Control of a double-inverted pendulum for nonlinear system

The aim of the paper is to compare two different techniques to design a stabilizing control the double inverted pendulum in an upright position. These techniques are the Pole Placement and Linear Quadratic Regulator. Techniques have been used to design controls for the nonlinear system. For our double pendulum system, it would be desirable to keep the values of the state variables small as a large displacement from the origin may cause the nonlinear system to be unstable we would also interested in the control that gives the largest region of stability for the system, as we then could allow a larger set of perturbations from upright position.