1. Introduction
Energy consumption is a crucial aspect of economic development and sustainability worldwide. The KSA has one of the highest energy-consumption rates in the world due to rapid economic and population growth. Air conditioning use is a major contributor to this trend, especially in the western region of the country, where temperatures can exceed 50 °C during the summer months [
1]. In this western region, which has the highest level of electricity consumption in the country, electricity is used by 99% of energy consumers, with the majority (80%) consuming less than 4000 kWh per month and a small percentage (1.4%) consuming more than 10,000 kWh per month [
1,
2].
According to the International Energy Agency (see
Figure 1), electricity consumption in Saudi Arabia has increased by more than 50% between 2007 and 2017 [
3]. Indeed, the use of air conditioners is responsible for more than 70% of peak electricity demand during the summer months in Saudi Arabia [
3]. This high level of energy consumption has created several challenges for the country.
The way energy is currently consumed in buildings is not suitable for the future. As a result, researchers and engineers are exploring different technologies and strategies to decrease energy usage while still providing comfort and well-being to occupants. In order to improve energy efficiency in the KSA and optimize energy consumption, recent studies have explored the use of intelligent building control systems using PNs.
Petri described PN theory as a network-like model used in research on automated communication that is relevant to the field [
4]. PNs have emerged as a powerful tool for modelling and analysing systems in various fields such as computer science, engineering and biology. They are characterized by their simplicity, flexibility, and ability to handle concurrency, making them suitable for a wide range of applications [
5].
In recent years, researchers have explored new directions for PNs, such as their use in modelling artificial intelligence systems and Big Data analysis. Researchers have developed several extensions and tools from PNs to model complex systems and analyse large-scale models, such as hierarchical and coloured PNs, as well as model checking techniques.
The basic theory of PNs and their formal properties, including the concepts of bounding and integrity are presented in [
6]. The authors in [
7] presented the extension of coloured PNs, allowing to model and control more complex data structures and systems with multiple interacting objects. The authors in [
8] introduced hierarchical coloured PNs, allowing modular and hierarchical modelling of complex systems. These papers have contributed significantly to the development and use of PNs in computer science and related fields, advancing our understanding of complex systems and their analysis techniques.
In the last two decades, there has been increasing interest in the use of PNs in building control applications. The authors in [
9] developed a hybrid PN model for building heating, ventilation, and air conditioning (HVAC) systems and proposed a control strategy based on the model. They demonstrated the effectiveness of their approach using a case study. A PN-based modelling approach for smart home appliances enabling a better understanding of their behaviour and interactions was proposed in [
10]. The proposed approach was applied to a smart washing machine and a smart dryer in a smart home environment. The PN models were able to capture the behaviour of the appliances and their interactions with the smart home environment.
In [
11], a PN-based framework for reducing building energy consumption by optimizing the temperature control was developed. The PN model incorporated real-time weather conditions and occupancy patterns to adaptively adjust the temperature set-points of HVAC systems. The results showed significant energy savings and improved thermal comfort for occupants. Authors in [
12] proposed an intelligent PN-based system to control and monitor the greenhouse temperature. The system utilizes wireless sensors to collect temperature and humidity data and control actuators to adjust the temperature in real-time. The results showed improved temperature control and energy efficiency, leading to higher crop yields. In [
13], the authors presented a design and implementation of a smart home system and a self-control window using a field programmable gate array (FPGA) and PN modelling techniques. The self-control window uses a PN model to detect changes in the environment and adjust its opening and closing accordingly.
In [
14], a PN was used to verify the feasibility and soundness of the system model and optimize its performance by eliminating improper states. The system aims to enhance safety and prevent property damage by enabling real-time monitoring and control of home appliances using IoT and machine learning technologies.
Fuzzy logic (FL) was first introduced by Lotfi Zadeh in 1965 [
15] as a mathematical framework for dealing with uncertainty and imprecision. FL allows the representation of a partial truth, useful in situations where information is incomplete or uncertain [
16]. In the last two decades, FL has gained significant popularity and has been widely utilized in numerous studies. For instance, the authors in [
17] employed FL in the development of an optimal energy management strategy for a hybrid power unmanned aerial vehicle (UAV) that integrates fuel cells and battery systems. A FL-based emulated inertia control was implemented in [
18] in a supercapacitor system to enhance inertia in a low-inertia grid with renewable energy sources.
FPN is a combination of FL and PN. Indeed, FPN is a formalism that inherits the graphical and mathematical foundations of the PN model, and it is used to construct, calculate, and make inferences in expert systems containing fuzzy data. FPN was originally proposed by Zimmermann in [
19]. FPN enables the modelling of complex systems with imprecise and uncertain information [
20]. Since their introduction, FPNs have been used in a variety of applications, including control systems, manufacturing systems, and decision support systems. They have also been extended in various ways, such as the use of interval-valued fuzzy sets or the incorporation of timed data.
