Through chemostat reactors, organisms can be observed under laboratory conditions. Hereby, the reactor contains the biomass, whose growth can be controlled via the dilution rate, respectively, the speed of a pump. Due to physical limitations, input constraints need to be considered. The population density in the reactor can be described by a hyperbolic nonlinear integro partial differential equation (IPDE) of first order. The steady-states and generalized eigenvalues and eigenmodes of these IPDE are determined. In order to track a desired reference trajectory, an optimal and an inversion-based feedforward control are designed. For the optimal feedforward control, the singular arc of the control is calculated and a switching strategy is stated, which explicitly considers the input constraints. For the inversion-based feedforward control, the IPDE is first linearized around the steady-state. To comply with the input constraints, a control system simulator is designed. For the simulation model, the IPDE is approximated using Galerkin's method. Simulations show the functionality of the designed controls and provide the basis for comparison. The inversion-based feedforward control operates well near the steady-state, whereas the performance of the optimal feedforward control is not bounded to the proximity to the steady-state.