State-Of-Art Precise Control in Foods Processing: Pasteurization and Lyophilization

Abstract

Food safety requires repeatability and precision in food processing and optimal signal-to-noise ratio, that is, robustness to environmental variables and interfering parameters in food processing, and processes must be traceable. A thermal process is controlled according to required temperature curves by methods from various areas of process control theory. Using the case study of industrially produced soft-boiled eggs with simultaneous pasteurization (disabling of Salmonella in the egg yolk), we demonstrate technological progress of the precise temperature process control in foods industry. The simplest thermal process control is implemented with on/off regulation of heating and cooling. Accuracy is improved with the introduction of proportional, integral, and derivative (PID) control. Fuzzy control is now used in many thermal process controls. The current state of the art is the use of artificial intelligence (AI) where we train a neural network in several iterations under different conditions. The trained neural network controls the thermal process according to the required sequence. Such a control is most insensitive to environment variables by its design. We present the drawbacks and complexity of individual approaches to precise thermal control in the food industry. One must note that the matter of the case study—egg’s pasteurization and preservation of yolk softness—have opposing temperature requirements, and coexistence of the two is not granted.

1. Introduction

Worldwide megatrends in food safety and food security are environmental sustainability, associated with climate change; improvement of food-chain robustness to economic and political factors; and last but not least, technological advancements and innovation. The latter two span various realms, each contributing to more robust and sustainable food systems. Key areas are biotechnology and genetic engineering [1], food traceability [2], precision agriculture [3], food packaging and distribution, monitoring for foods safety [4, 5], and food-processing control, which is about humidity, time, and temperature control. The latter is important in cooking and refrigeration, and it is critically important in lyophilization and pasteurization.

Lyophilization, a dehydration process, is used to preserve perishable materials, improve product stability, and extend shelf life [6]. Lyophilization removes water from the product while its structural integrity and biological activity is preserved. The method is widely used in pharmaceuticals, biotechnology, and the food industry for preservation of samples and food products. Pressure and temperature processing remove water, while they preserve biological activity in the matter. In the freezing, sublimation, and desorption stages of lyophilization, temperature control needs to be within + − 1 C to ensure uniform and adequate processing.

Pasteurization is a critical process in food safety [7]. It is about the inactivation of different pathogenic microorganisms. Pasteurization goals are extension of food shell life and prevention of poisoning with foods. Microorganisms are in most cases inactivated with thermal energy, which is the integral quantity of temperature over time. Foods’ organoleptic properties need to be preserved. Precise temperature control is essential to fulfill requirements of microorganism’s inactivation and organoleptic property preservation. Temperature control is about uniform heat distribution and precise temperature regulation. Variation in heat penetration results in some volumes being under-processed and some overprocessed, which affects food safety risk and deterioration of vitamins, enzymes, and the organoleptic quality of foods.

We demonstrate the challenges and progress in pasteurized food safety in a case study of pasteurized soft-boiled eggs.

1.1 Challenges in industrial food preparation

Industrial food preparation is at minimum about volumes of processed foods, transport, preservation of organoleptic properties, economics, and safety of foods. Involved are disciplines of supply chain management, sustainability and waste management, prevention of contamination and cross-contamination, regulatory compliance, workforce safety and training, and control of humidity, pressure, and temperature.

Requirements in industrial food preparation constitute a superset of domestic requirements, and production in volumes. Besides taste and appearance, the food needs to adhere systematically to microbiological constraints—it has to be pasteurized, or potential bacteria need to be incapacitated by some other means. The industrial food preparation process needs to be time invariant, and traceability needs to be built in according to Hazard Analysis Critical Control Points (HACCP) directives [8]. We focus on food safety, achieved with the application of state-of-art precise thermal process. Industrial production of pasteurized soft-boiled eggs is a suitable case study since requirements of preservation of soft yolk and egg pasteurization oppose each other. It is only a narrow temperature range where the thermal process fulfills both requirements.

1.1.1 Soft-boiled egg nutrition value

Eggs have a long-standing presence in the human diet, with evidence suggesting that early humans consumed eggs of various birds such as pigeons, ducks, and ostriches. Consumption of domesticated chicken eggs began around 7500 BC [9]. Today, eggs are a global dietary staple, consumed by people of all ages and genders.

The exceptional nutritional profile of eggs has earned them the reputation of being a nutritional powerhouse [10]. Over the decades, perspectives on the health implications of egg consumption have evolved. Eggs are known for their high nutrient-to-energy density ratio, providing a rich source of essential nutrients. However, they are also a primary source of dietary cholesterol [11]. Historically, concerns over high serum cholesterol levels and their association with cardiovascular disease led health professionals to recommend limited egg consumption [12]. Recent research, however, indicates that the impact of dietary cholesterol from eggs on serum cholesterol levels is minimal, and emphasizes the numerous health benefits of eggs.

While eggs can be consumed raw, they are more commonly prepared in various ways across different cultures. The primary method of preparation involves applying heat, with common techniques including hard and soft boiling, scrambling, frying (over easy and sunny-side up), and poaching [13]. An exception to the typical heat-based preparation is the century egg, a traditional Chinese delicacy that involves preserving the egg in a mixture of clay, ash, and other substances for several weeks to months, which transforms its flavor and texture without using heat [14].

These diverse preparation methods not only cater to different taste preferences but also influence the nutritional and sensory qualities of eggs, making them a versatile ingredient in global cuisine.

Monitoring the range of breakfast options available in hotels, schools, and hospitals reveals that soft-boiled eggs are notably absent from the typical menu. In contrast, other expected items such as hard-boiled eggs, cold cuts, cheeses, and salads are readily available.

A marketing survey conducted in the German-speaking regions of Europe indicates that there is a significant market potential for soft-boiled eggs in breakfast offerings at hotels, health resorts, hospitals, and similar institutions. These institutions can benefit from incorporating soft-boiled eggs into their menus as they are less expensive compared to many other breakfast items, and importantly, they offer a healthier alternative to various processed meats typically consumed at breakfast.

