## 4 Proposed Architecture of Model-Based Predictive Control for Thermal Comfort in Building
### Fuzzy Based Control Model  
A fuzzy control system is a control system based on fuzzy logic that has been widely employed in many areas such as air condition, refrigeration and robotic control systems. Some other approaches like genetic algorithms and neural networks can perform as well as fuzzy logic in many cases; however, fuzzy logic has the advantage that the solution to the problem can be cast in terms by using the common sense or experience that makes human operators understand easily. Among the most \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Gathering Period** & **Gathering Time** & **Data Interval** & **Predictive Mean Vote (PMV) Indices** & **Measure Data Range** & **International Standardization (ISO)** \\ \hline From June to the end & 9:00–21:00 & 10 min & \(T_{a}\) 0 & 18.5–32 & 10–30 \\  & - & - & \(V_{ar}\) (m/s) & 0.0–0.3 & 0.0–1.0 \\ - & - & - & \(T_{mr}\) () & 18.5–28.5 & 10–40 \\ - & - & - & \(H_{r}\) (%) & 15.0–40.6 & 30–70 \\ - & - & - & \(l_{cl}\) (m\({}^{2}\cdot\)K/W) & 0.5 & 0–2 \\ - & - & - & \(M\) (W/m\({}^{2}\)) & 1.2 & 0.8–4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Data set for building a multiple linear regression model. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **Coefficient** & **Error** \\ \hline Intercept & \(-4.4566\) & \(3.8\times 10^{-2}\) \\ \(T_{a}\) & 0.1153 & \(1.1\times 10^{-2}\) \\ \(T_{mr}\) & 0.1012 & \(1.3\times 10^{-2}\) \\ \(H_{r}\) & 0.0035 & \(2.2\times 10^{-4}\) \\ \(V_{ar}\) & 0.0015 & \(2.1\times 10^{-2}\) \\ R-square & 0.8945 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Multiple linear regression coefficient validation. successful applications of this theory has been the area of fuzzy logic control (FLC) initiated by the work of [PERSON] [46]. Mamdani fuzzy inference is the most commonly seen fuzzy methodology and was among the first control systems built using fuzzy set theory. The FLC provides an algorithm that can convert the linguistic control strategy based on expert knowledge into an automatic control strategy. A linguistic variable is a linguistic expression labeling an information granular, such as age for persons or temperature for weather. Since natural languages do not always contain enough value terms to express a fuzzy value scale, it is common practice to modify linguistic values with adjectives or adverbs. In this paper, the Mamdani rule structure with the linguistic fuzzy modeling has been applied in the PMV based thermal control. Two kinds of membership functions, triangular or trapezoidal functions, are contained in the fuzzy system to define the fuzzy variables. The characteristic function \(\mu_{A}(x)\) assigned by four quantified variables: (\(a\), \(b\), \(c\), \(d\)), describes the trapezoidal fuzzy set \(A\). Equation (8) interprets the mathematical representation of the proposed membership function:  
\[\mu_{A}(x)\left\{ \begin{array}{rl}0,&x<a\\ \frac{x-a}{b-d},&a<x<b\\ 1,&b<x<c\\ \frac{d-x}{d-c},&c<x<d\\ 0,&x>d\end{array} \right.\qquad(a<b\leq c\leq d). \tag{8}\]  
It is noteworthy that the trapezoidal function can be regarded as a triangular one if \(b=c\). Equation (9) defines the intersection operation between two fuzzy sets \(A\) and \(B\), where \(A\), \(B\in U\) and \(x\) can be any element in the \(U\) universe:  
\[\mu_{A\cap B}(x)=min\{\mu_{A}(x),\ \mu_{B}(x)\},\quad\forall x\in U, \tag{9}\]  
and their union is defined by Equation (10):  
\[\mu_{A\cup B}(x)=max\{\mu_{A}(x),\ \mu_{B}(x)\},\ \ \forall x\in U. \tag{10}\]  
The circumstance of the environment conditions can be described by means of linguistic rules, which opens to the adoption of fuzzy controller. The proposed fuzzy controller takes input variables including the PMV index value, the PMV index variation value, and outside temperature while the output variable of the controller is the fan coil speed.