UC San Diego

A pendulum which has its center of mass above its pivot point, is an inverted pendulum. Inverted pendulum is an unstable system, and without applying an acceleration at the bottom of it, it will fall over. The dynamics of the inverted pendulum are non-linear. In this paper, utilizing linear control design technique, specifically a Linear Quadratic Gaussian (LQG) controller is applied to stabilize two degrees of freedom inverted pendulum on a five-bar linkage mechanism. The linkage mechanism converts the rotational motion of two direct current (DC) motors into translational motion on the x-y plane, and it will provide the required acceleration that is needed in both x and y direction to stabilize the pendulum.

The equation of motion is obtained by the Lagrangian method instead of the Newtonian method. This method allows to neglect the reaction forces in the system and develops the equation of motion using the energy of the system. The other key aspect of this research paper is to simulate the non-linear model of the inverted pendulum rather than linearized version which makes controller more robust.