2. State-of-art precise thermal control project steps: case study - industrial preparation of soft-boiled pasteurized egg

2.1 Ensuring food safety in egg preparation, with focus on pasteurized soft-boiled eggs

The cooking process for eggs serves not only to alter their molecular structure but also to inactivate harmful bacteria. Among these, Salmonella is the most problematic. Studies consistently highlight that the consumption of raw or undercooked eggs is a significant factor in both sporadic cases and outbreaks of Salmonella infections [15].

While it is possible to determine if an egg is adequately cooked through various tests [16], these methods are often impractical for everyday use. Fortunately, the about-appropriate temperature range for preparing soft-boiled eggs has been established [17], which gives grounds to industrial approach in production of pasteurized soft-boiled eggs where precise temperature control is essential, not only in this project but also in ensuring food safety and success of various research applications. For instance, studies on egg gelation and digestibility [18], the abundance of lipids and their categories [19], changes in egg yolk metabolites [20], and the influence of yolk structure on gel state and taste [21] all require precise temperature management.

By maintaining proper temperature control during the cooking process, we can ensure the safety, that is, pasteurization and quality of soft-boiled eggs, thus making them a viable option for inclusion in diverse dietary settings.

2.2 Thermal simulation of egg interior

Thermal simulation of heat transfer within an egg is essential to establish a correlation between the transient temperature distribution and the egg’s dimensional and material properties. To achieve this, we developed a fast simulator of conductive transient heat transfer with a fixed grid of cells, applied in egg thermal simulation. The simulator is thoroughly elaborated in Ref. [22]. The user interface display is in Ref. [23]. The results from these simulations are crucial for designing a thermal process that ensures the production of certified pasteurized soft-boiled eggs.

The primary goal of developing this simulation is to identify how temperature distributes spatially within an egg during heating and how these temperature variations relate to the egg’s size and material characteristics. This understanding was vital for assessing the feasibility of the new thermal process. Subsequently, this knowledge was integral in designing both the thermal process and its control system, ensuring that the eggs are heated uniformly and to the required temperatures for pasteurization.

Thermal simulation not only yields insight into the safety and quality of pasteurized eggs but also contributes to broader applications in food safety. By employing such detailed simulations, food scientists can better understand and control thermal processes for a variety of food products, ensuring they meet safety standards while retaining their nutritional and sensory attributes.

The specific thermal model employed involves placing a cold egg into a pot of hot water. The simulator is designed to calculate the temperature at any given point inside the egg over time, considering the distinct thermal properties of the shell, egg white, yolk, and the air pocket. The initial assumption is that the egg’s temperature is uniform, and the water bath maintains a constant temperature throughout the process.

To describe the heat flow within the egg, this model utilizes Fourier’s law of heat conduction:

$$\frac{\mathit{dQ}}{\mathit{dt}}=\mathit{GA}\frac{\mathit{dT}}{\mathit{dx}},$$E1

where G is the thermal conductivity, and A is the heat flow area between two neighboring cells. Heat energy as a function of temperature is

$$Q=CVT$$E2

where V is the cell volume, and C is the specific heat of the cell material.

The differentials in Eq. (1) are to be replaced by finite differences:

$$∆Q=\mathit{GA}\frac{∆T}{∆x}∆t,$$E3

which must be sufficiently small for the simulation algorithm to converge.

The thermal properties used in the simulation are detailed in Table 1. This includes thermal conductivity and specific heat capacity values for the different components of the egg. These data points have been derived from several authoritative sources, specifically Refs. [24, 25, 26].

	Thermal conductivity G [W/(mm K)]	Heat capacity C [J/(K mm^3)]
Water bath	0.00060	0.00420
Shell	0.00050	0.00200
Egg white	0.00065	0.00120
Yolk	0.00040	0.00300
Air pocket	0.00010	0.00001

Table 1.

Thermal parameters used in the simulation.

The objective of these simulations is to understand how the properties of an egg influence the time required for the coldest spot within the egg to heat up. The initial temperature of the egg is set at 5°C, and it is immersed in a water bath maintained at 90°C.

Figure 1 presents a cross section of the simulated egg at various stages across three simulations. The central line in the egg’s cross section indicates the position of the temperature profile, which is depicted below the egg. This temperature profile is recorded at 30-second intervals throughout the heating process. The time required for the coldest spot within the egg to reach 60°C is specifically highlighted and annotated. Simulation scenarios are depicted in Table 2.

Figure 1.

Cross section of the simulated egg at various heating stages across the size of an egg simulation.

No.	Egg variant	No.	Egg variant
1	reference sized	8	yolk volume 90%
2	larger 1	9	yolk volume 110%
3	larger 2	10	yolk to left 10%
4	shell thickness 50%	11	yolk to right 10%
5	shell thickness 200%	12	white g 110%, white c 90%
6	air pocket 5% egg’s volume	13	white g 90%, white c 110%
7	air pocket 10% egg’s volume

Table 2.

Egg’s variants being simulated.

2.2.1 Influence of egg size on heating time (cases 1 to 3)

In the simulated scenarios, the size of the egg significantly impacts the heating time. 252, 314, and 386 s are the times of reaching a yolk center temperature of 60°C, Figure 1. For a spherical object, the surface area increases with the square of the radius, while the volume increases with the cube of the radius. This relationship is similar in the case of an egg. Since the volume absorbs the heat energy, which must first traverse the surface, it is not surprising that larger eggs require longer heating times.

2.2.2 Effect of shell thickness (cases 4 and 5)

Where the shell thickness was halved and doubled, the influence on heating time was minimal (−0.4 and + 0.8%, respectively, compared to the reference time in Case 1). Despite the shell and other components of the egg having similar thermal properties, the shell’s relative thinness compared to the overall geometry of the egg results in negligible differences in temperature distribution. Thus, altering the shell thickness has an insignificant effect on both the heating time and the internal temperature distribution of the egg.

2.2.3 Impact of air pocket formation (cases 6 and 7)

Formation of an air pocket impact in an older egg is examined. The presence of an air pocket increased the heating time by 0.8 and 2.4%, respectively, which is not considered significant. While the air pocket does affect the internal temperature distribution, it does not alter the location of the coldest spot, which remains at the center of the yolk.

