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 model:̇ X=μ(S)X−DẊ S=−μ(S)X∕YX∕S+D(Sf−S)X and S are the cell and substrate concentrations, respectively,and Sf is the substrate feed 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 sub-strate concentration S are the output variables. Typically, the rate of reaction is referred to as the specific growth rate μ and is modeled by a Monod equation, μ(S)=μmS/(Ks+S) Assume μm=0.20 h−1,Ks=1.0 g/L, and YX/S=0.5 g/g. Usea steady-state operating point of D=0.1h-1, X=4.5g∕L,S=1.0g∕L, and Sf=10 g∕L.Using linearization, derive a transfer function relating thedeviation variables for the cell concentration(X−X)to the dilution ration(D−D).
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 model:̇ X=μ(S)X−DẊ S=−μ(S)X∕YX∕S+D(Sf−S)X and S are the cell and substrate concentrations, respectively,and Sf is the substrate feed 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 sub-strate concentration S are the output variables. Typically, the rate of reaction is referred to as the specific growth rate μ and is modeled by a Monod equation, μ(S)=μmS/(Ks+S) Assume μm=0.20 h−1,Ks=1.0 g/L, and YX/S=0.5 g/g. Usea steady-state operating point of D=0.1h-1, X=4.5g∕L,S=1.0g∕L, and Sf=10 g∕L.Using linearization, derive a transfer function relating thedeviation variables for the cell concentration(X−X)to the dilution ration(D−D).
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