The Search for a Reduced Order Controller: Comparison of Balanced Reduction Techniques

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dc.contributor.authorCamp, Katie A. E.en
dc.contributor.committeechairKing, Belinda B.en
dc.contributor.committeememberRogers, Robert C.en
dc.contributor.committeememberBorggaard, Jeffrey T.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:35:36Zen
dc.date.adate2001-05-09en
dc.date.available2014-03-14T20:35:36Zen
dc.date.issued2001-05-01en
dc.date.rdate2002-05-09en
dc.date.sdate2001-05-08en
dc.description.abstractWhen designing a control for a physical system described by a PDE, it is often necessary to reduce the size of the controller for the PDE system. This is done so that real time control can be achieved. One approach often taken by engineers is to reduce the approximating finite-dimensional system using a balanced reduction method known as balanced truncation and then design a control for the lower order system. The unsettling idea about this method is that it involves discarding information and then designing a control. What if valuable physical information were lost that would have allowed a more effective control to be designed? This paper will explore an alternate balanced reduction method called LQG balancing. This approach allows for the designing of a control on the full order approximating system and then reducing the control. Along the way, the basic ideas of feedback control design will be discussed, including system balancing and model reduction. Following, there will be mention of the linear Klein-Gordon equation and the development of the one-dimensional finite element approximation of the PDE. Finally, simulations and numerical experiments are used to discuss the differences between the two balanced reduction methods.en
dc.description.degreeMaster of Scienceen
dc.identifier.otheretd-05082001-090500en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-05082001-090500/en
dc.identifier.urihttp://hdl.handle.net/10919/32354en
dc.publisherVirginia Techen
dc.relation.haspart1kcamp_thesis.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectBalanced Reductionen
dc.subjectKlein-Gordon Equationen
dc.subjectBalanced Truncationen
dc.subjectReduced Order Feedback Controlen
dc.subjectLQG Balancingen
dc.titleThe Search for a Reduced Order Controller: Comparison of Balanced Reduction Techniquesen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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