In [
21], the author applied FPNs to the control of complex industrial processes. They demonstrated how FPNs handle imprecise data and provide more accurate results. The paper highlighted the potential of FPNs as a tool for modelling and controlling complex systems. The authors in [
22] discussed various aspects of FPNs, such as their syntax and semantics, graphical representation, analysis and verification techniques, and applications in areas such as control, diagnosis, and scheduling. They also highlighted some of the advantages and challenges of using FPNs, such as their ability to capture both qualitative and quantitative aspects of a system, but also their potential complexity and computational cost. In [
23], a comprehensive review of the application of FPNs in knowledge representation and reasoning is described. The authors presented various examples of FPNs in action, including their use in medical diagnosis, fault diagnosis, and process control. In [
24], a robust and efficient system for decision making and control, in the GEMMA guide paradigm, was developed, utilizing FPNs as a modelling tool. The applications of FPNs in various domains such as control, optimization, and fault diagnosis and their recent advances and extensions, such as hybrid FPNs that combine fuzzy and crisp information, and dynamic FPNs that can model systems with changing structures or behaviour are discussed in [
25].
The motivation of this work is driven by the increasing demand for energy resources and the need for energy efficiency, particularly in countries such as the KSA. Energy consumption in buildings, particularly for air conditioning (AC) systems, represents a significant portion of the overall energy usage. Therefore, there is a pressing need to develop intelligent and energy-saving frameworks that can optimize energy use while ensuring a comfortable environment for occupants.
In [
11], a regular PN was utilized for temperature control based on a user-defined temperature. However, recognizing the subjectivity and variability of individual preferences for temperature, we have enhanced the framework by integrating FPNs. By considering fuzzy concepts such as “good temperature”, “warm temperature”, or “low temperature”, the system can accommodate the subjective and varying preferences of different users, providing a more personalized and adaptable solution. This integration allows for the modelling of uncertainty and imprecision, enabling a more effective approach to address diverse user preferences, ultimately improving user comfort and satisfaction. Furthermore, by optimizing energy consumption based on firing degrees within the FPN framework, the proposed approach offers significant improvements over the previous model. Through this advancement, we aim to provide a more effective and user-centric temperature control system that achieves both energy efficiency and occupant comfort.
The main goal of this paper is to explore the potential of FPNs in reducing energy consumption and promoting sustainable energy practices in smart buildings in the KSA. We propose a framework based on three different stages. The initial phase involves identifying the user through a user identification sub-system, and obtaining their preferred temperature. In the subsequent phase, an FPN utilizes the data gathered in the first stage to create the desired temperature patterns for the users and communicates it as a reference signal to the following stage. The third stage involves a regulatory process utilizing a PID controller, which synchronizes the actual room temperature with the preferred temperature generated by the user.
The paper is structured in the following manner:
Section 2 introduces FPNs, while
Section 3 discusses FL and its application in this paper. The PID controller and user identification processes are explained in
Section 4 and
Section 5, respectively. In
Section 6, the FPN-based smart temperature control framework developed in this paper is described. The experimental work conducted to test the framework is covered in
Section 7. The advantages and effectiveness of the developed framework are discussed in the subsequent two sections. Finally, the conclusion summarizes the accomplishments of the proposed approach.
5. Smart FPN-Based Temperature Control Framework
In this work, we developed a system that uses FPN to regulate the temperature of AC systems based on user preferences. The FPN used in the system enables modelling of complex systems that involve uncertain and ambiguous data. The decision-making mechanism of the FPN system receives data from different sources, such as the user preference model, the temperature prediction system, and the energy reduction system, to determine the ideal temperature set-point for the AC unit. This method reduces energy consumption and improves user satisfaction by considering an individual’s preferences. In addition, the integration of FL into different aspects of the system allows the system to deal with ambiguous and uncertain data, improving its versatility and adaptability to different scenarios.
The framework consists of three stages, as shown in
Figure 6, each dedicated to a specific task.
The most significant aspect of this work is the integration of several stages, including person identification, FPN-based monitoring, and temperature control using a PID controller. The framework combines the advantages of each component, making it feasible, easy to implement, and very flexible. In addition, it can be easily modified and customized to meet different requirements, such as incorporating additional sensors or temperature control algorithms. The framework can also be integrated with other systems to provide advanced features such as remote monitoring and control.
The initial stage of the framework involves identification of the user, the results are then passed to the next stage. The second stage generates the user’s preferred temperature based on the identification results, using FPN for modelling, supervision, and real-time implementation. The third stage uses a traditional PID controller to regulate the room temperature based on the user’s preferred temperature. The framework operates autonomously, monitoring the room and adjusting the temperature when users are present, and switching to sleep mode when no one is present to save energy. The most significant aspect of this work is the integration of several stages, including person identification, FPN-based monitoring and supervision and temperature control using a PID controller.
