Discussion of a Mathematical modeling of a non-ideal rotor-tower interaction

Abstract

In this article, we investigate a tower with a non-linear motor, in which we propose a mathematical model that describes the vibrations of a tower-type system with a non-ideal motor coupled, for a prototype of a wind turbine. With that, State-Dependent Riccati Equation Control (SDRE) to suppress the jump caused by the Sommerfeld Effect in the structure to a desired periodic orbit. And as a result, we control the system and suppress the bounce that is observed so that the amplitude of the vibrations decreases. Such a decrease in the amplitude of vibrations can prevent malfunctions, or even disasters. Vibration control in wind generators is important to ensure that wind turbine operation is safe, reliable, and efficient. Excessive vibrations can cause damage to components such as the wind turbine’s rotating blades and shorten their service life. In addition, vibrations can also affect the quality of the energy generated, making it less stable.