A chemostat is a continuous stirred tank bioreactor that can carry out fermentation of a plant cell culture. Its dynamic behavior can be described by the following equations:

X = ?(S)X ? DX

S = ? ?(S) X/Y _X/S?? D (S_f?? S)

X and S are the cell and substrate concentrations, respectively, and S_f is the substrate teed concentration. The dilution rate D is defined as the feed flow rate divided by the bioreactor volume. D is the input, while the cell concentration X and substrate concentration S are the state variables, Typically, the rate of reaction is referred to as the specific growth rate ? and is modeled by a Monod equation,

Assume ?_m = 020 hr^?1, K_S = 1.0 g/l, and Y_X/S = 0.5 g/g. Use a steady-state operating point of D = 0.1 hr^?1, X = 2.25 g/l, S = 1.0 g/l, and S_f?= 110 g/l. Using linearization, derive a transfer function relating the deviation variables for the cell concentration (X ? X) to the dilution rate (D ? D).

Ks + S H(S)