Modeling and simulation of a maglev vehicle

We will consider an attractive MAGLEV system made by a wagon and a base plate (carrying the electromagnets) that are stiffly connected. The complete dynamics of the MAGLEV can be represented by a set of second order non-linear differential equations. For small displacements around the equilibrium the previous system can be linearized and we obtain a MIMO system where the control variables are the electro-mechanical forces, the controlled ones are the wagon and base plate displacements and the disturbances are due to the actual rail way profile. By straightforward algebraic manipulations the angular displacements of the wagon can be related to the vertical ones of each suspension electromagnet. Assuming that the rail has a suitable profile, it is possible to control the position of the wagon via small horizontal electromagnet displacements. In this way the control of the MAGLEV is related to the fine position control of a bank of dc motor and the current in the electromagnets can be kept constant. The aim of this paper is to obtain a model of the system such that an optimal control law can be implemented. The study of the dynamic behavior of the MAGLEV system is then performed via simulations.