=Paper= {{Paper |id=Vol-3900/Paper5 |storemode=property |title=An Ontological Model of Peltier Thermoelement Control based on a Fuzzy Digital Filter and a PID-controller |pdfUrl=https://ceur-ws.org/Vol-3900/Paper5.pdf |volume=Vol-3900 |authors=Maxim Bobyr,Artem Aseev,Natalya Milostnaya |dblpUrl=https://dblp.org/rec/conf/dosier/BobyrAM24 }} ==An Ontological Model of Peltier Thermoelement Control based on a Fuzzy Digital Filter and a PID-controller== https://ceur-ws.org/Vol-3900/Paper5.pdf

An Ontological Model of Peltier Thermoelement Control
based on a Fuzzy Digital Filter and a PID-controller
Maxim B. Bobyr1,*,† , Natalya Milostnaya2 and Artem Aseev3
1
Southwest State University of Russia (SWSU), 94, 50 Let Oktyabrya St, Kursk, 305000, Russian Federation
2
Southwest State University of Russia (SWSU), 94, 50 Let Oktyabrya St, Kursk, 305000, Russian Federation
3
Southwest State University of Russia (SWSU), 94, 50 Let Oktyabrya St, Kursk, 305000, Russian Federation

Abstract
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 25°C to 75°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.

Keywords
PID-controller, Peltier thermoelement ontology, Fuzzy logic, Fuzzy digital filter, Exponential moving average
filter

1. 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

The 2024 Sixth Doctoral Symposium on Intelligence Enabled Research (DoSIER 2024), November 28–29, 2024, Jalpaiguri, India
*
Corresponding author.
†
These authors contributed equally.
$ maxbobyr@gmail.com (M. B. Bobyr); nat_mil@mail.ru (N. Milostnaya); asseeff.artem@gmail.com (A. Aseev)
0000-0002-5400-6817 (M. B. Bobyr); 0000-0002-3779-9165 (N. Milostnaya); 0009-0007-8271-7660 (A. Aseev)
© 2025 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).

CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
Figure 1: The ontological model of PTE control

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.

2. 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:
10 21 18
⟨ ⟩
𝑂𝑚 = 𝑂𝑐 , 𝑂𝑎 , 𝑂𝑟 , (1)
i=1 j=1 k=1

where 𝑂𝑐 is the ontology of concepts, 𝑂𝑎 is the ontology of attributes, 𝑂𝑟 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 interrela-
tions. 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
Table 1
Specification of concepts of the OMPTC
Concepts 𝑂𝑐 Attributes 𝑂𝑎 Relationships 𝑂𝑟
PTE 𝑂𝑐1 PTE type (Peltier element) Controlled by the drain current of the MOSFET
𝑂𝑎1 transistor 𝑂𝑟1 , the temperature is measured by the
Power 𝑂𝑎2 thermistor 𝑂𝑟2 .
Efficiency 𝑂𝑎3
Thermistor 𝑂𝑐2 Temperature 𝑂𝑎4 Measures the temperature of the PTE 𝑂𝑟3 . Transmits
Resistance 𝑂𝑎5 temperature data to the voltage converter 𝑂𝑟4 .
MC 𝑂𝑐3 Clock frequency 𝑂𝑎6 Controls the PID-controller and the MOSFET-transistor
Memory capacity 𝑂𝑎7 𝑂𝑟5 . Connected to the zero bus 𝑂𝑟6 .
User 𝑂𝑐4 Setpoint 𝑂𝑎8 Sets the specified value 𝑂𝑟7 . The value goes to the com-
parison block 𝑂𝑟8 .
Comparison block Tinput 𝑂𝑎9 Receives data from the voltage converter and the set
𝑂𝑐5 value 𝑂𝑟9 . Gives a signal about the need for regulation
Tsetpoint 𝑂𝑎10 𝑂𝑟10 .
PID-controller 𝑂𝑐6 Coefficient 𝐾𝑝 𝑂𝑎11
Coefficient 𝐾𝑖 𝑂𝑎12 Receives power data after a signal about the need for
Coefficient 𝐾𝑑 𝑂𝑎13 regulation 𝑂𝑟11 . Calculates the control signal for the
𝑑𝑡 𝑂𝑎14 FDF 𝑂𝑟12 .
Output PID𝑖 𝑂𝑎15
FDF 𝑂𝑐7 𝛼 𝑂𝑎16 Processes the control signal of the PID-controller using
𝛽 𝑂𝑎17 a smoothing algorithm 𝑂𝑟13 .
EMAF 𝑂𝑐8 Output value power 𝑂𝑎18 From the signal coming from the FDF, it forms an output
signal and transmits it to the MOSFET-transistor 𝑂𝑟14 .
MOSFET-transistor Current 𝑂𝑎19 Receives control signal from EMAF controller 𝑂𝑟15 .
𝑂𝑐9 Connected to zero bus 𝑂𝑟16 .
Voltage 𝑂𝑎20
Power supply 𝑂𝑐10 Voltage 𝑂𝑎21 Connected to the 12V TE 𝑂𝑟17 , zero bus 𝑂𝑟18 .

