A robustification of the two degree-of-freedom controller based upon multivariable generalized predictive control law and robust H ∞ control for a doubly-fed induction generator

Abstract

A robustification method of primary two degree-of-freedom (2-DOF) controllers is proposed in this paper to control the wind turbine system equipped with a doubly-fed induction generator DFIG. The proposed robustification method should follow the following three step-procedures. First, the primary 2-DOF controller is designed through the initial form of the multivariable generalized predictive control MGPC law to ensure a good tracking dynamic of reference trajectories. Second, the robust $H_{\infty }$ controller is independently designed for the previous system to ensure good robustness properties of the closed-loop system against model uncertainties, neglecting dynamics and sensor noises. Finally, both above mentioned controllers are combined to design the robustified 2-DOF-MGPC controller using Youla parameterization method. Therefore, the obtained controller conserves the same good tracking dynamic that is provided by the primary 2-DOF-MGPC controller. It ensures the same good robustness properties which are produced by the robust $H_{\infty }$ controller. A wind turbine system equipped with a DFIG is controlled by the robustified 2-DOF-MGPC controller. Its dynamic behaviour is modelled by an unstructured-output multiplicative uncertainty plant. The controller performances are valid by comparison with those given through both controllers, which are primary 2-DOF-MGPC and robust $H_{\infty }$ controllers in time and frequency domains.