@article{El-Borhamy2023, 
author = {Mohamed El-Borhamy and Essam Eddin M. Rashad and Arafa A. Nasef and Ismail Sobhy and Samah M. Elkholy},
title = {On the construction of stable periodic solutions for the dynamical motion of AC machines},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {4},
pages = {8902-8927},
keywords = {linear differential equations, stability theory, periodic solutions, perturbation techniques},
url = {https://www.sciopen.com/article/10.3934/math.2023446},
doi = {10.3934/math.2023446},
abstract = {This article discusses the stability of periodic responses for the dynamical motion of AC machines from the perspective of Lyapunov function approach. The dynamical motion of AC machines is prototypically modeled as an equivalent linear RLC series circuit with time-variant inductance represented by a linear differential equation with periodic coefficients. Based on the deduced stability conditions, some special identities among the equivalent circuit parameters to ensure the stability of responses and their periodic structures are concluded. Through these conditions, the periodic structure of responses is obtained by using the method of strained parameters. Through a comparison with the experimental results from the specialized practical literatures, a strong agreement with the obtained analytical results is achieved. In addition, from a practical point of views, some future points within the discussion are raised to improve the mathematical modeling of AC machines to obtain a better model and simulation.}
}