Estabilidad y diseño de un controlador LQR para un sistema Bola-Viga

This article presents the design of an LQR controller for a Ball-Beam system, as well as its stability analysis, the control of a Ball-Beam system is one of the most interesting for control engineering since it is a highly non-dynamic system linear. The objectives of this document focus on the performance of the system using an LQR control for different disturbances as well as obtaining the phase plans. The work starts with the modeling of the ballgirder system, which consists of two mechanical arms, a gear box and a DC servomotor, later the LQR control is designed, this allows simulation and obtaining the response of the controller under different conditions. In the system the input torque is generated from the DC servo motor to control the position of the ball on the beam, where the ball rolls freely on the beam. Performance analysis is performed using robust LQR and the performance characteristics of the system are presented. Finally, the stability analysis is carried out by plotting the phase planes.