Fuzzy Controllers Instead of Classical PIDs in HVAC Equipment: Dusting Off a Well-Known Technology and Today’s Implementation for Better Energy Efficiency and User Comfort

Abstract

Cutting-edge building energy management systems (BEMS) interact with heating, ventilation, air conditioning (HVAC) systems, which generally account for much of the energy consumption. Major attention is focused on the BEMS themselves, barring on-field equipment. In HVAC equipment, sub-optimal controller settings may lead to energy losses and user discomfort, for instance, due to oscillations of air temperature and fan speeds. The way to solve this problem could be to replace classical PID controllers with an alternative concept that does not require tuning and works optimally for a wide range of parameters. This paper compares a fuzzy logic controller (FLC) with a standard PID for a model-based simulation of an HVAC system in Simulink for different conditions using real building measurement data. The end result is the implementation of the developed methods in a newly designed universal control board for air handling units (AHU). The proposed FLC achieves better integral control quality indicators (IAE, ISE, ITAE, ITSE) by at least 27.4%, and smaller supply air temperature variation; the daily mean square error (MSE) was reduced by an average of 36%, which leads immediately to better occupant comfort and a presumed reduction in energy consumption. Compared to the untuned PID, energy consumption was 12.7% lower; this will ensure improved economy from the lowest level, and paves the way for interoperability with high-level energy management schemes.

1. Introduction

Buildings represent about a third of global energy consumption and a quarter of CO₂ emissions. They account for an even larger share of energy consumption in some of the most energy-intensive countries. In the EU, it is 41%; in the US, 34%; in Japan, 37%; and in Russia, 42% [1]. As a result, they have become an important element of climate policy.

Heating, ventilation, air conditioning systems (HVAC) are the most consumed service worldwide (38%) in residential and commercial buildings (Figure 1). HVACs’ contribution to building energy consumption depends largely on climate and wealth. It is highest in all countries (except for India, where it is warmer and there are lower income levels). For this reason, it is the largest area for savings and energy efficiency improvements in buildings [1,2].

Currently, much research is focused on the development of intelligent, high-level algorithms using machine learning [3,4], advanced multi-criteria optimization methods, incorporating external weather forecasts [2,5,6] and implementing pre-cooling and pre-heating strategies [7,8]. HVAC system management can include adjustment of energy consumption to energy tariffs [9,10]. The direct building blocks for these strategies are HVAC appliances, including air handling units (AHUs) (see Section 2.1), responsible for exchanging and maintaining the parameters of the supplied air and containing several controllers inside. It is possible to correctly select the parameters of the most commonly used proportional, integral, derivative (PID) controllers (see Section 2.2); however, considering the different features of the actuators, the parameters of the building, the installation site and other factors related to the operation of the unit such as refrigerant supply temperatures, it is challenging, and sub-optimal settings affect the control performance and final energy consumption.

The stage of tuning and observing the system after installation in the building does not always last long enough, and is sometimes omitted entirely; the AHU is started with default factory values. From our own experience as well as from the literature [11], controller and tuning problems are the most common and account for more than half of all problems that occur during the operation stage. Despite correct operation, the unit does not reach its maximum performance, both in terms of air conditioning quality and energy consumption.

In our previous work, we have faced the issue of untuned controllers in HVAC equipment and original low-level controllers that are impossible to modify. We solved this by designing additional modules deployed in high-level BMS (building management systems), based on NARMAX modelling and PSO optimization, to cyclically fine-tune the PIDs in AHUs [12]. However, this is not a versatile solution that can be applied to most AHUs.

Taking into account all the mentioned factors and the requirements of the project under which we carried out the presented work (see Section 3), the key assumptions were as follows:

• the best results would come from choosing a controller that does not require tuning;
• on-line auto-tuning methods are not robust enough to work right out of the box under vastly deviating operating conditions;
• the method should involve hardware and be computationally demanding, similar to classic PIDs;
• after deployment, it should work correctly within a wide range of conditions without the supervision of a qualified installer.

Additionally, the paramount requirement for funding the project was that the developed method could be adopted in a new type of hardware AHU controller using off-the-shelf electronic components. The key contributions of the paper are as follows:

• proposition of a fuzzy logic controller (FLC), with a structure similar to PID-like controllers found in the literature, that can accomplish all the necessary functions of a conventional PID controller whilst simultaneously eliminating the fine-tuning problem for the temperature control applications in AHUs;
• simulation verification of the control performance that is comparable to conventional PIDs (still used in the vast majority of facilities) in the target hardware, using a universal room model with the HVAC system in Simulink, thereby allowing simulations in real time and equivalent time with the hardware-in-the-loop (HIL) approach.

The developed type-1 FLC (see Section 3.3) has been adopted in a multi-purpose hardware controller dedicated to AHUs with a wide range of capacity and various types of peripheral equipment. The hardware controller likewise has enhanced communication capabilities for integration with modern BMS and BEMS systems, although it can also operate autonomously. It should achieve better performance than classic controllers while requiring less technical staff attention. It is also suitable for use as a retrofit controller for older AHUs that may not have the necessary technical documentation needed to tune classical PID-type controllers.

