Linear quadratic regulator (LQR) controller design for inverted pendulum

The Inverted Pendulum System is an under actuated, unstable and nonlinear system. The challenge of this project is to keep the inverted pendulum balanced and track the linear cart to a commanded position. This project presents investigations of performance comparison between conventional Proportional Integral Derivatives (PID) and modern control Linear Quadratic Regulator (LQR) schemes for an inverted pendulum system. The goal is to determine which control strategy delivers better performance with respect to pendulum’s angle and cart’s position. LQR algorithm needed to compute what the steady-state value of the states should be by multiply that by the chosen gain K, and a new value as the reference is used for computing the input. Gain k is the state feedback gain matrix, so the system becomes a closed loop control system. The LQR should produce a better response compared to PID control strategies in both discrete time and continuous time control.