Servo control and Stabilization of Linear Inverted Pendulum on a Cart using LQG

In this work, non-linear Mathematical model of Inverted Pendulum(IP)-cart system is obtained using Lagrange's equation. The linearization of the system about the vertical position is achieved by Tayler's series approximation. Linear Quadratic Gaussian(LQG) control strategy is used for solving servo problem and stabilization of angle of pendulum rod about vertically straight position. Reference signal used for tracking problem is, square wave. White Gaussian noises are injected as process/plant noise and sensor/measurement noise. Simulated results are obtained with and without noises in MATLAB. The performance of LQG is based on time response specification and noise rejection level.