Dynamic Equilibrium Control of a Ball-on-Beam System: Newtonian Modeling and Stabilization Techniques

This study presents the design of a teaching tool for feedback control classes that draws inspiration from the well-known ball-on-beam problem. The equipment was made with easily obtainable materials and packaged in kits that were simple to duplicate, highlighting a balance between cost-effectiveness and visual appeal. This work's main focus is on the development of two separate control loops and the physical apparatus design. While the second loop controls the ball's position along the beam, the first loop precisely controls the angle of the motor. A lead compensator was used to improve performance in both control loops. In addition, a second integrator was added to the motor control loop. This essential component ensures that the beam stays stable and level, successfully opposing gravity and preserving the ball's intended position. This tool offers a practical and efficient platform for control systems engineering education. The system consists of two interdependent control loops: the second loop regulates the ball's position along the beam, while the first loop regulates the motor angle, which directly affects the tilt of the beam. Lead compensators were used in the meticulous design of each loop to guarantee proper phase margins and transient response. In order to handle steady-state error and guarantee that the beam returns to a horizontal position upon reaching equilibrium, an integrator was also added to the motor loop. Classical control principles served as the basis for the design and tuning of these loops, and performance was verified against design objectives using simulations and empirical testing.