Stabilization of an under-actuated mechanical system by sliding mode control

The objective of this work is to stabilize an under-actuated mechanical system Ball and Beam by applying a sliding mode control. The model obtainted by Lagrange formalism, is strongly nonlinear, a classical linearization by feedback can't be applied due to the defect of the relative degree. We propose first to apply an approximate linearization by feedback associated with robust relative degree that linearize the Ball and beam, next, we stabilize the linearized system by a sliding mode control law.