Trajectory Tracking Control of the Planar Inverted Pendulum

This paper analyzed the physical structure of the planar inverted pendulum system, established the nonlinear dynamic model of the system with Lagrange equation. The same linear model and state-space expression in each direction is obtained, by decoupling the nonlinear model around the system's equilibrium position. On the basis of the linear optimal control theory, designs LQR controller, which the base cart positioning prior to the pendulum stabilization. Realizes the positioning, circular and infinity shape trajectories tracking control of the base cart, while ensuring the pendulum is inverted and stable. Real-time experiments show that the controller is simple and has good real-time performance. Under the different motion conditions, has high control accuracy, fast response speed, good robustness, validates the effectiveness of the algorithm.