## 4 Fuzzy Control Structure for Supervisory Ejector Cycle and Multi-Solar Collector Systems
### Layer 2: Supervisory Fuzzy Control of Ejector Cooling Cycle
According to our objective, which is to optimize the use of the refrigeration cycle, different cooling capacities, e.g., 3.0, 3.5, 4.0, 4.5 and 5 kW, are maintained for our analysis. Equation (5) helps us to calculate the necessary energy and mass flow to operate the ejector refrigeration cycle for different cooling capacities:  
\[Q_{R}=\dot{m}_{e}(h_{8}-h_{6}). \tag{5}\]  
For the development of the control strategy, it is necessary to calculate the mass flow rate of the evaporator and the generator for different powers. In relation to the analysis performed for the  
Figure 6: Entrainment ratio with respect to the generator temperature. To facilitate the control strategy, we proceed to calculate the average mass flow of the evaporator and the generator with the five cooling powers. Figure 10 and Table 3 show the linkage of the mass flows. The operation modes are determined by the end user. Mode 0 means economical use in energy; according to the analysis made in the previous section, the reference for the tank temperature control system should be low, and the outputs of references in flow generator and evaporator also should be moderately low, but within the limits that have been set for the ejector cooling cycle to work. In contrast, Mode 5 must set the reference temperature for the tank control to the maximum permissible by the previous analysis performed. Figure 11 shows the input variables for the fuzzy governor controller; this variable is the actual value \(T_{c}\), while \(dT_{c}/dt\) act as the derivative of temperature \(T_{c}\) in the solar collectors and allow one to know the behavior of solar radiation at all times. Finally, in Figure 12 are shown the governor outputs \(\dot{m}_{g}\) and reference temperature for fuzzy control of the solar collector. The following fifteen fuzzy sets: LL (Low Low), L (Low), M (Medium), H (High), HH (High High), NH (High Negative), NM (Medium Negative), Z (Zero), P (Positive), PH (High Positive), \(M_{1}\) (Mode 1), \(M_{2}\) (Mode 2), \(M_{3}\) (Mode 3), \(M_{4}\) (Mode 4) and \(M_{5}\) (Mode 5), represented as triangular and trapezoidal functions of the membership degrees, are defined for each of the input variables; see Figure 11. Output fuzzy set membership function for generator mass flow and input temperature reference to fuzzy control of solar collector, respectively, use the following fuzzy sets: \(Mg_{1}\) (Generator Mass Flow 1), \(Mg_{2}\) (Generator Mass Flow 2), \(Mg_{3}\) (Generator Mass Flow 3), \(Mg_{4}\) (Generator Mass Flow 4), and \(Mg_{5}\) (Generator Mass Flow 5) and output temperature set reference for fuzzy control of solar collector: LL (Low Low), L (Low), M (Medium), H (High) and HH (High High); see Figure 12. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Cooling Power (\(k\)W)** & \(\dot{m}_{e}\) (kg/s) & \(\dot{m}_{g}\) (kg/s) \\ \hline
3 & 0.01845 & 0.03382 \\
3.5 & 0.02153 & 0.03946 \\
4 & 0.02460 & 0.04510 \\
4.5 & 0.02768 & 0.05073 \\
5 & 0.03075 & 0.05637 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average of \(\dot{m}_{e}\) and \(\dot{m}_{g}\) for different cooling powers. Figure 10: Mass flow of the generator (\(\dot{m}_{g}\)) and evaporator (\(\dot{m}_{e}\)) considering five different powers (\(k\)W).