This paper presents the multivariable predictive control in the state space for a rotational inverted pendulum that acts as a underactuated system. It began with the dynamic modeling of the system by means of Euler-Lagrange formalism; later a basic CAD model of the mechanical structure of the system was designed, providing the physical variables necessary for the design of the controller, based on the material defined and the dimensions of the prototype. Finally, the controller required a predictive model of the process to obtain a set of properties of its future behavior, based on the desired forecasts and references for each variable to be controlled, future control signals were calculated, which led to the convergence of the system in relation to the necessary operating values and compliance with the respective restrictions.