## 8 Theoretical Results  
Figure 15 shows a comparison of the power delivered to the pump by the three controllers when the irradiance level is constant at 1000 Watt/m\({}^{2}\) (the comparison includes constant step input as in Figure 15 and varying step input as in Figure 16). In comparison to the SUI-PID and the normal FLC controllers, the MDOF-FLC has a faster response, a better rise time, and a lower error. It appears from Table 6, showing the comparative performance analysis associated with different controllers, that the proposed MDOF-FLC records the best values in rising time, settling time, and integral time absolute error (ITAE). The time required to attain a steady state was 2.3 milliseconds with the MDOF-FLC, 3.7 milliseconds with the SUI-PID controller, and 5.5 milliseconds with the normal FLC. (i.e., 37.8% and 58.1% enhanced response compared to the SUI-PID controller and the normal FLC, respectively). Also, the error, measured by the ITAE, was 29.4% and 62.5% lower, respectively. Figure 16 illustrates the capability of the MDOF-FLC, normal FLC, and SUI-PID controllers to track the MPP under various irradiance levels. The irradiance level was abruptly increased from 600 Watt/m\({}^{2}\) to 800 Watt/m\({}^{2}\), and subsequently to 1000 Watt/m\({}^{2}\). The three controllers responded well when following the MPP. However, the MDOF-FLC has a smaller rise and settling time. Pump performance under a range of operating circumstances was simulated. These situations include varying scenarios, constant irradiance levels, and abrupt irradiance level fluctuations from 300 Watt/m\({}^{2}\) up to 1000 Watt/m\({}^{2}\) for all pumps. The pump performance curve [27] can be used to estimate the volume flow rate \(Q\). The study analysis of the solar pump includes three different types: Kyocera SD (6-35), SD (12-30), and SD (3-70). The SD (6-35) was studied for heads of 15 m and the pump's maximum water head of 35 m. Figures 17 and 18 provide a comparative analysis of the amount of water for the heads under varied levels of irradiation using the proposed MPPT MDOF-FLC, MPPT FLC, MPPT SUI-PID, and without MPPT control. Next, the SD (12-30) was evaluated at heads of 20 m and the pump's maximum water head of 30 m. Figures 19 and 20 provide a comparative analysis of the amount of water for the heads under varied irradiance levels with the proposed MPPT-MDOF-FLC, the MPPT normal FLC, the MPPT SUI-PID, and without MPPT control. Finally, the SD (3-70) was evaluated at heads of 40 m and the pump's maximum water head of 70 m. Figures 21 and 22 provide a comparative analysis of the amount of water for the heads under varied levels of irradiation using the proposed MPPT MDOF-FLC, MPPT FLC, MPPT SUI-PID, and without MPPT control. Figures 23-26 demonstrate an increase in the amount of water provided at various irradiance levels when the MPPT control algorithms are used. The proposed MDOF-FLC provides a slight increase in the water flow rate compared to the FLC. \begin{table}
\begin{tabular}{l l l l} \hline \hline  & **MDOF-FLC** & **SUI-PID** & **FLC** \\ \hline ITEA & 0.12 & 0.17 & 0.32 \\ Rising Time & 0.0018 s & 0.0023 s & 0.0037 s \\ Settling Time & 0.0023 s & 0.0037 s & 0.0055 s \\ \hline \end{tabular}
\end{table} 
Table 6: Comparative performance analysis associated with different controllers. Figure 16: The output of different controllers under various irradiance levels. Figure 19: Performance analysis of the volume flow rate at a head of 20 m.  
Figure 17: Performance analysis of the volume flow rate at a head of 15 m.  
Figure 18: Performance analysis of the volume flow rate at a head of 35 m.  
Figure 21: Performance analysis of the volume flow rate at a head of 40 m.  
Figure 22: Performance analysis of the volume flow rate at a head of 70 m.  
Figure 23: Experimental setup of the system. Figure 24: _Cont._  
Figure 25: Cont. Figure 16:0 (**A**) Output power and voltage with MDOF-FLC under constant atmospheric conditions (T = 25 \({}^{\circ}\)C, G = 1000 Watt/m\({}^{2}\)).