# A Review on Applications of Fuzzy Logic Control for Refrigeration Systems
## 2 Fuzzy Controller Design Applied to RACs  
Logic fuzzy systems are based on the human ability to think, which has allowed controllers to adapt better to systems by finding an approximation to their real behavior. This has been observed mainly in those systems where their analytic functions are difficult to obtain. These controllers, through the creation of a database of knowledge with fuzzy linguistic expressions and rules, can make decisions about the control of a process using a method called inference. This method simulates the human thinking process allowing us to understand mathematically the knowledge represented in rules of the type IF-THEN to obtain an output value from the controller. In this sense, the inference method of [PERSON] (Max-Min) is most commonly used in the design of fuzzy controls for the RACs. Another method also used in the field of refrigeration is the Sugeno method or Takagi-Sugeno-Kang, TSK. Figure 1 shows the typical structure of a fuzzy control system. It has four stages: fuzzification, rule base, inference engine, and defuzzification. During the fuzzification stage, the crisp inputs (the numeric values), by using membership functions, will determine the fuzzy values (\(\mu(x)\)) in the range from zero to one. Then, the inference engine takes the fuzzy variables and evaluates the rules established in the rule base, and one or more fuzzy sets representing the output fuzzy variables can be obtained. Finally, defuzzification converts the fuzzy variables into crisp values that can be used by the actuator in a control system [20]. At this stage, it is possible to use different methods to perform this transformation from fuzzy values to real values. Generally speaking, the fuzzy control applied to the RACs focuses on the control of temperature and humidity. Consequently, variables, such as the duty cycle, the electric frequency of the compressor, the opening of the expansion valve, and the flux of the refrigerant are manipulated. Because of the similarity between the controlled variables (temperature and humidity) and the manipulated variables (operating duration or compressor frequency), the design of controllers for the RACs shares some characteristics independently of the system to which it is applied. The first element corresponds to the design of the membership functions for the input and output variables of the fuzzy system. Figure 2 shows the fuzzy sets most used for the RACs, these present a combination of triangular and Gaussian functions. In these sets, two of the functions are placed at the ends and they correspond to trapezoidal functions (Figure 2a) or Gaussian functions (Figure 2b). In the study of the RACs, the triangular function is most commonly used around 70% of the published research papers present controllers using a combination of triangular functions. This is because a triangle or a trapezius often provides an adequate representation of the expert knowledge, and at the same time, these two shapes simplify significantly the computation process [21] and they can additionally improve the dynamics of the system [22]. However, [PERSON] and [PERSON] [23] showed that the use of triangular or trapezoidal membership functions affects the performance of the controller and, in particular, for air conditioning systems, trapezoidal functions are the most suitable. The set of the membership functions may depend directly on the variable or the error. With low frequency, sets of fuzzy functions in which the domain depends directly on the variable are presented. In these cases, the domain of the set of membership functions (or universe) includes all possible values that the variable can take. In most cases, there are sets in which the membership functions depend on the error, the derivative of the error, or the integral of the error. Therefore, the range of the set of functions exhibits negative and positive values.