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In this paper, a robustification method of the primary fractional controller is proposed. This novel method uses the adjustable fractional weights on the H∞ mixed-sensitivity problem. It can achieve an enhancement in both nominal performance and robust stability margins for the uncertain plants while respecting the frequency-domain constraints, such as the tracking of the set-point references, load disturbance attenuation and measurement noise suppression. The proposed robustification holds two steps; in the first step, a primary fractional controller is designed from solving the H∞ mixed-sensitivity problem that uses fixed-integer weights. In the second step, the robustified fractional controller with adjustable fractional weights is designed in order to guarantee a good compromise between the nominal performance and the robust stability not only for the nominal plant, but also for all set of the neighbouring plants. The proposed robustified fractional controller is used to control the doubly fed induction generator. Its dynamic is modelled by the unstructured output-multiplicative uncertain plant. Simulation results given by both primary and robustified fractional controllers are compared in time and frequency domains with those given by the conventional integer H∞ controller in order to validate the effectiveness of the proposed method.

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