ODE network model for nonlinear and complex agricultural nutrient solution system
📝 Abstract
In closed hydroponic systems, periodic readjustment of nutrient solution is necessary to continuously provide stable environment to plant roots because the interaction between plant and nutrient solution changes the rate of ions in it. The traditional method is to repeat supplying small amount of premade concentrated nutrient solution, measuring total electric conductivity and pH of the tank only. As it cannot control the collapse of ion rates, recent researches try to measure the concentration of individual components to provide insufficient ions only. However, those approaches use titrationlike heuristic approaches, which repeat adding small amount of components and measuring ion density a lot of times for a single control input. Both traditional and recent methods are not only time-consuming, but also cannot predict chemical reactions related with control inputs because the nutrient solution is a nonlinear complex system, including many precipitation reactions and complicated interactions. We present a continuous network model of the nutrient solution system, whose reactions are described as differential equations. The model predicts molar concentration of each chemical components and total dissolved solids with low error. This model also can calculate the amount of chemical compounds needed to produce a desired nutrient solution, by reverse calculation from dissolved ion concentrations.
💡 Analysis
In closed hydroponic systems, periodic readjustment of nutrient solution is necessary to continuously provide stable environment to plant roots because the interaction between plant and nutrient solution changes the rate of ions in it. The traditional method is to repeat supplying small amount of premade concentrated nutrient solution, measuring total electric conductivity and pH of the tank only. As it cannot control the collapse of ion rates, recent researches try to measure the concentration of individual components to provide insufficient ions only. However, those approaches use titrationlike heuristic approaches, which repeat adding small amount of components and measuring ion density a lot of times for a single control input. Both traditional and recent methods are not only time-consuming, but also cannot predict chemical reactions related with control inputs because the nutrient solution is a nonlinear complex system, including many precipitation reactions and complicated interactions. We present a continuous network model of the nutrient solution system, whose reactions are described as differential equations. The model predicts molar concentration of each chemical components and total dissolved solids with low error. This model also can calculate the amount of chemical compounds needed to produce a desired nutrient solution, by reverse calculation from dissolved ion concentrations.
📄 Content
ODE Network Model for Nonlinear and Complex Agricultural Nutrient Solution System
Byunghyun Ban*
Andong District Office
Ministry of Employment and Labor
Andong, Republic of Korea
bhban@kaist.ac.kr
Minwoo Lee
Future Agriculture Team
Imagination Garden Inc.
Andong, Republic of Korea
hydrominus@sangsang.farm
Donghun Ryu
Machine Learning Team
Imagination Garden Inc.
Andong, Republic of Korea
dhryu@sangsang.farm
Abstract—In
closed
hydroponic
systems,
periodic
readjustment of nutrient solution is necessary to continuously
provide stable environment to plant roots because the
interaction between plant and nutrient solution changes the rate
of ions in it. The traditional method is to repeat supplying small
amount of premade concentrated nutrient solution, measuring
total electric conductivity and pH of the tank only. As it cannot
control the collapse of ion rates, recent researches try to
measure the concentration of individual components to provide
insufficient ions only. However, those approaches use titration-
like heuristic approaches, which repeat adding small amount of
components and measuring ion density a lot of times for a single
control input. Both traditional and recent methods are not only
time-consuming, but also cannot predict chemical reactions
related with control inputs because the nutrient solution is a
nonlinear complex system, including many precipitation
reactions and complicated interactions. We present a
continuous network model of the nutrient solution system,
whose reactions are described as differential equations. The
model predicts molar concentration of each chemical
components and total dissolved solids with low error. This
model also can calculate the amount of chemical compounds
needed to produce a desired nutrient solution, by reverse
calculation from dissolved ion concentrations.
Keywords— nutrient solution, smart farm, system engineering,
computational chemistry, simulation, complex system, IoT
I. INTRODUCTION
Recently, soilless culture takes center stage in agricultural
industry. Closed hydroponic system is one of the most
popular hydroponic method because it reduces the cost and
hazard of water pollution [1]. As plants continuously absorb
nutrients from the environment, the concentration of
individual ions continuously drops. Traditional methods
usually measure pH and electrical conductivity (EC) of the
nutrient solution to monitor the fertilization status [2-3].
When EC is low, they add premade concentrated solution to
the tank and then apply acids to maintain pH.
As the absorption rates of the ions are all different, those
approaches gradually destroy the ratio among ions [4] and
accumulates excessive ions (sodium, chloride, sulfate and
etc.) [5-6] which have low absorption rates or are supplied
too much. Many researchers recently have suggested to
measure individual ion with ion-selective sensors and to
provide insufficient ions only [1, 7-9]. However, their control
methods are slow and cannot avoid Na+ accumulation
problem caused by Fe-EDTA supply.
Nutrient solution is a complex system. It is a bi-directed
network model, whose nodes are chemical components and
edges are reactions. It is difficult to figure out the exact state,
and some input can cause unexpected results because almost
all the vesicles have self-feedback structures or bi-directed
interactions. And many reactions lead to undesired output
nodes such as sediment or unabsorbable ions. For example,
supplying additional chemicals does not just raise ion
concentrations directly. The components in the nutrient
solution make various reactions such as sedimentations or
reductions, producing compounds which plant does not
absorb. As researchers does not know what is happening in
the nutrient solution system exactly, they proposed some
models to predict salt accumulation [6] or ion rates [4].
Boolean network model and ordinary differential equation
(ODE) model are frequently applied to describe complex
system. Boolean system describes value of the components
as true or false binary. So construction of large-scale network
model such as cancer cell model [10-13] is a novel and useful
approach. ODE network describes interaction between
components as ordinary differential equations, which usually
have time t as independent variable [14-16]. It requires huge
computing power, and it is difficult to build differential
equations for the whole network. ODE model can describe
continuous system while Boolean model can describe
discrete phenomena only. Applying Boolean network on
nutrient system modeling can only show existence of a
component as true or false value but ODE network can
describe continuous changes of concentrations of ions and
sedimentation reactions.
Chemical reactions are time-dependent continuous process
so they can be modeled as ordinary differential equations,
whose independent variable is the time. For examp
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