# A Review on Applications of Fuzzy Logic Control for Refrigeration Systems
## 2 Fuzzy Controller Design Applied to RACs
The range of the values that the universe can take is very diverse and depends on the range of the measurement of the variables that are taken into consideration for the design of each controller. Figure 1: General scheme of a fuzzy controller. Additionally, it is very common in the design of a controller that the names of the linguistic variables are similar to the names of the membership functions. For instance, if the function is centered around zero, the name would be Z. On the other hand, if the function is positive, the name would be P. When the function is negative, the name could be N. In the same sense, it is customary to use the modifiers \"very\" (V), \"medium\" (M), \"low\" (L), etc. To establish some of the linguistic terms, such as \"very positive\" (VP) or \"slightly low negative\" (SLN), it is necessary to assign these names based on the number of functions in the controller. Table 1 shows a summary of the description of the linguistics variables most frequently used in the design of fuzzy logic controllers for the input and output variables. The output variables in the fuzzy logic controllers in the RACs correspond to variables of the actuators. For instance, temperature control is performed by modifying mainly the speed of the compressor, the duty cycle of the compressor, and the opening of the expansion valves. For humidity control, it is regulated by modifying the speed of the fans or opening the gates. The fuzzy sets for the input and output variables generally coincide in quantity and shape. For the RACs, systems with five membership functions for the input and the output are generally designed. However, [PERSON] et al. [24] presented a set of membership functions with different quantities and shapes for the input and output variables, showing that it is not necessary to use the same type and number of functions to attain satisfactory \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Inputs** & & & **Outputs** \\ \hline
**Variable** & **Linguistic Term** & **Description** & **Variable** & **Linguistic Term** & **Description** \\ \hline \multirow{8}{*}{Temperature} & VHP & Very high positive & & VHS & Very high speed \\  & MP & Medium positive & & MED & Medium \\  & LP & Low positive & & SLH & Slightly high \\  & Z & Zero & & VH & Very high \\  & SHN & Slightly high negative & & NM & Normal \\  & HN & High negative & & SLL & Slightly low \\  & VHN & Very high negative & & AISpeed, fan speed, & VLS & Very low speed \\ \hline \multirow{8}{*}{Humidity} & H & High & opening percentage & SLS & Slightly low speed \\  & VL & Very low & & LS & Low speed \\ \cline{1-1}  & SH & Slightly high & & MS & Medium speed \\ \cline{1-1}  & M & Medium & & SHS & Slightly high speed \\ \cline{1-1}  & L & Low & & VLS & Very low speed \\ \cline{1-1}  & SH & Slightly high & & OFF & Off \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Linguistic variables frequently used in RACs. Figure 2: Membership function sets for the input and output variables. (**a**) trapezoidal functions, (**b**) Gaussian functions. results in temperature control. Additionally, [PERSON] et al. [25] demonstrated that according to the defuzzification method, the behavior of the output variables is affected and values with considerable differences are obtained that directly affect the behavior of the system. Fuzzy Logic Integrated with Other Control Systems for RACsOne of the advantages of fuzzy logic is its ease of integration with other controllers; this integration has shown an improvement in the regulation of process variables. One of the most common integrations in RACs is with Proportional Integral Derivate, PID, controllers. Figure 3 shows the general diagram of a fuzzy PID controller. This diagram shows the most frequent application in RACs, where fuzzy control supervises the adjustment of the constants kp, ki, and kd of the PID control, generating self-adjusting controls or adaptive controllers. There are also alternatives in the application of PID fuzzy controllers.