Inverted Pendulum Simulation Program

This MATLAB source code implements a comprehensive simulation of a first-order inverted pendulum system with vertical cantilever-pendulum configuration. The program includes the following components: - Mathematical modeling of the inverted pendulum system, utilizing Lagrangian mechanics or Newton-Euler equations to derive the governing differential equations - Definition of system states including pendulum angle, angular velocity, cart position, and cart velocity - Control system design featuring PID control, LQR optimization, or state feedback controllers for stabilization - Simulation implementation using MATLAB's ODE solvers (ode45) with real-time visualization capabilities The code demonstrates key MATLAB functions such as ode45 for numerical integration, control law computation functions, and visualization tools like plot and animate for result analysis. This program serves as an educational resource for understanding inverted pendulum dynamics, control system design principles, and MATLAB-based simulation techniques for nonlinear systems.