Concerning the Optimal Control of the Relative Positions of the Sections of a Center-Pivot Irrigation Machine for Processing of the Fields of Non-Circular Shapes

Abstract

A center-pivot irrigation system is widely used all over the world. Its main drawback is its applicability only to the round fields. In order to avoid this limitation a possibility of changing the mutual arrangement of the sections of the center-pivot irrigation machine was proposed. So, the sections of the machine must be able to rotate one around the other. In order to achieve such a feature, the traditional wheeled vehicles must be replaced with the walking machines. The walking machines based on the rotary-orthogonal movers (for example, Orthonog walking robot developed in Volgograd State Technical University) have almost perfect maneuverability. This allows a machine to take the form of an arbitrary curved line. The optimality criterion was introduced, which was a minimal work of the drive motors during movement of the machine. The system of rigid sprinkling sections was replaced with a continuous curve, wherein each subsequent point was not closer to the center than the previous one. The optimal configuration of a sprinkler in a field plane was found by using the methods of calculus of variations. The resulting equation was solved by the numerical method. An analysis of the results was done in order to find the maximal range of the length change. The results are valid for the steady driving mode in the sector of constant radius. The proposed model can be improved by introduction of another optimality criterion and taking into account the errors arising from the replacement of a discrete system with a continuous curve. Thus, a possibility of the use of a center-pivot sprinkler for the fields of non-circular shape is substantiated.