These three stages cooperate for the best experience for users and most importantly to control temperature and reduce energy consumption. In FPN, the whole set of places indicates the previous or next state of the system and may have a token bound to a degree of truth between 0 and 1 that represents the confidence in these values. FL can be used to define the transition firing conditions and the marking change in the FPN. In a traditional PN, the transition firing condition is based on a binary value (0 or 1) depending on the marking of the input and the firing rule. However, in an FPN the transition firing condition can be defined as a continuous value between 0 and 1, representing the degree of activation of the transition. This degree of activation is calculated based on fuzzy rules accounting for the marking of the input, the firing rule, and other relevant factors. Therefore, the integration of FL with PN is performed by setting the transition into a rule associated with a certainty factor value between 0 and 1. The certainty factor represents the strength of belief in the rule. In this research, we use FPN as a decision support system based on specific rules of the form: IF condition THEN action.
Arc weights in an FPN can also be fuzzy sets that represent the degree of membership between two nodes. The arc weight between a transition and a place can represent the degree to which firing that transition will fill or empty the place. The degree of membership is determined by FL, based on the firing condition and other relevant factors. For instance, a rule might specify that if the temperature is “very cold” and the user’s preference is “very warm”, then the transition to increase the temperature should fire with a degree of membership of 0.8. The rule’s fuzzy set defines the degree to which the condition is satisfied. Therefore, FL offers a strong method for dealing with uncertainty and imprecision in the PN. This allows for greater flexibility and reliability in controlling complex systems.
For example, consider an FPN that models a temperature control system. The inputs are the current temperature and the desired temperature, and the output is the control signal that regulates the temperature. The transition firing condition can be defined as a degree of activation that reflects the degree of match between the current temperature and the desired temperature. This degree of activation can be calculated using fuzzy rules that account for the difference between the current and desired temperatures, the rate of temperature change, and other relevant factors.
Once the degree of transition activation is calculated, it is used to determine the probability of firing the transition. This probability is then used to update the marking of the input and output. The marking of the inputs is decreased according to the firing rule, while marking the output is increased. The degree of transition activation is also used to calculate the degree of change in marking the output, reflecting the degree of control signal needed to regulate the temperature.
5.1. Room Model
The system response analysis for the AC would be performed in the Laplace domain (s-space), instead of the time domain. For an AC space of a fixed volume, the parameters could be illustrated as in
Table 1.
The thermal mass includes the weights of the users and the thermal mass of the indoor air.
Figure 7 presents the modelling of the temperature control in the AC space [
42].
The equation representing the AC model is shown as follow:
where
is the exchanging air flow, and
is the heat capacity. Assuming
to be time-invariant, Equation (
1) can be rewritten as:
Taking the Laplace transform of Equation (
2), the result is:
The transfer function model of the AC space is:
5.2. Sensor Model
To measure the room temperature and close the control loop, a high-quality sensor is used inside the indoor AC unit, placed in the centre of the evaporator as shown in
Figure 8 [
42].
The relationship between the return air temperature (
T) and the measured temperature by the sensor (
) can be written as:
Taking the Laplace transform of Equation (
5), the result is:
Therefore, the transfer function representing the model of the sensor is:
5.3. Disturbance Model
The thermal leakage (
) of the AC space can be approximated by the temperature difference of the indoor and outdoor space as:
To maintain the air quality of the indoor space, according to the building technology rules, the minimum mechanical ventilation is 10 m
3/h per unit surface area m
2. The thermal leakage (
) due to the exchanged air flow is:
Regarding human disturbances inside the room, in order to maintain human functionality, body temperature has to be kept at a constant level. Therefore, thermal radiation from people (
n person) affect the internal temperature of the room. Typically, a person releases about 70 W during sleeping and 100 W performing light effort. In this work, human disturbance is presented as Equation (
10).
By installing a temperature sensor in the evaporator of the indoor split-type AC unit to obtain a feedback signal, the open-loop AC space model becomes a closed-loop model, as shown in
Figure 9.
The room transfer function of the AC space, sensor and controller are organized to simulate the responses of the indoor temperature and compressor output for the AC control design. The controller output relies on sensing differences between the setting point and real feedback signal to compute the power commands for either fixed- or convertible-frequency ACs. The compressor of the fixed-frequency AC is switched On or Off for a period of time, while the convertible-frequency AC changes the compressor output continuously to adjust the room temperature; both types are simulated later.
7. Energy Consumption Analysis
In this test, we sought to analyse the performance of the system over the course of a day. The simulation started at 12:00 and lasted 24 h to measure the energy consumption, temperature control, and compressor power. Three models were tested, namely, the PN model, the FPN model and the On/Off model. The room was occupied as shown in the
Table 6.
