Feedback Linearization of a Reduced Chemostat Model Under Inflow Disturbances

This paper investigates the stabilization of a chemostat system with biomass settling dynamics using feedback linearization and model reduction techniques. The original three-dimensional system, composed of substrate, free biomass, and settled biomass compartments, is reduced to a two-dimensional system by assuming quasi-steady-state for the settled biomass population. A nonlinear feedback control law for the dilution rate is then designed using feedback linearization, aiming to regulate the free biomass concentration around a desired set point. The proposed control strategy compensates for nonlinearities introduced by Monod-type microbial growth and biomass settling effects. To evaluate robustness, time-varying disturbances are introduced into the inflow substrate concentration. Numerical simulations in MATLAB confirm that the closed-loop system maintains stability and tracks the biomass target despite sustained inflow fluctuations. The results demonstrate the efficacy of the reduced-order feedback linearization approach in chemostat stabilization and its potential for bioreactor control under uncertain environmental conditions.