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In this paper, a model of a DC-DC (boost) converter is first expressed as a hybrid/switched/variable-structure system state model for the purpose of applying recently developed hybrid optimal control theory to control switching in a boost converter. Switching control is achieved by forming the embedded form of the hybrid state model, which enables the derivation of a control that solves for the switching function that minimizes a user-defined performance index. This approach eliminates the need to form average-value models and provides flexibility to balance competing objectives through appropriate weighting of individual terms in the performance index. Since, in practical situations, both the source voltage and the load resistance vary with time in unknown and unmeasurable ways, we introduce a sliding mode observer based on an enlarged state model which allows implicit estimation of the unknown variables. The combined optimal switching control and sliding mode observer are applied to a boost converter in which several nonidealities and losses are represented. The results of time-domain simulation and hardware experiments are used to validate and compare the response of the hybrid optimal control-sliding mode observer to that of a traditional current-mode control strategy.
Date of Publication: Sept. 2009