The dynamic response of a stirred-tank bioreactor can be represented by the transfer function C'(s) 4...

 

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The dynamic response of a stirred-tank bioreactor can be represented by the transfer function C'(s) 4 C(s) 2s +1 where C' is the exit substrate concentration , mol/L and C si the feed substrate concentration, mol/L. a. Derive an expression for c'(t) if c; (t) is a rectangular pulse with the following characteristics: t<0 Cr(t) = 4 0sts2 2 2sts0 b. What is the maximum value of c'(t)? When does it occur? What is the final value of c'(t)? c. If the initial value of c(0) = 1, how long does it take for c(t) to return a value of 1.05, after it has reached its maximum value? The dynamic response of a stirred-tank bioreactor can be represented by the transfer function C'(s) 4 C(s) 2s +1 where C' is the exit substrate concentration , mol/L and C si the feed substrate concentration, mol/L. a. Derive an expression for c'(t) if c; (t) is a rectangular pulse with the following characteristics: t<0 Cr(t) = 4 0sts2 2 2sts0 b. What is the maximum value of c'(t)? When does it occur? What is the final value of c'(t)? c. If the initial value of c(0) = 1, how long does it take for c(t) to return a value of 1.05, after it has reached its maximum value?