2.2.4 Influence of yolk size on heating time (cases 8 and 9)

The size of the yolk was varied to observe its impact on the heating time of the egg. A smaller yolk resulted in a 9% reduction in heating time, whereas a larger yolk caused a 7% increase. These outcomes are primarily due to the yolk’s lower thermal conductivity and higher thermal capacity compared to the egg white.

2.2.5 Effect of yolk position on heating time (cases 10 and 11)

We explored how the position of the yolk within the egg influences heating time. The results indicated no significant difference in heating times for various yolk positions. However, the temperature distribution within the egg showed a strong correlation to the yolk’s position, although the coldest spot consistently remained at the center of the yolk.

2.2.6 Impact of egg white’s thermal properties (cases 12 and 13)

The thermal properties of the egg white were altered to assess their effect on heating time. The heating time varied within a range of −4 to +10%. After the reference heating time, the temperature at the center of the yolk (the coldest spot) was found to be 1.30°C below and 2.53°C above the targeted 60°C, respectively.

Heat is transferred through three primary mechanisms: radiation, convection, and conduction. In the context of heating an egg in a bucket of hot water, radiative heat transfer is negligible and thus not considered relevant. However, convective heat transfer can play a role given that egg white is a thick liquid and could potentially contribute to heat transfer through convection. Despite this, our simulation did not incorporate convective heat transfer.

Our decision to exclude convective heat transfer from the simulation is based on findings from previous experiments related to the thermal treatment of eggs. These experiments indicated a strong correlation between egg size and the temperature measured at the center of the egg. While there was inherent noise in the measurements due to the invasive placement of the temperature sensor in the egg’s center, the data supported the exclusion of convection.

Furthermore, no significant correlation was observed between the egg’s orientation in the water (whether laid on its side, pointed end up, or rounded end up) and the organoleptic properties of the resulting soft-boiled egg. This observation justifies the simplification of the model by excluding convective heat transfer.

The relevant literature on the thermal simulation of eggs supports our approach and findings. The relevant similar literature on thermal simulation of eggs is provided in Refs. [24, 25, 27].

The implemented temperature profile for the circulating water in the basin with eggs, along with the measured temperatures at the centers of the eggs, is illustrated in Figure 2. The designed temperature profile begins at a sufficiently low temperature to prevent thermal stress and cracking of the immersed eggs. The heating power is regulated by electrical equipment standards (I_{EF MAX} = 16 A, single phase, P = 3700 W at U_EF = 230 V). The water temperature is capped at 90°C. After predetermined intervals, which vary based on egg size, the water temperature is reduced to 60°C. Concurrently, the coldest spot within the egg reaches the pasteurization temperature of 60°C. Ten minutes later (not shown in Figure 2), the water bath temperature is further lowered to 57°C, maintaining the egg’s organoleptic properties while keeping it warm until use.

Figure 2.

Measured and simulated temperature profiles [22].

The developed thermal process must be adjusted at the beginning of each run to account for egg size, classified according to standard Euro sizes: small (weight ≤ 53 g), medium (53 g < weight ≤ 63 g), large (63 g < weight ≤ 73 g), and very large (weight > 73 g). All eggs in the batch must be of the same declared size. The temperature of the circulating water bath is to be regulated in the best possible manner. This precise control minimizes variations in egg properties, ensuring consistent quality of the pasteurized soft-boiled eggs. Notably, the thermal process does not require adjustment for other egg parameters aside from size.

2.3 Verification of Salmonella incapacitation

Pasteurization is a temperature-dependent process designed to significantly reduce the number of microorganisms in food. Unlike sterilization, which aims to eliminate all active microorganisms, pasteurization seeks to drastically lower their numbers by several orders of magnitude. The goal is to ensure that the remaining concentration of pathogens is so low that the risk of disease is minimal, provided the food is stored properly at low temperatures for short periods.

When it comes to eggs, the primary concern is contamination with Salmonella. Different methods and procedures have been explored to decontaminate potentially contaminated eggs effectively. A combination of temperature, duration, and additional stress factors is necessary to reduce the concentration of live Salmonella to a harmless level.

Several studies have established specific combinations of temperatures and times required for effective pasteurization of eggs. These guidelines help ensure that the pasteurization process is both effective and efficient [28, 29, 30]. A method combining pasteurization with dry heat has been shown to effectively destroy bacteria in eggs [31]. Another approach focuses on inactivating bacteria on the shell’s surface through targeted temperature treatments [32].

Various sources of energy have been investigated for their potential to inactivate bacteria, including: utilization of microwave energy to heat the egg, effectively killing bacteria [33]; application of RF energy to achieve similar bactericidal effects [34]; combination of pulsed electric fields with heat to enhance bacterial inactivation [35]; and use of ionizing radiation to destroy bacteria, providing an effective alternative to traditional heat treatments [36].

To ensure effective pasteurization, a thermometer must be inserted into the coldest spot of the food product. This specific point must reach or exceed the minimum pasteurization temperature for the required duration [37]. Achieving this is critical for ensuring that all pathogenic microorganisms, including Salmonella, are effectively reduced to safe levels.

The most effective protection against Salmonella is to process foods at high temperatures. This principle underlies why industrial preparations of eggs for breakfast and supper buffets in hotels and restaurants commonly include hard-boiled and scrambled eggs, which undergo high-temperature processing. In contrast, soft-boiled eggs, which involve lower temperature processing, are not typically offered due to the increased risk of insufficient pasteurization.

To validate the pasteurization process, a series of test eggs were deliberately contaminated with Salmonella enteritidis at their centers. The survival rate of the bacteria was then measured across different combinations of temperature and time to determine the effectiveness of the pasteurization conditions [38]. This experimental approach helps to establish the optimal parameters for ensuring food safety while maintaining the desired qualities of the eggs.

The temperature versus time function, depicted in Figure 3, represents the optimized temperature profile for the medium in which the eggs were immersed. This carefully designed curve ensures the production of Salmonella-free soft-boiled eggs. The temperature profile has been patented [40, 41], and its pasteurization efficiency has been certified by an independent microbiological authority [42].

