# Fractional Order Controller Design for Wind Turbines
## 1 Introduction
Among these algorithms, this section considers genetic algorithms (GAs), artificial neural networks (ANNs), particle swarm optimization (PSO) and radial basis function neural networks (RBFNNs). In [9], the authors presented the use of a genetic algorithm to tune the parameters of an FOPID controller. The \"ranking method\" was used to select the best combinations of parameters, in which every combination was put into a \"dual\" and only the combination that produced the best results was compared to the other combinations. This process continued until the minimum \"fit\" was found. The cost function was represented by the sum of the error norm and the square of the control signal. This particular function was chosen in order to avoid large control inputs and to achieve good dynamic performance. Another GA was also used in [10]; however, instead of using the generalized rule of GAs in which optimization is achieved using strings, the authors used a set of equations that were determined by the imposed performance of the gain margin, phase margin, robustness, the sensitivity of the process and the complementary sensitivity. The process for identifying the optimal parameters was repeated until the integral of the absolute error (IAE) was minimal. In [11], an innovative idea was evinced for developing FOPID controllers that were tuned with the help of neural network (NN) algorithms. In this method, neural networks were assigned to each FOPID parameter and the weights from the NNs were updated using the extended Kalman filter so convergence was accomplished in fewer iterations. The activation function for the hidden layer was the hyperbolic tangent and a linear function was used to activate the neurons in the output layer, with the aim of mapping the data at the desired magnitude. Due to the fact that artificial neural network controllers provide adaptability and generalizability, researchers have started to use them more and more often because they offer the possibility of managing both linear and nonlinear systems [12]. Another useful optimization algorithm that has become more frequently used in control systems is PSO. The important benefit of this algorithm is the ability to avoid becoming trapped in local optima and in this way, the search area is reduced. Moreover, PSO has proved to be very efficient in tuning the parameters of FOPID controllers for various controlling systems, such as automatic voltage regulators (AVRs) [13], twin rotor aerodynamical systems (TRASs) [14], chemical processes (e.g., isotope separation columns) [15] and mobile robots [16]. The authors of [13] defined a new cost function in order to simplify their control strategy equally for the time domain and the frequency domain. Thus, when a particle generated instability in their system, a \"penalty\" in the closed-loop was applied. This penalty consisted of a large constant value that meant that the faulty particle was not able to resist during the updating process. In [14], a new initialization procedure for search areas was developed. By applying the spreading factor (SF) method, the inertia weight and the acceleration coefficient converged linearly toward predefined values. The authors of [15] highlighted the use of a hybridization method for transforming FOPID controllers into a discrete form. This hybridization method consisted of the interpolation of the Euler and Tustin methods of discretization. In order to approximate the parameters of the FOPID controller, the Oustaloup approximation method was used. Despite all of the advantages of the PSO algorithm, it also has its down sides: premature convergence and the need for a user to set both the values of the parameters and the value of the exploration capacity. Consequently, to address these disadvantages, the authors of [16] proposed an innovative hybridized form of the PSO algorithm that was combined with the fruit fly optimization (FFO) algorithm.