Tracking control of inverted pendulum on a cart with disturbance using pole placement and LQR

This paper presents the Mathematical non-linear model of Inverted Pendulum (IP) system on a cart based on Lagrange's Equation. The linearization is done through Tayler's series approximation. Linear Quadratic Regulator (LQR) and Pole Placement control strategy are used for solving tracking problem and stabilization of pendulum around upright position. Square wave is used as reference signal for IP tracking. Simulation results are compared with and without disturbances for both the control strategy. The performance of controllers is obtained based on specification of response time and disturbance rejection level. The performance of LQR is better than pole placement control.