Development of a Simple PID-Controlled Inverted Pendulum Model Using Simulink

This document presents the development of a simple PID-controlled inverted pendulum model using Simulink. The model serves as an effective platform for understanding inverted pendulum dynamics and implementing control strategies to achieve system stabilization. Within this framework, we implement a PID controller that processes position error, velocity error, and acceleration error to generate optimized control signals, thereby maintaining the pendulum in an upright vertical position. The implementation involves configuring three parallel control channels in Simulink: proportional (P) for immediate response to position deviation, integral (I) for eliminating steady-state error through historical error accumulation, and derivative (D) for predicting future behavior using rate-of-change calculations. The controller output is computed using the standard PID algorithm: u(t) = Kp*e(t) + Ki*∫e(t)dt + Kd*de(t)/dt, where tuning parameters Kp, Ki, and Kd are optimized through simulation experiments. This model enables detailed investigation of the inverted pendulum's dynamic behavior, including stability margins, transient response characteristics, and disturbance rejection capabilities. Researchers can utilize this foundation to refine control strategies through parameter tuning, controller structure modifications, or alternative control algorithms. As an educational tool, the model effectively demonstrates core control theory concepts and their practical application to real-world balancing systems, making it particularly valuable for engineering students learning control system design and implementation.