NB2 Demo

Ball and beam

The ball and beam is a classic control theory problem, consisting of a beam held in place at one end and attached to a servo or other device that tilts it up or down at the other end, and a ball that rolls along its length. The incline angle of the beam determines the motion of the ball.

The objective is to bring the ball to rest at some specified position. The following plot shows the performance on an NB2 controller on a virtual ball and beam system. The NB2 balances the ball through a series of setpoint changes and load disturbances, all without any controller tuning.

The position of the ball on the 1-meter length beam is plotted in red. The controller output, in this case representing the gear angle of a connected servo, is plotted in blue.

The load disturbances were as follows. At 15 seconds: 2x increase in ball radius. At 45 seconds: revert to original ball radius; one-half reduction in ball mass. At 75 seconds: ball mass increased to double its initial value. At 105 seconds: revert to original ball mass; 2x increase in gravity. At 135 seconds: revert to original gravity.