On nonlinear stabilization of a magnetic levitation system

The objective of this paper is to compare in a simple example three controller design techniques for stabilization of nonlinear systems which have emerged in the last few years: 1) Feedback linearization, which as the name says aims at achieving a linear system in closed-loop via nonlinearities cancellation, is probably the best well known and easier to understand; 2) Integrator backstepping, which is another widely publicized technique that has proven very succesful for systems with special triangular structures; 3) Passivity-based control, which has traditionally received a wide acceptance among practicioning engineers, achieves system stabilization solving an, apparently more natural, passivation problem. Application of these, seemingly unrelated, methodologies will typically lead to the definition of different control schemes. For some specific examples these differences blur and some interesting connections and similarities between the controller design techniques emerge. The careful study of such cases will improve our understanding of their common ground fostering cross-fertilization. In this paper we investigate these questions, both analytically and via simulations, for the simple problem of stabilization of a magnetically levitated ball. Our motivation in choosing this particular example stems, not just from the fact that due to its simplicity the connections between the controllers are best revealed, but also that such an equipment is available in many engineering schools, hence experimental work can be easily carried out to complement our studies.