Finite Approximation Models for Age-Structured Population Dynamics with Self-Competition in Chemostat Reactor Applications

Microorganisms are typically cultivated in chemostat reactors. If considering self-competition, their population is described by a nonlinear hyperbolic first order integro-partial differential equation with integral boundary condition. In order to validate control algorithms for this system class a finite-time simulation model is required. To obtain such an approximated model Galerkin's method is used. The resulting system is transformed to Byrnes-Isidori normal form to decouple the internal dynamics and the input/output dynamics. In addition to the analysis of the stability of the internal dynamics, a feedforward and a feedback controller is designed. In simulations the performance is shown and the stated theoretic stability properties are validated by means of numerical results.