High-gain observer for the nitrification process including sensor dynamics

TL;DR

This paper introduces a high-gain observer for nitrification process monitoring that accounts for sensor dynamics, enabling better inference of soil nitrate levels from limited sensor data.

Contribution

It develops a novel high-gain observer model incorporating sensor measurement dynamics and proposes a model reduction technique for improved spatial resolution.

Findings

Observer gain computed via linear matrix inequalities

Model discretization on a grid for system of ODEs

Simulation validates the effectiveness of the proposed approach

Abstract

Fertilization is commonly used to increase harvests. The lack of knowledge of soil properties and the excessive use of fertilizers can result in overfertilization. Current sensor technology is able to measure the concentrations of some of the involved substances only at selected locations and depths. Point measurements of adjacent sensors in coarse sensor networks can be used to infer upon the state of nitrate concentrations in the sensor surroundings. For this purpose, a high gain observer is proposed. Models of the nitrification process as well as the measurement dynamics for the observer design are derived and discretized on a grid to obtain a system of ordinary differential equations. It is shown that the nonlinearities of the model can be bounded and how the observer gain can be computed via linear matrix inequalities. Furthermore, a model reduction is proposed, which allows the consideration of more grid points. A simulation study demonstrates the proposed approach.