Nedashkovskii

pp. 217-234

pp. 308-327

The article concerns the harmonic linearization method in the identification of nonlinear dynamical systems problem by the example of a system with dry friction. It describes an algorithm for the systems identification with a known transfer function for an experimental frequency hodograph that contains random measurement accuracy. The transfer function of the system was adopted as a model. The authors suggested finding a solution of the identification problem in the hodograph class, defined by system model. The unknown coefficients transfer function is searched, according to authors’ proposal, by the minimizing a proximity measure of the experimental system hodograph and the hodograph of system model. As a result, the solution of the identification problem was reduced to solving a system of linear equations. An illustrative numerical simulation for the second-order system has shown that the accuracy of determining the values of the transfer function coefficients is comparable with the range of measurement accuracy of experimental samples of this system hodograph.

This article deals with the identification method for a linear dynamic element with known transfer function using an experimental frequency locus with random measurement errors. A transfer function of an element was selected as a model. It was proposed to search for the solution to the identification problem in the class of hodographs, defined by the element’s model. Search for unknown coefficients of a transfer function of the element’s model was carried out by minimizing the proposed proximity measure of the experimental element’s locus and the model’s locus. As a result, the specified problem was reduced to a system of linear equations. An illustrative computing experiment for a second-order element showed that an error of the transfer function’s coefficients was comparable with the range of measurement errors of experimental samples of this element’s locus.