## 5 Normal Fuzzy Logic Controller  
The FLC is an approach to attaining the MPP of photovoltaic systems based on an expert-type control method that uses human experience to make decisions. The fundamental concept is the use of language to specify control rules. The distinguishing feature is the transformation of human experience into control rules. Thus, fuzzy control is more advantageous when dealing with complex nonlinear systems whose mathematical model is unknown. Generally, the controller is divided into three phases: fuzzification, rule-based table, and defuzzification. In this study, a Mamdani type is presented as it is considered the most popular type, and the rules can be obtained from experienced human operators. At the same time, the Sugeno approach is suitable for generating fuzzy rules from a given input-output dataset. A membership function with a triangle form is employed due to its fewer complexes when splitting values (low, medium, and high) than other membership functions. When the controller is used with the PV pumping system, the inputs to the controller are error (\(E\)) and change in the error signal (\(CE\)). The controller's output is the duty cycle (\(CD\)). Five fuzzy sets are used to describe each input and output variable: NB (Negative Big), N (Negative), Z (Zero), P (Positive), and PB (Positive Big) [16; 17; 18; 19; 20; 21]. The following equations define the fuzzy controller's inputs and outputs:  
\[CE=E(n)-E(n-1) \tag{15}\]  
\[CD=f(E,CE) \tag{16}\]  
where \(E(n)\): is the present value of the error and \(E(n-1)\): is the previous value of the error.  
The maximum output power can be defined by examining the characteristics of the photovoltaic panel at various temperatures and irradiance levels. The simulation work is considered a membership function with a triangular shape. The membership of the input and output signals, which were designed using simulation data, is shown in Figure 9. Fuzzy rules consist of linguistic rules that relate fuzzy inputs to fuzzy outputs. These are based on an expert's knowledge and comprehension of the system's behavior, which is necessary to accomplish the control objectives. The fuzzy control rules comprise a series of IF-THEN statements that include all relevant information for the controlled parameters. The rules are designed to incorporate the following considerations:  
1. If a positive change in the error signal is followed by a positive change in the change of the error signal, the chopper duty ratio must be raised. If the error signal variation is negative, the chopper ratio should be lowered.
2. If the error signal change is zero or very close to zero, which means it has reached its maximum, the chopper ratio should not change.  
Figure 8: Simulink model of the system with the SUI-PID.  
3. If a negative change in the error signal is followed by a positive change in the error signal, the chopper duty ratio must be lowered. If the error signal variation is positive, then the chopper ratio should be increased.  
The design of the fuzzy rules can be illustrated in Table 3, and the system with the normal FLC Simulink model is shown in Figure 10.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**E** & **NB** & **N** & **Z** & **P** & **PB** \\
**CE** & & & & & \\ \hline NB & PS & PB & NB & NB & NS \\ N & PS & PS & NS & NS & NS \\ Z & Z & Z & Z & Z & Z \\ P & NS & NS & PS & PS & PS \\ PB & NS & NB & PB & PB & PB \\ \hline \hline \end{tabular}
\end{table}
Table 3: FLC rule-based table.  
Figure 9: Membership functions of the fuzzy system. (**a**) Error signal. (**b**) Change of error signal. (**c**) Change of duty cycle.