An Ontological Model of Peltier Thermoelement Control based on a Fuzzy Digital Filter and a PID-controller MaximBBobyr maxbobyr@gmail.com Southwest State University of Russia (SWSU)
94, 50 Let Oktyabrya St 305000 Kursk Russian Federation
NatalyaMilostnaya Southwest State University of Russia (SWSU)
94, 50 Let Oktyabrya St 305000 Kursk Russian Federation
ArtemAseev asseeff.artem@gmail.com Southwest State University of Russia (SWSU)
94, 50 Let Oktyabrya St 305000 Kursk Russian Federation
An Ontological Model of Peltier Thermoelement Control based on a Fuzzy Digital Filter and a PID-controller 1613-0073 C38D93E8FA0367CC2CE8C8D71396CB98 GROBID - A machine learning software for extracting information from scholarly documents PID-controller, Peltier thermoelement ontology, Fuzzy logic, Fuzzy digital filter, Exponential moving average filter 0000-0002-5400-6817 (M. B. Bobyr) 0000-0002-3779-9165 (N. Milostnaya) 0009-0007-8271-7660 (A. Aseev)

The ontological model of Peltier thermoelement control is presented in the article. It consists of a PID-controller, a fuzzy digital filter and an exponential moving average filter, implemented in software in the microcontroller. The ontological model calculates the voltage value, which is transmitted to the gate of the MOSFET-transistor. The field-effect transistor converts the applied voltage into a drain current signal, and this value is transmitted to the Peltier thermoelement. Voltage is removed from the Peltier thermoelement using thermistor, which is converted into a temperature value and limited from 25Β°C to 75Β°C. The technique for converting voltage to temperature is presented in the article. The temperature signal is transmitted to the input of the microcontroller. Also, a user-defined signal is fed to the input of the microcontroller, which must select the appropriate temperature value on the thermocouple. The fuzzy model, depending on the input signal, forms the coefficients of the exponential averaging filter. A limitation of the fuzzy method for calculating the coefficients used in the ontological model of thermoelement control is the use of triangular membership functions to describe the input variables. The experimental results presented in the article showed that when using a combination of a PID-controller, a fuzzy digital filter and an exponential moving average filter, the transient time during Peltier thermoelement control is reduced: overshoot reduced by 2.44%, achieved a 11.25% faster response time, and ensured 4.19% quicker stabilization.
Introduction

Systems with a PID-controller are often used in temperature control devices: a cutting tool cooling device [1], a device for regulating the temperature of a climatic chamber [2], a control system for electromechanical equipment [3], a temperature control system in a greenhouse [4], a controller for the performance and energy consumption of an industrial air conditioner [5], a control device for the air conditioning system of a car [6]. However, the PID-controller has two significant drawbacks: a large jump in the amplitude of the first harmonic of the output control signal (leading to a voltage jump that clearly accelerates the wear of the elements of the entire system) [7] and a long transient process time when the control signal goes to the specified values [8]. The third drawback of the PID-controller is the need to select the controlled coefficients Kp, Ki and Kd [9]. In one of the studies, this drawback was solved using a genetic method that allows for automatic selection of the controlled coefficients [10]. In [4], a neuro-fuzzy approach is used to solve the same drawback. In the study [2], scientists abandoned PID-control in favor of the Tsukamoto method. In this article, it is proposed to use a PID-controller modified using a combination of a fuzzy digital filter (FDF) and an exponential moving average filter (EMAF) [11] to control a Peltier thermoelement (PTE). FDF and EMAF allow to reduce the time of transient processes when controlling a PTE by reducing the jump in the amplitude of the first harmonic of the output control signal. With this approach, it is enough to set the controlled coefficients once and not change them. Thus, all the main problems of the PID-controller are eliminated at once. At present, there are already modifications of the PID-controller using fuzzy logic blocks [6], [10], [12]. There are also exponential averaging modifications [9], but the combination used in this article is presented for the first time.

Methodological basis of the ontological model of Peltier thermoelement control

The Ontological Model of Peltier Thermoelement Control (OMPTC) allows to organize the structure of the system and describe the interaction of its components. OMPTC is represented as the following formula:

𝑂 π‘š = ⟨ 10 𝑂 𝑐 i=1 , 21 𝑂 π‘Ž j=1 , 18 𝑂 π‘Ÿ k=1 , ⟩

where 𝑂 𝑐 is the ontology of concepts, 𝑂 π‘Ž is the ontology of attributes, 𝑂 π‘Ÿ is the ontology of relations [13].

The graphical representation of the ontological model is shown in Fig. 1.

A list of elements is used to describe the process of TE control, such as a MOSFET-transistor, PTE, thermistor, power supply and microcontroller (MC), in which the following are software implemented: comparison unit, PID-controller, FDF, EMAF; voltage converter, indicating their attributes and interrelations. The list of elements is summarized in Table 1.

