2.1 Variable rate irrigation (VRI)

Variable rate irrigation (VRI) is a specific management tool used to apply the adequate amount of water in the sectors or zones of a planting area, for example Figure 2, presents control regions where the zones in reddish colors need more water, and those of bluish colors are with the humidity within the limits that the plant needs. The development of the prescription of variable rate irrigation is a field of active research, studied in [13, 14, 35].

Once established, prescriptions can, within a management variability, remain fixed, or these zones can dynamically change a small number of times during a growing season. Characteristics of crops and soil type are the main factors that contribute to determine the space and time variability of a planted area. This information is incorporated into a geographic information systems (GIS) database and, therefore, used for interpretation and decision support [36].

#### 2.1.1 Irrigation system

Irrigation systems are a set of techniques aimed to distribute water to crops in adequate quantities in order to promote appropriate plant development with a

#### Figure 2.

Spatial variability of irrigation water needs. Source: VALLEY. (http://ww2.valleyirrigation.com/valley-irriga tion/pt/tecnologia-de-comando/rega-de-taxa-vari%C3%A1vel/vri-controle-de-velocidade).

## Integrating Remote Sensing Data into Fuzzy Control System for Variable Rate Irrigation Estimates DOI: http://dx.doi.org/10.5772/intechopen.87023

minimum of water consumption [37]. Irrigation systems can be divided into two subsystems: catchment and application subsystem. The way the water is applied depends on different methods of application, and each has its specificities. They are divided into three groups: surface irrigation, localized irrigation, and sprinkler irrigation.


Sprinkler irrigation is the method of irrigation in which water is sprayed on the surface of the land, like a rainfall, because the water jet is fractioned in drops. They are classified as: conventional spraying, central pivot, self-propelled, and linear system. Since this is the scope of this chapter, central pivot irrigation will be further detailed.

#### 2.1.2 Central pivot

2.1 Variable rate irrigation (VRI)

cnptia.embrapa.br/redeap2).

Figure 1.

of active research, studied in [13, 14, 35].

2.1.1 Irrigation system

Figure 2.

30

Variable rate irrigation (VRI) is a specific management tool used to apply the adequate amount of water in the sectors or zones of a planting area, for example Figure 2, presents control regions where the zones in reddish colors need more water, and those of bluish colors are with the humidity within the limits that the plant needs. The development of the prescription of variable rate irrigation is a field

Different management zones within the same planting area. Source: Embrapa. (https://www.macroprograma1.

Irrigation - Water Productivity and Operation, Sustainability and Climate Change

Once established, prescriptions can, within a management variability, remain fixed, or these zones can dynamically change a small number of times during a growing season. Characteristics of crops and soil type are the main factors that contribute to determine the space and time variability of a planted area. This information is incorporated into a geographic information systems (GIS) database

Irrigation systems are a set of techniques aimed to distribute water to crops in adequate quantities in order to promote appropriate plant development with a

Spatial variability of irrigation water needs. Source: VALLEY. (http://ww2.valleyirrigation.com/valley-irriga

tion/pt/tecnologia-de-comando/rega-de-taxa-vari%C3%A1vel/vri-controle-de-velocidade).

and, therefore, used for interpretation and decision support [36].

Among the sprinkler systems, the central pivot has been used with relative success due to the lower labor demand [37, 38]. It was first built in 1948 by Frank L. Zybach, who sent the invention for analysis, finally patented in 1952 in Colorado, United States (see Figure 3). In 1954, Zybach sold the manufacturing rights to the American company Valley, located in the State of Nebraska. In 1968, the Lindsay Company also started to produce pivots, and currently both companies share the leadership of the world market of pivots.

The speed of the lateral displacement of a central pivot is controlled in the last tower, which is established by a timer, installed in the central control box of the pivot, which controls the time of activation and the stop of the motor of the last tower. For example, the condition in which the motor standstill time is equal to the movement time corresponds to the setting of 50% of the maximum speed set by the timer control percentage. At maximum speed of 100%, the motor of the last tower is continuously moving [37, 39].

Irrigated agriculture does not allow reductions in crop productivity due to lack or excess of applied water. The application of little water (deficit irrigation) can be an obvious waste, since production could not obtain the expected benefit. On the other hand, the excessive application is much more destructive, because soil saturation occurs, which prevents its aeration and leaches the nutrients, inducing a higher rate of evaporation and salinization [40]. So, it is important to develop an irrigation scheduling program for deciding when and how much to irrigate. For this purpose, we used the fuzzy logic system to simulate the amount and the frequency of irrigation needed.

### 2.2 Fuzzy logic

Fuzzy sets theory was introduced in 1965 by the Iranian mathematician Lotfi Asker Zadeh, a professor at the University of Berkley, USA [41], especially intended to offer a mathematical treatment to some subjective linguistic terms such as "approximately" and "around", among others. This would be a first step in programming and storing vague concepts in computers, making it possible to produce calculations with inaccurate information, such as the human being [42].

analyzed according to a degree of pertinence, which indicates the level that the information belongs to a specific set in a universe of discourse, according to [44]. Fuzzy set theory provides a method for manipulating sets whose boundaries are imprecise rather than restricted. The uncertainty of an element, that is, its fractional degree of pertinence, can be conceived as a measure of possibility, in other words,

Integrating Remote Sensing Data into Fuzzy Control System for Variable Rate Irrigation Estimates

In many practical systems, relevant information comes from two sources: human experts, who describe their knowledge about the system in natural languages, and sensory measures and mathematical models proposed according to physical laws. An important task, therefore, is to combine these two types of

The fuzzy inference system consists of a fuzzification interface, a rule base, a database, a decision-making unit or inference unit, and finally a defuzzification

• A database that defines the functions of association of fuzzy sets used in fuzzy

• A defuzzification interface that transforms the fuzzy results of the inference

Based on natural language, a fuzzy logic system is simple to understand and enables the representation and processing of human knowledge in a computer. The inputs, outputs, and fuzzy logic rules are easy to modify. These fuzzy logic features make it particularly well suited for use in a decision support system and is able to assist in the construction of vague rate-based irrigation control maps based on results of an imaging system in real time or by prescriptive maps based on the

the possibility that an element is a member of the set [42].

interface. The functional blocks are shown in Figure 4.

• A rule base containing a number of "if-then" fuzzy rules;

• A decision unit that performs rule inference operations;

correspondence with linguistic values;

• A fuzzification interface that transforms crisp inputs into degrees of

2.2.1 Fuzzy inference systems

information into systems designs [45].

DOI: http://dx.doi.org/10.5772/intechopen.87023

The function of each block is:

into a crisp output.

soil-plant-atmosphere transfer.

Fuzzy inference system. Source: Adapted from Ross [46].

Figure 4.

33

rules;

In other words, while decision making in classical theory would be like Eq. (1), fuzzy logic would be like Eq. (2) [43].

$$f(\mathbf{x}) = \begin{cases} 1 \text{ if,} , \text{and } \text{only } \circ \text{f, } \mathbf{x} \in A \\ 0 \text{ if,} , \text{and } \text{only } \circ \text{f, } \mathbf{x} \notin A \end{cases} \tag{1}$$

$$f(\mathbf{x}) = \begin{cases} \mathbf{1} \circ f, \text{and only if, } \mathbf{x} \in A\\ \mathbf{0} \text{ if, and only if, } \mathbf{x} \notin A\\ \mathbf{0} \le \mu(\mathbf{x}) \le \mathbf{1} \circ f \propto \text{partial membership to } A \end{cases} \tag{2}$$

The most evident characteristic of fuzzy logic is to consider that between two values (zero and one) there may be intermediate values, and these values are
