Nonlinear controller for a modified design of the ball & beam system

The global stabilization of the classical ball & beam has been approached in the literature through saturated control which impose restrictions on the reactivity of the closed loop. In this work a modified design for the classical ball & beam system is presented. The beam is driven by two actuators (see figure 1). In comparison to the classical system, this design offers an additional degree of freedom which is the vertical motion of the beam. We show that the new design offers the possibility to get rid of the closed loop low reactivity restriction. We propose two nonlinear controllers to steer the trajectories of the system towards a final desired position. The first controller adapts, to the new design, existing controllers from the literature for the classical ball & beam. The second controller uses the additional degree of freedom to provide a faster stabilization.