Research on Control Scheme Based on Ball & Beam System

In the research of control theory, the open-loop unstable Ball & Beam system is one of the typical research objects. This article studies the PID（Proportion Integration Differentiation）controller design method and fuzzy PID controller design method based on the Ball & Beam system, aiming to achieve effective control of system stability and performance. Firstly, a force analysis was conducted on the Ball & Beam system, and a mathematical model was established based on the Lagrangian equation, providing a foundation for the subsequent design of control strategies. Next, we conducted an analysis of stability and performance indicators, including overshoot, adjustment time, etc., to evaluate the performance of the two PID controllers. Finally, the optimal PID controller is determined by adjusting their respective control parameters, and the accuracy, speed, and stability of the proposed algorithm and model are verified through their corresponding response curves. The simulation and experimental results show that the fuzzy PID controller can quickly stabilize the ball at the target position compared to the conventional PID controller and has good practicality, stability, rapidity, and accuracy.