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University of California, Davis
ECH 157  Process Dynamics and Control
Fall 2011
Homework Problem Set # 4
Assigned
: Wednesday, November 2.
Due
: Friday, November 11.
Reading Assignment
: Lecture notes, Chapters 7, 8, 10 and 11 of the textbook.
Instructions
: Please include your name on the ±rst 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 frst Four problems only
.
Required Problems:
1. A process is described by the transfer function
G
1
(
s
) =
K
(1

s
)(
τs
+ 1)
(a) Calculate and plot the response
y
(
t
)
to a step change in the input
u
(
t
)
of magnitude
M
, when
M
= 2
,
K
= 3
and
τ
= 3
.
(b) What would be the step response if the process also included a time delay, i.e.,
G
2
(
s
) =
e

2
s
G
1
(
s
)
?
(c) If a ±rstorder Pade approximation were used in place of the time delay, what transfer
function would approximate
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 Fall '08
 PALAGOZU

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