Control of an Inverted Pendulum Model Using LQR with Two Feedback Loops

This paper presents method of controller design for an inverted pendulum system via two close loops. The inner loop uses state feedback method to stabilize model around the up-right equilibrium point. The outer loop uses the cart position feedback to drive the whole model to its set point. The Linear Quadratic Regulator (LQR) is used for both two loops at the same time to optimize the operation of the model. To estimate the state variables for the inner loop coupled with the noise filter, we use the Kalman filter as a state observatory. Simulation results on Matlab demonstrate the advantages of using LQR for both two loops and the effect of the Kalman filter. This controller is tested on the pendulum model by experiment