The first person’s preferred temperature is 20 °C, the second person’s preferred temperature is 23 °C and the third person’s preferred temperature is 26 °C. In this simulation, we assume that the outdoor room temperature is 36 °C. When there is more than one person in the room, the desired temperature is set to the average of the preferred temperatures. When no one is inside the room, a standby temperature of 30 °C is set.
Figure 25 shows the temperature profile during the simulation when the PN model is used, and it is clear that the controller (convertible-frequency mode) is able to maintain the desired temperature successfully and accurately. The compressor power varies continuously from 0 W to the maximum power depending on the required power dissipation. The total energy consumption in this mode is about 210 Wh, which is low compared to the 850 Wh of the AC, as shown in
Figure 26.
The FPN model behaves similarly to the PN model in that it uses the designer’s experience to decide what action to take based on the situation. Therefore, the controller follows the commands of the FPN model to maintain the desired temperature.
Figure 27 shows that the temperature of the room is precisely controlled, similar to the PN model, but the main difference is the total energy consumption. The FPN model can perform the same test scenario using only 45 Wh.The steady-state temperature error is about 0.5 °C, larger than the error obtained in the PN model, as shown in
Figure 28, because the fuzzy rules interfere in the control and affect the PID controller input.
A second similar simulation was performed with a fixed-frequency compressor; as shown in
Figure 29, the room temperature is regulated approximately around the desired temperature because the compressor is either On (room temperature decreases) or Off (room temperature increases) and it is difficult to achieve zero error. The total energy consumption in this mode is around 345 Wh, corresponding to around 40% of the rated AC power. The AC power is always On and Off, which is inefficient and uncomfortable for the person in the room. The steady-state temperature error shown in
Figure 30 is large compared with the FPN and PN models.
From the results presented above, we find that the error rate when using the PN is lower than the error rate with the FPN. However, it is important to consider the energy consumption. The difference in energy consumption between the PN and FPN is noticeable and large compared to the difference in the temperature error, with no effect on user comfort and flexibility.
The results presented in
Table 7 compare the energy consumption and temperature error for the different compressor modes in the implemented models. The On/Off switching model, which utilizes a fixed-frequency compressor, shows a temperature error of approximately ±2.5 °C, with an energy consumption of 345 Wh. The PN model, incorporating a convertible-frequency compressor, demonstrates a significantly reduced temperature error of less than 0.1 °C, with a energy consumption of 210 Wh. The FPN model, also employing a convertible-frequency compressor, achieves further improvement with a temperature error of approximately ±0.5 °C, resulting in a remarkably reduced energy consumption of only 45 Wh. These findings indicate that both the PN and FPN models outperform the On/Off switching approach in terms of temperature control accuracy and energy efficiency. Furthermore, the FPN model demonstrates superior performance, effectively reducing energy consumption compared to the PN model. Overall, the integration of FL into the PN framework enhances the temperature control precision and energy efficiency, with the FPN model yielding the most favourable results.
9. Conclusions
The proposed framework utilizes FL to enhance the performance of the PN-based control system for regulating building temperature and optimizing energy usage. By implementing a facial recognition system to identify individuals and adjust the temperature according to their preferences, a comfortable indoor environment is achieved. A database is created to store user information, including names, ID numbers, temperature preferences, and facial features. The system is controlled using an FPN controller, effectively managing different operational modes based on user presence.
Initially, the system remains in an Off state until the designated start time, entering Standby mode with an ambient temperature set to 30 °C to conserve energy. Once a registered user is recognized, the temperature is adjusted to their preferred level. In cases where multiple users are present, the system calculates the average of their preferred temperatures. The FPN controller ensures that the AC unit is turned Off when a predefined time limit is reached.
Simulations conducted using two types of compressors, a convertible-frequency AC compressor and a fixed-frequency compressor, demonstrate the effectiveness of the proposed system. Evaluation of the system reveals significant energy savings, with the FPN model and the convertible-frequency compressor reducing energy consumption by 94% (45 Wh). When only using the PN model a 25% reduction in energy consumption (210 Wh) is achieved, while employing a fixed-frequency compressor leads to a 40% increase in energy usage (345 Wh). The incorporation of FL into the PN model proves highly advantageous, effectively reducing energy consumption by half.
In conclusion, this research presents a framework that effectively utilizes FL to improve the performance of a PN-based control system for building temperature regulation and energy optimization. The implementation of a facial recognition system and user preferences further enhances user comfort. Future research should focus on exploring the use of alternative control algorithms within the proposed framework, or studying the impact of external factors on energy efficiency. By addressing these areas, new advances can be made in the development of energy-efficient building control systems.