As a verification model, a ready-made model for the Simulink package modelling the car ventilation and air-conditioning system was used, adjusting its parameters so as to best reflect the conditions of the real building (see Section 4.1). This model was chosen because of its availability and ease of evaluation by HVAC engineers.

2. Problem Definition and Other Works

2.1. Air Handling Units

An AHU is a device that removes stale air from a rooms, supplies fresh air, or performs both activities simultaneously. A typical AHU (Figure 2) may contain from several to even dozens of controllers that control their actuators, such as fans (F1, F2), cooler and heater valves (C1, H1), and air dampers, with sensors for the unit maintenance supply air (T%H), internal room parameters (CO₂) and air volume (MAF). The AHU may have the ability to mix both air flows or be equipped with a heat exchanger for heat exchange between the two air streams. Additionally, using supplementary actuators, the supplied fresh air may be cooled by water or gas cooling coils cooperating with the external chiller, or heated with water or an electric heater [13,14,15].

It can be assumed that the most beneficial method, both from the point of view of energy consumption and control quality, is the use of smooth control of executive elements with the use of PID regulators and similar continuous control methods. In the case of two-state regulation, there are working cycles (unintentional bang-bang control) connected with switching executive elements which, apart from, e.g., generated noise, may cause discomfort, e.g., in the form of noticeable changes in the temperature of the supplied air [14,16]. In some applications (e.g., hospitals and food storage spaces) such control is unacceptable due to temperature fluctuations of a single degrees.

All these factors, and the consideration of operation over a wide range of external parameters, except for several fixed operating points, makes the AHU a nonlinear system; it is possible for it to be stable, but it is difficult to control optimally.

2.2. PID Controllers and Tuning Methods

The automatic control system reacts to a change or imbalance in the variable it controls by adjusting some system parameters to restore the system to the desired state. The key component of the system is the controller (Figure 3), which observes changes in the controlled value (PV, or process value) and modifies the state of its output accordingly, so that the controlled value equals the setpoint (SV, or setpoint value). The input signal of the controller is the control error (EEEE)), which is the difference between the setpoint (SV) and the current value in the system (PV). Thus, it is a closed-loop control, and a controller’s response pattern and timing is dependent on its type and settings. The principles of closed-loop control and the operation of PID controllers are an industry mainstay, being taught in all engineering schools, and their detailed descriptions are broadly available in the literature [13,14,15,16,17,18,19].

PID controllers are the most widely adopted solution for many sectors, such as the industrial, building automation, automotive sectors, etc. The internal structure of the controller can be varied, but the common and most frequently used design is shown in Figure 3. This is known as a parallel layout, and can be represented by Equation (1):

$$output\left(t\right)=K_pϵ\left(t\right)+K_i{\int }_0^tϵ\left(t\right)dt+K_d\frac{dϵ\left(t\right)}{dt}$$

(1)

where t is time, and ε is the control error defined as the difference between the setpoint SV and the current process value PV; K_p, K_i, K_d are the tuning gains (proportional, integral, derivative).

The appropriate selection of these gains is crucial for correct operation of automatic control in any field. Tuning of PIDs in general is a still challenging problem. Numerous traditional tuning methods, such as analytical methods based on the system model, heuristic rule-based methods such as Ziegler–Nichols, Cohen–Coon or the damped oscillation method, which generally require some experiments on the running system with the participation of an experienced system operator or automation engineer, can be found in the literature [17,18] and engineering handbooks [14,16]. They are also commonly used frequency response methods [20,21], and sometimes, computational intelligence [22], FL [23], and evolutionary algorithms and PSO [24] are used. This is discussed further in Section 2.4.

The controller being used for a fully equipped AHU, with recovery of all external actuators, as is shown in Figure 2, must contain up to six controllers. If classic PIDs are used, the settings of every single controller depend on the individual configuration of a given AHU and applied actuators, but also on the conditions in the building. The place of installation of the AHU and the way the building is used, including the habits of the users, have an influence on the regulators’ tuning. Proper selection of the settings requires laboratory and on-field tests; additionally, after some time, e.g., with a change of season and in a particular installation, it may be necessary to fine-tune them. An improperly tuned regulator may cause various negative effects, such as increased electricity consumption or increased noise generated by the AHU, not to mention the deterioration of thermal comfort.

It is worth noting that despite the presence of PID controllers in most dedicated controllers for AHUs, due to large time constants, the derivative block D is omitted by introducing K_d close to 0 and the controllers act similar to a PI-type.

Most of the actuators are modelled as a second-order object with a delay, particularly for temperature control. Measurement noise from temperature or airflow signals can be removed with averaging filters, and the lag coming from them also legitimises very low participation (small K_d) or fully bypassing the derivative (D) block of the controller. This approach also reduces complexity in fine-tuning and is being used by technicians; it achieves tolerable performance, but not peak performance.

