This paper compares two linear control methods, LQR and MPC, in the context of controlling and stabilizing the Double Inverted Pendulum, a highly unstable and nonlinear system. While the use of LQR to control this system is well-established, MPC has emerged as an alternative that has shown to be effective. The study examines the impact of incorporating Laguerre functions in the MPC approach, as it has the potential to reduce computational load while maintaining dynamic performance. The results were obtained through simulations conducted in MATLAB.