2. A process is subjected to a unit step change in input and responds in the way shown in Figure 1. Fit a first order plus dead-time model to this process and find the values of the model parameters. Figure Q2 15.0 14.8 14.6 14.4 14.2 14.0 13.8 13.6 13.4- 13.2- 13.0- 12.8 12.6 12.4 12.2 12.0 0 I 10 1 20 30 40 50 Time (sec) 1 60 70 80 Figure 1: Model response to a step change. 90 100

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Answered: 2. A process is subjected to a unit step change in input and responds in the way shown in Figure 1. Fit a first order plus dead-time model to this process and…

Introduction to Chemical Engineering Thermodynamics

8th Edition

ISBN: 9781259696527

Author: J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Publisher: McGraw-Hill Education

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steps how to reach these please

2. The idea was not to overcomplicate (after all, we are reading numbers from a graph)
the analysis but to find parameter values that make sense in terms of fitting the curve
given in the question.
T =
t90-t30
In(7)
; ta = t90 - Tln (10)
My (very rough) estimates are:
t30≈ 30s t90≈ 50s T≈ 0.5 * (5030) 10s ta 1.2 × 30 – 0.2 × 50≈ 26s
Note that this short-cut method of fitting the FOPDT model is based on forcing agreement
with the process data where it reaches 30% and 90% of its ultimate value.
It should be noted that this approximation doesn't necessarily give us the best fit to all the
data (since we're considering the two selected points only), but it can representative enough
to give a useful quick indication.

2. A process is subjected to a unit step change in input and responds in the way shown
in Figure 1. Fit a first order plus dead-time model to this process and find the values
of the model parameters.
Figure Q2
15.0
14.8
14.6
14.4
14.2
14.0
13.8
13.6
13.4-
13.2-
13.0-
12.8
12.6
12.4
12.2
12.0
0
I
10
1
20
30
40
50
Time (sec)
1
60
70
80
Figure 1: Model response to a step change.
90
100

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Step 1: Given data

$T r a n s f e r space f u n c t i o n space i s space G subscript p left parenthesis s right parenthesis space equals space fraction numerator Y left parenthesis s right parenthesis over denominator U left parenthesis s right parenthesis end fraction space equals space fraction numerator K subscript P e to the power of negative theta subscript P s end exponent over denominator Z subscript P S space plus 1 end fraction w h e r e space K subscript p space i s space g a i n space c o n s tan t theta subscript p space i s space d e a d space t i m e Z subscript p space i s space t i m e space c o n s tan t w e space h a v e space t o space f i n d space m o d e l space p a r a m e t e r s space n o w$

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