Optimizing Energy Efficiency in a Peltier-Module-Based Cooling Microunit through Selected Control Algorithms

Abstract

This research covers the process of heat exchange in a cooling microunit equipped with Peltier modules. We put forward that by choosing the control algorithm, not only the control signal quality in such a system is affected but also its energy consumption. Tests were carried out for the following algorithms: relay, parallel PID, serial PID, and PID + DD. An experimental setup was developed that allowed for recording the step response of the investigated plant. Next, the transfer function of the plant was formulated, and a simulation model of the control system was developed using the MatLab^®-Simulink environment. Through computer simulation for a selected system operation procedure (cooling down to three set temperatures and maintaining them for 5000 s), the quality of control signals and the influence on energy use were investigated. The cumulative energy value for each of the algorithms and the cumulative difference in energy consumption between the controllers were calculated. The best results in terms of control quality were obtained for the parallel PID controller. The lowest energy consumption was observed for the relay controller, with the difference compared to other investigated controllers reaching 4.3% and 9.0%, without and with the presence of signal disturbances, respectively.

1. Introduction

Refrigeration processes are widely used in everyday life, enabling essential applications such as air conditioning, food storage, and the transportation of temperature-sensitive pharmaceuticals. One of the basic technical solutions used in refrigeration is vapor compression technology, which has dominated refrigeration systems since its commercial design by W.H. Carrier in 1911 [1]. However, the increasing demands for energy efficiency and the need for environmentally friendly cooling solutions are driving a search for alternative refrigeration technologies. The use of harmful refrigerants such as chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs) raises significant environmental concerns due to their difficulty in disposal and potential to degrade the ozone layer [2,3]. Consequently, the disadvantages of vapor compression systems—primarily their high energy demand, low efficiency, and adverse environmental impact—highlight the need for innovative refrigeration technologies [4].

Among the alternatives gaining attention in research on refrigeration are thermoelectric systems that utilize thermoelectric phenomena. The Seebeck effect, discovered in 1821, allows thermoelectric devices to convert heat into electricity, while the Peltier effect, identified by J. Ch. Peltier in 1834, enables these devices to provide cooling or heating [5,6]. Thermoelectric coolers (TECs) offer several advantages over conventional cooling devices, including no working fluid, quiet and vibration-free operation, no moving parts, negligible direct emission of greenhouse gases throughout their lifetime, compact size and low weight, high reliability, ease in switching between cooling and heating modes, DC power supply, and easy and low-cost maintenance [7,8]. Their versatility extends to applications in air conditioning, electronic device cooling, temperature control in vehicles, and biomedical uses such as preserving biological materials [9,10,11,12,13].

Nevertheless, a significant limitation of thermoelectric cooling systems is their relatively low energy efficiency [14]; hence, many research works are focused on new materials and structures enhancing TEC performance [15,16,17]. Key factors influencing the cooling efficiency of systems based on Peltier modules include spatial configuration, flow rates over the modules, and module packaging and connections [18,19,20,21,22].

To improve the energy efficiency of cooling processes in Peltier-module-based systems, modeling and simulations have been employed in various research activities [23,24]. For instance, Najafi and Woodbury [25] investigated the use of Peltier modules for cooling photovoltaic (PV) systems through MatLab^® simulations, identifying optimal power inputs to enhance PV performance. Similarly, Ari and Kribus [26] developed a mathematical model to analyze the impact of the Peltier effect at the junction of TECs and PV cells. Many studies focus primarily on modeling and simulations of specific applications or configurations, such as the performance of TECs combined with magnetic cooling [27] or optimizing microprocessor cooling using Peltier modules [28]. Other authors, including Mannella et al. [29], Astrain et al. [30], and He et al. [31], concentrate their research on developing and validating mathematical models for various Peltier-based refrigeration systems to enhance the design stage of these systems in practice.

Despite these advancements, research exploring ways to reduce energy consumption in the heat exchange process through optimization of the control algorithm remains limited. The algorithm is understood here as the method of shaping the control signal, for which the controller in the control system is responsible [32]. Therefore, by changing the type of controller, the control algorithm is modified. A review of the literature demonstrates several studies focused on improving energy efficiency by adjusting control algorithms in diverse fields, including steam boilers in thermal power plants [33,34], distillation columns in the chemical industry [35,36], and seawater desalination systems [37]. Notably, Shi et al. [38] proposed an interesting approach for energy savings in applications such as plastic injection molding, using robust predictive fault-tolerant switching control. However, the potential impact of control algorithm optimization on the overall energy efficiency of Peltier-module-based systems is not adequately explored. Existing studies often prioritize achieving stable temperatures rapidly [14] or maintaining stable temperature in the refrigerated space [39], neglecting the energy efficiency implications of different control strategies. In this work, we compare various control algorithms for cooling systems, taking into account both the signal quality and energy efficiency of the process. Such methodology has been applied in research by Śmierciak and Ziółkowski [40,41], who analyzed the control of resistance furnaces in foundries, and by Knaga et al. [42], who studied the bioethanol production process using a rectification column. To the best of our knowledge, no similar study has been conducted regarding Peltier-module-based cooling systems thus far.

There is extensive literature in the field of control quality, or the optimization of controller settings and their impact on the quality of control signals [43,44,45,46]. However, these works generally do not take into account the fact that a change in control algorithms may affect the total energy efficiency of the processes for which they are responsible. In this paper, an additional criterion for evaluating the algorithms regarding energy consumption is introduced. This research focuses on developing a methodology that allows for assessing the energy efficiency of various control algorithms through modeling and computer simulation at the design stage. In this study, the following hypothesis is put forward: “In a Peltier-module-based cooling system in which heat exchange processes occur, the control algorithm affects not only the quality of the control signal but also energy consumption”. By establishing an additional criterion for evaluating control algorithms based on energy use, this work aims to provide a comprehensive analysis of energy consumption in cooling scenarios, setting the stage for future innovations in thermoelectric cooling applications.

2. Materials and Methods

In order to test the hypothesis, an experimental setup was constructed and the step response for the investigated plant was recorded, which enabled system identification. Next, using MatLab^®-Simulink, a simulation model of the control system was created. Then, using the developed model, the quality of control signals and the impact of the control algorithm on energy consumption were investigated in a series of computer simulations. Control systems using a relay controller and three variants of a proportional–integral–derivative controller (PID), i.e., parallel PID, serial PID, and PID plus second-order derivative (DD), were analyzed.

2.1. Experimental Setup

In the first stage of the research procedure, the dynamic characteristics of the investigated plant were determined. Figure 1 presents a scheme of the experimental setup constituting the plant, which is a cooling microunit equipped with Peltier modules.

The essential element of the experimental setup is the physical model of the plant, namely a cooling microunit based on four Peltier modules, which are thermally connected in parallel and electrically in series. This unit is shown in Figure 2.

Peltier modules, such as the ones used in this study, are semiconductor thermoelectric elements, in which one can distinguish an electric circuit (a series connection of semiconductors, or “poles”, with a conductor or copper plates) and a thermal circuit (a parallel system connecting the cold plate with the hot plate through a semiconductor/conductor connection). When voltage is applied to a Peltier module, the flowing current causes heat to be transferred from one side (plate) of the Peltier device to the other. As a result, one side of the module is cooled while the other side is simultaneously heated [18].

The physical model comprised four standard Peltier modules (TEC1-12706 40 × 40), which were installed in a specially constructed thermal insulation board with dimensions of 200 × 200 mm. This board had a sandwich structure made of three layers of ArmaFlex^® insulation placed alternately with three Novotext layers (one layer 3 mm thick, two others 1 mm thick). Such a board is characterized by good thermal insulation and appropriate structural rigidity, allowing for the attachment of Peltier modules, as well as radiators, both on the hot and cold side. The cold side was equipped with passive radiators made of aluminum, whereas on the hot side active copper–aluminum radiators with a cooling tube were used (Figure 2). Active radiators display better heat dissipation, which allowed for reducing the temperature difference between both sides of the modules. The developed model of the cooling unit was mounted on a polystyrene box with a capacity of 30 dm³, in which a fan ensuring air circulation in the cooling chamber was mounted.

In order to register the step response, a power supply unit linked to a PC was used ((4) in Figure 1) The PT-100 resistance thermometer was applied as a temperature sensor. It was switched through the signal amplifier to an input–output card (PCLD-8710 wiring terminal board) connected to the PC, which recorded the data at 0.5 s intervals. The role of the temperature sensor was to enable registering the plant’s response to the forced signal.

2.2. Step Response

The first stage of developing a model of the plant was to identify its dynamic characteristics by experimentally determining the step response [47]. At the beginning of the experiment, the system was in a steady state at a temperature of 19.0 °C. The step response was triggered by a forced step increase in power supplied to the system, ΔP = 100 W. The response of the system to such a drive was a change in temperature in the chamber, which is shown in Figure 3. The step response was recorded until the temperature stabilized at 2.86 °C. Figure 3 shows the discussed characteristics (left axis) along with the course of the supplied power (right axis).

2.3. Model of the Plant

The obtained step response (Figure 3) was the basis for the development of the plant model G(s), which in general form is described by the following equation [47,48]:

$$G\left(s\right)=k_{ob}·{\displaystyle \frac{1}{Ts+1}}·e^{-T_{o}s}$$

(1)

where the components of the above equation are as follows:

• s—Laplace operator;
• T—time constant;
• T_o—delay;
• k_ob—coefficient of static amplification.

The value of the time constant T and delay T_o were initially read from the graph (Figure 3). The coefficient of static amplification k_ob was calculated as the ratio of the change in the output signal (ΔY) to the change in the input signal (ΔX) [48]:

$$k_{ob}={\displaystyle \frac{∆Y}{∆X}}$$

(2)

2.4. Model Validation

In order to determine the values of the model parameters that ensure that the model accurately represents the behavior of the plant, a validation procedure was applied [49]. It was carried out during subsequent computer simulations, during which the model parameters were modified in such a way that the sum of squared absolute errors ɛ_mod determined on the basis of dependence (3) approached zero.

$${\epsilon }_{mod}=\sum _{i=1}^N{{\epsilon }_i}^2$$

(3)

where the components of the above equation are as follows:

• ɛ_mod—sum of squared absolute errors;
• N—number of measurements;
• ɛ_i—absolute error of the model fit:

$${\epsilon }_i=\left(T_i-{\widehat{T}}_i\right)$$

(4)

where the components of the above equation are as follows:

• T_i—output signal in a real system;
• ${\widehat{T}}_i$—output signal calculated using the model.

The final form of the model resulting from the model fitting process is presented in Figure 4.

Having considered the curves presented in Figure 4, it should be stated that the developed model (curve no. 2) describes the plant (curve no. 1) with high accuracy. The model fit error ɛ (curve no. 3) is in the range between −0.6 and 0.6 °C.

The final form of the plant model after validation is presented by the following dependence [42]:

$$G\left(s\right)=0.16{\displaystyle \frac{1}{350s+1}}$$

(5)

where s denotes the Laplace operator.

2.5. General Concept of the Control System

According to good practice recommendations [32,48], the control system should maintain the value of the process variable at a predetermined constant level while ensuring resistance to external disturbance factors. In this study, control in a typical closed-loop control system was analyzed (Figure 5). In addition, for the purposes of the study, energy consumption of the plant was included in the control system design.

The blocks presented in Figure 5 refer to the following functions: “Setpoint” represents the set temperature, “Controller” denotes the analyzed algorithms, and “Transfer Fcn” and “Transport Delay” symbolize the plant. There is also an additional block in the control loop, which is not part of the system structure—“Signal Generator”. This block simulates a disturbance input. Its presence during simulation tests enables the analysis of the influence of the interfering signal on the control quality. In addition, the diagram shows the following signals: set value r(t), control error e(t), control u(t), and system output y(t). The following controllers were included in the study: relay, parallel PID, serial (interactive) PID, and PID + DD.

2.6. Control Algorithms

The first controller analyzed in the study is a relay. Its control signal takes only two values: minimum and maximum. Such controllers are recommended for controlling thermal objects [50].

Next, modifications of a PID controller were analyzed. Manufacturers of controllers for industrial processes use three PID controller algorithms, i.e., serial (interactive), parallel, and ideal (non-interactive). Typically, there is some available controller software which allows for choosing between the listed algorithms.

In this study, serial and parallel algorithms were analyzed. The serial (interactive) PID controller algorithm consists of three functional terms (proportional, integral, and derivative) in series. Such a connection causes the terms to interact with each other. Thus, the gain factor P affects all three correction actions, and the derivative time constant D affects the integral time constant I. Using a series controller as P, PI, or PD gives the same results as a parallel one. It is related to the possibility of using analogous setting values in both cases. The block diagram of the interactive PID controller is shown in Figure 6 [51,52,53].

The correction actions of a parallel PID controller are based on three functional terms (proportional, integral, and derivative) that work in parallel. The output signal of the controller is a sum of the proportional gain of the error signal, its integral, and its derivative. With this algorithm, each term is independent and does not affect the others. This means that the gain factor k works only in the proportional path, and it does not affect the integral or derivative terms. The algorithm of the parallel PID controller as a block diagram is shown in Figure 7.

A PID + DD controller was developed by adding the second-order derivative path to three functional terms (proportional, integrating, and differentiating) of a parallel PID controller [51]. In this case, the proportional gain of the error signal, its integral, its derivative, and its second derivative are summed to calculate the output signal. Similarly to the parallel PID controller, each term is independent and can be adjusted without affecting the others. The structure of the PID + DD controller is shown in Figure 8.

2.7. Model of the Control System

Based on the general control concept (Figure 5) and the plant model (Equation (5)), a simulation model of the control system was developed in the Matlab^®-Simulink environment. Four versions of the control system were implemented, each including a different controller: relay, serial (interactive) PID, parallel PID, and PID + DD (Figure 9).

The modeled system (Figure 9) was the basis for computer simulations enabling the selection of settings for the controllers, analysis of the control quality, and evaluation of the impact that the control algorithms have on energy consumption in the process.

2.8. Simulation

The plant model and the model of the control system were subjected to computer simulations. As a result, the data on the control signal at the controller output were obtained. This signal, together with the information on the actuator power (in the range of 0–100 W), allow for estimating the energy consumption. The obtained results may facilitate the controller selection for Peltier-module-based cooling systems at the design stage.

In the simulations, a scenario representing typical operation of the investigated cooling system was applied. The process duration was set at 250 min. The set signal was shaped according to the following algorithm: reaching the temperature of 15 °C and maintaining it for 83.3 min (i.e., 5000 s), then lowering it to 10 °C and maintaining it for the next 83.3 min, and finally the temperature drops to 5 °C and remains maintained at this level for 83.3 min.

At the start, the simulations did not include any disturbance signals. Subsequently, the control process was evaluated by introducing an interfering signal representing bounded and unknown disturbances. These disturbances have a frequency of 2 mHz and an amplitude equivalent to 5% of the maximum value of the set signal. This aligns with the methodology applied in studies by Śmierciak i Ziółkowski [40,54]. A fragment of the disturbance signal is shown in Figure 10.

For the relay controller, the hysteresis value set throughout the simulations was at the level of 0.5 °C. The settings (values of gains for PID-type controllers) were selected by trial and error during successive computer simulations.

2.9. Indicators of Signal Quality and Energy Use

The control quality was assessed on the basis of QI1 and QI2 quality indicators, where QI1 is the integral of the absolute value of the control error (6) and QI2 is the integral of the absolute value of the control signal derivative (7) [40,55,56].

$$QI1={\int }_{tp}^{t_f}\left|e\right|dt$$

(6)

$$QI2={\int }_{t_p}^{t_f}\left|{\displaystyle \frac{du}{dt}}\right|dt$$

(7)

where the components of the above equation are as follows:

• e—error between the set value and the output;
• ${\displaystyle \frac{du}{dt}}$—control signal derivative;
• t—time;
• t_p—start of the control time interval;
• t_f—end of the control time interval.

QI1 informs about the quality of control, while QI2 provides information on the dynamics of the control signal. The lower the value of QI1, the better the control quality. Higher QI2 values indicate that the dynamics of the signal is higher, which may influence the durability of the actuator since it has to react to more dynamical changes in the control signal.

The influence of the control algorithm on energy consumption was analyzed on the basis of the cumulative energy AE (8) and the cumulative difference of energy consumption ADE (9) [42].

$$AE={\int }_{t_p}^{t_f}Pdt$$

(8)

$$ADE={\int }_{t_p}^{t_f}\left(P_A-P_B\right)dt$$

(9)

where the components of the above equation are as follows:

• P—power at the controller output;
• P_A—power in the system with the controller A;
• P_B—power in the system with the controller B;
• t—time;
• t_p—start of the control time interval;
• t_f—end of the control time interval.

On the basis of the ADE value, the energy efficiency of the system was assessed. In this study, as the refence controller (index A in the Equation (9)) for calculations, the relay controller was applied, to which variations of PID controllers were compared (index B in Equation (9)). Thus, the following notation was used to indicate the difference in cumulative energy consumption for individual controllers: relay–PID-serial, relay–PID-parallel, and relay–PID + DD.

3. Results and Discussion

3.1. Control Signals

The simulations were carried out for the process in ideal conditions (without disturbances) and in the presence of a disturbing signal of a random nature, with a frequency of 2 mHz and an amplitude equaling 5% of the maximum value of the set signal. Figure 11 presents the changes in the control signals over time for ideal conditions (no disturbances).

The characteristics of the relay and PID + DD controllers make the analysis of their control signals shown in Figure 11 difficult, so to better highlight the nature of changes in those signals, a part of the process was isolated and is shown in Figure 12 and Figure 13.

The control signals of the applied controllers (Figure 11) represent the power input to the plant. A significant similarity can be observed for both serial and parallel PID-type algorithms. The difference in the signal of the relay controller (Figure 12) results from the fact that its corrective action consists in alternating only two values: 0 or 100 W. In the analyzed case, the hysteresis value set for the relay was 0.5 °C. Hysteresis should be a compromise between minimizing the control error and durability of the actuator. The result of too high a frequency of the control signal (on and off operations) would be a shortening of the actuator’s service life (surge current effect).

In the case of the PID + DD controller (Figure 13), it should be noted that the main curve of its control signal is analogous to that of the PID controllers. However, there are also numerous vertical peaks corresponding to the signal waveform of the relay controller.

The simulation results including the influence of the disturbance signal on the modeled system are shown in Figure 14.

In order to highlight the specific nature of changes in the signals in the presence of disturbances, short time intervals were separated for the analyzed controllers (Figure 15).

The waveforms of the presented control signals (Figure 15) result from the reaction of the controller algorithms to the interfering signal (Figure 10). It can be observed that in order to maintain the controlled value at the set level, the controller has a feedback effect on the plant through control signals with high dynamics of change. The rate of change in control signals corresponds to the dynamics of changes in the interfering signal.

3.2. Analysis of the Control Quality

Figure 16 illustrates the obtained results for temperature control simulations performed for the modeled system (Figure 9) without disturbances.

In order to show the nature of the signal changes more clearly, a part of the process was selected and is presented in Figure 17.

Table 1. Control quality indicators in ideal conditions (without disturbances).

	Controller	Relay	Parallel PID	Serial PID	PID + DD
Indicator
QI1		5141	2332	3438	2332
QI2		2.78 × 108	6206	6567	1.07 × 105

presents the values of control quality indicators, calculated according to Formulas (6) and (7).

Taking into account the output signals (Figure 16) and the values of the control quality indicators (Table 1), it should be stated that the best result was obtained for the parallel PID and PID + DD controllers. The values of QI1 in both cases are 2332. However, it should be emphasized that to achieve the same effect, the dynamics of the control signal in the case of the PID + DD controller was much higher (high value of QI2). In a real system, this would contribute to a much greater load on the actuator. A slightly worse result in terms of control quality was provided by the serial PID controller (QI1 = 3438). The relay controller was characterized by the highest value of both QI1 (QI1 = 5141) and QI2 (QI2 = 2.78 × 10⁸), which indicates the worst control signal quality and high dynamics of the signal. In general terms, it should be stated that the algorithms of the tested controllers during the computer simulation for ideal conditions (without disturbances) ensure the control quality that allows for maintaining the controlled parameter at a level close to the set value (not exceeding 0.5 °C difference from the set value).

The simulation results including the influence of the disturbance signal on the modeled system are shown in Figure 18.

The quality control indicators calculated for the simulations including disturbances are presented in

Table 2. Control quality indicators in non-ideal conditions (including random disturbances, 2 mHz frequency, and 5% amplitude).

	Controller	Relay	Parallel PID	Serial PID	PID + DD
Indicator
QI1		8881	7937	1.23 × 104	8065
QI2		7.50 × 108	3.61 × 1010	2.15 × 108	4.56 × 107

.

Based on the analysis of the simulation results for the process with disturbances (Figure 18 and Table 2), a significant increase in the values of the QI1 and QI2 indicators can be noticed compared to the simulation for ideal conditions. The best result was obtained for the control system with a parallel PID controller (QI1 = 7937). Slightly worse results were observed for systems with PID + DD and relay controllers (QI1 equaling 8065 and 8881, respectively). The highest value was noted for the system with a serial PID controller (QI1 = 1.23 × 10⁴). In this case, the output signal in the second half of the analyzed time significantly differs from other systems. This observation, as well as the one resulting from the analysis of the signal changes presented in Figure 14, may indicate that in this case (serial PID) the controller was not able to react to the disturbances. The values of QI2 for the mentioned controllers range from 4.56 × 10⁷ to 3.61 × 10¹⁰. Such high values are the result of the disturbance signal, which induces high dynamics of the control signals.

Knaga et al. [42], who performed similar simulations for the periodic rectification process taking into account the relay, parallel PID, and I-PD controllers, found that the best results in terms of signal quality were obtained for the relay, both in ideal conditions and in the presence of disturbances. Additionally, in the case of disturbances, the relay controller was also characterized by the lowest QI2 index (the lowest dynamics of changes). These observations differ from the research results presented above. However, Knaga et al. [42] tested a heating system, with the heating temperature set to over 93 °C, while for the Peltier-module-based system in this study, the cooling process was analyzed, in which the temperature settings were lower than the ambient temperature. This indicates that different objectives for the controller and operating temperature ranges influence the quality and dynamics of the control signal.

3.3. Impact of the Control Algorithm on Energy Consumption

After the control quality analysis, additional simulation tests were carried out to determine the impact of the control algorithms on energy consumption in the heat transfer process under study. For ideal conditions (without disturbances), similar values of AE (cumulative energy consumption) were noted (Figure 19), namely 0.233 kWh at the end of the simulated scenario for the control system with a relay controller and approx. 0.24 kWh for all the systems with PID-type controllers. It can be stated that in the case of no disturbances present, the difference in energy consumption during the analyzed time does not exceed 4.3%, with the lowest consumption obtained for the simplest relay controller and the highest for PID + DD.

Subsequently, the influence of the control algorithms on energy consumption in the presence of disturbances was analyzed. Figure 20 shows the results of simulations regarding the cumulative energy consumption AE.

Based on the diagram (Figure 20), it should be stated that in the presence of disturbances, there are greater differences in cumulative energy consumption for individual types of controllers than in the case of simulations for ideal conditions. The change in the value of AE is caused by the high dynamics of the control signal resulting from interference. The following values of cumulative energy consumption were obtained at the end of the simulated scenario: relay—0.233 kWh, serial PID—0.254 kWh, parallel PID—0.243 kWh, and PID + DD—0.244 kWh. The AE value for the relay is the same as in the simulation without disturbances. Applying PID-type controllers resulted in slightly higher AE values, with the differences, however, being not considerably greater than in the case of no disturbances present (up to 9.0% for the serial PID).

Next, the difference in cumulative energy consumption (ADE) was calculated for each controller pair (Equation (9)). The results of the simulations not including disturbances are shown in graphical form (Figure 21).

The nature of the cumulative difference in energy consumption for “relay–parallel PID” and “relay–PID + DD” is comparable throughout the analyzed process, both in values and shape (Figure 21). A different characteristic was observed for the pair “relay–serial PID”. In this case, there is a smaller difference in energy consumption, up to 2 × 10⁻³ kWh less than for other pairs, and a significant curvature of the diagram can be noticed, which proves the evident influence of the integrating and derivative terms.