The structure of the computational processes for controlling the PTE is presented as a two-level system in Fig. 2. This structure allows to reduce the time of transient processes and reduce the jump in the amplitude of the first harmonic of the output control signal of the PID-controller. The first level includes the following computational processes: converting the thermistor voltage into temperature; calculating the PIDi control signal using the PID-controller; smoothing this signal using the FDF based on fuzzification of input data and the area ratio defuzzification method, forming the optimal voltage for the MOSFET-gate using the EMAF.

The second level of the system is designed to control the intensity of cooling or heating of the PTE. It includes the following computational processes: regulating the PTE power using the MOSFET-transistor, measuring the temperature on the PTE using the thermistor, transmitting the voltage by the thermistor to the voltage converter.

At the initial stage of the OMTC operation, data is received from the thermistor. For this purpose, it is necessary to calculate the temperature value Tinput based on the dependence of the voltages at the analog output of the thermistor, using a formula based on polynomial regression [14], which is obtained empirically:

𝑇 𝑖𝑛𝑝𝑒𝑑 = 7.39 Γ— π‘ˆ 2 + 62.17 Γ— π‘ˆ + 131.24,

where U is the voltage at the analog input of the MC. Thus, according to Eq.2, the MC calculates the temperature of the PTE using information coming from the thermistor, which is fixed on the surface of the PTE.

PID-controller is used to control the thermoelement, ensuring that the set temperature is maintained. For this purpose, a controlled signal is calculated, the task of which is to reduce the difference between the temperature set by the user 𝑇 π‘ π‘’π‘‘π‘π‘œπ‘–π‘›π‘‘ and the actual 𝑇 𝑖𝑛𝑝𝑒𝑑 received from the thermistor in the MC:

π‘’π‘Ÿπ‘Ÿ = 𝑇 π‘ π‘’π‘‘π‘π‘œπ‘–π‘›π‘‘ βˆ’ 𝑇 𝑖𝑛𝑝𝑒𝑑 β†’ π‘šπ‘–π‘›.

The coefficients proportional 𝐾 𝑝 , integrating 𝐾 𝑖 , differentiating 𝐾 𝑑 , integration step dt have specific values and do not need to be calculated. Thus, the following signal is generated at the output of the PID-controller [15]:

𝑃 𝐼𝐷 𝑖 = π‘’π‘Ÿπ‘Ÿ Γ— 𝐾 𝑝 + π‘’π‘Ÿπ‘Ÿ Γ— 𝑑𝑑 Γ— 𝐾 𝑖 + (π‘’π‘Ÿπ‘Ÿ 𝑖 βˆ’ π‘’π‘Ÿπ‘Ÿ π‘–βˆ’1 ) Γ— 𝐾 𝑑 𝑑𝑑 .

From the control signal of the PID-controller 𝑃 𝐼𝐷 𝑖 , a delay signal 𝑃 𝐼𝐷 π‘–βˆ’1 is formed, determined after a specified time interval 𝑑 π‘‘π‘’π‘™π‘Žπ‘¦ . Both signals are transmitted to the FDF for further smoothing using a fuzzy rule base. After the PID-controller generates the control signal, it is necessary to smooth it to eliminate sharp jumps and reduce the load on the MOSFET-transistor. For this purpose, a FDF is used, which eliminates high-frequency interference in the signal. The EMAF signal smoothing formula is formulated as follows:

𝐷𝑋 = 𝑃 𝐼𝐷 𝑖 βˆ’ 𝑃 𝐼𝐷 π‘–βˆ’1 .

(

)

where 𝑃 𝐼𝐷 𝑖 is the current signal of the PID-controller, 𝑃 𝐼𝐷 π‘–βˆ’1 is the delay signal determined after a specified time interval 𝑑𝑑.

Transform the variable DX (see Eq.5) into a linguistic variable with terms DX = DX1, DX2, DX3, DX4, DX5. The core of the input linguistic variable is the range of values from 0.0 to 7.0. The graph of the input membership function is shown in Fig. 3.

