{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/22831"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/22831","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Large-signal tools for power electronics: State space analysis and averaging theory","abstract":"This thesis explores the application of nonlinear methods to the practical problems of switching power converter analysis and design. Based on switching algebra, a formalism for large-signal component modeling is developed. The governing equation is formulated for a general class of mixed-mode circuit models containing ideal switches. The geometric interpretation of the governing equation in the state space is developed. This interpretation provides a cogent framework for understanding feedback control and unusual instability phenomena. The classical theory of averaging for systems of ordinary differential equations is applied to power electronic systems. A theoretical basis for widely used averaging approximation techniques is developed. Three new large-signal tools are introduced which are an outgrowth of the basic theory developed. Three large-signal experiments are reported which test the modeling formalism and the geometric and averaging concepts introduced.","abstract_html":"This thesis explores the application of nonlinear methods to the practical problems of switching power converter analysis and design. Based on switching algebra, a formalism for large-signal component modeling is developed. The governing equation is formulated for a general class of mixed-mode circuit models containing ideal switches. The geometric interpretation of the governing equation in the state space is developed. This interpretation provides a cogent framework for understanding feedback control and unusual instability phenomena. The classical theory of averaging for systems of ordinary differential equations is applied to power electronic systems. A theoretical basis for widely used averaging approximation techniques is developed. Three new large-signal tools are introduced which are an outgrowth of the basic theory developed. 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