## 1 Introduction  
The generation of large amounts of electricity is necessary to meet the growing demand; generating it through natural renewable resources is essential for the care of the environment. Within clean energy, wind energy has had great momentum in recent years. The Global Wind Energy Council reported 60.4 GW of new installations in 2019, and a global capacity of 651 GW and an expectation of growth of more than 100 GW in annual installations over the next decade [1]. However, the technological trend points to the development and construction of increasingly large wind turbines. Currently, the highest-capacity wind turbine is produced by Siemens Gamesa that generates 14 MW of nominal power, has a swept area diameter of 222 m, and requires an annual average wind speed of 10 m/s [2]. In places with lower wind resources, it is necessary to install small horizontal-axis wind turbines (SHAWTs). IEC 61400-1: 2014 defines \"small wind turbines\" as those with a swept area less than 200 m\({}^{2}\) and generation voltage less than 1000 V AC or 1500 V DC [3]. SHAWTs require a cut-in wind speed of 4 m/s [4]. Fifty percent of the planet has an average wind speed greater than 6.04 m/s at a height of 10 m [5]. These areas include buildings, trees, or mountains that are obstacles to the wind path, causing a decrease in wind speed and an increase in turbulence. The turbulence area reaches 2 or 3 times the height of the obstacles, while in the frontal contact part, it is 2 to 10 times [6]. Disorderly wind motion and fluctuating wind speed magnitude hinder the efficiency of a wind turbine and can be prone to failures, even catastrophic ones [7]. Therefore, a wind turbine should operate with variable wind speed and regulate the effect of the wind force on the rotor by controlling the angle of incidence between the blade and the wind flow [8]. The classical method of pitch angle control is the proportional integral derivative (PID), which is based on a mathematical model of the system with feedback of the controlled variable, as it calculates the error between the measured and desired values [9]. To adjust the controller, the weights of the proportional constant, the integral time, and the derivative time (gains) are determined [10]. This adjustment of optimum values of gains is performed for the desired control response. However, in a variable-speed wind turbine, the optimal response changes as a function of the magnitude of the wind speed variation. This variability makes a PID controller unstable with drastic changes in the wind speed [11; 12]. Pitch control methods in a wind turbine that mitigate changes in wind speed were found in the literature reviewed. In [13; 14; 15], a fuzzy logic controller (FLC) selects the previously calculated PID gains for the negative or positive error of the process variable, or if the error is very large. In [16], an artificial neural network determines the PID gain values. In [17], the \"differential evolution\" optimization algorithm is used to change the PID gain values as the operating point changes. In [18; 19], the proportional and integral gains of a proportional integral (PI) controller are adjusted by a \"particle swarm\" optimization algorithm. In [20], a \"flame-moth\" optimization algorithm is proposed, the candidate solutions are moths, and the PID parameters are the position of the moths in a 3D search space. In [11], an optimization algorithm based on the teaching-learning model of a classroom is used to calculate the gains of a PI controller. These known methods have different disadvantages. They improve the response of the control signal for different wind speed ranges, as the controller is adjusted for each of these ranges. However, when there is a sudden change in wind speed, the response of the controller is not optimal, due to the inertial impulse generated in the rotor. If the gain tuning is done using a search algorithm or neural networks, the global optimum solution is not guaranteed, because it can be set to a local minimum/maximum solution.