Dynamic System Transfer Function Identification Based on the Experimental Results

Abstract

The paper deals with identifying linear dynamical systems from the experimental data obtained through applying the test signals to the system. The paper objective is to determine both the form and the coefficients of the transfer function retrieved from the hodograph samples experimentally at bench test. The order of the frequency transfer function of the system being identified was assumed to be unknown. It was expected that in obtaining the frequency characteristics of a real system there would be noise during the experiment as a result of which the points of the experimentally obtained hodograph would be randomly shifted. As a model, a certain transfer function of the system was adopted. The authors proposed to find a solution of the identification problem in the class of hodographs specified by the model of the system. The search for unknown coefficients of the transfer function of the system model is carried out by minimizing a proximity criterion (measure) - described and published earlier by one of the authors - between the experimentally received system hodograph and the system model on an entire set of the experimental points of the system hodograph and the hodograph of the system model. The solution of linear dynamic system identification from the frequency hodograph was reduced to solving a system of equations of the system model frequency transfer function that is linear with respect to unknown parameters. The proposed identification algorithm allows us to determine the order of the frequency transfer function of the identified system from the experimentally obtained samples of the frequency hodograph of the system. For dynamic systems of the fifth order at most there is software developed to simulate the process providing the pseudo-experimental data with random errors and determining the parameters of such systems. A computational experiment has been carried out to evaluate the error with which the proposed algorithm determines the parameter values of the system to be identified. The illustrative computational experiment has shown that using the proposed algorithm for identifying a linear dynamic system from the frequency hodograph the error in determining the coefficient values of the frequency transfer function of the system is comparable with a range of measuring error in the experimental samples of the hodograph of this system. In known sources on identification of linear dynamic systems there is no method of identification this publication describes. This identification method of linear dynamic systems can find application in experimental testing, verification tests in situ and iron bird tests for vehicles of various purposes.