Другие журналы
scientific edition of Bauman MSTU
SCIENCE & EDUCATION
Bauman Moscow State Technical University. El № FS 77 - 48211. ISSN 1994-0408
Identification of Nonlinear Dynamical Systems with the Specified Nonlinearity Types in Hodographs
# 10, October 2014
DOI: 10.7463/1014.0727229
Article file:
SE-BMSTU...o327.Pdf
(1065.07Kb)
SE-BMSTU...o327.Pdf
(1065.07Kb)
This work concerns the problem of identification of nonlinear dynamic systems from the experimental data obtained by applying test signals to the system.
The goal is to determinate the coefficients of differential equations of systems by the experimental frequency hodographs and separation of similar, but different in essence forces: dissipative forces of the first derivative in the motion equations and dissipative action force of dry friction.
It was suggested to use the harmonic linearization method and to approximate the nonlinearity of "dry friction" by linear friction with the corresponding harmonic linearization coefficient.
It was assumed that the frequency transfer function of the identified system is a well-known value.
It was also assumed that there are disturbances while obtaining frequency characteristics of the real-world system. As a result, the points of experimentally obtained hodograph move randomly.
A solution of the identification problem was searched in the hodograph class, specified by the system model, which had the same form of the frequency transfer function as a form of the frequency transfer function of the system identified.
Searching for the unknown coefficients of the frequency transfer function of the system model was carried out by minimizing a criterion (measure) of proximity of the experimentally obtained hodograph system, which was previously described and published by one of the authors, and the system hodograph model for all the experimental points.
A solution of the nonlinear dynamic system identification in frequency hodograph was reduced to solving an equations system, linear relative to the unknown parameters of the frequency transfer function of the system model.
For the second-order dynamic system with combination of nonlinearity of the type "dry friction" and linear friction was developed the simulation software to provide pseudo experimental data of random accuracy and determine parameters of this system.
A computational experiment of accuracy evaluation was made with which the proposed algorithm determines the parameters of the system.
Illustrative numerical simulation has demonstrated that the accuracy of determining the values of the coefficients transfer function does not exceed the range of measurement accuracy of experimental samples of this system hodograph.
This method of the identification of nonlinear dynamic systems is not mentioned in the well-known publications.
The identification method of nonlinear dynamical systems, described in the article, can be used to determine the parameters of a variety of power actuators.
Using the method of harmonic linearization and identification of dynamical systems hodographs is promising for solving the problem of the identification of nonlinear systems with different types of nonlinearities.
References
- Zhdanov A.I., Katsiuba O.A. Identification by the method of least squares of autoregression equation parameters with additive measurement errors. Avtomatika i telemekhanika , 1982, no. 2, pp. 29-38. ( English translation: Automation and Remote Control , 1982, vol. 43, no. 2, pp. 158-166.).
- Bolkvadze G.R. Hammerstein Models for Identification of Stochastic Systems. Avtomatika i telemekhanika , 2003, no. 1, pp. 42-55. ( English translation: Automation and Remote Control , 2003, vol. 64, iss. 1, pp. 37-48. DOI: 10.1023/A:1021820307806 ) .
- Pavlenko S.V. Application of wavelet filtering in the process of identification of nonlinear systems in the form of kernels of Volterra. Vostochno–evropeiskii zhurnal peredovykh tekhnologii = Eastern-European Journal of Enterprise Technologies , 2010, vol. 6, no. 4 (48), pp. 65-70. (in Russian).
- Raibman N.S., Kapitonenko V.V., Ovsepian F.A., Varlaki P.M. Dispersionnaia identifikatsiia [Dispersion identification]. Moscow, Nauka Publ., 1981. 336 p. (in Russian) .
- Pavlenko S.V. Identification of Nonlinear Dynamic Systems in the Form of the Volterra Kernels on the Basis of the Data of Pulse Response Measurements. Elektronnoe modelirovanie , 2010, vol. 32, no. 3, pp. 3-18.
- Rajbman N.S. Extensions to nonlinear and minimax approaches. In: Eykhoff P., ed. Trends and Progress in System Identification . Oxford, Pergamon Press, 1981, pp. 185-237. (Russ. ed.: Rajbman N.S. Metody nelineinoi i minimaksnoi identifikatsii. In: Eykhoff P., ed. Sovremennye metody identifikatsii sistem: sb. Moscow, Mir Publ., 1983, pp. 177-277.).
- Popov E.P., Pal'tov I.P. Priblizhennye metody issledovaniya nelineynykh avtomaticheskikh system [Approximate methods of study of nonlinear automatic systems]. Moscow, GIFML Publ., 1960. 790 p. (in Russian) .
- Pugachev V.S., ed. Osnovy avtomaticheskogo upravleniya [Basics of automatic control]. Moscow, Nauka Publ., 1968. 680 p. (in Russian) .
- Boevkin V.I., Pavlov Yu.N. Regressionnyy analiz v prikladnoy zadache identifikatsii [Regression analysis in applied problem of identification]. Moscow, Bauman MSTU Publ., 1990. ( Trudy MGTU im. N.E. Baumana [Proceedings of the Bauman MSTU]; no. 546). (in Russian).
- Boevkin V.I., Nedashkovskii V.M., Pavlov Iu.N. Identification of linear dynamic elements using a frequency locus. Nauka i obrazovanie MGTU im. N.E. Baumana = Science and Education of the Bauman MSTU, 2013, no. 9, pp. 349-360. DOI:10.7463/0913.0618917(inRussian).
- Pavlov Iu.N., Nedashkovskii V.M, Tikhomirova E.A., Shavyrin I.B. Harmonic linearization method in the identification of nonlinear dynamical systems. Nauka i obrazovanie MGTU im. N.E. Baumana = Science and Education of the Bauman MSTU, 2014, no. 4. S, 382-397. DOI:10.7463/0414.0704613(in Russian).
Publications with keywords: identification, harmonic linearization, nonlinear dynamical system, dry friction, frequency locus, linear friction
Publications with words: identification, harmonic linearization, nonlinear dynamical system, dry friction, frequency locus, linear friction
See also:
Thematic rubrics:
Поделиться:
| Authors |
| Press-releases |
| Library |
| Conferences |
| About Project |
| Phone: +7 (915) 336-07-65 (строго: среда; пятница c 11-00 до 17-00) |
|
 |
|||
| © 2003-2024 «Наука и образование» Перепечатка материалов журнала без согласования с редакцией запрещена Phone: +7 (915) 336-07-65 (строго: среда; пятница c 11-00 до 17-00) | |||||
