This dissertation is divided into two parts. In the first part we consider the problem of feedback stabilization of nonlinear systems described by state-space models. This approach is inherited from the methodology of sector bounded or passive nonlinearities, and influenced by the concept of absolute and quadratic stability. It aims not only to regionally stabilize the nonlinear dynamics asymptotically but also to maximize the estimated region of quadratic attraction and to ensure nominal performance at each equilibrium. In close connection to gain scheduling and switching control, a path of equilibria is programmed based on the assumption of centered-epsilon-cover which leads to a sequence of linear controllers that regionally stabilize the desired equilibrium asymptotically.
In the second part we tackle the problem of control for fluid flows described by the incompressible Navier-Stokes equation. We are particularly interested in film cooling for gas turbine engines which we model with the jet in cross-flow problem setup. In order to obtain a model amenable to the controller design presented in the first part, the well-known Proper Orthogonal Decomposition (POD)/Galerkin projection is employed to obtain a nonlinear state-space system called the reduced order model (ROM). We are able to stabilize the ROM to an equilibrium point via our design method and we also present direct numerical simulation (DNS) results for the system under state feedback control.
| Identifer | oai:union.ndltd.org:LSU/oai:etd.lsu.edu:etd-12062012-162954 |
| Date | 21 December 2012 |
| Creators | Alvergue, Luis Donaldo |
| Contributors | Jorge Pullin, Guoxiang Gu, Sumanta Acharya, Kemin Zhou, Dimitris Nikitopoulos |
| Publisher | LSU |
| Source Sets | Louisiana State University |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lsu.edu/docs/available/etd-12062012-162954/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached herein a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to LSU or its agents the non-exclusive license to archive and make accessible, under the conditions specified below and in appropriate University policies, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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