homework5_f10

homework5_f10 - University of California, Davis Department...

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University of California, Davis Department of Chemical Engineering and Materials Science ECH 157 Process Dynamics and Control Ahmet Palazoglu HOMEWORK 5 Fall 2010 (60 points) 1. (10 pts) For the following process and the controller transfer functions, determine if the closed-loop system exhibits stability using the Bode Stability Criterion, + = + + + + = s s g s s s s s g c p 1 1 1 . 0 ) ( ; 1 4 2 3 1 2 ) ( 2 3 If the system is stable, determine the Gain Margin and the Phase Margin. Show your work clearly. 2. (10 pts) The following transfer function is given for a process: 1 3 6 2 1 ) ( 2 3 + + + = s s s s g p If a P controller is used with a gain of 10, show, using Nyquist Stability Criterion, that the system is unstable. What value of the gain would make this system stable? Show, again, using the Nyquist Stability Criterion. 3. (20 pts) An unstable exothermic reactor is modeled by the following transfer function: ) ( ) 1 )( 2 ( 1 ) ( s m s s s y + = A PI controller is chosen to stabilize the process. Using the Routh’s Criterion, find
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This note was uploaded on 04/01/2011 for the course ECH 157 taught by Professor Palagozu during the Spring '08 term at UC Davis.

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homework5_f10 - University of California, Davis Department...

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