Stabilize the planar single inverted pendulum based on LQR

This paper firstly analyses the physical model of planar single inverted pendulum system, then builds the mathematical model of this system based on Lagrangian mechanics. These characteristics: multi-parameter, less-driven, strong coupling and highly nonlinearity make it difficult to stabilize the planar inverted pendulum system. But nearby the upright equilibrium of this system, the nonlinear mathematical model of the system can be linearized and get decoupled in X-axis and Y-axis. Then two LQR controllers are designed for each linear inverted pendulum in each axis respectively, and they are almost the same. At last, the simulation experiments in MATLAB test and verify the mathematical model is right and the control policy is effective.