Construction of a method for representing an approximation model of an object as a set of linear differential models

• Main Authors: Olexander Brunetkin, Konstantin Beglov, Vladimir Brunetkin, Оleksiy Maksymov, Oksana Maksymova, Oleh Havaliukh, Volodymyr Demydenko
• Format: Article
• Language: English
• Published: PC Technology Center 2020-12-01
• Series: Eastern-European Journal of Enterprise Technologies
• Subjects: object approximation model; structural identification; padé approximant; linear differential models
• Online Access: http://journals.uran.ua/eejet/article/view/220326
• ISSN: 1729-3774; 1729-4061

This paper has demonstrated the need to use models not only at the stage of theoretical research and design operations but also when studying existing objects. The techniques to build them on the basis of identification methods have been analyzed. The identification methods have been shown when determining the parameters of processes and objects. The difficulty of defining the models' structures has been emphasized. A method has been proposed to determine the structure of an arbitrary object's model as the approximating set of linear differential models. The data on the object's response to external impact have been used as source data. Demonstrating the method's feasibility employed a set of standard links and a standard external influence in the form of a stepped function as a model. This approach helps assess the adequacy of the obtained approximation results based on the precise solutions available. In a general case, there are no specific requirements for the form of an external influence and an object's reaction. The data that reflect the object's response should allow their approximation using a polynomial. That makes it possible to represent them following a Laplace transform in the form of a truncated power series in the image domain. The transfer function is written in a general form as a rational fraction. It underlies a Padé approximant of the truncated power series. The comparison of the available accurate calculation results and those derived on the basis of the built model has shown good agreement. In the cases under consideration, the computation error did not exceed the 5 % value permissible for engineering calculations. This is also the case when using the approximation of original data over a limited period. The response of the resulting model to the external influence that simulates a real pulse was investigated. The comparison with precise results showed a discrepancy not exceeding the value permissible for engineering calculations (<5 %)