Engineering, Energy, Transport AIC

Oleg IVANOV – Сandidate of technical sciences, Аssociate professor, Associate Professor of the Department of Construction and Vocational Education, Poltava State Agrarian University (1/3 Skovorody St., Poltava, Ukraine, 36003, е-mail: oleg.ivanov@pdau.edu.ua, https://orcid.org/0000-0002-1761-9913).
Oleksii BURLAKA – Сandidate of technical sciences, Аssociate professor, Associate Professor of the of the Department of Agroengineering and Road Transport, Poltava State Agrarian University (1/3 Skovorody St., Poltava, Ukraine, 36003, е-mail: oleksii.burlaka@pdau.edu.ua, https://orcid.org/0000-0002-2296-7234).
Anton KELEMESH – Сandidate of technical sciences, Аssociate professor, Associate Professor of the of the Department of Agroengineering and Road Transport, Poltava State Agrarian University (1/3 Skovorody St., Poltava, Ukraine, 36003, е-mail: anton.kelemesh@pdau.edu.ua, https://orcid.org/0000-0001-9429-8570).
Sergii LIASHENKO – Сandidate of technical sciences, Аssociate professor, Head of the Department of Agroengineering and Road Transport, Poltava State Agrarian University (1/3 Skovorody St., Poltava, Ukraine, 36003, е-mail: sergii.liashenko@pdau.edu.ua, https://orcid.org/0000-0002-3227-3738).

The paper presents a mathematical model of the system for automatic water level control in a hydraulic pressure tank of an irrigation system. The object of control is the water level, which changes as a result of the supply of liquid by a centrifugal pump. The system is implemented according to the feedback principle, which uses an ultrasonic level gauge as a measuring element, an electric actuator of the pump and a proportional-integral controller for correcting the control signal. To simplify the analysis of dynamics, the system is linearized in the vicinity of the operating point, which corresponds to a stable operating mode, and is presented in the form of transfer functions of individual links. The transfer function of the control object describes the inertial properties of the change in the liquid level in the tank.
Based on the constructed mathematical model, an analysis of the dynamic characteristics of the system was performed, in particular, transient processes and root trajectories were investigated at different values of the controller gain coefficient Kp. The range of its change was taken from 0 to 8 with an increase step of 0.1. The simulation results showed that at small values of Kp < 0.2 the system reacts slowly, demonstrating an aperiodic but prolonged nature of water level establishment. In the range of Kp =0.6…2 the transient characteristic takes on an optimal form - the system reaches the set level without significant fluctuations, providing a compromise between speed and stability. Further increase of Kp > 2.5 leads to a decrease in the transient process time, however, the system acquires an oscillatory character with possible overregulation. At Kp > 7.0 there is a risk of loss of stability, which is confirmed by the location of the roots in close proximity to the imaginary axis.
Graphical analysis of transient characteristics confirmed that an increase in the Kp coefficient reduces the system establishment time, but at the same time increases the amplitude of oscillations. The constructed response time curves and root trajectories allow us to quantitatively assess the stability limits and the influence of the controller parameters on the quality of the regulation process. The results obtained indicate that the use of a PI controller provides effective stabilization of the water level, reduces the static error and increases the reliability of the pumping unit.
The developed methodology can be used to optimize the settings of automatic control systems in hydraulic and irrigation systems, as well as for the further synthesis of controllers with improved dynamic properties.

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