Trajectory Tracking Simulation of the Planar Inverted Pendulum Based on LQR

This paper establishes the nonlinear model of the planar inverted pendulum system by using Lagrange equation, then decouples the model around the system's equilibrium position with Taylor series expansion, gets the same linear model in the direction of and. According to the linear optimal control theory, designs a LQR controller, its base cart positioning prior to the pendulum stabilization. Finally, realizes the simulation of positioning, circular and shape of infinity trajectories tracking control of the base cart, while keeping the pendulum stable. The experiments show that, the controller is simple, and in different forms of motion with good stability, high control precision, validates the effectiveness of the algorithm.