Miguel F. Acevedo
ABSTRACTS
Modelling and control of a simple
trophic aquatic system
Ecological Modelling 131:269-284.
2000.
Miguel F. Acevedo(1,2,3) and William T. Waller(1)
(1) Institute of Applied Sciences and (2) Department of Geography,
University of North Texas, Denton, Texas 76203
(3) Center for Simulation and Models, Universidad de Los Andes,
Mérida
Venezuela
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. 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.
Keywords: Control strategy, Cladocera, Daphnia, harvesting,
closed
system, trophic systems, life support, monitoring, real-time.