the analog output of the thermistor, using a formula based on polynomial regression [14], which is
obtained empirically:

𝑇𝑖𝑛𝑝𝑢𝑡 = 7.39 × 𝑈 2 + 62.17 × 𝑈 + 131.24, (2)
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 𝑇𝑠𝑒𝑡𝑝𝑜𝑖𝑛𝑡 and the actual 𝑇𝑖𝑛𝑝𝑢𝑡 received from the thermistor in the MC:

𝑒𝑟𝑟 = 𝑇𝑠𝑒𝑡𝑝𝑜𝑖𝑛𝑡 − 𝑇𝑖𝑛𝑝𝑢𝑡 → 𝑚𝑖𝑛. (3)
The coefficients proportional 𝐾𝑝 , integrating 𝐾𝑖 , differentiating 𝐾𝑑 , 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]:

(𝑒𝑟𝑟𝑖 − 𝑒𝑟𝑟𝑖−1 ) × 𝐾𝑑
𝑃 𝐼𝐷𝑖 = 𝑒𝑟𝑟 × 𝐾𝑝 + 𝑒𝑟𝑟 × 𝑑𝑡 × 𝐾𝑖 + . (4)
𝑑𝑡
From the control signal of the PID-controller 𝑃 𝐼𝐷𝑖 , a delay signal 𝑃 𝐼𝐷𝑖−1 is formed, determined
after a specified time interval 𝑡𝑑𝑒𝑙𝑎𝑦 . Both signals are transmitted to the FDF for further smoothing
using a fuzzy rule base.
Figure 2: The structure of computational processes in a two-level PTE control system

Figure 3: Input membership functions, where the labels 𝐿𝑖𝑚1 , 𝐿𝑖𝑚2 , 𝐿𝑖𝑚3 are designated for the second
membership function 𝐷𝑋2

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 𝐼𝐷𝑖 − 𝑃 𝐼𝐷𝑖−1 . (5)
where 𝑃 𝐼𝐷𝑖 is the current signal of the PID-controller, 𝑃 𝐼𝐷𝑖−1 is the delay signal determined after a
specified time interval 𝑑𝑡.
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:

if 𝐷𝑋 > 0 and 𝐷𝑋 < 𝐿𝑖𝑚1
⎧
⎨1,
⎪
−𝐷𝑋
𝜇(𝐷𝑋)1 = 𝐿𝑖𝑚22−𝐿𝑖𝑚1 , if 𝐷𝑋 > 𝐿𝑖𝑚1 and 𝐷𝑋 < 𝐿𝑖𝑚2
𝐿𝑖𝑚 (6)
else;
⎪
0,
⎩
Figure 4: Output membership functions

