Stabilizing and Swinging-Up the Inverted Pendulum Using PI and PID Controllers Based on Reduced Linear Quadratic Regulator Tuned by PSO

Abstract

The inherited instabilities in the Inverted Pendulum (IP) system make it one of the most difficult nonlinear problems in the control theory. In this research work, Proportional –Integral and Derivative (PID) Controller with a feed forward gain is used with Reduced Linear Quadratic Regulator (RLQR) for stabilizing the Cart Position and Swinging-up the Pendulum angle. Tuning the Controllers' gains is achieved by using Particle Swarm Optimization (PSO) Technique. Obtaining the combined PID controllers' gains with a feed forward gain and RLQR is a multi-dimensions control problem. The Proposed Controllers give minimum Settling Time, Rise Time, Undershoot and Over shoot for both the Cart Position and the Pendulum angle. A disturbance with different amplitudes is applied to the system, and the results showed the robustness of the systems based on the tuned controllers. The overall results are promising.