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 ifeld-efect 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 coeficients of the exponential averaging filter. A limitation of the fuzzy method for calculating the coeficients 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.
Systems with a PID-controller are often used in temperature control devices: a cutting tool cooling
device [
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 ⟩ , , , i=1 j=1 k=1 (1) where is the ontology of concepts, is the ontology of attributes, 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
Measures the temperature of the PTE 3 . Transmits temperature data to the voltage converter 4 .
Controls the PID-controller and the MOSFET-transistor 5 . Connected to the zero bus 6 .
Sets the specified value 7 . The value goes to the comparison block 8 .
Receives data from the voltage converter and the set value 9 . Gives a signal about the need for regulation the analog output of the thermistor, using a formula based on polynomial regression [14], which is obtained empirically: (2) (3) = 7.39 × 2 + 62.17 × + 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 diference between the temperature set by the user and the actual received from the thermistor in the MC: = − → .
The coeficients proportional , integrating , diferentiating , 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]:
= × + × × + ( − − 1) × . (4) From the control signal of the PID-controller , a delay signal − 1 is formed, determined after a specified time interval . 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: = − − 1. (5) where is the current signal of the PID-controller, − 1 is the delay signal determined after a specified time interval .
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 coeficient , 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: ( )1 = ⎪⎧1, if > 0 and < 1 ⎨ 22−− 1 , if > 1 and < 2 (6) ⎪⎨⎧ 23−3−−− 112 ,, iiff >> 12 aanndd << 23 ⎪⎨⎧ 2−− 11 , if > 1 and < 2 if > 2 and < 3 else; 1 1 2 2 3 3 4 4 5 5 The graph of the output membership function is shown in Figure 4.
The control coeficient is calculated using the following formula: Calculating the coeficient: = ∑︀5=1 − ∑︀5 =1
.
= 1 − .
The coeficient is necessary for the final calculation of the output voltage value from EMAF . The value is calculated according to the following form:
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]: = − 1 × + × .
= × 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]. (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17)
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 = 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 from the PTE obtained via a thermistor. When value1 changes, the control system adjusts the PTE temperature to approach the target value, demonstrating efective regulation.
Signal value3 (green): This is the control signal representing the voltage 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.
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.
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.
The author(s) have not employed any Generative AI tools.