Well-tuned PIDs or another type of regulator, such as modern optimal regulators (linear quadratic control, linear-quadratic-integral control) would fulfil their task properly [19] without the mentioned negative effects, but their fitting requires a lot of work and knowledge, and in real conditions within a building, it is actually challenging to achieve.

2.3. Fuzzy Logic Controllers

The concept of fuzzy sets was introduced in 1960 by L. Zadeh, and fuzzy logic is based on these sets, generalizing classical two-valued Boolean logic to multiple-valued logic [25]. The multi-valued sets and the relationships between them are used to build the rule base; this gives an often straightforward description of a phenomenon using natural language. For phenomena for which there is no proper mathematical model, or whose construction is difficult but whose general principles of control are known, fuzzy logic may become the only solution to obtain satisfactory control performance [26,27].

Fuzzy control was initiated by Mamdani in 1974, inspired by Zadeh’s earlier works; the first application was performed on a laboratory steam engine [28]. Applying fuzzy logic principles in practice to build controllers and decision blocks consists of three steps (Figure 4):

• fuzzification: the process of mapping crispy input values x${}_n$ to fuzzy values, which describes degree of membership µ(x${}_n$) to the fuzzy sets;
• inferencing: using the rule base, the membership degrees of the input signals are mapped to the membership degrees of the fuzzyfied output signals y${}^{*}$;
• defuzzification: the process of determining the precise, crisp values of the output signal y based on the rule activation degree y${}^{*}$; defuzzification is similar to the first fuzzification stage, but occurs in the opposite direction.

The rule base can describe a decision block that determines the output signal based on the contained rules; in the case of building a fuzzy controller, this block is enclosed in a feedback loop, as for a PID controller. The fuzzy controller can use a specific description of a phenomenon or its generality in his rule base. Mamdani-type fuzzy systems are linguistically understandable.

The most common shapes of membership functions are trapezoidal, triangular or Gauss features. The most common methods used for defuzzification are the maximum method (first, middle, last), the centre of gravity method and the centre of area method. The details of how to choose the shape, design the controllers and formulate the rules are widely available in the literature [26,27,29].

The replacement of the PID controller with an FLC, but in the form of a sole controller and not an additional unit to improve the performance of the typical PID, should meet all design objectives. A large number of works on fuzzy control were published in the years 1990–2000, but they were analysed only from the theoretical side and compared with PID-type controllers. The results achieved seem to be satisfactory, and the quality of control was generally improved [27,29,30]. However, there are not many reports in the literature of their practical applications, especially in buildings and HVAC fields.

The application of FL, although the techniques are now well explored, also has its drawbacks. Mamdani-type systems are understandable linguistically, but strict mathematics frameworks for their synthesis and the creation of rules are still developing, and most of the practical methods are based on heuristics. Also, the systematic analysis of stability is difficult [31]. Takagi–Sugeno systems do not have linguistic variables, but functional membership functions without labels; because of this, their synthesis can be performed with strict procedures [32,33], and their stability examined as in classical systems (e.g., with the Lyapunov criterion) [31].

Current works mainly focus on type-2 [34] and the gradually spreading type-3 fuzzy, although here, too, most of the works address the topic from a theoretical perspective and in more practical applications than the improvement of the core. Additionally, ubiquitous design blocks such as standard controllers focus on more sophisticated plants from various fields [35,36]. State-of-the-art fuzzy methods such as type-2-fuzzy sets can achieve even greater accomplishments, but their adoption is more difficult and could reduce versatility, so for the proposed controller and its hardware deployment, the Mamdani system and FL type-1 were chosen, and were proven to be sufficient.

Using type-2 fuzzy would allow for further improvement of the achieved results, but due to the low dynamics of the system, large time constants and the use of averaging filters for input measurement signals, type-1 fuzzy seems to be an acceptable compromise between control quality and hardware requirements.

2.4. Other Works

Most of the papers analysed below, [20,21,24,37], despite the use of often advanced computational methods, still use a PID controller as the main part, for which they attempt to optimize the settings or use an approach such as gain scheduling [38] (see Figure 5). Already, some ways to create more robust controllers have been proposed, one example being internal model control (IMC) [39,40], or attempts to design fuzzy controllers that streamline the tuning [41].

In real HVAC application, however, the classical PID designs still dominate, and all others outgrow them by a considerable margin of complexity. A review and a practitioner interview of common human errors of AHU control systems was presented by Torabi et al. [11]. According to their paper, controller problems account for 67% of all issues. Leaving aside other problems with the HVAC system and assuming correct design and component selection, the authors’ practice and discussions with both integrators and practitioners also confirm that tuning problems occur most often and account for more than half of all problems occurring at the operation stage.

