Modelling and control of a simple trophic aquatic system

Artificially assembled and maintained trophic systems require real-time mea surement and control of environmental and biological variables, either beca use 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 ecologi cal life support systems (CELSS). The design of control strategies needed i n these two cases benefit from a model of the system dynamics. As an exampl e, we modelled closed-loop controllers of a two-level artificial aquatic tr ophic system consisting of a cladoceran population feeding on algae supplie d from a culture. The control of the cladoceran is based on a stage-structu red model of its population dynamics and the food density, obtained as a ba lance of the rates of supply from the algae culture and of consumption by t he cladoceran. The animal model assumes that females switch from asexual to sexual reproduction at low food density. The control strategy maintains th e animal population in the asexual cycle and is based on two controllers. O ne to limit animal population growth by harvesting in accordance to food su pply availability and another to adjust food supply in order to maintain th e food density at a. constant reference level above the threshold for sexua l reproduction. Both controllers require real-time estimates of food densit y and total animal density; however, measurements of animal density by stag e (adults and neonates) are assumed to be unavailable. The second controlle r, a proportional-derivative linear law, maintains the cladoceran in the as exual cycle by avoiding changes in reproductive behavior due to lack of ade quate food density. The first controller calculates a harvest rate based on departures of the food consumption from a reference value, which was selec ted conservatively as only a fraction of food supply availability. Two alte rnative designs, linear and nonlinear, for the harvest controller were simu lated and compared. Simulations of the model system (controllers, animal an d food) are employed to investigate the effect of the controllers on short- term stability and transient behavior. All simulations started from zero an imal density and a pulse inoculation of resting eggs ready to hatch. After post-inoculation transients, sudden changes in the consumption reference we re also implemented to evaluate tracking response to these changes. As expe cted, the nonlinear control yielded better consumption rate transient behav ior for both post-inoculation and tracking. Animal density fluctuations dur ing the post inoculation period were not dampened due to the conservative a ssumptions of unavailability of real-time measurements of density by stage. We conclude that this control strategy is feasible but that further work i s needed for implementation. In future work, we plan to address issues that limit current applicability of the model: generate real data for calibrati on and validation, extend controls to long-term behavior, and include other limiting factors and processes. (C) 2000 Elsevier Science B.V. All rights reserved.