The use of a Mamdani-type fuzzy model for assessing the performance of a boom stabilization systems in a field sprayer

Abstract

Fuzzy logic models are increasingly used to control simple and complex devices, as well as entire operating systems. In this study, a fuzzy logic model was applied to assess the performance a boom stabilization system in a field sprayer. The model was tested on a field sprayer with a trapezoid system for stabilizing the sprayer boom with a length of 21 m. Measuring cables for registering the displacement of the boom's terminal segments (right and left) in the vertical and horizontal plane were installed on the sprayer. The field sprayer was connected to a tractor. The model was based on two linguistic variables: "absolute displacement of the boom's terminal segments" and "boom stability index". It was assumed that the sprayer boom was stable when the displacement of the boom's terminal segments did not exceed 0.25% of boom length. The study demonstrated that the proposed model can be reliably used to assess boom stability in real time (during field operations). The time required to achieve boom stability was more than 2.5 times shorter in the vertical than in the horizontal plane, which can be attributed mainly to the structure of the stabilization system. The proposed model is universal, and it can be applied to evaluate other boom stabilization systems in field sprayers.

Figure 1

Fuzzy control diagram.

Figure 2

System for measuring the sprayer boom's displacement from a state of equilibrium: (a) general view; (b) support arms with reel spools and cable tension springs; (c) loop screws for attaching measuring cables.

Figure 3

Displacement of the boom's terminal segments in two planes (speed – 8 km h⁻¹, without an air sleeve): A—point of contact between the tractor’s rear wheel and the obstacle, B—point of contact between the sprayer unit’s wheel and the obstacle, C—point at which the sprayer boom was stabilized, t₁—time directly before the tractor's rear wheel came into contact with the obstacle, t₂—time interval between points at which the tractor wheel and the sprayer wheel came into contact with the obstacle, t₃—time of unstable boom operation after the sprayer wheel came into contact with the obstacle, t₄—time of stable boom operation.

Figure 4

Membership functions: (a) admissible displacement, (b) threshold displacement, (c) excessive displacement; a₁, a₂, a₃—coefficients, d_l—threshold displacement.

Figure 5

Membership function of the stable boom state (a) and the result function (b): p₁—parameter, S_s—coordinate on the x-axis, μ_smax—coordinate on the y-axis.

Figure 6

Membership function of threshold boom displacement (a), the result function (b), and the membership function of unstable boom state: p₂… p₅—coefficients; S_l1, S_l2—coordinates on the x-axis; μ_lmax—bounding coordinate on the y-axis.

Figure 7

Membership functions of boom stability states (a) and the result of rule aggregation (b) for a field sprayer boom: |d_l|, |d_r|—absolute values of threshold displacement of the boom's left and right terminal segments; μ_lmax, μ_nmax, μ_smax—bounding coordinates on the y-axis for: threshold displacement, unstable boom state, and stable boom state.

Figure 8

Time of boom displacement and boom stabilization in the vertical plane (speed—6 km h⁻¹, without an air sleeve): A—point of contact between the tractor’s rear wheel and the obstacle, B—point of contact between the sprayer unit’s wheel and the obstacle, C—point at which the sprayer boom was stabilized, t₁—time directly before the tractor's rear wheel came into contact with the obstacle, t₂—time interval between points at which the tractor wheel and the sprayer wheel came into contact with the obstacle, t₃—time of unstable boom operation after the sprayer wheel came into contact with the obstacle, t₄—time of stable boom operation.

Figure 9

Time of boom displacement and boom stabilization in the horizontal plane (speed—6 km h⁻¹, without an air sleeve): A—point of contact between the tractor’s rear wheel and the obstacle, B—point of contact between the sprayer unit’s wheel and the obstacle, C—point at which the sprayer boom was stabilized, t₁—time directly before the tractor's rear wheel came into contact with the obstacle, t₂—time interval between points at which the tractor wheel and the sprayer wheel came into contact with the obstacle, t₃—time of unstable boom operation after the sprayer wheel came into contact with the obstacle, t₄—time of stable boom operation.

Figure 10

Stabilization system of a field sprayer boom: 1—slide bushings, 2—fixed-length bar, 3—hydraulic cylinder with adjustable length, 4—boom displacement damper in the vertical plane.