Nonlinear Model & Controller Design for Magnetic Levitation System

This paper aims at development of non linear dynamic model for Magnetic Levitation System and proposed linear and nonlinear state space controllers. The linear controller was designed by linearizing the model around equilibrium point, while nonlinear controller was based on feedback linearization where a nonlinear state-space transformation is used to linearize the system exactly. Relative degree of the system was determined and conditions were found that ensure relative degree be well defined. Magnetic Levitation system considered in this study is taken as a ferromagnetic ball suspended in a voltage controlled magnetic field. Dynamic behaviour of the system was modeled by the study of electromagnetic and mechanical subsystems. State space model was derived from the system equations. Linear full state feedback controller along with linear observer was designed and was compared with nonlinear full state feedback with nonlinear observer. Both linear and nonlinear controllers were simulated using matlab and results are presented. Key-Words: Magnetic Levitation System; Nonlinear Model; Exact Linearization; Electromagnet; unstable