Kasahara et al. [20] presented a strategy of robust PID tuning for temperature control for HVAC systems in a single-zone environmental space. The PID gains are obtained by solving a two-disk type mixed sensitivity problem and, contrary to the traditional Ziegler–Nichols method, it can be modified during operation. Based on simulations and experiments, the paper concludes that the proposed procedure is successful enough and suitable for use in practical applications.

Pandey et al. [21] proposed a solution developed in Matlab/Simulink, utilizing a robust and practical algorithm which uses only the output signal of the object to automatically tune the parameters of the PID controller. It was evaluated with various first-order systems for temperature control. Hongli et al. [23] showed a fuzzy control strategy based on PID parameter tuning in HVAC systems. The fuzzy logic part modifies the gains of the PID controller. Simulations performed by the authors show less overshoot, a shorter settling time and better robustness.

Approaches utilizing optimization algorithms are presented in the papers [24,37]. A design method for optimal PID using particle swarm optimization (PSO) was described by Jun et al. [24]. The authors’ proposition for the temperature control application of an HVAC system requires mathematical modelling to approximate the operating point. Based on the model, a global optimum is searching in the solution space of K_p, K_i, K_d. Almabrok et al. [37] using an evolutionary algorithm called Big Bang–Big Crunch (BB–BC), proposed the fast PID tuning technique dedicated to HVAC applications. The authors also reached satisfactory performance in the simulation when comparing the accuracy and speed of the convergence achievement with other optimization methods such as the genetic algorithm (GA) and PSO. A merit of this work that is rarely seen in other papers is the presentation of the method of hardware implementation.

In their paper, Zhu et al. [22] present the application of a neural regulator. It is a direct adaptive controller based on a two-layer neural network. Experimental results performed on the HVAC system showed an improvement over the PID controller in terms of response speed to changing operating conditions and robustness to external disturbances.

Unfortunately, most of the published works ignored the hardware layer and its implementation in controllers. From the overall reviews of control strategies presented in [42,43], some conclusions can be drawn to better select system settings and components.

Additionally, there are very complex control strategies, such as the use of IoT [44] and blockchain with smart-contracts [45], that are currently being worked on, but the field level is being overlooked and is treated as something outmoded; however, it is necessary for the implementation of such strategies. Engagement at this level, as shown in this work, can also bring positive outcomes.

3. Proposed Solution

3.1. Method Selection

The desired control method should be numerically lightweight and able to be implemented in relatively low-cost and stock micro-controllers, working in parallel with the other control routines of the AHU. The advantage should be the versatility of the code and the ability to use a single, unified software module, with scaling of the input and output signals to match the control board inputs and outputs. Some algorithm elements can be simplified; for instance, the type of used heater can be omitted, because no matter if an electric heater with PWM power regulation or a water heater with a three-way valve is used, the output signal is always a value in the range of 0–1 or 0–255, only at the level of hardware GPIO will the calculated output value be converted into a proper physical output signal. The regulator should operate only on control error and error difference in given time period.

The previously analysed (in Section 2.4) approaches used so far with various auto-tuning, PSO, or neural networks (NN) do not seem to be adequately efficient and robust in such an application, or ready for deployment in hardware controllers. Other works being considered most often use a PID controller with an additional module designed as shown in Figure 5 in order to optimize its settings [20,21,22,24,30,37,38,43]. Such a module can use an additional FLC [23,28,30], an NN or complex optimization methods such as metaheuristic algorithms, for example, PSO [12,24,37].

There are only a minority of solutions for the HVAC field [22], including the one proposed in this paper, that propose a new type of controller that does not require or significantly simplifies the tuning stage. The use of the first approach is easier in larger systems, wherein several AHUs cooperate with the BMS, thereby allowing both the visualization of data and the activation of additional optimization modules [12]. In such installations, the AHU controls the supply air temperature, and a higher-level controller is most often responsible for the controlling room conditions. Negative effects or incorrect settings can be compensated by this higher-level controller. In the case of single, individual home installations or upgrading the control of already installed AHUs, the unit can operate independently, directly controlling the conditions in the room. Improving the control quality should produce positive effects in all the cases described above. In summary, extending the requirements previously stated in the introduction, the main requirements are as follows:

• the desired approach should have a computational complexity and technical maintenance needs similar to those of the standard PIDs, whilst eliminating the tuning stage or significantly simplifying this step;
• despite the elimination of the tuning stage, the approach should work better over a wider range of parameters and in different types of HVAC installations;
• it should be capable of being implemented with stock-available electronic components, taking into account the costs efficiency;
• it should be suitable for both autonomic work, to control a single AHU, as well as for work in advanced multi-unit installations, in cooperation with a higher-level controller or BEMS system.

