Non linear dynamics of an electromagneticsuspension/levitation system

1
Abstract—This paper presents a mathematical model and the
performance evaluation of a kind of electromagnetic
levitation/suspension system, where the static and dynamic
magnetic fields are linked through conductor bodies. The
complex and nonlinear dynamic of the system, allows it to
illustrate in a practical form, different aspects of automatic
control like mathematical modelling,nonlinear analysis,
simulating, controllers design, evaluation and validation of linear
and nonlinear controllers. Also, the system allows to illustrate the
basic principles of operation of the big developments in power
applications, force generation and energy conversion. The
performance evaluation is started from a model obtained by
direct evaluation of mechanical forces of electromagneticorigin
and virtual work method.
Index terms—Electromagnetic Suspension, Electrodynamic
Suspension, Electrostatic, Magnetostatic, Magnetodynamic,
Nonlinear multivariable systems.
I. INTRODUCTION
EVITATION techniques, have allowed the realization of big
developments on power, force generating and energy
conversion applications [1].
Electromagnetic suspension (EMS) [2][3][4] and
electrodynamicsuspension (EDS) [6][7][8] are two categories
to obtain mechanical contactless developments. On these,
controlled magnetic fields are induced by means of the use of
coils and in some cases superconductive coils.
In EMS, levitation is obtained by attractive magnetic force
applied to adjacent sides of an air gap [2] whereas in EDS,
levitation is obtained by the repulsive force between anincident magnetic field and an induced one on a movable body
[6][8].
With the mechanism shown in figure 1 it is possible to
illustrate and experiment operation principles in EMS and
EDS, controlling the electrical current that excites conductor
magnets.
This document was sent for revision on September 19th, 2005.
Eisenover Cabal, eisecaba@univalle.edu.co, Rodrigo Martínez,rmartin@univalle.edu.co, work in Control system and Drivers in the School
of Electrical and Electronic Engineering, Universidad del Valle, calle 13 #
100-00 Cali Colombia. http://eiee.univalle.edu.co/
This suspension/levitation mechanism can meet experimental
requirements for courses on automatic control, modern control
engineering, experimentation of principles, axioms and
models related to electrostatic,magnetostatic and magnetodynamic
[10].
Figure 1. Suspension / Levitation system driven by electrical
current
Complex dynamic and multivariable of the system allow
nonlinear analysis of multivariable systems with structure of
uncertainty [12], feedback linearization and the evaluation of
algorithms based on intelligent techniques [16].
The system can be represented in the companion form orcontrollability canonical form [11]:
•
x = f (x, p) + g(x)u .
In order to deduce the dynamics of the system represented in
state space, a direct evaluation of mechanical and
electromotive forces of electromagnetic origin and the virtual
work method for electro-mechanical complex systems
modelling [13] are used.
Non Linear Dynamics of an Electromagnetic
Suspension/Levitation System
EisenoverCabal, Rodrigo Martínez D
L
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II. SUSPENSION /LEVITATION SYSTEM MODELLING
Any change in the energy of the system shown in figure 1,
must satisfy the conservation equation:
  


  


Energy
electrical
Input
+
  


  


Energy
Mechanical
Input
=  


 

Energy
Accumulated
-
 

 

Energy
Dissipated
(1)
Applying the basicprinciples of energy conservation, the
direct evaluation of Maxwell’s equations and the virtual work
method [13] it is possible to calculate present forces on the
suspension/levitation mechanism and to obtain a model for the
system, covering the following basic goals:
• Nonlinear dynamic analysis for multivariable systems
with an uncertainty structure.
• Design and evaluation of linear and...