answers given 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 curvegiven in the question.T =t90-t30In(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≈ 26sNote that this short-cut method of fitting the FOPDT model is based on forcing agreementwith 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 thedata (since we're considering the two selected points only), but it can representative enoughto give a useful quick indication. 2. A process is subjected to a unit step change in input and responds in the way shownin Figure 1. Fit a first order plus dead-time model to this process and find the valuesof the model parameters.Figure Q215.014.814.614.414.214.013.813.613.4-13.2-13.0-12.812.612.412.212.00I10120304050Time (sec)1607080Figure 1: Model response to a step change.90100

Answered: Image /qna-images/answer/b85c0038-547f-4a0a-9094-808f54172bb2.jpg

Answered: 2. A process is subjected to a unit…

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

Chapter1: Introduction

Section: Chapter Questions

Problem 1.1P

See similar textbooks

Related questions

Question

answers given

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

Expert Solution

Step 1: Given data

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