Model-Based Feedforward Control of an Intra- and Interspecific Competitive Population System

Abstract

Intra-and interspecific competitive population systems are relevant for a variety of applications, such as bioreactors or wastewater treatment plants. These systems are described by coupled hyperbolic semilinear integro partial differential equations with non-local integral boundary conditions. This type of population system has not been considered in the context of control theory in the literature to date. It is assumed that it is possible to measure both species separately, but only one control input is available, namely the dilution rate. A system analysis allows for the determination of infinitely many, but uniquely determined steady-states that are used to derive nonlinear input-output dynamics via the relation of hyperbolic partial differential equations to integral delay equations. A model inversion yields a feedforward control to control the two different outputs, which are a weighted integral over the population density. This results in a restriction in the choice of reference trajectories due to the undercount of inputs. Simulations show the great potential that can be achieved with model-based feedforward control in the context of population systems.