Youla-Kucera adaptive feedback disturbance rejection in the presence of plant uncertainties

The stability of an adaptive disturbance rejection scheme based on the Youla-Kucera parameterization is investigated, in case of an uncertain plant model is used in the synthesis of the central controller. It is shown that stability is guaranteed provided that two conditions are satisfied at the same time: the first one is linked to the internal model principle, and the second one depends on the closed-loop poles location. For some uncertainties, these constraints cannot be met simultaneously with the minimal Q-filter. That leads to propose an over-parametrized Youla-Kucera filter, in order to relax the said conditions. Simulations on relevant examples illustrate the procedure for stabilizing the Youla-Kucera adaptive rejection scheme, in the presence of plant model uncertainties.