Control-Oriented Modelling of Wind Turbines Using a Takagi-Sugeno Model Structure S¨ oren Georg Control Group, Department of Engineering I HTW Berlin, Berlin, Germany Email: soeren.georg@htw-berlin.de Horst Schulte Head of Control Group, Department of Engineering I HTW Berlin, Berlin, Germany Email: horst.schulte@htw-berlin.de Harald Aschemann Chair of Mechatronics Universit¨ at Rostock Rostock, Germany Email: harald.aschemann@uni-rostock.de Abstract—For a horizontal-axis wind turbine (HAWT), a dynamic nonlinear model with four degrees of freedom is derived and transformed into a Takagi-Sugeno (TS) model structure using the sector nonlinearity approach. Thereby, an exact transformation of the nonlinear model is obtained as a weighted combination of linear models. This structure allows for a convenient design of controller and observer structures. The maps of the rotor thrust and torque coefficients can be implemented in the model as look-up tables or, alternatively, as analytical nonlinear functions. Open-loop simulation results of the derived TS model for a reference model turbine are compared to those obtained with the aero-elastic code FAST. The small deviations obtained demonstrate the high model quality of the control-oriented TS model. In future work, the derived TS model shall be used as a basis for the design of fault detection and isolation (FDI) concepts. I. I NTRODUCTION As wind turbines are gaining a growing significance in the global energy supply, the demand for advanced control strategies aiming at higher efficiency and availability as well as load reduction also rises. Therefore, it is essential to develop model-based control algorithms that exceed the possibilities of classical frequency-domain control design concepts. Based on dynamic wind turbine models with few degrees of freedom, various control design concepts have already been employed to address different issues arising in wind turbine control. For example, LQG controller concepts were used in [1] and [2] to reduce loads. Classical gain-scheduling tech- niques have been replaced by more rigorous linear parameter- variable (LPV) approaches to design the wind turbine speed control for the different operating regions in [3]. The purpose of this paper is to present a wind turbine model that shall be used as a basis for fault detection and isolation (FDI) concepts in wind turbine control in future work. By using the Takagi-Sugeno model structure with sector nonlinearities, an exact representation of the nonlinear model can be obtained as a weighted combination of linear state- space models. For this structure, both controllers and observers can be designed by solving linear matrix inequalities (LMIs) [4]. Fault detection schemes can be developed by extending the standard TS observer structures to sliding mode TS observers [5]. In [6], this is used for the detection of sensor faults in the pitch system of wind turbines. The same methodology shall be applied in order to detect and isolate more sensor and actuator faults occurring in the operation of wind turbines, for which the model presented here serves as a starting point. The derived wind turbine model is validated against the aero-elastic simulation code FAST by NREL [7] using a 5 MW reference wind turbine described in [8]. There are a lot of papers that make use of a TS model structure for wind turbine models and controller design. For example, in [9] maximum wind power tracking is tackled by designing a TS controller along with an observer for a turbine model including an explicit generator/converter model. In [10] a robust power tracking controller is designed using linear matrix equalities to account for disturbances and parametric uncertainties. In [11] a Fuzzy clustering approach is applied to obtain a TS model in order to achieve maximum energy extraction. In most cases, however, the controllers are not validated against more detailed structural simulation models (like FAST) normally used in the wind energy industry. This, however, is important in order to test both the quality of the design models and the controller performance with more realistic models. This paper is organised as follows: In Section II, the wind turbine model is derived and written in state-space form. In Section III, the state-space model is transformed into a TS model structure. In Section IV, model parameters for the 5 MW reference wind turbine are given including the nonlinear aero maps for the rotor thrust and torque coefficients. In addition, these maps are approximated by nonlinear functions. In section V, simulation results are presented which are compared to the results obtained with the FAST aero-elastic simulation. Conclusion and outlook are given in section VI. II. WIND TURBINE MODEL The aero-elastic codes normally used for wind turbine load simulation contain models with more than twenty degrees of freedom which are derived by employing modal analysis techniques. For control design purposes, these models are too complicated and also capture dynamic effects that are not directly influenced by the control action. For these reasons, the models used for control design have to be as simple as possible but must capture the dominant system dynamics [3]. U.S. Government work not protected by U.S. copyright WCCI 2012 IEEE World Congress on Computational Intelligence June, 10-15, 2012 - Brisbane, Australia FUZZ IEEE