Stabilization of a circular ball-and-beam system

The ball on a circular beam system is an under-actuated mechanical system that is challenging control problem compared to its variant: the ball on a horizontal beam. The control challenge stems out from the fact that the ball on a circular beam system has two unstable eigenvalues unlike its variant which has one. A stabilizing controller synthesized using backstepping methodology is presented. In doing so, a series of nonlinear coordinate transformations is applied on the equations of motion to arrive at a state-space representation which is in the so called quadratic non-triangular normal form. Simulation results are presented to demonstrate the effectiveness of the proposed controller in stabilizing the system while respecting the physical constraints on the system.