Title page for ETD etd-06062008-154655
|Type of Document
||Jump, Addison B.
||Mathematical analysis of a large-gap electromagnetic suspension system
|Rogers, Robert C.
|Beattie, Christopher A.
|Burns, John A.
|Herdman, Terry L.
|Russell, David L.
|Date of Defense
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
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
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