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Homework 06 - Transfer Functions

Homework 06 - Transfer Functions - concentration c Ai The...

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Chemical Engineering Department University of Florida ECH 4323 Process Control Theory HOMEWORK No. 6 — TRANSFER FUNCTIONS 1.0 A constant-volume stirred-tank heater can be modeled as ( ) ( ) Q T T hA T T wC dt dT C V a i + ! ! ! = " . Assume that w , T i , and T a (the ambient temperature) are constant. The area available for heat losses is A and an appropriate heat transfer coefficient is h . Obtain a transfer function that relates liquid outlet temperature T to Q , the heating rate of the element. 2.0 A process follows the differential equation model: x dt dx y dt dy dt y d dt y d 3 2 4 8 5 2 2 3 3 + = + + + . Find the transfer function relating Y(s) to X(s). Both y and x are deviation variables with zero initial values. 3.0 Exercise 4.5 4.0 A stirred tank reactor is operated with a feed mixture containing reactant A at a mass
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Unformatted text preview: concentration c Ai . The feed flow rate is w i , as shown below in the drawing. Under certain conditions the system operates according to the model ( ) A A Ai i A i Vkc wc c w dt Vc d w w dt V d ! " " = " = ) ( Derive transfer functions for the outlet concentration c A with respect to (a) c Ai , and (b) w i . Assume that w remains equal to w i for both parts (a) and (b). OPTIONAL: 5.0 Exercise 4.3 Note : Equation (2-45) is d( ! V) dt = w i " w Equation (2-46) is dT dt = w i ! V T i " T ( ) + Q V ! C Eq. (2-46) has a typo in the textbook; use the equation given above instead. Hint : Applepolsher obtained the wrong answer because he did not notice that = V f (show that this indeed the mistake he made)....
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