Identification of a nonlinear system with an insensitivity zone of an elastic element

Abstract

The article considers the problem of identifying nonlinear dynamic systems using experimental data obtained by applying test signals to the system. The goal is to determine the unknown parameters of the (frequency) transfer function of a nonlinear dynamical system with a deadband of an elastic element from experimental frequency hodographs. It was assumed that the type of transfer function of the identified system is 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 a solution to the identification problem was carried out in the class of hodographs specified by the system model. The view of transfer function of the model is the same as the view of transfer function of the identifiable system. The search for unknown parameters of the transfer function of the system model was carried out by minimizing a given criterion (measure) of 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 nonlinear 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 nonlinear system with an insensitivity zone of an elastic element, a program has been developed for simulating the process of obtaining pseudo-experimental data containing random errors and determining the parameters of this system. A computational experiment was conducted to estimate the error 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.