3.2. Fuzzy Controller

The FLC with the internal layout shown in Figure 6 has been matched, relying on the variety of approaches available in the literature [13,15,17,29] and our own experiments. To the controller, the setpoint (SV) and process value (PV) from the room temperature sensor are supplied, and the control error ε which is the base input signal, is calculated. The delta of the control error Δε_1min is computed with a one-minute interval. Such a period of time is adequate to achieve a responsiveness to events in the interior (the arrival of a large number of people, the opening of a window), e.g., simultaneously avoiding the cons of controllers with a D component in the sense of reacting to the measurement noise and short-term disturbances.

Both crispy input signals ε, Δε_1min are fuzzificated with seven fuzzy sets (negative big, negative medium, negative small, zero, positive small, positive medium, positive big) to corresponding degrees of membership: µ${}_{NB}$, µ${}_{NM}$, µ${}_{NS}$, µ${}_Z$, µ${}_{PB}$, µ${}_{PM}$, µ${}_{PS}$.

In the next step, the activation degrees for the output intervals in the inference process are determined based on the rule base. The final signal is in fact a change of output which depends on whether the sign is added or subtracted from the stored previous output value. This is responsible for the presence of the I (integrating) component in the controller.

The sign of the control determines whether a heater or a cooler is activated, while a bypass is controlled by the difference between the outside temperature and room temperature. If the difference is higher than 0 and the working mode is heating, the bypass dumper is open for free heating. If the difference has a negative sign and the unit mode is cooling, the bypass is open for free cooling (and an analogically positive sign activates the free-heating mode).

The controller was implemented using a Mamdani model, making the rules understandable linguistically. The inference process in this model consists of the following steps:

• performing minimum operations $min\left(\right)$ for memberships degrees on “AND” connectors for rules;
• performing a maximum operation $max\left(\right)$ as an operator for combining inference results obtained from single rules.

A triangular membership function was used. As noted above, the width of the membership function is defined by the user and and is the only tunable parameter. By default, it is 2 ${}^{\circ }$C. Changing the width will indirectly affect the dynamics of the controller; for instance, decreasing this value with constant control error $ϵ$ will cause the input to be triggered faster. In the rule evaluation process, the conclusions are aggregated with $max\left(\right)$ operation. A defuzzifier uses on the centre of area (COA) method.

When developing a temperature controller, it is suitable to take the input sets as $warm$, $cold$, $optimum$, and for example the output as heater power and the sets low–power, medium–power, high–power; however, the better solution is to use generalization with the reference to the overall control process and control error $ϵ$, for example, positive–small, positive–large, zero, negative–small, negative–large, using corresponding sets for the output. The number of membership function intervals has a final influence on the control plane (by smoothing it, if rising) and the number of rules (which can increase the computation effort). The choice of seven intervals and 49 rules was a trade-off due to these factors.

The main investigations were conducted for temperature control because it has the greatest influence on energy consumption and comfort of users; however, the developed method provides a universal controller module which can be implemented to control other values occurring in the AHU, such as supply air volume in variable air volume (VAV) mode.

Considering the approachability of its implementation in hardware, its low computational complexity, and, as the evaluation described next revealed, the achievement of satisfactory results in comparison with classical PIDs, the controller was created using type-1 fuzzy logic. It will be suitable for temperature control using actuators in the form of valves or through the 0–10 V signal provided to the controller of an electric heater or an outdoor cooling unit or heat pump.

It was also assumed that settings made by the user would be eliminated as the controller has only one parameter that can be modified (the width of the intervals of the membership functions). Narrower intervals result in faster reaching of subsequent sets, and therefore a more aggressive controller response.

3.3. Practical Implementation in Controller Board

The proposed FLC has been deployed on a prototype version of the control board based on the ESP32 microcontroller running FreeRTOS. The use of this type of operating system ensures reliability and isolation of the functions performed. A view of the board is shown in Figure 7. The control board has eight relay outputs, eight analogue outputs for controlling actuators according to the 0–10 V standard, twelve digital potential-free inputs and ten analogue inputs as well as an I${}^2$C bus for handling sensors (e.g., temperature, humidity, CO₂, MAF, etc.). This allows operation of the full AHU configuration and equipment with all auxiliary components (as shown in Figure 2).

The controller, working as a separate task with higher priority, was supervised by a watchdog timer which in the event of program failure, restarts and restores the functionality of the AHU. Two basic tasks are running on separate cores. The first task is responsible for executing the whole HVAC algorithm, and the second one for handling network connections, communication with the user, external control panels, etc. A partial graphical documentation of the firmware source code is shown in Figure 8. To make the software fault-tolerant and interactive, it was decided to use the EventQueue [46] design pattern. Both tasks exchange data through access to a common memory area implemented on a queue basis. The main control task, responsible for controlling not only the temperature but all other functionalities of the AHU, is executed cyclically, with measurement data averaged every minute; however, the controller execution itself depends on measurement data and queue events. The communication part is executed asynchronously. The entire code was written in C++ language.

