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, while 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].

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

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons © 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

can produce further problems to the design of the control method. In general, commercial codes are not able to adequately describe the wind turbine overall dynamic behaviour; 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 task of the control law consists of maintaining safe and reliable working 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 chapter [2].

the controller model. In particular, a recursive Frisch scheme extended to the adaptive case for control design is considered in this study, as proposed, e.g. in Simani and Castaldi [9], which makes use of exponential forgetting laws. This allows the online application of the Frisch

Robust Control Applications to a Wind Turbine-Simulated System

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Finally, the chapter is organised as follows. Section 2 recalls the wind turbine model considered for control design purposes. Section 3 addresses the data-driven scheme exploited for the derivation of the fuzzy controller, proposed in Section 3.1. On the other hand, the model-based control design is considered in Section 3.2, based on its mathematical derivation also described in Section 3. The achieved results and comparisons with different control strategies are outlined in Section 4.

This section outlines the wind turbine model, whose sampled inputs and outputs will be used

The wind turbine system exploited in this chapter uses a nonlinear dynamic model representing the wind acting on the wind turbine blades, thus producing the movement of the low-speed rotor shaft. The higher speed required by the electric converter is produced by means of a gear box. The simulator is described in more detail, e.g. in Odgaard et al. [10]. A block scheme of the

Both the generator speed and the generator power are controller by means of the two control inputs representing the generator torque τg(t) and the blade pitch angle β(t). Several signals can be acquired from the wind turbine simulator. In particular, the signal ωr(t) represents the rotor speed measurement, whereas ωg(t) represents the converter velocity. Concerning the electric generator, τg(t) refers to its required torque, which is controlled by the converter. Therefore, this signal represents the measurement of the torque setpoint, τr(t). The aerodynamic model defining the aerodynamic torque provides the τaero(t) signal, which is a nonlinear function of the wind speed v(t). This measurement is very difficult to be acquired correctly, as

<sup>τ</sup>aeroðÞ¼ <sup>t</sup> Cp <sup>β</sup>ð Þ<sup>t</sup> ; <sup>λ</sup>ð Þ<sup>t</sup> <sup>r</sup>Av<sup>3</sup>ð Þ<sup>t</sup>

(t) r

<sup>2</sup>ωrð Þ<sup>t</sup> (1)

Generator

P (t) <sup>g</sup>

(t) <sup>g</sup>

g(t)

wind turbine simulator considered in this chapter is represented in Figure 1.

The aerodynamic model reported in Figure 1 is described as follows:

Wind

(t)

Aerodynamic model

*v*(t)

scheme to derive the parameters of a time-varying controller.

2. Wind turbine simulator model

described in Odgaard et al. [10].

Controller

(t) <sup>g</sup>

(t) P (t) <sup>g</sup> <sup>r</sup>

Figure 1. Scheme of the wind turbine process.

for the proposed control designs, as shown in Section 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 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 modelling 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 maximise 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 [3].

Regarding the regulation strategies proposed in this chapter, two control design examples are described and applied to a wind turbine system. The wind turbine model exploited in this chapter is freely available for the Matlab® and Simulink® environments and already proposed as benchmark for an international competition regarding the validation of fault diagnosis and fault-tolerant control approaches [2].

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 modelling represents an alternative tool for obtaining the mathematical description of the controlled process. In contrast to purely nonlinear identification schemes, see, e.g. [4], fuzzy modelling and identification methods are able to directly provide nonlinear models from the measured input-output signals. Therefore, this chapter suggests to model the wind turbine plant via Takagi-Sugeno (TS) fuzzy prototypes [5], whose parameters are obtained by identification procedures. This approach is also motivated by previous works by the same authors [6].

Regarding the second model-based strategy presented in this chapter, it relies on an adaptive control scheme [7]. Again, with respect to pure nonlinear control methods [8], it does not require a detailed knowledge about the model structure. Therefore, this chapter suggests the implementation of controllers based on adaptive schemes, used for the recursive derivation of the controller model. In particular, a recursive Frisch scheme extended to the adaptive case for control design is considered in this study, as proposed, e.g. in Simani and Castaldi [9], which makes use of exponential forgetting laws. This allows the online application of the Frisch scheme to derive the parameters of a time-varying controller.

Finally, the chapter is organised as follows. Section 2 recalls the wind turbine model considered for control design purposes. Section 3 addresses the data-driven scheme exploited for the derivation of the fuzzy controller, proposed in Section 3.1. On the other hand, the model-based control design is considered in Section 3.2, based on its mathematical derivation also described in Section 3. The achieved results and comparisons with different control strategies are outlined in Section 4.