The output linguistic variable is the control coefficient 𝛼, consisting of five terms: M1, M2, M3, M4, M5, which is set by a proportional value in the range from 40% to 80% [0.4; 0.8] of its maximum value [17]. The bases of the input membership functions (see Eqs.6-8) and fuzzy rules (see Eqs.9-13) are presented below:

πœ‡(𝐷𝑋) 1 = ⎧ βŽͺ ⎨ βŽͺ ⎩ 1, if 𝐷𝑋 > 0 and 𝐷𝑋 < πΏπ‘–π‘š 1 πΏπ‘–π‘š 2 βˆ’π·π‘‹ πΏπ‘–π‘š 2 βˆ’πΏπ‘–π‘š 1 , if 𝐷𝑋 > πΏπ‘–π‘š 1 and 𝐷𝑋 < πΏπ‘–π‘š 2 0, else;πœ‡(𝐷𝑋) 2,3,4 = ⎧ βŽͺ ⎨ βŽͺ ⎩ π·π‘‹βˆ’πΏπ‘–π‘š 1 πΏπ‘–π‘š 2 βˆ’πΏπ‘–π‘š 1 , if 𝐷𝑋 > πΏπ‘–π‘š 1 and 𝐷𝑋 < πΏπ‘–π‘š 2 πΏπ‘–π‘š 3 βˆ’π·π‘‹ πΏπ‘–π‘š 3 βˆ’πΏπ‘–π‘š 2 , if 𝐷𝑋 > πΏπ‘–π‘š 2 and 𝐷𝑋 < πΏπ‘–π‘š 3 0, else;πœ‡(𝐷𝑋) 5 = ⎧ βŽͺ ⎨ βŽͺ ⎩ π·π‘‹βˆ’πΏπ‘–π‘š 1 πΏπ‘–π‘š 2 βˆ’πΏπ‘–π‘š 1 , if 𝐷𝑋 > πΏπ‘–π‘š 1 and 𝐷𝑋 < πΏπ‘–π‘š 2 1, if 𝐷𝑋 > πΏπ‘–π‘š 2 and 𝐷𝑋 < πΏπ‘–π‘š 3 0, else;𝐼𝐹 𝐷𝑋 1 𝑇 𝐻𝐸𝑁 𝑀 1𝐼𝐹 𝐷𝑋 2 𝑇 𝐻𝐸𝑁 𝑀 2𝐼𝐹 𝐷𝑋 3 𝑇 𝐻𝐸𝑁 𝑀 3

𝐼𝐹 𝐷𝑋 4 𝑇 𝐻𝐸𝑁 𝑀 4

𝐼𝐹 𝐷𝑋 5 𝑇 𝐻𝐸𝑁 𝑀 5 (13) The graph of the output membership function is shown in Figure 4.

The control coefficient 𝛼 is calculated using the following formula:

𝛼 = βˆ‘οΈ€ 5 𝑖=1 𝐷𝑋 𝑖 βˆ’ 𝑀 𝑖 βˆ‘οΈ€ 5 𝑖=1 𝐷𝑋 𝑖 .

Calculating the 𝛽 coefficient:

𝛽 = 1 βˆ’ 𝛼.

The coefficient 𝛽 is necessary for the final calculation of the output voltage value from EMAF π‘ˆ 𝑔 . The π‘ˆ 𝑔 value is calculated according to the following form:

π‘ˆ 𝑔 = 𝑃 𝐼𝐷 π‘–βˆ’1 Γ— 𝛼 + 𝑃 𝐼𝐷 𝑖 Γ— 𝛽. ()

After calculating the voltage Ug, it is converted into a range suitable for the eight-bit DAC at the output of the MC (Arduino) [16]:

π‘π‘œπ‘€π‘’π‘Ÿ π‘šπ‘Žπ‘ = π‘ˆ 𝑔 Γ— 100/255.

The output voltage Ug after processing by the EMAF is transferred to the drain of the MOSFETtransistor, which is used to switch the power of the PTE [17].

Experimental research

The characteristics of the OMPTC were determined by conducting experimental studies. The experimental setup of the control system with software-implemented FDF, EMAF and PID-regulator is shown in Fig. 5.

The objective of the experiment was to compare the performance of the OMPTC system using the default PID-regulator against the enhanced PID-regulator with FDF and EMAF. During the experiment, the user set a target temperature of 𝑇 π‘ π‘’π‘‘π‘π‘œπ‘–π‘›π‘‘ = 45Β°C, represented by the value1 signal (blue). This signal remained constant over time, indicating that the system was maintaining the desired temperature.

Signal value2 (orange) represents the current measured temperature 𝑇 𝑖𝑛𝑝𝑒𝑑 from the PTE obtained via a thermistor. When value1 changes, the control system adjusts the PTE temperature to approach the target value, demonstrating effective regulation.

Signal value3 (green): This is the control signal representing the voltage π‘π‘œπ‘€π‘’π‘Ÿ π‘šπ‘Žπ‘ applied from MC (Arduino) to the MOSFET-transistor. The MOSFET-transistor regulates the power supplied to the PTE. The sharp spikes and subsequent drops in this signal indicate the process of power regulation to minimize the deviation from the target temperature. The behavior of the default PID-regulator and the enhanced PID-regulator (with FDF and EMAF) is shown in Figs. 6-8:

The results of the experiment are summarized in Table 2.

