## 3 Model Development
The change in the temperature of the room air with the effect of heat loss due to the heat loss in the room caused by the cooling and the heat gains (\(Q_{dist_{room}}\)) due to the deteriorating effects is determined by using Equation (5). \[\left(\frac{\partial Q_{dist_{room}}}{\partial t}-\frac{\partial Q_{cooler}}{ \partial t}\right)\frac{1}{M_{air}c}=\frac{\partial T_{room}}{\partial t} \tag{5}\]  
Thus, the instantaneous room temperature, which is fed back into the control, is obtained. By adjusting the fan speeds of the air taken from the atmosphere, the temperature of the cooler outlet air is changed, and thus the temperature of the room is adjusted, and the whole system temperature change equations are obtained. An error input is created for the controller by comparing the instantaneous temperature of the room with the desired reference temperature. For this reason, the correlation between the fan speed and the change in room temperature is of great importance. After the temperature change modeling was completed, a similar modeling process was performed for the mass transfer process. The change in the relative humidity of the air taken into the cooler is mostly realized during the desiccant-wheel-based cooling process. For this reason, in the control strategy developed, the dehumidification amount is adjusted by changing the speed of the desiccant wheel. There is a direct proportionality between these two parameters and the relationship between the change in the relative humidity of the air dehumidified in the cooler and the speed of the desiccant wheel and the change created by this less humid air fed into the room in the room air need to be modeled. For this purpose, the relation between the desicant wheel's speed and mass transfer is determined, firstly. The speed of the desiccant wheel is converted to vapor mass in the air as follows. The relative humidity of the intake air (\(RH_{dw}\)) is assumed to equal the relative humidity of the atmospheric air (\(RH_{atm}\)):  
\[V_{dw}K_{conv_{dw}}=RH_{dw}=RH_{atm}=\frac{\partial M_{dw}}{\partial t} \tag{6}\]  
where \(V_{dw}\), \(K_{conv_{dw}}\) and \(M_{dw}\) indicate the speed of the desiccant wheel, the converting coefficient between the speed and vapor mass variation, and the vapor mass, respectively. Then, the variation of the relative humidity in the cooler is determined by using the variation of vapor mass due to DW's speed change. The relative humidity of the air at the outlet of the cooler is:  
\[\frac{\partial RH_{cooler}}{\partial t}=\frac{1}{K_{rhdpc}}\bigg{(}\frac{ \partial M_{dw}}{\partial t}+\frac{\partial M_{dist,c}}{\partial t}\bigg{)} \tag{7}\]  
\(M_{dist,c}\) represents the disturbing effects due to uncertainty and unknown mass transfer in the cooler. They lead to increase in the relative humidity of the air. \(K_{rhdpc}\) is the coefficient for converting vapor mass to relative humidity. Finally, the relation between the speed of the desiccant wheel and the variation in the relative humidity of the air is obtained for the cooler. After that, the air is supplied into the room and the variation of the relative humidity of the room's air is determined as a function of supplied cooler air's relative humidity. Similar to the temperature variation process, a balance will be tried to be established by mass transfer between the less humid air fed and the humid air in the room. For this purpose, firstly, the mass change caused by the relative humidity of the air at the cooler outlet was calculated:  
\[RH_{room}-\frac{RH_{cooler}+RH_{room}}{2}=\frac{\partial M_{cooler}}{\partial t} \tag{8}\]  
where \(M_{cooler}\) represents the vapor mass. Then, the variation of the relative humidity of the room's air (\(RH_{room}\)) is determined by using Equation (9) as a function of vapor gains due to disturbance effects (\(M_{dist_{room}}\)) and vapor loss due to the dehumidification process in the cooler.