Figure 3.

The reference temperature curve [39].

Maintaining precise temperature control is critical to achieving effective pasteurization. The required temperature precision in the constant regions of the temperature curve, shown in Figure 3, is within ±0.20°C. Pump-induced circulation of heating water minimizes temperature gradients around eggs. Residual gradients add to temperature inaccuracy. Systemic accuracy ensures that the eggs are heated adequately to eliminate Salmonella without compromising their quality.

2.4 Design of apparatus for production of Salmonella-free soft-boiled eggs

2.4.1 The mechanical system design

Figure 4 illustrates the schematic representation of our egg cooker.

Figure 4.

Schematic representation of the egg cooker [39].

2.4.1.1 Design and operation of the egg cooker

The hot water tank has a capacity of 9 liters and is used to immerse anywhere from one to thirty eggs simultaneously for thermal processing. A hot water pump ensures the circulation of water around the eggs, maintaining consistent temperatures within the tank. During the cooling phase, the pump transfers water from the cold-water tank into the hot-water tank. Any excess water flows back into the outer tank through an interconnection at the top of both tanks. For cleaning purposes, the pump can also expel water from the system.

The heating element is designed in a flat spiral shape. The heating power is controlled analogously using a thyristor circuit, which adjusts the amount of electrical energy converted into heat every 10 milliseconds (corresponding to a 50 Hz electrical grid with a sine wave).

2.4.1.2 Insulation and cooling mechanism

The tanks are insulated with 20 millimeters of expanded polystyrene to maintain temperature stability. The cold-water tank has a capacity of 12 liters and is used to mix with hot water to lower its temperature when necessary.

An electromagnetic three-way valve facilitates the circulation of hot water in one position, and in the other position, it allows cold water to enter the hot-water tank. This increases the hot water level, causing water to flow back into the cold-water tank through the interconnection.

A cold-water pump circulates water through a radiator, and a fan dissipates the heat from the radiator. This cooling system ensures that the cold water remains sufficiently cool for sequential cooking operations.

2.4.1.3 Operational efficiency

The egg cooker can produce batches of up to 30 pasteurized soft-boiled eggs every 15 minutes. This system ensures high efficiency and consistency in egg pasteurization, meeting both safety and quality standards.

2.4.2 Ratiometric temperature measurement

Ratiometric measurement involves determining the ratio between an unknown quantity and a reference quantity. This method is generally more resilient to environmental influences compared to direct variable measurements. The fundamental reason for this resilience is that environmental variables tend to affect both the reference and unknown values similarly. Consequently, these influences cancel out when calculating the ratio, thereby minimizing their impact on the measurement.

Environmental factors, such as temperature fluctuations, humidity changes, or power supply variations, usually affect both the unknown and reference values in a similar manner. Therefore, their impact is neutralized when the ratio is calculated, leading to more stable and accurate measurements.

By focusing on the ratio rather than absolute values, ratiometric measurements can achieve higher accuracy. This is particularly important in environments where maintaining constant conditions is challenging.

In the context of food safety and security, ratiometric measurement can be employed in various scenarios such as sensor calibration where sensor systems used in food processing are accurately calibrated once and later affected by environmental changes at minimum. When assessing food quality, samples are compared against reference standards, thereby improving the reliability of assessments.

The optimal choice for a temperature sensor is a platinum-resistance-based sensor, such as the PT 100 or PT 1000. In our application of ratiometric measurement, we continuously monitor the ratio between a precision resistor and the temperature-dependent platinum resistor. This method ensures high accuracy and stability by effectively compensating for any potential disturbance to the temperature measuring system.

There is implementation of ratiometric temperature measurement with two resistors, by Jenko [43]:

When discharging a capacitor through a resistor, the capacitor voltage V_C is

$$V_{\mathrm{C}}=V_{C0}{e}^{\frac{-t}{\mathrm{RC}}}.$$E4

The discharge time can be measured by counting clock cycles N, as in

$$t=-\mathit{RC}\mathit{ln}\frac{V_{\mathrm{C}}}{V_{\mathrm{C}0}}=N{f}_{\mathrm{C}}.$$E5

For two resistors, a reference one and a resistive temperature sensor, the ratio of discharge times is

$$\frac{N_{R\left(\mathrm{T}\right)}}{N_{\text{Rref}}}=\frac{R\left(T\right)}{R_{\mathrm{ref}}}.$$E6

Implementation of temperature measurement by Eq. (6) is in Figure 5 left, where

Figure 5.

Two ratiometric implementations of a circuit for measuring R(T).

$$R\left(T\right)+R_{S3}=\frac{N_{R\left(T\right)}}{N_{\mathit{\text{Rref}}}}\left(R_{\mathit{ref}}+R_{S2}\right).$$E7

R_S in Eq. (7) corresponds to the resistance of analog switch S, which is below 1 Ω but cannot reach 0 Ω. To eliminate measurement uncertainty indicated by the analog switches, one can introduce a second reference resistor. The circuit in Figure 5 left is modified to the circuit in Figure 5 right.

Taking into account resistances of switches S2 to S4 in Figure 5 right, Eq. (7) changes to Eq. (8):

$$R\left(T\right)+R_{S3}=\frac{N_{R\left(T\right)}-N_{\mathit{\text{Rref}}1}}{N_{\mathit{\text{Rref}}2}-N_{\mathit{\text{Rref}}1}}\left(R_{\mathit{ref}2}+R_{S4}-R_{\mathit{ref}1}-R_{S2}\right)+R_{\mathit{ref}1}+R_{S2}$$E8

Since switches S2 to S4 are made within the same analog switch monolith, it is reasonable to assume that their resistances are about equal. Then, Eq. (8) changes to Eq. (9):

$$R\left(T\right)=\frac{N_{R\left(T\right)}-N_{\mathit{\text{Rref}}1}}{N_{\mathit{\text{Rref}}2}-N_{\mathit{\text{Rref}}1}}\left(R_{\mathit{ref}2}-R_{\mathit{ref}1}\right)+R_{\mathit{ref}1}$$E9

The thermal process is to maintain approximately 12 cubic decimeters of water and eggs within ±0.2°C of the specified temperature profile. This stringent requirement necessitates highly accurate and stable temperature measurements that can withstand years of industrial use. The professional kitchen appliance market typically demands minimal servicing over a product’s lifespan, which is expected to be no less than 15 years. Recalibrations of the temperature measurement system in apparatus lifetime are not feasible.