The controller module as initially envisaged remains universal, and its other instances, apart from temperature control, are able to control other parameters such as air volume and the anti-freeze heater for heat exchange. The controller code was also written in C/C++ language and can be used in other types of microcontrollers, both in programs written natively and using libraries that facilitate prototyping such as Arduino Core or the HAL (hardware abstraction layer) provided by µC manufacturers.

The developed AHU control board, in addition to the use of the described control method, contains several more functions that allow it to work as a stand-alone, AHU master controller. Thanks to its extended communication properties, it can also be integrated into more sophisticated indoor climate management systems, such as BMSs and BEMSs.

4. Evaluation and Results

4.1. Verification Model

A variety of approaches to performance verification were considered, but since the development of the controller was started in the industry-standard Matlab/Simulink package, which is familiar to most people working in the field, it was used throughout the verification stage using the hardware-in-the-loop (HIL) method, with the controller code physically implemented. During the development of the final version of the controller, it was necessary to perform multiple iterations with various setups. However, the parameters should be repeatable, with real-time and equivalent execution. An important issue is the proper selection of the room model operated by AHU; for the same reasons as in the selection of the package, it was decided to use a ready-made model and adapt it.

The vehicle HVAC system from the Matlab package was used [47] but was adjusted to match the parameters of the room in the building, walls and glass areas. Thermal conductivities and indoor volumes have been modified in the heat transfer subsystem (see Figure 9). The room is represented as a volume of moist air exchanging heat with the external environment. The moist air flows through a recirculation flap, a blower, an evaporator, a blend door, and a heater before returning to the room. The recirculation flap selects flow intake from the room or from the external environment. The blender door diverts flow around the heater to control the temperature. The evaporator and the heater are implementations of heat exchangers using the e-NTU method [48]. They are components based on the Simscape^™ Foundation Moist Air library.

Additionally, the authors were able to verify the feasibility of the simulation based on their experience with controlling an AHU in a comparable real-world room. Once the final version of the verification model was prepared, its behavior was compared with an existing room that was available to the authors, with the same volume and similar HVAC system performance (Figure 10). However, in order to avoid the influence of the controller and other control circuit components, the test was carried out by driving the chiller and heater to 100% and comparing ramp-up times; in addition, the simulation used the same weather data as those used in the physical test. The adopted oversimplifying ensured similar thermal dynamics in the model as in real conditions, making the model usable for further exploration.

The walls consisted of one concrete layer, 40 cm thick (a simplification that ignores the true thinner thickness of the concrete and the presence of an insulating layer). An additional load was the heat from two occupants of the room. The HVAC system with an efficiency of 0.08 kg/s consisted of an air mix chamber with a bypass, a 1.5 kW chiller and a 3.5 kW heater for small rooms (<100 m${}^3$) and 7 kW heater and 3.6 kW chiller for large rooms (≥100 m${}^3$). Rooms with volumes ranging from 48 to 300 m${}^3$ were studied during tests, leading to the creation of the final regulator structure. The improvement of control quality was observable for all the cases, and the two edge cases (small room, large room) and the averaged results for all tests are presented next.

4.2. Examination Method

The single simulation included 24 h of air temperature control carried out for three different weather conditions: winter (heating), summer (cooling) and a transition period in spring (mixed cycle). The weather data came from actual measurements taken in Poland (moderate climate) during these three periods. The base set-point temperature was 24.5 ${}^{\circ }$C for summer and spring and 23 ${}^{\circ }$C for winter. The control algorithm was run on an Arduino Uno R1 board in HIL convention during the development stage, and in the newly designed control board in final stage. Simulink sent the data necessary for the controller to run via a serial interface, in response, the controller sent the computed signals to back the simulation (see Figure 11 and left part of Figure 9). The proposed solution was compared with two variants of the standard PID regulator:

• variant 1: an untuned PID with default settings (K_p = K_i = 0.5, K_d = 0.00001);
• variant 2: a fine-tuned PID for for a particular room size using Z-G method (K_p = 0.001, K_i = 0.01, K_d = 0.00001).

The plots of indoor temperature for one of the model rooms plotted together with external temperature for single days are shown in Figure 12 and Figure 13. All simulations started from an initial temperature (T_init, T_cabin in Simulink model) of 25 ${}^{\circ }$C (A) with a constant air volume. The setpoint was constant for the entire simulation time. AHUs generally operate with a fixed temperature, or it is changed at most a few times during the day (working according to a programmed schedule); therefore, it is more important to respond to external disturbances than to change the setpoint. The response to the unit jump of the setpoint at a constant outdoor temperature was used in the tuning stage of the fine-tuned controller; due to the standard use of this and conditions deviating from normal operation of the AHU, description of this examination was omitted.

