Identification of nonlinear models of the components of the "elastic aircraft – flight control system" loop

Аuthors

Liseikin G. V.^*, Safin K. Z.^**

Central Aerohydrodynamic Institute named after N.E. Zhukovsky (TsAGI), Zhukovsky, Moscow region, Russia

*e-mail: gleb.liseykin@tsagi.ru
**e-mail: kamilsafin1997@mail.ru

Abstract

The process of identifying a control system involves creating a model in the time or frequency domain, which is expressed as a set of mathematical rules. This representation can be in the form of a set of objects whose behavior is assumed to be known, or by other means. Based on this mathematical model, a digital twin can be generated that can be used to conduct virtual tests or optimize various parameters of a real object. Currently, an important aspect in the field of automatic control theory is the development of methods for identifying nonlinear control systems. This article discusses the development of such methods in the context of modeling dynamic systems using data collected during testing of contour "elastic aircraft – integrated control system". The main goal is to develop a method for creating a model that would be trained based on data obtained from a finite number of experiments, so that it could accurately describe the behavior of the control system at any given input signal in a given amplitude range. For this purpose, the nonlinear Hammerstein–Wiener model is used in the work. This model has a number of advantages over other approaches, including its ability to take into account the physical parameters of the system in question, ease of implementation and speed of operation compared to neural networks or Volterra models. In addition, the model allows you to obtain a linear approximation, which can be useful under certain circumstances. It should also be noted that it can be applied to systems with multiple input/output channels (MIMO), which expands its capabilities. At the initial stage, the goal was to identify a system created in a dynamic modeling environment based on data collected in a virtual experiment. Various nonlinearities with known parameters were introduced into the oscillatory link, in particular: dead zone, saturation, transmission delay and quantization. As part of the dynamic system simulation, a model has been developed that reproduces the behavior of the above-mentioned system. Based on the NRMSE (normalized root mean square error) indicator, it was determined that the accuracy of the model exceeds 99%. At the next stage of the project, real control objects were identified using methods developed to identify the model from the dynamic systems modeling environment, using data collected during wind tunnel tests. According to the NRMSE assessment, the quality of the model turned out to be more than 90% accurate.

Keywords:

identification, nonlinear systems, Hammerstein-Wiener model, virtual experiment

References

1. Brunton S.L., Kutz J.N. Data-Driven Science and Engineering. Cambridge, Cambridge University Press, 2022, pp. 360-392. DOI: 10.1017/9781009089517
2. Gus'kov A.A, Spirin A.A., Norinskaya I.V. Trudy MAI, 2019, no. 111. URL: https://trudymai.ru/eng/published.php?ID=112813. DOI: 10.34759/trd-2020-111-14
3. Vataeva E.Yu. Trudy MAI, 2023, no. 128. URL: https://trudymai.ru/eng/published.php?ID=171404. DOI: 10.34759/trd-2023-128-16
4. Burenko E.A. Trudy MAI, 2023, no. 132. URL: https://trudymai.ru/eng/published.php?ID=176855
5. Egorchev M.V., Tyumentsev Yu.V. Trudy MAI, 2017, no. 94. URL: https://trudymai.ru/eng/published.php?ID=81171
6. Nelles O. Nonlinear system identification: From classical approaches to neural networks, fuzzy models and Gaussian processes. Cham, Springer, 2021, pp. 1-20. URL: https://doi.org/10.1007/978-3-030-47439-3_1
7. Fadin D.A. Trudy MAI, 2015, no. 80. URL: https://trudymai.ru/eng/published.php?ID=57021
8. Ezrokhi Yu.A., Kalenskii S.M. Trudy MAI, 2022, no. 122. URL: https://trudymai.ru/eng/published.php?ID=164276. DOI: 10.34759/trd-2022-122-19
9. Kalyagin M.Yu., Voloshin D.A., Mazaev A.S. Trudy MAI, 2020, no. 112. URL: https://trudymai.ru/eng/published.php?ID=116625. DOI: 10.34759/trd-2020-112-20
10. Wills A., Schön T.B., Ljung L., Ninness B. Identification of Hammerstein-Wiener models, Automatica, 2013, vol. 49(1), pp. 70–81. DOI: 10.1016/j.automatica.2012.09.018
11. Alesenko V.V., Bol'shikh A.S., Genkin M.D. et al. Vibratsii v tekhnike: Spravochnik. V 6-ti t. Izmereniya i ispytaniya. T. 5. (Vibrations in technology: A reference book. In 6 volumes. Measurements and tests. Vol. 5.), Moscow, Mashinostroenie, 1981, pp. 366-374.
12. Morozov A.Yu. Trudy MAI, 2022, no. 124. URL: https://trudymai.ru/eng/published.php?ID=167168. DOI: 10.34759/trd-2022-124-24
13. Rodionova D.A. Trudy MAI, 2015, no. 84. URL: https://trudymai.ru/eng/published.php?ID=63137
14. Semakov S.L., Semakov I.S. Trudy MAI, 2018, no 100. URL: https://trudymai.ru/eng/published.php?ID=93446
15. Vavilov A.A. Chastotnye metody rascheta nelineinykh sistem (Frequency methods for calculating nonlinear systems), Leningrad, Energiya, 1970, pp. 50-75.
16. Lavrent'eva M.V., Govorkov A.S. Trudy MAI, 2017, no. 96. URL: https://trudymai.ru/eng/published.php?ID=85930
17. Popov E.P. Prikladnaya teoriya protsessov upravleniya v nelineinykh skhemakh (Applied theory of control processes in nonlinear circuits), Moscow, Glavnaya redaktsiya fiziko-matematicheskoi literatury, 1973, pp. 20-34.
18. Popov E.P. Teoriya nelineinykh sistem avtomaticheskogo regulirovaniya i upravleniya (Theory of nonlinear automatic control and control systems), Moscow, Nauka. Glavnaya redaktsiya fiziko-matematicheskoi literatury, 1979, pp. 7-26.
19. Kirillov V.V., Moiseev V.S. Analogovoe modelirovanie dinamicheskikh sistem (Analog modeling of dynamic systems), Leningrad, Mashinostroenie, 1977, pp. 59-94.
20. Kostin S.V., Petrov B.I., Gamynin N.S. Rulevye privody (Steering drives), Moscow, Mashinostroenie, 1973, pp. 150-164.

Download