Ensuring long-term accuracy and stability in temperature measurement systems is crucial for maintaining the integrity of the thermal process. This involves using high-quality sensors and ratiometric design technique to nullify drift and ensure consistent performance over extended periods. The industry standard emphasizes reliability, durability, and only minimal maintenance.

The expectation of longevity and reliability means that the temperature measurement system must be designed to remain accurate without requiring recalibration throughout its’ operational lifetime. This approach not only reduces maintenance costs but also ensures continuous compliance with food safety standards.

The temperature measurement chain is calibrated in the apparatus production. The water temperature, measured using a PT1000 sensor, class B, and conditioned within a microcontroller, is accurate to within ±0.04°C compared to a reference thermometer in the range of 30 to 95°C.

2.5 Thermal process control

2.5.1 Prototype control of the thermal process

In the pasteurization process, eggs are immersed in hot water heated by a resistive coil. The rate at which the temperature increases is determined by the power output of the coil. To maintain a constant temperature within the hot-water reservoir, a pump continuously circulates the hot water, ensuring most uniform heat distribution. To decrease the water temperature efficiently, simply turning off the heating coil and relying on natural heat loss are inadequate due to its slow nature. Instead, the system includes a specialized reservoir of cold water surrounding the hot-water reservoir. An electromagnetic valve controls the mixing of hot and cold water. By adjusting the valve, the system can regulate the amount of cold water introduced, allowing for rapid cooling of the hot water. The extent of the cooling effect depends on the initial temperature of the hot water, as illustrated in Figure 6 left.

Figure 6.

Apparatus temperature curves.

Initially, on/off regulation was evaluated not as a final design option but to understand temperature delay characteristics. As anticipated, significant temperature fluctuations (up to 6°C) were observed, indicating substantial heat capacitance of the volume filled with eggs and water. This method proved inadequate for even coming close to the precise temperature control requirements.

The most common feedback control systems typically utilize a Proportional-Integral-Derivative (PID) controller, which assumes symmetrical actuating actions. However, in our system, this assumption does not hold true, as illustrated in Figure 6 right.

The rate of temperature change (temperature derivative) varies significantly between the heating and cooling phases. Additionally, the system exhibits vastly different time delays for heating and cooling actions. These discrepancies render a standard PID controller unsuitable for our needs.

2.5.2 Fuzzy control of a thermal process

Fuzzy regulation is based on principles akin to human manual control of various processes. Through experimentation, we demonstrated the ability to manually control the cooking process after several days of practice. The primary challenge encountered was the slow response in readouts and adjustments needed to maintain a constant temperature. Given this experience, designing a control system using fuzzy logic principles is a logical and appropriate choice.

In this application, the system includes at least one input variable: Temperature Error (TE), which is the difference between the setpoint temperature and the measured temperature.

The system has two output variables: heating power (H - heater), which is regulated by controlling the electric current through the heating element, and cooling power (V - valve): This is managed by adjusting the influx of cold water through the valve settings.

To achieve improved precision in temperature regulation, we introduce a second input variable: the time derivative of the temperature error, also known as the Temperature error gradient (TEG).

The membership functions for the input variables (temperature error and its time derivative) are depicted in Figure 7, upper part. These functions define how each input variable is categorized into fuzzy sets, which are then used to determine the control actions.

Figure 7.

Membership functions for input and output variables.

Similarly, the membership functions for the output variables (heater power and valve position for hot/cold water flow) are shown in Figure 7, lower part. These functions translate the fuzzy logic decisions into precise control actions, regulating the heating and cooling processes.

The second step in developing a fuzzy control algorithm involves defining fuzzy behavioral rules, which are a critical component of the control system. Given that there are two input variables—one with six fuzzy values and the other with five—there are 30 possible input combinations. Each combination requires a corresponding rule to govern the system’s response. However, since the time derivative of the temperature error becomes less relevant when the temperature error is high, the number of necessary rules is reduced to 14, as shown in Table 3.

Rule number	Temperature	Temperature derivative	Heater power	Valve opening
1	very low		full	closed
2	low		modest	closed
3	normal low	very low	full	closed
4	normal low	low	modest	closed
5	normal low	neutral	low	closed
6	normal low	high	minimum	closed
7	normal low	very high	zero	closed
8	normal high	very low	low	closed
9	normal high	low	minimum	closed
10	normal high	neutral	zero	closed
11	normal high	high	zero	closed
12	normal high	very high	zero	partially open
13	high		zero	partially open
14	very high		zero	open

Table 3.

Fuzzy behavioral rules for implementation [44].

The rules for managing negative and positive temperature errors are not symmetrical. This asymmetry arises from the inherent differences between the heating and cooling processes, as well as the varying rates of energy flow available for each. Heating and cooling have distinct dynamics, which must be accounted for to ensure precise and effective temperature regulation.

The third step in developing a fuzzy control algorithm is defuzzification, which we implemented using discrete centroid computation. The detailed source code in C++, along with figures and explanations, is available for display and download at Ref. [45].

The membership functions illustrated in Figure 7 serve as inputs.

The resulting control surfaces, depicted in Figure 8, are outputs. They are used to regulate heating and cooling power.

Figure 8.

Heating intensity—left, and cooling intensity—right, as functions of temperature error and its gradient [44].

When implementing fuzzy control algorithms in microcontroller code, there are two primary approaches to consider:

1. Recode and modify existing code, which involves adapting the downloadable C++ code available at Ref. [45]. The modified code is then compiled and loaded onto the chosen microcontroller.

