In this article, optimal control methods based on a metabolite-constrained fish growth model are applied to the operation of fish production in an aquaponic system. The system is formulated for the twin objective of fish growth and plant fertilization to maximize the benefits by optimal and efficient use of resources from aquaculture. The state equations, basically mass balances, required by the optimization algorithms are given in the form of differential equations for the number of fish in the stock, their average weight as mediated through metabolism and appetite, the water recirculation and waste treatment, hydroponic nutrient requirements and their loss functions. Six parameters, that is, water temperature, flow rate, stock density, feed ration size per fish, energy consumption rate and the quality of food (percentage of digestible proteins) are used to control the system under dynamic conditions. The time to harvest is treated as a static decision variable that is repeatedly adjusted to find the profit-maximizing solution. By modeling the complex interactions between the economic and biological systems, it is possible to obtain the most efficient decisions with respect to diet composition, feeding rates, harvesting time and nutrient releases. Some sample numerical results using data from a tilapia-tomato farm are presented and discussed.
- dynamic modeling