Doğrusal Olmayan Sistemlerin Frekans Boyutunda Modellenmesi ve Analizi İçin Yeni Bir Hesaplama Algoritması Tasarımı ve Uygulaması

Abstract

ABSTRACT When the modeling and analysis of nonlinear systems are considered, it is seen that the methods are divided into two main classes: time and frequency. It is very difficult to examine nonlinear behaviors such as bifurcation and chaos in time-domain methods. Therefore, the methods in the frequency dimension are more preferred for the analysis of nonlinear systems. When the methods used in analytical modeling and analysis of nonlinear systems are examined, it is seen that the methods based on Volterra Series are widely used. Volterra Series provides frequency response values such as amplitude gain and phase angle in frequency dimension of nonlinear systems. There are different methods for obtaining amplitude and phase responses based on Volterra series. One of these methods is the Definition Functions method used for nonlinear systems defined by differential equations containing polynomial type nonlinear terms. This method is preferred both for ease of presentation in two dimensions and its applicability to various systems. In this project, the definition functions based on Volterra series which are widely used in frequency analysis of nonlinear systems are studied. Volterra series and Description Functions are described in an exemplary embodiment. An interface has been designed to make the Description Functions more usable and popular. Frequency analysis was performed with interface and simulink for different nonlinear systems. In addition, analog electronic circuit designs of different nonlinear systems have been made. Simulation results were obtained using analog electronic circuits and experimental results were obtained. The validity of the Identification Function has been shown by comparing the interface design and frequency response results and simulation results. As a result, the frequency responses obtained by four different methods were compared and the results were interpreted and the usability of the Identification Function method was demonstrated.