⎨ 𝐿𝑖𝑚2 −𝐿𝑖𝑚1 , if 𝐷𝑋 > 𝐿𝑖𝑚1 and 𝐷𝑋 < 𝐿𝑖𝑚2
⎧ 𝐷𝑋−𝐿𝑖𝑚
1
⎪
−𝐷𝑋
𝜇(𝐷𝑋)2,3,4 = 𝐿𝑖𝑚33−𝐿𝑖𝑚2 , if 𝐷𝑋 > 𝐿𝑖𝑚2 and 𝐷𝑋 < 𝐿𝑖𝑚3
𝐿𝑖𝑚 (7)
else;
⎪
0,
⎩

⎨ 𝐿𝑖𝑚2 −𝐿𝑖𝑚1 , if 𝐷𝑋 > 𝐿𝑖𝑚1 and 𝐷𝑋 < 𝐿𝑖𝑚2
⎧ 𝐷𝑋−𝐿𝑖𝑚
1
⎪
𝜇(𝐷𝑋)5 = 1, if 𝐷𝑋 > 𝐿𝑖𝑚2 and 𝐷𝑋 < 𝐿𝑖𝑚3 (8)
else;
⎪
0,
⎩

𝐼𝐹 𝐷𝑋1 𝑇 𝐻𝐸𝑁 𝑀1 (9)
𝐼𝐹 𝐷𝑋2 𝑇 𝐻𝐸𝑁 𝑀2 (10)
𝐼𝐹 𝐷𝑋3 𝑇 𝐻𝐸𝑁 𝑀3 (11)
𝐼𝐹 𝐷𝑋4 𝑇 𝐻𝐸𝑁 𝑀4 (12)
𝐼𝐹 𝐷𝑋5 𝑇 𝐻𝐸𝑁 𝑀5 (13)

The graph of the output membership function is shown in Figure 4.
The control coefficient 𝛼 is calculated using the following formula:
∑︀5
𝑖=1 𝐷𝑋𝑖 − 𝑀𝑖
𝛼= ∑︀5 . (14)
𝑖=1 𝐷𝑋𝑖
Calculating the 𝛽 coefficient:

𝛽 = 1 − 𝛼. (15)
The coefficient 𝛽 is necessary for the final calculation of the output voltage value from EMAF 𝑈𝑔 .
The 𝑈𝑔 value is calculated according to the following form:

𝑈𝑔 = 𝑃 𝐼𝐷𝑖−1 × 𝛼 + 𝑃 𝐼𝐷𝑖 × 𝛽. (16)
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]:

𝑝𝑜𝑤𝑒𝑟𝑚𝑎𝑝 = 𝑈𝑔 × 100/255. (17)
The output voltage Ug after processing by the EMAF is transferred to the drain of the MOSFET-
transistor, which is used to switch the power of the PTE [17].
Figure 5: The experimental setup OMPTC with FDF

Figure 6: OMPTC reaction when user set 𝑇𝑠𝑒𝑡𝑝𝑜𝑖𝑛𝑡 : A is default PID-regulator, B is PID-regulator with FDF and
EMAF

3. Experimental research
The characteristics of the OMPTC were determined by conducting experimental studies. The experi-
mental 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 𝑇𝑠𝑒𝑡𝑝𝑜𝑖𝑛𝑡 = 45°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 𝑇𝑖𝑛𝑝𝑢𝑡 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 𝑝𝑜𝑤𝑒𝑟𝑚𝑎𝑝 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.

Table 2
OMPTC default PID-regulator and FDF EMAF PID-regulator comparison
Characteristics default PID-regulator FDF and EMAF PID-regulator
Overshoot reduction 82 80
Response time 1:20 1:11
Stabilization time 5:34 5:20
Figure 7: 𝑇𝑖𝑛𝑝𝑢𝑡 equal 𝑇𝑠𝑒𝑡𝑝𝑖𝑜𝑛𝑡 moment: A is default PID-regulator, B is PID-regulator with FDF and EMAF

Figure 8: Convergence of 𝑇𝑠𝑒𝑡𝑝𝑜𝑖𝑛𝑡 and 𝑇𝑖𝑛𝑝𝑢𝑡 at the end of PID-adjustment: A is default PID-regulator, B is
PID-regulator with FDF and EMAF

4. 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 sta-
bilization. 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.

5. 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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