2. Simplify with direct rule coding, which involves coding straightforward rules that define the control surfaces shown in Figure 8. This method is preferred by the authors because it requires less code, resulting in simpler implementation and reduced complexity.

The primary benefit of using the direct rule coding against rule-based approach is the reduced likelihood of introducing bugs. Debugging an embedded system application running on a microcontroller is inherently more complex than debugging an isolated piece of code on a workstation. Thus, minimizing code complexity is crucial for maintaining system reliability.

The design and implementation of temperature control using fuzzy logic is well-suited for processes requiring high precision. Although the product has been successful, intensive use has revealed some limitations:

• Load variability. The controller performs optimally with a full load of eggs and water. However, when users process fewer eggs, thermal load changes. This change affects the system model, making the control algorithm suboptimal for partial loads.

• Power supply variations. The heat output correlates with the voltage of the power supply. Field monitoring at many sites has shown us that the supply voltage at the appliance’s socket can be between U_eff = 200 V and U_eff = 240 V at maximum heating power, which has an effect on the efficiency and stability of the heating process.

• Limescale deposition. Over time, limescale accumulates on the surface of the heater, altering its power output and reducing its efficiency.

To overcome these issues, the idea of developing a controller based on artificial intelligence (AI) has been proposed. An AI-based controller could adapt to varying loads, compensate for power supply fluctuations, and adjust for changes in heater efficiency due to limescale buildup. This approach aims to enhance the robustness and flexibility of the temperature control system, ensuring consistent performance under diverse conditions.

2.5.3 Thermal process control by a deep neural network trained with reinforcement learning (RL)

2.5.3.1 Main elements of the reinforcement learning system

The proposed method for temperature control in this study employs RL, a type of machine learning designed to learn sequences of actions that yield favorable outcomes in the both short term and over extended periods. The fundamental components of an RL system are:

• Environment: The setting in which the agent operates and interacts. Environment provides observations to the agent, receives its’ actions, and gives rewards.

• Agent: The entity that interacts with the environment, making decisions and taking actions. The agent learns to interact with the environment and adapts its working to maximize its cumulative reward.

• State, that is, agent’s observation: State is the situation of the environment at time t. Before taking an action, the agent observes the current state of the environment. The current state and agent’s recollection of past states and its activities form its integral knowledge, which is needed for the agent to decide on its next action.

• Action is the agent’s activity between times t and t + ∆t. Based on its current and past observations, and on its current policy, the agent decides on its current action, and it is consequentially altering the environment state.

• Reward is the immediate feedback the agent receives as a consequence of its action. During the learning phase, the reward quantity guides the agent to learn the value of different actions.

• Step: Steps take place at discrete times t, t + ∆t, t + 2∆t, …. The agent receives the observation, makes the decision, and takes the action at the step.

• Episode: A sequence of steps. For example, a cooking episode corresponds to one cooking batch.

• Model is used in model-based RL to predict the environment’s response. Model allows planning by simulating potential future states and rewards.

• Policy maps states to actions. Policy can be represented by functions or by multidimensional tables. The agent creates and uses its policy to decide on its actions, based on observations. During the learning phase, the agent interacts with the environment to develop a behavior policy aimed at maximizing cumulative rewards over episodes. This policy can be seen as a predictive model that determines the best action to take, based on current and previous observations. The policy is essentially the activity of the object, a software entity where inputs are observations and outputs are actions. This object contains several parameters that are approaching to optimal values during the learning phase.

Different RL algorithms exist, aimed at use in different applications. Not all RL algorithms are suitable for every application, but typically, more than one algorithm can be applied to a specific problem, offering some flexibility in the approach.

The successful application of RL in temperature control requires careful selection of the most appropriate algorithm and later continuous refinement of the policy, based on real-time feedback. This approach ensures that the system adapts to changing conditions, maintaining optimal temperature control to ensure food safety and quality.

In the proposed method, the cooking apparatus model serves as the environment for the RL agent. We use the Deep Q-Network (DQN) algorithm [46] for the cooking process control.

The agent can perform one of four actions at each step:

1. Turn/keep heating OFF & Turn/keep cooling OFF

2. Turn/keep heating ON & Turn/keep cooling OFF

3. Turn/keep heating OFF & Turn/keep cooling ON

4. Turn/keep heating ON & Turn/keep cooling ON

The first three actions are self-explanatory: stand by, heating, and cooling. The last activity results in a slower rate of cooling than activity no. 3.

Each action is applied for a duration of 1 second (∆t), defining a single step. An episode consists of up to 3600 steps (1 hour, 3600 seconds total). The goal is to produce the required temperature profile with high signal-to-noise ratio. That is, being the most insensitive to environment variables.

In our current implementation of RL, the agent receives an observation (O) at each step n

$$O_{\mathrm{n}}=\left[T_{\text{Meas}\mathrm{n}},T_{\mathrm{Ref}\mathrm{n}}\right]$$E10

The agent possesses its private functions and data, consisting of a log of measured and reference temperatures, in our case, for the last 30 time ticks t_n, then corresponding temperature gradients, temperature offsets from reference values, and logs of its’ previous actions and rewards received at each step. The agent uses this information in its reasoning to decide on its action for the next step.

At each step, the agent receives a reward. It is up to the system designer to carefully formulate the reward in such a way that it best reflects adequacy of the agent’s decision. We started the agent’s learning process with a reward that is inversely proportional to temperature offset.

