Model-based determination of optimal PID controller tuning parameters for technological processes
DOI:
https://doi.org/10.33216/1998-7927-2026-304-6-186-194Keywords:
PID controller, optimal tuning, quadratic optimisation function, integral quality criterion, identification of the controlled system, second-order elementAbstract
This article examines a model-based approach to determining the optimal parameters of PID controllers for industrial processes.
The relevance of this work stems from the need to improve the accuracy, response time and stability of automatic control systems without the need for repeated active experiments on industrial equipment. The proposed approach combines the identification of an equivalent mathematical model of the plant with the optimisation of controller parameters within a single calculation procedure. The plant is a second-order model with transport delay, the parameters of which are determined from characteristic points of the transient response using the least squares method. The input data for the theoretical generalisation are the transient responses of technological systems, obtained and validated in previous studies. To evaluate the quality of control, the integral quadratic criterion is used, which characterises the total deviation of the controlled variable from the setpoint during the transient process. The optimal values of the gain, integration time and differentiation time of the PID controller are determined using the conjugate gradient method. The sequence of steps for identification, construction of the closed-loop system, calculation of the quality criterion and iterative adjustment of the controller parameters has been formalised.
The procedure developed makes it possible to compare different tuning options and select the parameters that ensure the required transient response characteristics. The scientific novelty lies in the combination of second-order model identification with transport delay and the numerical optimisation of PID controller parameters. The practical significance of the results is determined by the possibility of implementing the method in software for automated controller tuning in chemical-technological and other inertial systems.
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