The correctness of the proposed solution was evaluated by monitoring the process value (PV) signal and the controller output. Oscillations or overshoots noticeable by a human operator, but as objective indicators of the tuning, the following integral quality metrics are most typically used: Integral of Absolute Error (Equation (2)), Integral of Square Error (Equation (3)), Integral of Absolute Error multiplied by Time (Equation (4)), Integral of Square Error multiplied by Time (Equation (5)).

$$IAE=\sum _{k=0}^N\left|ϵ\left(t_k\right)\right|$$

(2)

$$ISE=\sum _{k=0}^N{ϵ}^2\left(t_k\right)$$

(3)

$$ITAE=\sum _{k=0}^N\frac{t_N}{N}\left|ϵ\left(t_k\right)\right|$$

(4)

$$ITSE=\sum _{k=0}^N\frac{t_N}{N}{ϵ}^2\left(t_k\right)$$

(5)

$t_0$ = 0, and N is the number of samples in the analysed time period; so, $\frac{t_N}{N}$ corresponds to the sampling time.

These indicators are the typical ones known in the control engineering field; those shown above are modified, discrete versions, which can be applicable to simulations and digital data sampled from physical devices.

The base metrics used in simulation tests may also be the mean absolute error (Equation (6)) which describes the averaged control error $ϵ$ over a certain simulation time from $t_0$ to $t_N$:

$$MAE=\frac{1}{N}\sum _{k=0}^N\left|ϵ\left(t_k\right)\right|$$

(6)

If the SV always corresponds to the PV, the value of all these indicators (Equations (2)–(6)) becomes 0, which is unattainable in real systems. The goal is to minimize them, and tuning requires trade-offs between steady-state and transient behaviour; this is a tricky task, especially in building automation and ventilation applications [11,31].

4.3. Single Case Description—A Small Room, Three Seasons

The results for room of 48 m${}^3$ volume with single 3.5 m${}^2$ window, a 1.5 kW chiller and a 3 kW heater are shown in Figure 12. The negative effects of mistuning are more perceptible in small rooms, in which it an averaging effect associated with the large heat accumulation of large rooms does not occur; while the AHU serves single rooms, users are more likely to change settings and use the on-demand mode (which can negatively affect energy performance). However, due to the smaller volume and the associated time constant of the room, the oscillations presented in Figure 12 are also smaller than in Figure 13, which occurred in a large room.

The part marked (A) in Figure 12 presents another important piece of information: the overshoot increases with the change of season. This is related to the more frequent use of the mixing chamber for cooling. In order to achieve optimum savings, the PID settings would have to be adapted to the actuator used by the HVAC system, as well as to the external conditions. In addition, the fuzzy controller regardless of the season reaches the set temperature faster, and its upkeep is more stable than with a PID (B in Figure 12).

4.4. Single Case Description—A Large Room, Three Seasons

The large room had volume of 300 m${}^3$ with a window area of 38 m${}^2$. The chiller had power of 3.6 kW and the heater 7 kW. The negative effects of untuning are more perceptible in a large room. Prima facie (Figure 13), it can be assessed that the fuzzy controller behaves correctly, much better than the untunned variant and comparably to the fine-tuned. In the case of using flaps, a blending chamber and external air thermal, during the equivalence of external and internal temperatures, there were oscillations in all cases; however, they are partially related to the simulated model (B). Nevertheless, a similar phenomenon is also observable in the real systems and may be related to the presence of still air zones around the heat exchanger.

For the untuned variant, oscillations occurred in a settled state for all cases (C), but the amplitude was of the order of single degrees, and the period was in the range of about 30–65 min. As practice shows, without monitoring and data visualization, it would probably remain unnoticed; however, it can cause some negative implications such as higher energy consumed or faster wear of components (e.g., valves).

4.5. Overall Results

Apart from the visual assessment of the waveforms, in order to objectively evaluate the effects, the average control quality indicators given in Section 2.2 were calculated (Equations (2)–(5)). As can be seen in Figure 14, FLC was better for all comparisons with the untuned variant, and the differences in the magnitude of the indicators are even several times smaller.

The first plot in Figure 14 shows a comparison of mean-square error MSE, which may be physically interpreted as the average daily deviation from the setpoint. Except in the summer (a small difference of 0.05 ${}^{\circ }$C favourable to fine-tuned variant), the FLC has always had a slightly better performance. The MSE for FLC was 0.36 ${}^{\circ }$C on average for all three seasons, and it improved by 36% compared to the fine-tuned variant (with MSE = 0.56 ${}^{\circ }$C) but relatively improved by 72.5% compared to untuned version, in which the MSE value was 1.31 ${}^{\circ }$C.

It could be presumed that the smaller the MSE, the better the user comfort (excluding other factors such as air flow, humidity, etc.), but even the worst averaged values for the untuned PID are at the limit of human temperature perception [49]. Yet, this could induce some occupants to modify the setpoint, which may negatively affect energy efficiency, not obviously improving their comfort after the change is made.

The last graph in Figure 14 is a compilation of the averaged daily control value of actuators (0 for off-state and 1 for on-state, all day, with 100% power). Based on this value, the energy consumption can be roughly estimated (

Table 1. Estimated energy consumption for simulated 3 days (H—heater 3 kW, C—cooler 1.5 kW).

