Title page for ETD etd-06062008-154655


Type of Document Dissertation
Author Jump, Addison B.
URN etd-06062008-154655
Title Mathematical analysis of a large-gap electromagnetic suspension system
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Rogers, Robert C. Committee Chair
Beattie, Christopher A. Committee Member
Burns, John A. Committee Member
Herdman, Terry L. Committee Member
Russell, David L. Committee Member
Keywords
  • Large-Gap systems
Date of Defense 1996-04-18
Availability restricted
Abstract
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 •/x =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.

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