Control of age-structured population dynamics with intraspecific competition in context of bioreactors

Abstract

Bioreactors are used for commercial manufacturing of products or as a simplified representation of wastewater treatment plants. If it is taken into account that individual organisms from the population in the bioreactor behave differently, an additional structure such as age can be added to the population. This leads to a nonlinear, hyperbolic, integro-partial differential equation (IPDE) with non-local integral boundary conditions (BC) in the modeling. The steady-states of this system can be uniquely determined by a substitution due to the non-local BC. Using the asymptotic properties of the system, the IPDE is split into finite-dimensional dynamics and infinite dimensional internal dynamics. The internal dynamics are globally exponentially stable. Therefore, a feedforward control based on the finite dimensional dynamics is designed, augmented with a feedback control to compensate for the remaining influence of the internal dynamics on the output. Finally, the control concept is supplemented by an observer. Global exponential attractiveness of certain reference trajectories is proven. The overall control concept is validated experimentally with a bioreactor. A system parameter is identified and it is shown that by applying the control concept, the biomass can track various reference trajectories with small errors.