# Mathematical model of closed irrigation system as an object of control

• S. Karpenko
• H. Rudakova

## Keywords:

pumping unit, valves, closed irrigation system, irrigation equipment, mathematical model

## Abstract

Irrigation machines of the Frigate series are mainly used in closed irrigation systems in the south of Ukraine. During the operation of such systems there are problems with pressure control in the system, the problem of remote control of irrigation. A possible solution to these problems is to control the pressure in the water supply line of sprinklers, by automatically controlling the pumping equipment and installing appropriate sensors (pressure, flow meters, etc.) for feedback to the control system. By controlling the pumping equipment that creates pressure in the mains, it is possible to ensure proper modes of operation in the water supply mains of the DMU. Appropriate software for statistical data collection and management is also needed to improve watering and remote monitoring of the system. The aim of the study is to build a mathematical model of a closed irrigation system as an object of management, which will analyze the processes occurring in the system and evaluate the effectiveness of management methods being developed. The article considers the scheme of relationships between the main components of a closed irrigation system such as pump unit, distribution and irrigation pipeline, shut-off valves, universal sprinklers, control system with further mathematical description of each component. The main parameters of the system that affect its operation are identified. Set quality indicators that are put forward to the control system. The system as an object of control is analyzed, input, output and internal parameters of the system are revealed. The mathematical model of ZSS is built from the considered models of components, gives the chance to analyze the processes proceeding in system, and to estimate efficiency of the management methods developed. To determine the adequacy of the mathematical model, which is created by the proposed approach, it is advisable to simulate the operation of the ZSS for real conditions in different modes of operation. To determine the properties of ZSS as an object of control, such as inertia, controllability, stability, observation, it is necessary to obtain a model of the complex in the space of states.

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2022-04-08

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