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This study presents the control of a variable-speed wind energy conversion system based on a brushless doubly fed reluctance machine. The control objectives are the tracking of the maximum power conversion point and the regulation of the reactive power injected by the generation system into the grid. The control design is approached using multi-input second-order sliding techniques which are specially appropriate to deal with non-linear system models in the presence of disturbances and model inaccuracies. The controller synthesised through this theoretical framework presents very good robustness features, a finite reaching time and a chattering-free behaviour. The performance of the closed-loop system is assessed through representative computer simulations.