4. A chemical process has the overall transfer function: Y'(s) G'(s) 10 X(s) (30s +16s+2) a) Classify this second order transfer function (undamped, overdamped, underdamped, etc., and stable or unstable). b) Find the response y'(t) if the system is subjected to a step function increase at time t = 0 in x'(t) of magnitude M = 2.0. c) Plant engineers are disappointed in the system time response and have decided to install a lead-lag unit to the input in hopes of speeding up the response time. The new transfer function is: G(S)= Y'(s) X(s) 10(+1) (30s+16s+2) == (T₁₂s+1)G'(s) Find the new response ynew(t) in terms of ta (leave ta as a variable), if the system is subjected to the same step function increase at time t = 0 in x'(t) of magnitude M = 2.0. d) Both an inverse response and an overshoot would ruin product output. If you want the system to approach new steady state as fast as possible what value of t₂ would you suggest? e) Compare the original response as a function of time to that of the new response with the lead-lag [i.e., zero in numerator, and the value you choose in part e)] by graphing both responses in Excel. Has the response improved?
4. A chemical process has the overall transfer function: Y'(s) G'(s) 10 X(s) (30s +16s+2) a) Classify this second order transfer function (undamped, overdamped, underdamped, etc., and stable or unstable). b) Find the response y'(t) if the system is subjected to a step function increase at time t = 0 in x'(t) of magnitude M = 2.0. c) Plant engineers are disappointed in the system time response and have decided to install a lead-lag unit to the input in hopes of speeding up the response time. The new transfer function is: G(S)= Y'(s) X(s) 10(+1) (30s+16s+2) == (T₁₂s+1)G'(s) Find the new response ynew(t) in terms of ta (leave ta as a variable), if the system is subjected to the same step function increase at time t = 0 in x'(t) of magnitude M = 2.0. d) Both an inverse response and an overshoot would ruin product output. If you want the system to approach new steady state as fast as possible what value of t₂ would you suggest? e) Compare the original response as a function of time to that of the new response with the lead-lag [i.e., zero in numerator, and the value you choose in part e)] by graphing both responses in Excel. Has the response improved?
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
Related questions
Question
![4. A chemical process has the overall transfer function:
Y'(s)
G'(s)
10
X(s) (30s +16s+2)
a) Classify this second order transfer function (undamped, overdamped, underdamped, etc.,
and stable or unstable).
b) Find the response y'(t) if the system is subjected to a step function increase at time t = 0
in x'(t) of magnitude M = 2.0.
c) Plant engineers are disappointed in the system time response and have decided to install a
lead-lag unit to the input in hopes of speeding up the response time. The new transfer
function is:
G(S)=
Y'(s)
X(s)
10(+1)
(30s+16s+2)
== (T₁₂s+1)G'(s)
Find the new response ynew(t) in terms of ta (leave ta as a variable), if the system is
subjected to the same step function increase at time t = 0 in x'(t) of magnitude M = 2.0.
d) Both an inverse response and an overshoot would ruin product output. If you want the
system to approach new steady state as fast as possible what value of t₂ would you suggest?
e) Compare the original response as a function of time to that of the new response with the
lead-lag [i.e., zero in numerator, and the value you choose in part e)] by graphing both
responses in Excel. Has the response improved?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9b629bd-7b7c-4b52-85cc-46a95271ddc8%2F0702103b-4e09-46ba-8785-d2e3149ab097%2Fpetp1l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. A chemical process has the overall transfer function:
Y'(s)
G'(s)
10
X(s) (30s +16s+2)
a) Classify this second order transfer function (undamped, overdamped, underdamped, etc.,
and stable or unstable).
b) Find the response y'(t) if the system is subjected to a step function increase at time t = 0
in x'(t) of magnitude M = 2.0.
c) Plant engineers are disappointed in the system time response and have decided to install a
lead-lag unit to the input in hopes of speeding up the response time. The new transfer
function is:
G(S)=
Y'(s)
X(s)
10(+1)
(30s+16s+2)
== (T₁₂s+1)G'(s)
Find the new response ynew(t) in terms of ta (leave ta as a variable), if the system is
subjected to the same step function increase at time t = 0 in x'(t) of magnitude M = 2.0.
d) Both an inverse response and an overshoot would ruin product output. If you want the
system to approach new steady state as fast as possible what value of t₂ would you suggest?
e) Compare the original response as a function of time to that of the new response with the
lead-lag [i.e., zero in numerator, and the value you choose in part e)] by graphing both
responses in Excel. Has the response improved?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Introduction to Chemical Engineering Thermodynami…
Chemical Engineering
ISBN:
9781259696527
Author:
J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:
McGraw-Hill Education
Elementary Principles of Chemical Processes, Bind…
Chemical Engineering
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY
Elements of Chemical Reaction Engineering (5th Ed…
Chemical Engineering
ISBN:
9780133887518
Author:
H. Scott Fogler
Publisher:
Prentice Hall
Introduction to Chemical Engineering Thermodynami…
Chemical Engineering
ISBN:
9781259696527
Author:
J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:
McGraw-Hill Education
Elementary Principles of Chemical Processes, Bind…
Chemical Engineering
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY
Elements of Chemical Reaction Engineering (5th Ed…
Chemical Engineering
ISBN:
9780133887518
Author:
H. Scott Fogler
Publisher:
Prentice Hall
Industrial Plastics: Theory and Applications
Chemical Engineering
ISBN:
9781285061238
Author:
Lokensgard, Erik
Publisher:
Delmar Cengage Learning
Unit Operations of Chemical Engineering
Chemical Engineering
ISBN:
9780072848236
Author:
Warren McCabe, Julian C. Smith, Peter Harriott
Publisher:
McGraw-Hill Companies, The