems with Structural, Parametric, and Signal Disturbances, IEEE Multi-Conference on Systems and Control, 2012. DOI: 10.1109/CCA.2012.6402352

3. Bernal Miguel, Sala Antonio, Lendek Zsofia, Guerra Thierry-Marie. Analysis and Synthesis of Nonlinear Control Systems: A Convex Optimisation Approach. 2022. DOI: 10.1007/978-3-030-90773-0

4. Pyrkin A., Bobtsov A., Kolyubin S., Vedyakov A., Borisov O., Gromov V. Stabilization of Nonlinear System with Input Delay and Biased Sinusoidal Disturbance, IFAC Proceedings Volumes (IFAC-PapersOnline), 2014, vol. 47, no. 3, pp. 12104-12109. DOI: 10.3182/20140824-6-ZA-1003.00602

5. Lendek Zs., Guerra T., Lauber J. Controller design for TS models using delayed nonquadratic Lyapunov functions, IEEE Transactions on Cybernetics, 2015, vol. 45 (3), pp. 453–464. DOI: 10.1109/TCYB.2014.2327657

6. Vladimir Sinyakov, Antoine Girard. Controller Synthesis for Nonlinear Systemswith Reachability Specifications Using Monotonicity, IEEE Conferenceon Decisionand Control, 2019, Nice, France. DOI: 10.1109/CDC40024.2019.9029740

7. Shashihin V.N. Synthesis of Control for Nonlinear Systems, Synthesis of Control for Nonlinear Systems, 2019, vol. 53, pp. 97–106. DOI: 10.3103/s0146411619020068

8. Yang Z., Zhang L., Zeng X., Tang X., Peng C., Zeng Z. Hybrid Controller Synthesis for Nonlinear Systems Subject to Reach-Avoid Constraints. In: Enea, C., Lal, A. (eds) Computer Aided Verification. CAV 2023. Lecture Notes in Computer Science, vol. 13964. Springer, Cham. DOI: 10.1007/978-3-031-37706-8_16

9. Pyrkin A.A., Kolyubin S.A., Bobtsov A.A. Simple output controller for nonlinear systems with multisinusoidal disturbance, 21st Mediterranean Conference on Control and Automation, MED 2013, Conference Proceedings, 2013, pp. 1087-1091. DOI: 10.1109/MED.2013.6608856

10. Wang L., Ortega R., Bobtsov A. Observability is sufficient for the design of globally exponentially stable state observers for state-affine nonlinear systems, Automatica, 2023, vol. 149, pp. 11083.

11. Shakir Saat, Sing Kiong Nguang, Alireza Nasiri. Analysis and Synthesis of Polynomial Discrete-Time Systems, Butterworth-Heinemann, 2017. DOI: 10.1016/B978-0-08-101901-6.00001-3

12. Mel'nikov D.V., Shirokova Z.G. Nauka, tekhnika i obrazovanie, 2016, № 3 (7), pp. 36-44.

13. Hassan K. Khalil. Nonlinear Systems, USA, 2013, 560 p.

14. Dybok V.V., Khodunkov V.P., Baskakov V.A. Tekhniko-tekhnologicheskie problemy servisa, 2014, no. 1 (27), pp. 53-56.

15. Ibragimov D.N. Trudy MAI, 2015, no. 87. URL: https://trudymai.ru/eng/published.php?ID=69797

16. Uryupin I.V. Trudy MAI, 2018, no. 100. URL: https://trudymai.ru/eng/published.php?ID=93440

17. Khrustalev M.M., Rumyantsev D.S., Tsar'kov D.S. Trudy MAI, 2013, no. 66. URL: https://trudymai.ru/eng/published.php?ID=40831

18. Podaruev V.Yu. Trudy MAI, 2017, no. 95. URL: https://trudymai.ru/eng/published.php?ID=84610

19. Akopov V.S., Polyakova T.G., Timofeev S.S. Issledovanie i sintez potentsiometricheskoi malomoshchnoi sledyashchei sistemy (Research and synthesis of a potentiometric low-power tracking system), Saint Petersburg, Izd-vo GUAP, 2021, 59 p.

20. Akopov V.S., Polyakova T.G., Timofeev S.S. XIV mezhdunarodnaya konferentsiya po elektromekhanike i robototekhnike “Zavalishinskie chteniya-2019”: sbornik trudov. Saint Petersburg, GUAP, 2019, pp. 11-15.

21. Nikitin A.V., Shishlakov V.F. Parametricheskii sintez nelineinykh sistem avtomaticheskogo upravleniya: monografiya (Parametric synthesis of nonlinear automatic control systems), Saint Petersburg, GUAP, 2003, 358 p.

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