Exercise: Exploring the dynamics of the ball and beam system

Download the Ball and Beam Simulation, which contains a SIMULINK model of a “ball and beam” experiment, in which you apply a torque to a beam and try to balance a ball that rolls along the beam (see below for a more complete description).

1. Run the simulation with default parameters and create a plot of the ball position versus time. Note that the desired action of the system is to move the ball from its initial position at the center of the beam to a new resting point at r = 0.25 m.
2. While keeping the gain on α fixed at its default value, vary the gain on α from 75% to three times the default value. Plot the “overshoot” (the maximum amount by which the ball goes past the desired resting point, expressed as a percentage of the commanded position) as a function of this gain for stable cases.
3. While keeping gain on α fixed at its default value, vary the gain on ̇α from zero to twice its default value. Give the numerical range of this gain for which the system is stable.

Plot the “settling time” (amount of time required for the system to get within 5% of the desired resting point) as a function of this gain for the stable cases. All plots should included a title, labeled axes (with units), and reasonable axis limits.

Note: It is not necessary for you to understand the dynamics of the system and control law at this point. This model makes use of some advanced features in MATLAB and SIMULINK, which you may need to spend some time learning.