Nonlinear backstepping control design applied to magnetic ball control

The backstepping nonlinear control design scheme has been used for many years. The paper presents the use of backstepping nonlinear control design to asymptotically track the position of a magnetic ball-levitated ball. The model of the magnetic ball used is nonlinear. The design uses the backstepping nonlinear control to make the ball able to track an output signal x, a vertical position from some reference point, to a continuous twice-differentiable positive reference signal x_r, asymptotically. This design suggests the use of 2 inputs u₁ and u₂ working mutually exclusively together to generate a piecewise continuous control law u