Physics and differential geometry in modern control theory applied to a synchronous generator

This article will show how to address non-linear systems by means of state feedback linearization, through it we can have the stability of the system, which in most of the industry systems usually occurs. As the main contribution, tools of differential geometry will be presented, which is a recent branch of mathematics and physics which expands the concepts and definitions of classical mathematics, therefore, the model will be presented in terms of the definitions of space Tangent, derivative and Lie bracket all this allows us to understand and propose new solutions more efficiently since traditionally the techniques used revolve around the definitions of fields on finite spaces. The model on which the control techniques will be applied will be implemented on an electrical machine such as the synchronous generator, with the purpose of applying a control law that allows the outputs of the synchronous machine to adjust to the desired references, said the model is of great importance in the electricity sector industry because it can control the variables of the system.