Abstract The rotational inverted pendulum (Furuta pendulum) was designed and built in the laboratory of the school of mechanical engineering of the Universidad Industrial de Santander as a learning challenge of implementing control strategies for graduate students. In this research work, it’s developed a full dynamics model using Lagrangian formulation. The math dynamic model includes real physic parameters, the mass of each component, inertia terms, dimensions, viscous frictions, and DC high torque motor dynamics. With a linearized state-space model of the system dynamics, the PID approach and the optimal control gain for the linear quadratic regulator (LQR) controller and the linear quadratic Gaussian (LQG) regulator were computed and the dynamic and disturbance response were evaluated and compared for each control strategies to determine the best performance: a lower percentage of Peak Overshoot (PO). Steady-State Error (Ess), lower settling time (Settling Time (Ts)) and control (u) cost. PID controller presented the lowest performance in the control response to disturbances, unlike LQR, this does not take into account the cost-performance ratio, the controllers LQG and LQR modeled in the state space produce a feedback gain matrix which allows the Furuta pendulum to have regulated behavior making the pendulum quickly find the equilibrium point.