Conclusion

The experiment aimed to compare the performance of the OMPTC system with a default PID-regulator against the OMPTC system enhanced with FDF and EMAF in terms of temperature control and stabilization. Based on the results, the FDF and EMAF PID-regulator demonstrated better performance across all key indicators: it reduces overshoot by 2.44%, achieves a 11.25% faster response time, and ensures 4.19% quicker stabilization.

Figure 1 :Figure 1: The ontological model of PTE control
Figure 2 :Figure 2: The structure of computational processes in a two-level PTE control system
Figure 3 :Figure 3: Input membership functions, where the labels πΏπ‘–π‘š 1 , πΏπ‘–π‘š 2 , πΏπ‘–π‘š 3 are designated for the second membership function 𝐷𝑋 2
Figure 4 :Figure 4: Output membership functions
Figure 5 :Figure 6 :Figure 5: The experimental setup OMPTC with FDF
Figure 7 :Figure 8 :Figure 7: 𝑇 𝑖𝑛𝑝𝑒𝑑 equal 𝑇 π‘ π‘’π‘‘π‘π‘–π‘œπ‘›π‘‘ moment: A is default PID-regulator, B is PID-regulator with FDF and EMAF
Table 1Specification of concepts of the OMPTC Receives data from the voltage converter and the set value 𝑂 π‘Ÿ9 . Gives a signal about the need for regulation 𝑂 π‘Ÿ10 . Tsetpoint 𝑂 π‘Ž10 PID-controller 𝑂 𝑐6 Coefficient 𝐾 𝑝 𝑂 π‘Ž11 Receives power data after a signal about the need for regulation 𝑂 π‘Ÿ11 . Calculates the control signal for the FDF 𝑂 π‘Ÿ12 . Coefficient 𝐾 𝑖 𝑂 π‘Ž12 Coefficient 𝐾 𝑑 𝑂 π‘Ž13 𝑑𝑑 𝑂 π‘Ž14 Output PID 𝑖 𝑂 π‘Ž15 FDF 𝑂 𝑐7 𝛼 𝑂 π‘Ž16 Processes the control signal of the PID-controller using a smoothing algorithm 𝑂 π‘Ÿ13 . 𝛽 𝑂 π‘Ž17 EMAF 𝑂 𝑐8 Output value power 𝑂 π‘Ž18 From the signal coming from the FDF, it forms an output signal and transmits it to the MOSFET-transistor 𝑂 π‘Ÿ14 . MOSFET-transistor 𝑂 𝑐9 Current 𝑂 π‘Ž19 Receives control signal from EMAF controller 𝑂 π‘Ÿ15 . Connected to zero bus 𝑂 π‘Ÿ16 . Voltage 𝑂 π‘Ž20 Power supply 𝑂 𝑐10 Voltage 𝑂 π‘Ž21 Connected to the 12V TE 𝑂 π‘Ÿ17 , zero bus 𝑂 π‘Ÿ18 .Concepts 𝑂 𝑐Attributes 𝑂 π‘ŽRelationships 𝑂 π‘ŸPTE 𝑂 𝑐1PTE type (Peltier element)Controlled by the drain current of the MOSFET𝑂 π‘Ž1transistor 𝑂 π‘Ÿ1 , the temperature is measured by thePower 𝑂 π‘Ž2thermistor 𝑂 π‘Ÿ2 .Efficiency 𝑂 π‘Ž3Thermistor 𝑂 𝑐2Temperature 𝑂 π‘Ž4Measures the temperature of the PTE 𝑂 π‘Ÿ3 . TransmitsResistance 𝑂 π‘Ž5temperature data to the voltage converter 𝑂 π‘Ÿ4 .MC 𝑂 𝑐3Clock frequency 𝑂 π‘Ž6Controls the PID-controller and the MOSFET-transistorMemory capacity 𝑂 π‘Ž7𝑂 π‘Ÿ5 . Connected to the zero bus 𝑂 π‘Ÿ6 .User 𝑂 𝑐4Setpoint 𝑂 π‘Ž8Sets the specified value 𝑂 π‘Ÿ7 . The value goes to the com-parison block 𝑂 π‘Ÿ8 .Comparison blockTinput 𝑂 π‘Ž9𝑂 𝑐5
Table 2OMPTC default PID-regulator and FDF EMAF PID-regulator comparisonCharacteristicsdefault PID-regulator FDF and EMAF PID-regulatorOvershoot reduction8280Response time1:201:11Stabilization time5:345:20
Acknowledgments

The work was prepared as part of the implementation of the RSF project No. 24-21-00055. The authors are grateful to the Foundation for their support.

Declaration on Generative AI

The author(s) have not employed any Generative AI tools.

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