Mathematical analysis of a large-gap electromagnetic suspension system

In a form of controlled electromagnetic suspension, a permanent magnetic is levitated by a magnetic field; the field is produced by electrical currents passing through coils. These currents are the control input. In a Large-Gap system the coils are at some distance from the suspended body; in general, there is no closed form expression relating the currents to the flux at the point of the suspended body. Thus, in the general case, it is not possible to establish control-theoretic results for this kind of Large-Gap suspension system. It is shown, however, that if the coil placement configuration exhibits a particular cylindrically symmetric structure, expressions can be found relating the coil positions to the flux. These expressions are used to show the existence of a unique equilibrium point and controllability, in five dimensions of control, for a generic form of Large-Gap system. The results are shown to remain true if the suspended body is rotated about a particular axis. Closed form expressions are found for the currents required to suspend the body at these variable orientations. An inequality between difference classes of experimental inputs is shown to be a necessary condition for suspension of the body. It is demonstrated that the addition of coils to the system cannot lead to six dimensions of controllability. Let the system be given by the standard control equation 𝑥̇=𝐴𝑥+𝐵𝑢 Closed form expressions are found for the eigenvalues of 𝐴. In the course of proving that some coil placement restrictions may be relaxed, 𝐵 is shown to be related to the Vandermonde matrix.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1996

Author dc:creator

• Jump, Addison B.

Chair dc:contributor.committeechair

• Rogers, Robert C.

Committee members dc:contributor.committeemember

• Burns, John A.
• Herdman, Terry L.
• Russell, David L.
• Beattie, Christopher A.

• Large-Gap systems

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

etd-06062008-154655

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/38087