Inverted Pendulum Modeling and LQR Control Implementation Using MATLAB

The inverted pendulum represents a classic control problem with significant importance in control theory and engineering applications. In this documentation, we present the modeling and control methodology for inverted pendulum systems using MATLAB programming. The modeling process involves deriving motion and force equations to describe the pendulum's dynamics, while the control strategy implements a Linear Quadratic Regulator (LQR) controller for achieving stable pendulum balance. Our implementation includes MATLAB code for solving the state-space equations and designing the optimal LQR gain matrix using the 'lqr' function. The simulation results demonstrate control performance through comprehensive curve analysis, showcasing system response, stability margins, and controller efficiency. Through this documentation, you will gain understanding of the inverted pendulum's significance in control engineering and learn practical MATLAB implementation techniques for system modeling and advanced control design.