Nonlinear control via approximate input-output linearization: the ball and beam example

The authors present an approach for the approximate input-output linearization of nonlinear systems, particularly those for which relative degree is not well defined. They show that there is a great deal of freedom in the selection of an approximation and that, by designing a tracking controller based on the approximating system, tracking of reasonable trajectories can be achieved with small error. The approximating system is itself a nonlinear system, with the difference that it is input-output linearizable by state feedback. The authors demonstrate some properties of the accuracy of the approximation and, in the context of the ball and beam example, show it to be far superior to the Jacobian approximation. The results are focused on finding regular SISO systems which are close to systems which are not regular and controlling these approximate regular systems