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.

Pan-artifact Removing with Deep Learning, on ISEs

“…We used Yamazaki's nutrient solution for lettuce [9] because it is very popular around the world and its chemical phenomenon and interactions of every solvent are fully understood. [2] But We did not applied some ions whose population is very little. KNO3, Ca(NO3)2-4H2O and NH4H2PO4 were used to make the nutrient solution.…”

“…Nowadays, the replacement of experience based know-how is main trend of Farm-tech area. [2,3] On fertilization area, the hottest application is hydroponics aqua culture). Open hydroponic system does not recycle the nutrient solution while closed hydroponic system does.…”

Mathematical Model and Simulation for Nutrient-Plant Interaction Analysis

“…Recently, ODE network simulation is applied on nutrient solution system to understand the black-boxed behavior of complex chemical system. [1] The network-model based approach describes sedimentation and complex bidirected interactions among chemical compounds which the nutrient solution contains. It provided time-series simulations to investigate nutrient solution system with high accuracy.…”

“…This method is based on ordinary differential equation (ODE) expression of chemical reactions. For example, ionization of NaCl(aq) is described as equation (1)(2)(3), where k1 is forward reaction rate and k2 is backward reaction rate.…”

Mathematical Model for Secondary Transport of Cations at the Root of Plants

“…Recently, ODE network simulation on nutrient solution system to understand the black-boxed behavior of complex chemical system (Byunghyun Ban et al 2019). The network based approach describes sedimentation and complex bidirected interactions among chemical compounds which the nutrient solution contains.…”