Adding substance to the reward improved the agent’s decision-making process and consequently increased its learning efficiency (less episodes are needed). The current reward R_n at step n is structured in temperature differences and bonuses B_i, by Eq. (11).

$$R_{\mathrm{n}}=-\left|T_{\text{Meas}\mathrm{n}}-T_{\mathrm{Ref}\mathrm{n}}\right|+\left(\left|T_{\text{Meas}\mathrm{n}}-T_{\mathrm{Ref}\mathrm{n}}\right|-\left|T_{\text{Meas}\mathrm{n}-1}-T_{\mathrm{Ref}\mathrm{n}-1}\right|\right)+\sum _{i=1}^4{B}_{\mathrm{i}}$$E11

where

$$B_{\mathrm{i}}=\left|T_{\text{Meas}\mathrm{n}}-T_{\mathrm{Ref}\mathrm{n}}\right|<\mathrm{\Delta }{T}_{\mathrm{i}}?20,0.$$E12

In Eq. (12), an integral part of Eq. (11)

$$\mathrm{\Delta }{T}_1={0.50}^{°}C,\mathrm{\Delta }{T}_2={0.20}^{°}C,\mathrm{\Delta }{T}_3={0.15}^{°}C,\mathrm{\Delta }{T}_4={0.10}^{°}C.$$E13

To focus the learning process on regions where clear control rules are less defined, the RL agent only controls the system when the difference between the actual and reference temperatures is less than 8°C. This ensures the agent’s efforts are concentrated on fine-tuning the temperature within a critical range and us staying simple where being simple suffices.

2.5.3.2 Learning in a simulated environment

A significant limitation of reinforcement learning (RL) is the requirement for a large number of episodes or steps—often exceeding a million—to achieve acceptable performance. Conducting learning phase directly on the target real-world system is typically impractical and uneconomical. Therefore, a viable solution is to perform the learning phase within a simulated environment and then transfer the trained agent to the real-world system. This study adopts this approach due to the impracticality of real-world learning.

The agent learns within a simplified, linearized simulation model of the apparatus.

The hot-water tank heat Q at simulation step n is

$$Q_{\mathrm{n}}=Q_{\mathrm{n}-1}+P_{\text{heating}}\mathrm{\Delta }t-P_{\text{cooling}}\mathrm{\Delta }t$$E14

where

$$\mathrm{\Delta }t=t_{\mathrm{N}}-t_{\mathrm{N}-1},\text{and}$$E15

$$P_{\text{heating}}=\eta P_{\text{heater}},\text{where}0\le \eta \le 1,\text{and}$$E16

$$P_{\text{cooling}}=\left(T_{\mathrm{hot}\text{water}}-T_{\text{cold water}}\right){\Phi }_{\mathrm{eff}\text{cold water}}{c}_{\mathrm{p}\text{water}}.$$E17

The hot-water temperature at the step n is

$$T_n=\frac{Q_{\mathrm{n}}}{m_{\mathrm{hot}\text{water}}{c}_{\mathrm{p}\text{water}}}.$$E18

Our learning parameters for the DQN algorithm [47] and our detailed RL equations, accounting for heating and cooling delays, are in Ref. [48].

2.5.3.3 Parameter randomization and noise simulation

To handle variability and uncertainty of the real system, we use domain randomization. Parameters such as heating power ($P_{\mathit{\text{heater}}}$), mass of water in the apparatus ($m_{\mathit{\text{water}}}$), mass flow rate of water in the cooling system (${\Phi }_{\mathit{eff}\mathit{\text{cold water}}}$), environment temperature ($T_{\mathit{\text{environment}}}$), heating system response delay (${\mathit{\text{delay}}}_{\mathit{\text{heating}}}$), and cooling system response delay (${\mathit{\text{delay}}}_{\mathit{\text{cooling}}}$) are randomly set at the beginning of each episode. The values are distributed uniformly within the expected ranges of actual system values (Table 4).

Parameter	Min. value	Max. value
$P_{\mathit{\text{heater}}}\left[W\right]$	3217 (@ 190 V)	3861 (@ 240 V)
$m_{\mathit{\text{water}}}\left[\mathit{kg}\right]$	5 kg	10 kg
$m_{\mathit{\text{eggs}}}\left[\mathit{kg}\right]$	45 g (1 * S)	2400 g (30 * XXL)
${\Phi }_{\mathit{eff}\mathit{\text{cold water}}}$[kg/s]	0.01 kg/s	0.02 kg/s
$T_{\mathit{eff}\mathit{\text{cold water}}}\left[{}^{°}\mathrm{C}\right]$	12 °C	50 °C
$T_{\mathit{\text{environment}}}\left[{}^{°}\mathrm{C}\right]$	15 °C	35°C
${\mathit{\text{delay}}}_{\mathit{\text{heating}}}$[s]	2 s	10 s
${\mathit{\text{delay}}}_{\mathit{\text{cooling}}}$[s]	1 s	5 s

Table 4.

Upper and lower limits for randomly setting simulation model parameters at the beginning of each episode.

We do not add measurement noise, which is available in the RL programming environment. The reason is simple: The agent is taught in a simulated reality, where parameter values are randomly set by the virtual experiment environment. At this stage of design, we do not depend on physical measurements and associated uncertainty, which results in measurement noise.

Specific heat c_p of water is 4182 J/(kg °C) and specific heat c_p of an egg is 3180 J/(kg °C).

2.5.3.4 RL algorithm and parameters

The Deep Q-Network (DQN) algorithm [46] was selected to develop the policy for controlling the apparatus. The learning process was executed using the Python programming language and the RL library Stable-Baselines3 [47]. Default DQN parameter settings, which have been empirically validated and recommended by the RL library, were utilized during the training phase. The total number of timesteps for learning was set to 3 million.

During the learning phase, the agent must adhere to an adjusted target temperature profile: 5 minutes at 90 ± 0.2°C, 10 minutes at 60 ± 0.2°C, and then maintaining 57 ± 0.2°C. The adjustment involves extending the duration at 90°C from the original 1 to 5 minutes. This modification ensures that the agent places sufficient importance on maintaining the reference temperature of 90°C, as well as the temperatures of 60 and 57°C.

2.5.3.5 Transferring the learned control model and testing on the real system

Upon completion of the training process, the trained model is exported and implemented in the real system for performance evaluation [48]. The evaluation includes comparing the model’s performance against a benchmark approach. During the test phase, the model must follow a target temperature profile: maintaining 1 minute at 90 ± 0.2 °C, 10 minutes at 60 ± 0.2°C, and then 57 ± 0.2°C until completion.

Performance evaluation involves rigorous testing to ensure the trained model can effectively manage the temperature control process (Figure 9), adhering to the specified temperature profile. The comparison with benchmark methods helps to validate the efficacy and robustness of the RL approach.

