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Identification parameters of the dynamic damper of vibrations

Keywords:

Yu.N. Pavlov – Dr.Sc.(Eng.), Professor, Department «Information Systems and Telecommunications»,  Kaluga branch of the Bauman MSTU
E-mail: pavlov@bmstu.ru
V.M. Nedashkovsky – Ph.D.(Eng.), Associate Professor, Department «Information Systems and Telecommunications», Kaluga branch of the Bauman MSTU
E-mail: vmniu3@bmstu.ru
E.A. Tikhomirova – Associate Professor, Department «Information Systems and Telecommunications», Kaluga branch of the Bauman MSTU
E-mail: elizarti@mail.ru
I.B. Shavirin – Ph.D.(Eng.), Associate Professor, Department «Information Systems and Telecommunications», Kaluga branch of the Bauman MSTU
E-mail: shavirin@bmstu.ru


The problem of identification of linear dynamical systems based on experimental data obtained by feeding test signals to the system is considered in the article. The goal is to determine the unknown coefficients of the (frequency) transfer function of linear dynamical systems from experimental frequency hodographs using the example of a dynamic vibration damper consisting of two bodies: the main body, the forced oscillations of which must be extinguished, and the damper itself.
The energy introduced by the perturbing periodic force is dissipated a damper with viscous friction by relative motion of the bodies. The form of the transfer function of the system being identified was assumed to be known. It was assumed that in obtaining the frequency characteristics of a real system hindrances intervenes with the experiment, as a result of which the points of the experimentally obtained hodograph are randomly shifted.
The search for the solution of the identification problem was carried out in the class of hodographs given by the model of the system, the species of the transfer function of which is the same as the species of the transfer function of the system being identified. The search for unknown coefficients of the transfer function of the system model was carried out by minimizing the predetermined criterion (measure) of the proximity of the experimentally obtained hodograph of the system and the hodograph of the system model over the entire set of experimental points. The solution of the problem of identifying a linear dynamical system using a frequency hodograph is reduced to solving a system of equations that is linear with respect to unknown parameters of the transfer function of the model of system.
For a dynamic damper of vibrations, a program has been developed for simulating the process of obtaining pseudo-experimental data containing random errors and determining the parameters of the dynamic damper of vibrations.A computational experiment was per-formed to evaluate the errors with which the proposed algorithm determines the values of the parameters of this system.An illustrative computational experiment has shown that the error in determining the values of the system parameters is comparable with the measurement error range of the experimental values (counts) of the hodograph of this system.The presented method of identification of linear dynamical systems can find application in determining the parameters of not only the dynamic damper of vibrations, but also other similar systems.

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May 29, 2020

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