The dynamic modeling of a Furuta pendulum using Euler-Lagrange formalism which allows to find the equations of motion described by the model is presented. A basic design of the system mechanical structure was built in SOLIDWORKS software, which provided the required physical variables for modeling based on the defined material and dimensions of the pendulum prototype. Taylor series were used to obtain a linear model of the system and to design the predictive control in state space. This strategy allows control over the Furuta pendulum taking into account restrictions in its manipulated and controlled variables.