Ball and beam : model

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.

BallAndBeamModel

We will make the following assumptions:

  • m is the mass of the ball

  • \Theta is the angle of the beam

  • x is the position of the ball on the beam

  • b 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:

 m.a = m.\ddot{x} = \sum{\vec{F}} = m.g.sin(\Theta) - b.\dot{x}

In conclusion, the differential equation of the system is:

 \ddot{x} = - \frac{b}{m}.\dot{x} + g.sin(\Theta)

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