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The performances of the available adaptive controllers are strongly related to the magnitude of modelling error, i.e. the larger the modelling error, the worse the performances. In this paper, the authors present a new approach for designing model reference adaptive controllers that can achieve a high performance level in the presence of not necessarily small modelling error. The main design feature of such an approach is an additional feedback control signal that counteracts the effect of unmodelled dynamics on the output tracking error. To this end, the modelling error is estimated from a truncated expansion involving an appropriate basis of orthogonal functions. The underlying truncation order arises as a new design parameter for tuning the performance level, i.e. the higher the truncation order, the better the performances. This leads to a new compromise between the performance enhancement and the implementation simplicity.