This document proposes a solution to the problem of physical sciences, such as control systems, this happens since in the industry almost all systems with applications necessarily need to guarantee stability and controllability. For this case we will implement a discrete linear quadratic regulator controller for a back-to-back converter, with a genetic algorithm, for the selection of the design matrices Q and R, for a doubly fed induction generator connected to a wind power system. The optimization technique that is presented is an alternative to techniques based on the reduction of errors through a measure, and the application problem is very current due to renewable energies that are becoming increasingly important in the energy sector. The description of the mathematical model of the converter in the state space is also relevant as a spearhead for other types of application, such a technique is shown in detail.