{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/70910"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/70910","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Multidimensional Effects in Optimal Control Calculations for Time-Dependent Nuclear Systems","abstract":"Physically realistic step function control rod models are shown to be unsolvable under traditional formulations of distributed parameter optimal control theory. Extensions to the theory are proposed, and the method of reduced dimensional control is derived to allow systems of this type to be analyzed using generalized optimality conditions. Distributed parameter optimal control is shown to be a special case of this theory. Reduced dimensional control is shown to be adequate for the analysis of most optimality problems where there are differences in the number of dimensions on which the state variables are defined. The method is then applied to a xenon-iodine oscillation problem in two dimensions. A step function control rod model is examined and compared with an axially homogeneous model. The conditions of optimality are found, and analytical insights concerning the importance of the control rod tip for the optimality condition are obtained. The optimality and normalization conditions are solved numerically for a severe xenon transient. Differences are noted between the cases which can be directly attributed to the proper axial modeling of the control rod.","abstract_html":"Physically realistic step function control rod models are shown to be unsolvable under traditional formulations of distributed parameter optimal control theory. Extensions to the theory are proposed, and the method of reduced dimensional control is derived to allow systems of this type to be analyzed using generalized optimality conditions. Distributed parameter optimal control is shown to be a special case of this theory. Reduced dimensional control is shown to be adequate for the analysis of most optimality problems where there are differences in the number of dimensions on which the state variables are defined. The method is then applied to a xenon-iodine oscillation problem in two dimensions. A step function control rod model is examined and compared with an axially homogeneous model. The conditions of optimality are found, and analytical insights concerning the importance of the control rod tip for the optimality condition are obtained. The optimality and normalization conditions are solved numerically for a severe xenon transient. Differences are noted between the cases which can be directly attributed to the proper axial modeling of the control rod.","abstract_has_math":false,"creators":["Wyss, Gregory Dane"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Nuclear Engineering","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-16T04:17:42Z","date_published":"2014-12-16T04:17:42Z","updated_at":"2026-07-22T22:26:03Z","subjects":["Engineering, Nuclear"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8721788"],"render_values":[{"text":"(UMI)AAI8721788","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/70910","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Wyss, Gregory Dane"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T04:17:42Z","10000-01-01","1987"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Nuclear Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Engineering, Nuclear"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/70910","(UMI)AAI8721788"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Physically realistic step function control rod models are shown to be unsolvable under traditional formulations of distributed parameter optimal control theory. Extensions to the theory are proposed, and the method of reduced dimensional control is derived to allow systems of this type to be analyzed using generalized optimality conditions. Distributed parameter optimal control is shown to be a special case of this theory. Reduced dimensional control is shown to be adequate for the analysis of most optimality problems where there are differences in the number of dimensions on which the state variables are defined. The method is then applied to a xenon-iodine oscillation problem in two dimensions. A step function control rod model is examined and compared with an axially homogeneous model. The conditions of optimality are found, and analytical insights concerning the importance of the control rod tip for the optimality condition are obtained. The optimality and normalization conditions are solved numerically for a severe xenon transient. Differences are noted between the cases which can be directly attributed to the proper axial modeling of the control rod.","Made available in DSpace on 2014-12-16T04:17:42Z (GMT). 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Extensions to the theory are proposed, and the method of reduced dimensional control is derived to allow systems of this type to be analyzed using generalized optimality conditions. Distributed parameter optimal control is shown to be a special case of this theory. Reduced dimensional control is shown to be adequate for the analysis of most optimality problems where there are differences in the number of dimensions on which the state variables are defined. The method is then applied to a xenon-iodine oscillation problem in two dimensions. A step function control rod model is examined and compared with an axially homogeneous model. The conditions of optimality are found, and analytical insights concerning the importance of the control rod tip for the optimality condition are obtained. The optimality and normalization conditions are solved numerically for a severe xenon transient. Differences are noted between the cases which can be directly attributed to the proper axial modeling of the control rod.","Made available in DSpace on 2014-12-16T04:17:42Z (GMT). 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