# Fractional Order Controller Design for Wind Turbines
## 1 Introduction
Firstly, the global best value was obtained using the PSO algorithm, then the previous best locations of the swarm particles were updated with the help of the FFO. In [17], the PSO algorithm was used to tune the FOPID controller of an automatic voltage regulator system. The practical implementation of FOPID controllers was detailed in [18], which highlighted the advantages of using FOPID controllers for multicopter systems that require high levels of stability and maneuverability. The radial basis function (RBF) is an artificial neural network that utilizes the Gaussian function as the activation function for the hidden layer neurons. Structurally, the algorithm is simple: it has one input layer, one hidden layer and one output layer, which uses a linear function to activate its neurons. As a result of this simplified structure and logic, researchers (such as the authors of [19] and [20]) have identified the opportunity to use these networks for tuning the parameters of FOPID controllers. The architecture of the RBF algorithm that was used in [19] was similar. The input layer consisted of a control signal, output signal and time-delayed output. Another strategy for the use of the RBF algorithm was presented in [20]. The FMINCON function from MATLAB was used to find the optimal parameters for an FOPID controller. The main functions that needed to be minimized included the gain margin and the phase margin, while robustness, process sensitivity and complementary sensitivity were used as constraints. Other powerful optimization methods include the artificial bee colony (ABC) method [21] and the flower pollination algorithm (FPA) [22]. The present study used three optimization methods to tune FOPID controllers for two-mass wind turbine systems and compared their performance. For the FOPID controller tuning, the considered parameters were steady-state error, settling time, overshoot, stability and robustness. The controller design was realized in the frequency domain, in which the gain crossover frequency, system sensitivity and robustness equations could secure the management of the system performance, with the help of the phase margin. The equations in the frequency domain were used to compute the FOPID parameters with the help of the following optimization algorithms: a genetic algorithm (GA), a multi-objective genetic algorithm (MOGA) and particle swarm optimization (PSO). Another objective of the present study was to compare the obtained results to those in the specific literature of the field, particularly for ABC-PID, PSO-PID, FOPID and PI controllers that were evaluated using the IAE. This paper consists of four main sections. After this introductory section, Section 2 describes the wind turbine model and the mathematics behind the system. The structures of the FOPID controllers are also detailed, along with the optimization algorithms that were used to tune the controllers. Then, the third section presents the simulation results from our experiments using the two-mass wind turbine model. The results are presented in tables for easier interpretation. In the conclusions section, the main findings of this paper are highlighted, along with a discussion about the benefits of using this control strategy.