Figure 9.

Apparatus without enclosure in the laboratory setup.

Figure 10 left displays designed and actual temperature curves on a large scale. Figure 10 right displays detailed view of the constant temperature region. Ticks on the time scale are 10 s apart; the whole t axis is 600 s; that is, 10 minutes, which is the time of pasteurization at 60 ± 0.20°C. Ticks on the temperature scale are 0.10°C apart. The measured temperature is at 60 ± 0.13°C.

Figure 10.

Left—comparison of designed and actual temperature curves over time on a large scale, and right—detailed view of the constant temperature region.

3. Discussion

High-temperature processing remains the best defense against Salmonella, which guides industrial practices in food preparation. Experimental validation through deliberate contamination and subsequent measurement of bacterial survival rates are crucial for establishing safe and effective pasteurization protocols.

The process of soft-boiled eggs pasteurization requires precise control of temperature and time to ensure safety without compromising the quality of the food. By utilizing precise thermal control, it is possible to achieve the desired reduction in pathogenic microorganisms while delivering expected organoleptic egg properties. Food safety, which is a mandatory essential in the food industry, is preserved.

Meeting the precision requirements for thermal processes in food safety demands advanced temperature measurement solutions that are both stable and accurate over long periods. The professional kitchen appliance market’s intolerance for frequent servicing further underscores the need for durable, low-maintenance systems capable of maintaining high performance and reliability for at least 15 years.

Ratiometric measurement is a powerful technique that enhances the reliability and accuracy of measurements by mitigating the influence of environmental factors. This makes it particularly useful in applications where maintaining consistent measurement conditions is difficult, such as in food safety and security.

Implementing a fuzzy logic control system enables precise temperature management in the pasteurization process, ensuring the production of safe and high-quality soft-boiled eggs. This method leverages human-like reasoning to adjust heating and cooling actions dynamically, accommodating the complexities of the thermal process. The fuzzy logic approach is particularly effective in dealing with the non-linearities and time delays observed in the system.

Implementing fuzzy control in microcontrollers can be efficiently achieved by coding simple rules to define control surfaces, enhancing the reliability and ease of debugging. This approach ensures precise temperature management, critical for maintaining food safety and quality in pasteurization processes.

Implementing AI in temperature control systems offers a promising solution to address the limitations identified in the current fuzzy logic-based system. By leveraging AI, it is possible to achieve greater adaptability while preserving precision, thereby improving the overall reliability and efficiency of the food pasteurization process. Signal-to-noise ratio is increased to the sufficient level with even some safety margin for industrial precise thermal control in harsh environment with many influential parameters, such as, in our case, the exact value of electric grid voltage, environment temperature, amount of simultaneously cooked eggs in the water bath, initial temperature of the heat-transfer water, temperature of the cooling water, heat residue in apparatus from n previous cooking cycles, and potential formation of limestone lining on the heater at apparatus due to sloppy cleaning.

By training the RL agent in a simulated environment, it is possible to overcome the practical limitations of direct real-world learning. This approach ensures that the agent can achieve high performance when transferred to the actual system, providing robust and resilient temperature control.

The final result of cost-performance optimization for the control functions of the apparatus is shown in Figure 11. The electronic system is built from integrated circuits and passive components on a custom-made PCB. The MSP430 processor on the PCB, and any other similar processor, has enough memory space for changes or additions of thousands of C code lines in potential control process upgrades as new control technologies become available.

Figure 11.

Enclosed apparatus, front and top view, and its embedded control system hardware.

The current state-of art temperature control process in a cost-efficient apparatus yields temperature trajectory control in volume of 9 dm3, filled with water and arbitrary amount of water-immersed eggs, within + − 0.2°C of reference values, in the presence of substantial system noise. The safety and reliability of thermal processing in a delicate food application is achieved. Extensive testing of the apparatus in practical settings confirms these findings.

The environment in the food industry is rich on influential parameters, that is, system noise is substantial. Food industry apparatuses sell for an order of magnitude less then laboratory apparatuses. The apparatus designer needs to adhere to cost constraint at the early onset of a design project and further through the apparatuses’ lifetime. In the food industry, a need for periodic recalibrations either in the field or in a service station is not accepted. The goal of cost-performance optimization is clear: The required performance has to be assured at minimal cost for the lifetime of the product. Maintenance should be minimalistic and performed mostly by kitchen staff. The presented design systematics result in precise thermal process control in the presence of environmental disturbances, while it adheres to inherent food industry constraints.

4. Conclusion

Our contribution to food safety is exemplified through the detailed development steps of controlling the thermal process for producing Salmonella-free soft-boiled eggs. The outcome is a device capable of industrially preparing soft-boiled eggs that are certified Salmonella-free. The systemic result is a methodology for controlling the thermal process with high accuracy, a high signal-to-noise ratio, and relatively short development time. The resulting control systems are applicable across the entire food processing chain, enabling new types of food processing that were previously unfeasible due to the lack of precise, robust, and cost-effective thermal processes.

In yet-mature thermal processes, temperature accuracy will be improving through the continuous modernization of existing equipment, aligning closer with the ideal thermal process implementation.

Precise temperature control is crucial in processes such as pasteurization and freeze-drying. Moreover, in robust thermal treatments like roasting, baking, and braising, precise temperature control represents an asset as it can be perfectly aligned with the economic demands of foods processing.

The benefits of precise control and a high signal-to-noise ratio during thermal processes, associated with the longevity of equipment without the need for maintenance or calibration over its lifetime and enhanced economic viability of the equipment by design, are substantial. These features collectively contribute significantly to food processing safety.

Acknowledgments

Author thanks to colleagues at the institution:

Prof. Dr. Primož Podržaj for contribution and consultation on fuzzy control.

Assist. Prof. Dr. Dominik Kozjek for contribution and consultation on reinforced learning.

Tomaž Gruden, eng, at Kogast.d.d., Grosuplje, SI, for contribution and consultation in the apparatus mechanical construction.

This work is supported by the Slovenian Research Agency, grant no. P20270.

Conflict of interest

The authors declare no conflict of interest.