NutrientMixingAlgorithm

A Python-based Algorithm for Nutrient Mixing in Hydro- and Aquaponics systmes created by the Automatic Control & System Dynamics Lab at Chemnitz University of Technology.

Introduction

The program features an algorithm for automatically mixing a nutrient solution based on a target volume and reference concentrations for the nutrients that are considered by the user. To achieve the desired solution the algorithm optimally chooses the volumes of a set of water sources and masses of a set of fertilizers, that are flowing into a mixing tank. Both sets can be specified by the user of the program.

The optimal choice of inputs (water volumes and fertilizer masses) is based on the solution of a convex static optimization problem

$$\begin{align} \min_{u \in R^n}\ & f(u), \\ \text{s.t.}\ & g_L \le g(u) \le g_U, \\ & u_L \le u \le u_U. \end{align}$$

The optimization problem features two objectives:

1. Minimized error between a given reference concentration and the resulting nutrient concentration in the mixed solution,
2. Optimized use of the given water sources and fertilizers -> specified by the user.

The priority of both objectives and the optimal ressource consumption can be affected by setting the weights of the optimization problem.

Implementation

The program is implemented as a python script (Version 3.11). The interface between the program and the user is done via xml-files. These files are set up as tables, in which every parameter of the optimization problem is stated. Parameters include:

• Weights to affect the optimal consumption of ressources and the priority of the objectives
• Reference concentrations, max/min concentrations of the final solution,
• Nutrient composition of every water source and fertilzer,
• Mixing tank geometry, ...

Reading from and writing to the xml-files is done via the pandas-library and the lxml-parser. With the help of the read in parameters the optimization problem is set up with the Python API of CasADi and Solved by the IPOPT-Solver. References can be found in the associated article that is presented at the end of the README-file.

A more extensive investigation into the structure of the program can be found in the documentation.

Citation

We provide this program open source and hope it will help you for your research and/or for setting up your aquaponics, hydroponics or a similar system. However, if you do so, please cite the following article in your work:

• Kobelski, A.; Nestler, P.; Mauerer, M.; Rocksch, T.; Schmidt, U.; Streif, S. An Algorithm for Nutrient Mixing Optimization in Aquaponics. Appl. Sci. 2024, 14, 8140.

Note: The ReadMe-File is currently being edited.