This post deals describe the model of the ball and beam. The system consists of a long beam which can be tilted by an actuator together with a ball rolling back and forth on top of the beam.
We will make the following assumptions:
- is the mass of the ball
- is the angle of the beam
- is the position of the ball on the beam
- is the friction coefficient of the ball
Based on the fundamental principle of dynamics and considering that the friction is proportional to the speed, we can write:
In conclusion, the differential equation of the system is: