# Robust Control Examples Applied to a Wind Turbine Simulated Model
## 1 Introduction  
Wind turbine plants represent complex and nonlinear dynamic systems usually driven by stochastic inputs and different disturbances describing gravitational, centrifugal and gyroscopic loads. Moreover, their aerodynamic models are uncertain and nonlinear, whilst wind turbine rotors are subject to complex turbulent wind fields, especially in large systems, thus yielding to extreme fatigue loading conditions. In this way, the development of viable, robust and reliable control solutions for wind turbines can become a challenging issue [1; 2]. Usually, a model-based control design requires an accurate description of the system under investigation, which has to include different parameters and variables in order to model the most important nonlinear and dynamic aspects. Moreover, the wind turbine working conditions can produce further problems for the design of the control method. In general, commercial codes are not able to adequately describe the wind turbine overall dynamic behavior; usually, special simulation software solutions are used. On the other hand, control schemes have to manage the most important turbine dynamics, without being too complex and unwieldy. Control methods for wind turbines usually rely on the signals from sensors and actuators, with a system that connects these elements together. Hardware or software modules elaborate these signals to generate the output signals for actuators. The main feature of the control law consists of maintaining safe and reliableworking conditions of the wind turbine, while achieving prescribed control performances and allowing for optimal energy conversion, as shown, e.g., in recent works applied to the same wind turbine model considered in this work [3]. Today's wind turbines can implement several control strategies to allow for the required performances. Some turbines use passive control methods, such as in fixed-pitch, stall control machines. In this case, the system is designed so that the power is limited above rated wind speed through the blade stall. Therefore, the control of the blades is not required [1]. In this case, the rotational speed control is proposed, thus avoiding the inaccuracy of measuring the wind speed. Rotors with pitch regulation are usually used for constant-speed plants, in order to provide a power control that works better than the blade stall solution. In these machines, the blade pitching is controlled in order to provide optimal power conversion with respect to modeling errors, wind gusts and disturbance. However, when the system works at constant speed and below rated wind speed, the optimal conversion rate cannot be obtained. Therefore, in order to maximize the power conversion rate, the rotational speed of the turbine must vary with wind speed. Blade pitch control is thus used also above the rated wind speed [1]. A different control method can introduce the yaw regulation to orient the machine into the wind field. A yaw error reference from a nacelle-mounted wind direction sensor system must be included in order to calculate this reference signal [4]. Regarding the regulation strategies proposed in this paper, two control design examples are described and applied to a wind turbine system. The wind turbine model exploited in this work is freely available for the MATLAB(r) and Simulink(r) environments, and already proposed as benchmark for an international competition regarding the validation of fault diagnosis and fault tolerant control approaches [3]. In particular, a first data-driven method relying on a fuzzy identification approach to the control design is considered. In fact, since the wind turbine mathematical model is nonlinear with uncertain inputs, fuzzy modeling represents an alternative tool for obtaining the mathematical description of the controlled process. In contrast to purely nonlinear identification schemes (see, e.g., [5]), fuzzy modeling and identification methods are able to directly provide nonlinear models from the measured input-output signals.