Modelling and control of a simple trophic aquatic system

Abstract

Artificially assembled and maintained trophic systems require real-time measurement and control of environmental and biological variables, either because these are part of the system’s purpose, as it occurs in biosensing, or because they are needed for performance and stability, as in closed ecological life support systems (CELSS). The design of control strategies needed in these two cases benefit from a model of the system dynamics. As an example, we modelled closed-loop controllers of a two-level artificial aquatic trophic system consisting of a cladoceran population feeding on algae supplied from a culture. The control of the cladoceran is based on a stage-structured model of its population dynamics and the food density, obtained as a balance of the rates of supply from the algae culture and of consumption by the cladoceran. The animal model assumes that females switch from asexual to sexual reproduction at low food density. The control strategy maintains the animal population in the asexual cycle and is based on two controllers. One to limit animal population growth by harvesting in accordance to food supply availability and another to adjust food supply in order to maintain the food density at a constant reference level above the threshold for sexual reproduction. Both controllers require real-time estimates of food density and total animal density; however, measurements of animal density by stage (adults and neonates) are assumed to be unavailable. The second controller, a proportional-derivative linear law, maintains the cladoceran in the asexual cycle by avoiding changes in reproductive behavior due to lack of adequate food density. The first controller calculates a harvest rate based on departures of the food consumption from a reference value, which was selected conservatively as only a fraction of food supply availability. Two alternative designs, linear and nonlinear, for the harvest controller were simulated and compared. Simulations of the model system (controllers, animal and food) are employed to investigate the effect of the controllers on short-term stability and transient behavior. All simulations started from zero animal density and a pulse inoculation of resting eggs ready to hatch. After post-inoculation transients, sudden changes in the consumption reference were also implemented to evaluate tracking response to these changes. As expected, the nonlinear control yielded better consumption rate transient behavior for both post-inoculation and tracking. Animal density fluctuations during the post inoculation period were not dampened due to the conservative assumptions of unavailability of real-time measurements of density by stage. We conclude that this control strategy is feasible but that further work is needed for implementation. In future work, we plan to address issues that limit current applicability of the model: generate real data for calibration and validation, extend controls to long-term behavior, and include other limiting factors and processes.