Thermal Modeling of Heating Actuator
Summary
In control systems, a transfer function is known as the mathematical relationship between the inputs and the outputs of a system. This relationship aids greatly in enhancing the controller of the system and increasing its stability.
The system in question is a greenhouse prototype system that is designed to control and adjust the environment inside a confined area, in order to produce a suitable environment for the growth of plants. Out of the various variables that can affect the environment, the temperature is one of the most crucial of them all. In the designed hardware, the temperature is controlled by using two subsystems; heating actuator system and cooling actuator system.
This article presents the physical modeling and simulation of the heating actuator system that is used to heat the greenhouse. The method that was followed will be briefly explained, while the key equations will be discussed. The project was initiated in February 2015, and it was concluded in June 2015.
Background of the system I/Os
The following figure shows a schematic diagram of the system that was simulated. The two inputs to the system are the PWM (Pulse Width Modulation) duty cycle of the heating elements (T%) and the duty cycle of the fans (T%). On the other hand, the outputs are the temperature of the sink (Tsink) and the temperature of air (Tair). The temperature input (Tin) and the environment temperature (Tenv) will be external inputs to the system.
Heating Actuator Schematic
The lumped capacitance model, which is described by the following equation was used for modeling the heating actuator system:
Where Pin is the power input in Watts, Pout is the power output in Watts, C is the heat capacitance in J/K, T is the temperature in K and t is the time in seconds. This equation is basically a statement of conservation of energy. The above equation is used twice, once for the heat sink and once for the air inside the heating actuator. We assume that the electrical power input to the PTC heating elements will be transferred from the heat sink to the air due to convection and radiation. The air will gain power from the heat sink due to convection and radiation, and will lose power due to the flow of air out of the heating actuator system, while also losing some power due to conduction losses from the walls of the actuator. We have the following two equations:
Results
By using Matlab’s toolbox ‘Simulink’, the system was created in order to simulate the model and compare it to actual experimental results. The figure shows the results of one of the experiments. The fans were assumed to be turned off, while the heating elements start with a duty cycle of 0.4 for the first 300 seconds, and then switch off for a time period of 900 seconds before switching on for 200 seconds at a duty cycle of 0.8. Finally, the last 400 seconds of the experiment are spent at 0 duty cycle. The purpose of this case is to study the effect of heating and cooling for both the heatsink and the air temperatures.
The results suggest that the variation between the model and the experiment is not more than 7 degrees Celsius for the heatsink, and even less than that for the air. This confirms that the system is operating in a very good manner that is very close to the actual operation of the heating actuator.
Wrap-up
Overall, the author believes that the behavior of the modeled system is well within the acceptable limits and reasonably close to the results of the actual system (even though some slight differences exist). The model is predicting the actual system’s behavior in a very good manner in the compared cases which suggests that the followed methodology is reasonably accurate and can produce results that are valid. Therefore, the remaining parts of the greenhouse system can all be modeled by following the same methodology and even some of the same analytical equations and formulas. Once all the components are modeled, the subsystems can be connected to create an overall model of the whole greenhouse system.
In terms of the effect of the project on the perspectives of Bahrain, it will be possible to implement the methodology on full-scaled greenhouse system is order to create a greenhouse that is automatically controlled efficiently and accurately without wasting significant amount of energy. Nevertheless, if the heating actuator system is modeled, then most of the systems can also be modeled by using similar methodologies, that can greatly enhance the control design technologies in Bahrain, which is not a very common field in this region.
Special thanks to Dr. Christakis Papageorgiou (Head of Engineering School in Bahrain Polytechnic) for his continuous support and feedback throughout the project duration, and to Ahmed Sadriwala (the constructor of the hardware and the software programmer) for preparing and running the experiments that were useful for validating the model.