Modeling and simulation of a fractional order bioreactor system

Abstract In this paper, we propose a fractional order model for a well known bioreactor system. The model comprises a fractional differential equation for the ‘biomass’ and an integer order differential equation for the 'substrate’ dynamics. With an appropriate tuning of the ‘dilution rate’ control parameter, the proposed fractional order model behaves in a similar fashion to the parent integer order model, thus offering the advantage of model reduction while retaining the same qualitative steady state behavior. The dynamical responses are inherently slower than those obtained from the integer order model, and their speed increases with the system order. We also present a conjecture that for a fractional order bioreactor model of order 1 + α , biomass washout is obtained for dilution rates in excess of ‘ α ’ times the dilution rate for washout in the integer order model.