2025 , Volume 30, № 5, p.7-20

Purpose. Development of a simulation modelling method for fuzzy-logic control systems of complex objects to optimize parameters of the proportional-integral-derivative (PID) controller and PID with a fuzzy-digital filter (FDF) using the Peltier thermoelement control system as an example. The method accounts for nonlinear dependencies, first-order dynamics, and minimizes design costs of mechatronic systems by eliminating physical prototype assembly.

Methodology. A numerical model of the Peltier thermoelement was developed, describing nonlinear dependencies of its temperature on voltage and current through a field-effect transistor. PID and PID+FDF controllers were applied, with FDF smoothing the control signal to enhance stability. Discretization with a 0.1 s step, Euler method integration, and Gaussian noise were used to simulate temperature sensor inaccuracies. System stability was analyzed via Bode diagrams and BIBO (bounded-input bounded-output) stability assessment. Control quality was evaluated using IAE (integral absolute error) and ISE (integral squared error) metrics. Experiments conducted in Python using NumPy, Matplotlib, and python-control libraries investigated controller parameters and noise effects.

Findings. PID+FDF demonstrated reduced overshoot and faster achievement of target temperatures compared to the standard PID controller, particularly at high temperatures. The system confirmed BIBO stability, maintaining bounded temperature deviations under noise influence. PID+FDF showed superior performance at low-frequency disturbances, achieving lower IAE errors.

Originality/Value. The method, combining a fuzzy-digital filter with a PID controller, enables precise control without physical prototype assembly, reducing design costs and risks. It is versatile for mechatronic systems and promising for multi-variable systems with parameter optimization under complex disturbances.