Transfer functions obtained by integral transforms

In order to understand the behavior or characteristic feature of any system in electrical electronics and control engineering, it is necessary to express that system with mathematical equations. However, these mathematical expressions are often difficult to understand and have a complex structure. To get an idea about these expressions, they need to be converted to a simpler form. At this point, some mathematical transformations are needed. The most widely used of these is the Laplace transform. However, the discovery of the Sumudu transformation in recent years has brought a different perspective. Inevitably, "Is the Sumudu transform an alternative to the Laplace transform?" question comes to mind. The existence of a relationship between Laplace and Sumudu brought with it some differences. For example, when the Laplace transform of an odd function is taken, the even function will be obtained. But the Sumudu transform of even functions is even. The Sumudu transformation of odd functions is also odd. Since the Sumudu transform itself is a linear transformation, it does not break the linearity of the functions. In this study, obtaining the transfer functions of the circuits/systems used in electrical and electronics engineering, stability analysis, and behavior of the system were made with both Laplace transform and Sumudu transform. Simulations were carried out in the MATLAB/Simulink program. The output graphs of the system are realized and compared with both transformations. In the second part, systems and their classifications are given and in the third part, control systems are discussed. In the fourth chapter, the mathematical models of electrical and electronic systems are explained, and in the fifth and sixth chapters, Laplace and inverse Laplace transform, which are necessary for transfer functions, are mentioned. In the seventh chapter, transfer functions are explained and the transfer functions of electrical and electronic systems are obtained by Laplace transform. In the eighth chapter, stability analyzes of control systems are mentioned. In the ninth chapter, the acquisition of transfer functions of electrical electronic circuits/systems with the Sumudu transform is explained and compared with the Laplace transform. The simulations of the circuits/systems for which the transfer function is obtained by both transformations were carried out in the MATLAB/Simulink program. Then, output graphs and bode diagrams are obtained by applying various inputs. The graphs obtained by both Laplace and Sumudu are compared and interpreted. In addition, the stability analysis of the transfer functions obtained by both transformations was performed. Keywords: Stability analysis, Control systems, Laplace and Sumudu relationship, Routh-Hurwitz criterion, Sumudu transform, Transfer functions