{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/36668"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/36668","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Modeling and LQR Control of a Two-Dimensional Airfoil","abstract":"In this paper we develop a mathematical model of a two-dimensional aeroelastic airfoil. This model is used to design a flutter suppression controller. Flutter is a vibration in a wing caused by airstream energy being absorbed by the lifting surface. Flutter increases with increasing speed. For simplicity, we consider a flat plate in a two-dimensional flow. The model is developed in the frequency domain and then transformed into the time domain. The uncontrolled model is numerically simulated using MATLAB. Linear Quadratic Regulator (LQR) theory is used to design a state feedback controller. The LQR control scheme consists of using a full state feedback controller of the form u=-Kx, where K is a control gain matrix. The goal is to use LQR theory to supress flutter and to maintain stability of the closed loop system.","abstract_html":"In this paper we develop a mathematical model of a two-dimensional aeroelastic airfoil. This model is used to design a flutter suppression controller. Flutter is a vibration in a wing caused by airstream energy being absorbed by the lifting surface. Flutter increases with increasing speed. For simplicity, we consider a flat plate in a two-dimensional flow. The model is developed in the frequency domain and then transformed into the time domain. The uncontrolled model is numerically simulated using MATLAB. Linear Quadratic Regulator (LQR) theory is used to design a state feedback controller. The LQR control scheme consists of using a full state feedback controller of the form u=-Kx, where K is a control gain matrix. The goal is to use LQR theory to supress flutter and to maintain stability of the closed loop system.","abstract_has_math":false,"creators":["Olds, Shana D."],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Burns, John A."],"committee_members":["Rogers, Robert C.","Herdman, Terry L."],"year":1997,"date_issued":"1997-04-21","date_published":"1997-04-21","updated_at":"2026-07-22T22:19:22Z","subjects":["LQR","stability","pitch","plunge","flap angle"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-4128132049721391"],"render_values":[{"text":"etd-4128132049721391","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/36668","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Burns, John A."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Rogers, Robert C.","Herdman, Terry L."]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Olds, Shana D."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T20:51:26Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T20:51:26Z","1997-04-21"]},{"key":"dc:date.issued","label":"Date","values":["1997-04-21"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["LQR","stability","pitch","plunge","flap angle"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-4128132049721391"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/36668"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this paper we develop a mathematical model of a two-dimensional aeroelastic airfoil. This model is used to design a flutter suppression controller. Flutter is a vibration in a wing caused by airstream energy being absorbed by the lifting surface. Flutter increases with increasing speed. For simplicity, we consider a flat plate in a two-dimensional flow. The model is developed in the frequency domain and then transformed into the time domain. The uncontrolled model is numerically simulated using MATLAB. Linear Quadratic Regulator (LQR) theory is used to design a state feedback controller. The LQR control scheme consists of using a full state feedback controller of the form u=-Kx, where K is a control gain matrix. The goal is to use LQR theory to supress flutter and to maintain stability of the closed loop system."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:title","label":"Title","values":["Modeling and LQR Control of a Two-Dimensional Airfoil"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Burns, John A."],"dc:contributor.committeemember":["Rogers, Robert C.","Herdman, Terry L."],"dc:contributor.department":["Mathematics"],"dc:creator":["Olds, Shana D."],"dc:date.accessioned":["2014-03-14T20:51:26Z"],"dc:date.available":["2014-03-14T20:51:26Z","1997-04-21"],"dc:date.issued":["1997-04-21"],"dc:description.abstract":["In this paper we develop a mathematical model of a two-dimensional aeroelastic airfoil. This model is used to design a flutter suppression controller. Flutter is a vibration in a wing caused by airstream energy being absorbed by the lifting surface. Flutter increases with increasing speed. For simplicity, we consider a flat plate in a two-dimensional flow. The model is developed in the frequency domain and then transformed into the time domain. The uncontrolled model is numerically simulated using MATLAB. Linear Quadratic Regulator (LQR) theory is used to design a state feedback controller. The LQR control scheme consists of using a full state feedback controller of the form u=-Kx, where K is a control gain matrix. 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