Analogous calculations were carried out, including the introduction of disturbances into the feedback loop (Figure 22). Similarly to the simulation for ideal conditions, during this analysis, it was also observed that changes in ADE for “relay–parallel PID” and “relay–PID + DD” do not differ significantly in terms of values and nature, while the graph for “relay–serial PID” is shaped differently. The final value of ADE in this case is approx. twice as low as for other pairs, which proves higher energy consumption. However, the ADE changes in time are interesting, because for the 1st- and 2nd-degree regulation (for temperature set at 15 °C and 10 °C, respectively), the energy consumption for the serial PID controller is comparable to that of the relay controller. Only lowering the set temperature to 5 °C causes a sharp increase in energy consumption. It has to be stated that at this stage of the simulated scenario, the serial PID controller was not able to react to the disturbances anymore, which influenced the high deviation of the achieved temperature from the set one (Figure 18).

The analysis shows that the best solution in terms of energy consumption for controlling the cooling unit based on Peltier modules is the relay controller. However, this controller maintains the set temperature within a certain range, which results from its characteristics. In this case, the temperature value oscillates in the range of 0.5 °C. The second-best controlling solution in terms of energy efficiency is parallel PID, while PID + DD is slightly worse. On the other hand, the use of a serial PID controller is beneficial, but only in a limited temperature range. Undoubtedly, it can be concluded from this that a combined controller should be used to control Peltier module-based cooling systems, switching from a serial PID controller to another, e.g., parallel PID, depending on the desired temperature.

The research presented by Knaga et al. [42] demonstrated that in heating systems, the lowest energy consumption was achieved for algorithms other than relay; specifically, the I-PD controller and the parallel PID controller proved to be more advantageous during the rectification process. In contrast, this study reveals that for cooling applications in microcircuits based on Peltier modules, the relay controller facilitates a measurable reduction in energy consumption. In turn, Ziółkowski and Śmierciak [41] found that fuzzy controllers are optimal for foundry resistance furnaces. However, it should be noted that these furnaces are characterized by a long delay in response to changes in power supply parameters. These findings underscore the importance of simulation studies for various types of heat exchange processes, as they allow for the comparison of control algorithms and can contribute to the selection of the optimal solution already at the design stage. Furthermore, incorporating novel control strategies that have demonstrated improvements in control quality and resistance to disturbances (such as robust predictive fault-tolerant switching control [38], two-dimensional model-free Q-learning-based output feedback fault-tolerant control [57], and two-dimensional iterative learning robust asynchronous switching predictive control [58]) could also provide additional energy savings. Nevertheless, it is crucial to recognize that each process has its own specific characteristics, and optimal solutions cannot be transferred from one type of process/system to another, as the outcomes may vary significantly.

4. Conclusions

Our study addresses a recognized gap in the literature by proposing a novel approach to optimizing control algorithms for Peltier-module-based cooling systems. It posits that control strategies not only influence the quality of control signals but also can affect energy consumption in cooling processes. The conducted research and the subsequent analysis of the results have led to the following conclusions:

• The best result in terms of control quality for the simulations in ideal conditions (without disturbances) was obtained for the parallel PID and PID + DD controllers. In both cases, the QI1 indicators reached the same value. However, on the basis of the QI2 values, it was found that to achieve the same effect, the dynamics of the control signal for the PID + DD controller was much higher. The worst result in terms of control quality was obtained for the relay controller.
• During the simulation tests assuming the presence of a disturbance signal, the best result in terms of control quality was obtained for the control system model with the parallel PID controller. The worst result was recorded for the system with the serial PID controller.
• In terms of energy consumption, the best control solution for a cooling unit based on Peltier modules is the relay controller. However, the temperature value maintained by this controller oscillates in the range of 0.5 °C.
• Considering the quality of the maintained temperature and energy consumption, a parallel PID or PID + DD controller should be recommended to control the power supply to the cooling unit equipped with Peltier modules.
• A detailed analysis showed the possibility of applying an interesting solution, namely a combined controller consisting of a serial PID and one of the other PID-type controllers (parallel PID or PID + DD), with the switch between controllers depending on the temperature. This conceptual solution will be subjected to simulation tests in our future research.