Balanced Control Analysis of Single Inverted Pendulum Systems Using PID Methodology

This research provides an in-depth exploration of balance control mechanisms for single inverted pendulum systems. We initially establish a detailed mathematical model capturing various dynamic influences on system motion, implemented through state-space representation with nonlinear differential equations. The control design phase employs PID methodology, featuring proportional, integral, and derivative gain adjustments through Ziegler-Nichols tuning techniques. Simulation experiments conducted in MATLAB/Simulink environment incorporate real-time parameter optimization algorithms. Performance analysis confirms PID effectiveness in stabilization while revealing control quality attributes through rise time, settling time, and overshoot metrics. Further investigation examines parameter sensitivity impacts on system performance, leading to proposed optimization schemes enhancing control robustness and stability. The study integrates transfer function modeling with practical implementation code snippets for actuator response calibration. Overall, this work delivers comprehensive solutions with significant theoretical and practical implications for inverted pendulum control systems.