Unformatted text preview: University of California, Davis
Department of Chemical Engineering & Materials Science
ECH 157 – Process Dynamics and Control
Fall 2011 – Quiz # 2
Instructions: This is a 30minute closedbook closednotes quiz. Please print your name on all
answer sheets, label the problems clearly and put them in the right order. Read all questions
carefully; answer them concisely and neatly. Point values for each problem are based on 10
points total for the quiz. Good Luck!!
Problem 1: The question has been raised whether an openloop unstable process can be
stabilized with a proportionalonly controller. Ysp Gp = K
1−τ s G c = Kc Y Fig.1
(a) [3 points] For the process and controller shown in Fig.1, find the range of Kc values that
yield a stable closedloop response. (Note that τ is positive.)
(b) [3 points] For K = 10 and τ = 20, find the value of Kc that yields a pole at s =  0.1. What
is the offset for these conditions?
(c) [4 points] Suppose that you had designed the controller neglecting the dynamics of the
measurement sensor. Would the controller still yield a stable closedloop response
when the sensor is in the loop? To check the "robustness" of your design, suppose that
the sensor dynamics can be modeled by the following transfer function:
1
Gm ( s ) =
τm +1
Find the general conditions on Kc and τm for stability if the system is as shown in Fig.2.
Show for τm = 5, that your value of Kc from part (b) does or does not still yield a stable
system. Ysp Gp = K
1−τ s G c = Kc Gm
Fig.2 Y ...
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 Fall '08
 PALAGOZU
 Kc, stable closedloop response

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