Backstepping Control for Ball and Beam: Simulation and Experiment

Abstract

This paper presents the modeling and control of the Ball and Beam system, a commonly used Single Input – Multiple Output (SIMO) system in control research experiments. In the study, the Backstepping method is applied to model and control the system. The linear differential equations describing the system's dynamics are derived based on fundamental mechanical principles, using the Euler-Lagrange method to develop an accurate mathematical model. Subsequently, the backstepping method is employed to design a controller that ensures the global stability of the system. Lyapunov theory is applied to prove the system's stability, with an appropriate Lyapunov function selected to guarantee the global stability of the controller. In addition to simulations, the study also conducts experiments to test the system's stability under Backstepping control. The results show that this controller is not only effective in maintaining balance and controlling the position of the ball on the beam but also addresses the limitations of traditional linear control methods. Both simulation and experimental results demonstrate the high performance and stability of the system, confirming the stability according to Lyapunov theory.