scientific edition of Bauman MSTU
SCIENCE & EDUCATION
Bauman Moscow State Technical University. El № FS 77 - 48211. ISSN 1994-0408
# 04, April 2014
DOI: 10.7463/0414.0704613
Tikhomirova_E.pdf
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The subject of this work is a problem of identification of nonlinear dynamic systems based on the experimental data obtained by applying the test signals to the system.
The goal is to examine the opportunity for using the obtained experimental samples of the hodograph to define the parameters of this system by the specific example of a second-order dynamical system with a type of nonlinearity “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 well-known value.
It was assumed also that there are disturbances while obtaining frequency characteristics of the real-world system. As a result of that, the points of experimentally obtained hodograph move randomly.
Searching for the solution of the identification problem is accomplished in the hodograph class, specified by the system model, which has the form of the frequency transfer function the same as the form of the frequency transfer function of the system identified.
Searching for the unknown coefficients of the frequency transfer function model of the system was carried out by minimizing the previously described and published by one of the authors proximity criterion (measure) of experimentally obtained system hodograph and the hodograph of system model for all the experimental points.
The problem solution to identify 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 dynamical system with nonlinearity of the type "dry friction" the simulation software was developed to provide the pseudo experimental data containing random accuracy of and determine the parameters of the system.
A computational experiment of accuracy evaluation was made with which the proposed algorithm determines the values of the system parameters.
The illustrative numerical simulation has demonstrated that the accuracy of determining the values of the coefficients transfer function is comparable with 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 method of identification of nonlinear dynamical systems, which is described in the article, can be used to determine the parameters of various kinds of actuators.
Using the method of harmonic linearization and identification of dynamical systems hodographs is promising for solving the problem of identification of nonlinear systems with different types of nonlinearities.
References
1. Polyanin A.D., Zaytsev V.F., Zhurov A.I. Metody resheniya nelineynykh uravneniy matematicheskoy fiziki i mekhaniki [Methods for solving nonlinear equations of mathematical physics and mechanics]. Moscow, Fizmatlit, 2005. 256 p. (in Russian).
2. Timoshenko S. Vibration Problems in Engineering. 3rd ed. D. Van Nostrand Company, Inc.Toronto New York London, 1955. 468 p. (Russ. ed.: Timoshenko S.P. Kolebaniya v inzhenernom dele. Moscow, Nauka, 1967. 444 p.).
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4. Deych A.I. Metody identifikatsii dinamicheskikh ob"ektov [Methods of identification of dynamic objects]. Moscow, Energiya, 1979. 240 p. (in Russian).
5. 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).
6. Pugachev V.S., ed. Osnovy avtomaticheskogo upravleniya [Basics of automatic control]. Moscow, Nauka, 1968. 680 p. (in Russian).
7. 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).
8. Boevkin V.I., Nedashkovskiy V.M., Pavlov Yu.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. DOI:10.7463/0913.0618917 (in Russian).
Publications with keywords: identification, harmonic linearization, nonlinear dynamical system, dry friction, frequency locus
Publications with words: identification, harmonic linearization, nonlinear dynamical system, dry friction, frequency locus
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