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A recursive algorithm for the automatic tuning of PID regulators is described. The tuning strategy is based on the minimisation of a performance index which considers the quadratic deviations of the predicted output, over the set point, as well as the control efforts, over a time horizon. The adaptive version of this algorithm follows an explicit scheme so that the applications are not limited to self-tuning in the commissioning phase. It can also be applied to parameter adaptive control. The method has been successfully tested and some results are presented.