## 4 Results: MPPT Techniques Review
The Lyapunov functions are used to derive the update rules. For the pitch controller, two RBF networks solve the non-linear space state equation. In [74] an RBFNN is used with an input layer for the power supply error, a hidden layer with 25 neurons and an output layer with the approximate non-linear part. The training algorithm is a descending gradient. The result is greater stability in the extraction of wind energy. This control strategy is explained with Figure 16.  
In [75], the author proposes an individual pitch controller based on RBFNN. The controller requires two inputs variables, the error in the speed of the rotor axis and the measurement of the wind speed by Light Detection and Range (LIDAR). Better performances are obtained than with a PI controller, but with wind speed disturbances, the controller does not work properly. This is because LIDAR measurements delay the controller and cannot anticipate wind speed. The design of this methodology is shown in Figure 17. The design of this methodology is shown with Figure 17.  
Figure 16: ANN control strategy, acts on the control pitch and the speed of the generator. Uses as input, the error in the generator speed and the power generated [74]. Figure 13.0 Block diagram of an ANN controller that selects the control signal according to the measured wind speed [71]. Figure 13.1 In the control strategy two techniques are used, Multy Layer Perceptron Neural Network (MLPNN) regulates the pitch angle and Integral Sliding Mode Control (ISMC) adjusts the rotor speed reference independently of external disturbances [72]. In [76], the author works with two adaptive neuro-fuzzy inference system (ANFIS), combining ANN with FLC decision process without requires sensor for wind speed. The first ANFIS for wind speed estimation uses generated power and rotor speed as inputs and the output is wind speed. The second ANFIS uses the wind speed estimation of first ANFIS as input to give the optimum rotor speed. In [77], an ANN based on reinforcement learning (RL) is proposed. RL process learns the optimal relationship between rotor speed and electric power. The algorithm changes online, the RL process to application process when it has the optimal relationship. The RL process can be reactivated online any time the actual optimal relationship deviates due to a change in the environment. The block diagram of this strategy is presented in Figure 13.2  
In [78], a function of Nussbaum type is proposed to solve the non-linearity of the system and an RBFNN to determine the set-point values of the variable speed and variable angle controllers. The strategy is to control the generator torque before the rotor speed reaches the nominal speed. At the rated speed, the generator torque also reaches its nominal value and cannot be used as a control strategy, so the angle control of the blade is adopted as an input to maintain the rotor speed at its nominal value. In [79], the author presents a pitch angle controller that is based on equaling \(\text{CP}_{\text{ref}}=\text{Cp}_{\text{opt}}\). If the wind speed is higher than nominal speed, \(\text{Cp}_{\text{opt}}\) must be a small value, so ANN calculates a high value of \(\beta_{\text{ref}}\); and if the wind speed is lower than nominal speed, \(\text{Cp}_{\text{opt}}\) must be a higher value, so ANN calculates a low value of \(\beta_{\text{ref}}\). The training process is performed using the Levenberge-Marquardt algorithm to search for optimal synaptic weights. In [80], a control method is presented, based on an adaptive ANN-PID in which the PID parameters are regulated automatically. The gradient descent method is used to optimize ANN weights. This control strategy is shown in Figure 13.3  
In [81], a PI generator torque control is presented. In order to tune the PI gains, a RBFNN is used. The optimal dataset to train this neural network is provided by the Gravitational Search Algorithm (GSA).