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Center Manifold of a Nonlinear PDE That Models Compressor Systems
Probability| Speaker: | Dr. MingQing Xiao, UC Davis |
| Location: | 693 kerr |
| Start time: | Tue, Jun 8 1999, 4:10PM |
Description
A commonly used mathematical model that captures the flow behavior of a
compression system, due to Moore and Greitzer, consists of a
PDE and two ODEs. The PDE describes the behavior of disturbances in the inlet
region of compression system, and the two ODEs describe the coupling of the
disturbances with the mean flow.
In this talk it will be shown that the PDE
system features a local center manifold. The significance of this result is
that a study of the behavior of the local flow in the compressor can thus be
translated into a study of the flow of two scalar differential equations on
the center manifold. The result is obtained by converting the original PDE system
into an evolution equation on a Hilbert space, and showing that this equation and its
linearized version (around a desired equilibrium) are not topologically equivalent. The stability of the flow will be discussed through the reduced two
dimensional system.
The talk will conclude with a discussion
of some control issues that arise in the
stabilization of the flow through compressor systems, and some underlying
mathematical challenges.