Stabilizing Controller Design for Self Erecting Single Inverted Pendulum using Robust LQR

This paper describes the method for trajectory tracking and balancing the Self Erecting Single Inverted Pendulum (SESIP) using Linear Quadratic Regulator (LQR). A robust LQR controller for stabilizing the SESIP is proposed in this paper. The first part of the controller is a Position Velocity (PV) controller to swing up the pendulum from its hanging position by moving the pendulum left and right repeatedly until the pendulum swings up around the upright position. The second part is the stabilization controller which is obtained by the optimal state feedback control law determined using LQR to balance the pendulum around upright position. Both the dynamic and steady state characteristics of controller are investigated by conducting experiments on linear inverted pendulum system and the results are compared with the conventional double PID controller response to evaluate the effectiveness of the proposed scheme. Experimental results prove that the LQR controller can guarantee the inverted pendulum a faster and smoother stabilizing process with less oscillation and better robustness than a conventional double PID controller.