LQR Control of Single Inverted Pendulum System

The LQR control system for a single inverted pendulum consists of two main components: a Simulink model and an m-file. The Simulink model establishes the simulation environment for the inverted pendulum system, modeling the physical dynamics and real-time control response. The m-file contains the MATLAB code implementing the Linear Quadratic Regulator (LQR) control algorithm, which calculates optimal feedback gains by solving the Riccati equation to minimize a quadratic cost function. By integrating these two components, we achieve precise control of the single inverted pendulum system with enhanced disturbance rejection capabilities. The LQR algorithm implementation typically involves system linearization around the equilibrium point, state-space representation, and optimal gain computation using MATLAB's built-in lqr() function. This LQR control approach is widely applied in control engineering fields, providing a robust solution for maintaining stable operation of inverted pendulum systems under various operating conditions.