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For a multistage bioseparation process described by the
Chapter 7, Problem 7.4(choose chapter or problem)
For a multistage bioseparation process described by the transfer function,
\(G(s)=\frac{2}{(5 s+1)(3 s+1)(s+1)}\)
calculate the response to a step input change of magnitude, 1.5.
(a) Obtain an approximate first-order-plus-delay model using the fraction incomplete response method.
(b) Find an approximate second-order model using a method of Section 7.2.
(c) Calculate the responses of both approximate models using the same step input as for the third-order model. Plot all three responses on the same graph. What can you conclude concerning the approximations?
Questions & Answers
QUESTION:
For a multistage bioseparation process described by the transfer function,
\(G(s)=\frac{2}{(5 s+1)(3 s+1)(s+1)}\)
calculate the response to a step input change of magnitude, 1.5.
(a) Obtain an approximate first-order-plus-delay model using the fraction incomplete response method.
(b) Find an approximate second-order model using a method of Section 7.2.
(c) Calculate the responses of both approximate models using the same step input as for the third-order model. Plot all three responses on the same graph. What can you conclude concerning the approximations?
ANSWER:Step 1 of 12
Consider the given data:
\(\begin{array}{l} G(s)=\frac{2}{(5 s+1)(3 s+1)(s+1)} \\ X(s)=\frac{1.5}{s} \end{array}\)
(a) The output of the system is calculated as,
\(\begin{aligned} Y(s) & =G(s) X(s) \\ & =\frac{2}{(5 s+1)(3 s+1)(s+1)} \frac{1.5}{s} \end{aligned}\)
Solving the above equation gives,
\(Y(s)=\frac{0.2}{s\left(s+\frac{1}{5}\right)\left(s+\frac{1}{3}\right)(s+1)}\)