2D and 3D Control and Simulation of Simple Pendulum and Inverted Pendulum Systems

This documentation provides a comprehensive overview of control methodologies and simulation techniques for simple pendulum and inverted pendulum systems in both two-dimensional and three-dimensional configurations. The content begins with fundamental concepts of pendulum dynamics, establishing the mathematical foundation necessary for understanding control approaches. Subsequently, we explore various control strategies including PID (Proportional-Integral-Derivative) controllers and LQR (Linear Quadratic Regulator) methods, with implementation details covering system linearization and state-space representation. The MATLAB 7.0 simulation section demonstrates practical implementation using Simulink blocks and custom MATLAB scripts, featuring code examples for dynamic modeling using Euler-Lagrange equations and controller tuning parameters. This guide serves as a complete technical reference for control theory enthusiasts, offering hands-on simulation experience to validate control algorithm performance through graphical output and stability analysis.