This article demonstrates a strategy to design multivariable and multi-objective controllers based on the H ∞ norm reduction applied to a wind turbine. The wind turbine model has been developed in the GH Bladed software and it is based on a 5 MW wind turbine defined in the Upwind European project. The designed control strategy works in the above rated power production zone and performs generator speed control and load reduction on the drive train and tower. In order to do this, two robust H ∞ MISO (Multi-Input Single-Output) controllers have been developed. These controllers generate collective pitch angle and generator torque set-point values to achieve the imposed control objectives. Linear models obtained in GH Bladed 4.0 are used, but the control design methodology can be used with linear models obtained from any other modelling package. Controllers are designed by setting out a mixed sensitivity problem, where some notch filters are also included in the controller dynamics. The obtained H  controllers have been validated in GH Bladed and an exhaustive analysis has been carried out to calculate fatigue load reduction on wind turbine components, as well as to analyze load mitigation in some extreme cases. The analysis compares the proposed control strategy based on H  controllers to a baseline control strategy designed using the classical control methods implemented on the present wind turbines.

The non-linear behaviour of wind turbines demands control strategies that guarantee the robustness of the closedloop system. Linear parameter-varying (LPV) controllers adapt their dynamics to the system operating points, and the robustness of the closed loop is guaranteed in the controller design process. An LPV collective pitch controller has been developed within this work to regulate the generator speed in the above rated power production control zone. The performance of this LPV controller has been compared with two baseline control strategies previously designed, on the basis of classical gain scheduling methods and linear time-invariant robust H ∞ controllers. The synthesis of the LPV controller is based on the solution of a linear matrix inequalities system, proposed in a mixed-sensitivity control scenario where not only weight functions are used but also an LPV model of the wind turbine is necessary. As a contribution, the LPV model used is derived from a family of linear models extracted from the linearization process of the wind turbine non-linear model. The offshore wind turbine of 5 MW defined in the Upwind European project is the used reference non-linear model, and it has been modelled using the GH Bladed 4.0 software package. The designed LPV controller has been validated in GH Bladed, and an exhaustive analysis has been carried out to calculate fatigue load reductions on wind turbine components, as well as to analyse the load mitigation in some extreme cases.

This paper shows a strategy to carry out a wind turbine LPV (Linear Parameter Varying) and MIMO (Multivariable Input and Multivariable Output) model from a family of LTI (Linear Time Invariant) models. The family of LTI models is obtained from a linearization process in different operational points of the wind turbine model in GH Bladed. The procedure is valid for any family of LTI models obtained from other simulation packages, as for instance, from FAST. The wind turbine model chosen is based on a 5 MW wind turbine defined in the Upwind European project. The LPV model is represented by the LFT (Linear Fractional Transformation) representation and its dynamics varies according to a selected parameter: blade pitch angle or wind speed. The MIMO LPV model has been developed in Matlab/Simulink. This model is validated analyzing some quality values in the frequency domain and in the time domain. These values determine the quality of the approximation of the LPV model to the family of LTI models.

the Control Engineering and Power Electronics department and, especially, to the people who have been working in the L3 research group during these years. To Aron and Joseba, because they are the professional parents of this work and they entrusted me to carry out this research project.