Stable Adaptive Ball and Beam Control

The paper proposes a model based adaptive control algorithm to control the ball and beam system with unknown parameters. The algorithm is based on an error metric which combines the trajectory tracking of the ball and the stabilization of the beam. The proposed adaptive control algorithm is improved in such a way to avoid the singularity problem which can arise in nonlinear adaptive control systems. Using the Barbalat lemma, it can be shown that the tracking error of the ball motion on the beam converges to a small residual set even in the presence of parameter uncertainty. Experimental results are provided to show the performances of the proposed control scheme