		Winter	Spring	Summer	Total
fuzzy	H	61.9	2.16	0.72	70.18 kWh
	C	0	3.6	1.8
fine-tuned PID	H	52.9	2.88	3.6	61.18 kWh
	C	0	1.08	0.72
untuned PID	H	46.9	9.36	4.32	80.38 kWh
	C	0	7.2	12.6

), assuming some simplifications: 0.65 achieved with a 3 kW heater in winter will consume 46.9 kWh in a day (24 h). This estimation is valid for the heater and cooler, and can be directly derived from the averaged value of the output control signal. Energy usage for the steering of flaps and dampers in recovery mode and other parts of AHU (control board, sensors, etc.) can be ignored, because in practice it represents single percentages of the total AHU consumption. In addition, these estimates assumed the unit was operated at a constant air volume (CAV) mode.

4.6. Discussion

The comparison shows that the fine-tuned variant achieved 12.8% lower energy consumption relative to the FLC variant, but achieved worse control quality (all integral indicators values given in Figure 14 after averaging were reduced by 27.4% in favour of FLC). The difference in energy consumption between untuned PID and FLC is close to the previous value, and is 12.6%. So, there was a difference of a similar order between the untuned variant, FLC and fine-tuned version for energy consumption, but for the control quality and MSE, the significant advantage of the proposed FLC emerged. The minor notable exception was the summer period, in which the performance of FLC was 25.4% worse in terms of control quality relative to fine-tuned PID.

The behaviour of a fine-tuned regulator, working well for most conditions, for some specific cases (here, the days of spring and winter), such as that shown in Figure 13, is characterized by apparent overshoot; its elimination would require additional tuning, but with no guarantee of not spoiling its performance in other cases. However, this has not been the case for the FLC described in the article, and the projected method avoids these drawbacks.

To conclude, for all the investigated cases, it was confirmed that the control quality compared to the classical PID controllers is similar, and in the case of the untuned scenario, the FLC always performed at a better level. In scenarios in which the AHU operates under established conditions (industrial, laboratories, special purpose rooms) and it is possible (or cost-effective) to fine-tune the controller on-site, the classic PID is sufficient.

Nevertheless, in most uses, especially in moderate climates with all seasons and heating, cooling and transient cycles, in real buildings with a variable number of people with different thermal preferences, the correct selection of settings to guarantee optimal operation of the PID controller would be challenging. This is because detecting issues caused by its mistuning without detailed analysis of the measurement data and system observation is also demanding [50].

Still, most of the HVAC solutions available on the market include standard PIDs, and as practice shows, they often work with initial and factory settings, without reaching peak performance [11,50]. For all these cases, the solution may be FLCs, as proposed in these work, which basically eradicate the fine-tuning process, having similar computational complexity which allows deployment in dedicated AHUs’ logic boards and in general purpose automation controllers (e.g., programmable logic controllers and programmable automation controllers) such as typical PIDs.

5. Conclusions and Future Works

Modern methods such as those using machine learning and neural networks are currently among the most widely exploited, but they are often studied mainly by simulation outside hardware research work, and there are rarely pilot deployments; this means that the implementation aspect is neglected due to the lack of readiness for practical use. At the same time, there are many more adult methods of computational intelligence that are somewhat omitted for this reason, but this is more due to the rapid development of consumer electronics that are reliable and have a large practical aspect, much like the FLC presented in this paper.

For all the investigated cases, the control quality compared to the standard PID is comparable, but in the case of the untuned scenario, the FLC always outperformed it. If the AHU operates under constant conditions (industrial, laboratories, special-purpose rooms) and it is reasonable to fine-tune the controller on-site, the PID seems to be sufficient. In real buildings, especially in moderate climates with a variable number of people with different thermal preferences and widely varying weather conditions, correct tuning of the PID would be challenging. Detecting issues without detailed analysis of measurement data and system observation in practice is difficult to manage.

Most of the HVAC systems available on the market still use classical PIDs. They often work with initial factory settings, not reaching peak performance. FLC solutions, basically eliminating the fine-tuning, have similar computational complexity which allows deployment in many real systems and can also help to boost the performance of higher-level BEMS.

The approach proposed in this paper achieved better results both from the point of view of control quality (based on integral indicator, by 27.4%, in comparison with the fine-tuned PID; the approach was even several times better than the untuned variant) and estimated energy consumption (by 12.7% in comparison with untuned variant). It was finally deployed to the newly designed control board with an ESP32 microcontroller (Figure 7). The board has wider features and performs other tasks related to the correct operation of AHU, but this paper mainly focuses on the temperature control block because it affects energy consumption the most.

However, the obtained results should be confirmed by tests on a real, physical HVAC system in a wide range of conditions. The next, planned stages of development are industrial tests in connection with a few type of AHUs, and testing of the controller’s operation in applications other than temperature control, such as volume flow control. The first attempts are consistent with those obtained in HIL simulations.