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F11_ECH157_HW6 - University of California Davis Department...

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University of California, Davis Department of Chemical Engineering & Materials Science ECH 157 - Process Dynamics and Control Fall 2011 Homework Problem Set # 6 Assigned : Monday, November 21. Due : Wednesday, November 30 (at the beginning of lecture). Reading Assignment : Lecture notes, Chapters 9, 13 and 16 of the textbook. Instructions : Please include your name on the first page, label the problems clearly and put them in the right order, and staple your papers. You are required to work on, and submit your solutions to, the first five problems only . Required Problems: 1. The block diagram of a conventional feedback control system contains the following transfer functions: G c = K c parenleftbigg 1+ 1 5 s parenrightbigg , G v =1 , G m = 1 s +1 , G p = G d = 5 e - 2 s (10 s +1) (a) Plot the Bode diagram for the open-loop transfer function. (b) For what values of K c is the system stable? (c) If K c =0 . 2 , what is the phase margin? (d) What value of K c will result in a gain margin of 1.7? 2. Hot and cold liquids are mixed at the junction of two pipes. The temperature of the resulting mixture is to be controlled using a control valve on the hot stream. The dynamics of the
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