# Fractional Order Controller Design for Wind Turbines
## 1 Introduction  
Over recent years, renewable energy generation has been demanded more frequently for social and environmental reasons, including climate change and the dangers of the consumption of fossil fuel resources. In view of this increased demand, energy generation from wind turbine systems has been proved to be clean and efficient in many places, such as China, the USA and Europe [1]. However, due to their complex nonlinear structures, wind turbine systems come with great challenges because they have uncertain parameters, unknown disturbances and unmodeled dynamics. Nonetheless, these challenges could be overcome using advanced control strategies that contribute to improving turbine functionality. Bearing this in mind, the current study focused on obtaining electrical energy efficiently and reducing mechanical stress. Numerous control techniques have been proposed for this purpose, from conventional to artificial intelligence-based methods. The authors of [2] presented an innovative solution for controlling the mitigation of loads on wind turbines using a combination of nacelle acceleration feedback and the LiDAR-based feedforward control method. The authors of [3] highlighted the importance of improving estimation strategies for both the rotor flux and rotor speed; therefore, an adaptive Kalman filter was used to estimate the rotor flux and the concept of artificial neural networks was applied to estimate the rotor speed. This method proved to be very effective and resulted in enhanced robustness against parametric variations and uncertainties in the adaptation mechanisms. A generalized version of a PID controller is a fractional order PID controller, which has two more degrees of freedom. Over recent years, the use of FOPID controllers has become more and more common for a wide range of applications. In particular, numerous studies have shown that the FOPID control strategy leads to better closed-loop performance,as well as increased robustness. In [4], advanced tuning methods for FOPID controllers were compared to those for classic PID structures. An artificial bee colony PID (ABC-PID) controller and a particle swarm optimization FOPID controller were used for controller tuning. In [5; 6; 7; 8], the advantages of FOPID controllers and new tuning methods were studied and developed. In [5], a non-smooth optimization technique called \(\mu\)-synthesis was applied to tune the parameters of an FOPID controller that was used to control a multiple-input and multiple-output (MIMO) system. This methodology was proved to ensure the robust and stabile performance of a TRAS mechanism. The authors of [6] developed a new tuning method for FOPID controllers in order to improve the disturbance attenuation of periodic disturbances with estimated frequencies. The reference-to-disturbance (RTD) ratio was used as a quantitative measure of the control system's ability to reject disturbances. The authors of [7] proposed a tuning method for FOPID controllers that was inspired by the symmetrical optimum principles of Kessler. The main advantage of this technique was its simplicity in comparison to other methods. It could also be applied in a wide range of process models, from integer order models to fractional order models, which assured also both its robustness and the desired closed-loop characteristics. Although FOPID controllers present many advantages for system performance, the hardware requirements for FOPID implementation are high when higher order systems need to be controlled. Due to this drawback, the authors of [8] proposed a new implementation method for FO-IMC controllers. Their method consisted of event-based implementation in order to optimize the bandwidth allocation and energy usage. This method was tested using first-order plus dead-time (FOPDT) processes and produced better results in terms of reference tracking, disturbance rejection and robustness compared to a classic PI controller. Baseline research has focused on the use of state-of-the-art optimization algorithms for tuning FOPID parameters.