Parametric Identification of an Inertial Object from a Fragment of a Transient with Non-Zero Initial Values

Abstract

The article analyzes two approaches to solving the problem of parametric identification of a linear inertial object from a fragment of a transient with nonzero initial values. This formulation of the problem is relevant in practice not only for the stepwise form of the input signal, but also when a rectangular testing pulse is applied to the dynamic object input. With such statement, the parameters of input test signals are considered to be known. In the latter case, the maximal duration of the processed fragment of the recorded transient fragment is limited by the duration of the testing pulse. The problem is reduced to estimating the parameters of the dominant time constant in the description of the object’s transfer function and the object’s total transfer coefficient from the intermediate fragment of the transient taking into account nonzero initial conditions. A comparative analysis of two considered approaches to solving the problem is carried out. The first approach uses inverse digital transformation (differentiation) algorithms, and the second approach uses an estimate of the parameters of the function approximating the recorded fragment as the identified object’s model. In all cases, the least squares method is used to approximate a fragment of the transient. The test examples show better accuracy of the second approach in the presence of a random noise component in the processed signal. Using the example of processing fragments of electroretinograms in ophthalmology, the possibility of expanding the space of informative signs for the diagnosis of retinal diseases is shown. For these purposes, it is possible to use the results of parametric identification a fragment of a general electroretinogram, which is an intermediate part of the retinal reaction in response to a light pulse.