Can systems obeying a first-order transfer function (with no zeroes)exhibit an oscillatory response to a step change in an input?Will all systems with a transfer function that is second order andhigher exhibit an oscillatory response?Using the block diagram below, what is the transfer function betweenYıand U1?-. Using the block diagram below, what is the transfer function betweenYjand U3?5. Assuming K1, K2,T1 > 0 in the figure below, what qualitativefeatures do you anticipate in the response of Y1 to a unit step changein U1 (s) = 1/s? By qualitative features, comment on whether youexpect oscillations, an approach to a new steady state or a return tothe old steady state, exponential divergence, etc.

Answered: an systems obeying a first-order…

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

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Question

Can systems obeying a first-order transfer function (with no zeroes)
exhibit an oscillatory response to a step change in an input?
Will all systems with a transfer function that is second order and
higher exhibit an oscillatory response?
Using the block diagram below, what is the transfer function between
Yıand U1?
-. Using the block diagram below, what is the transfer function between
Yjand U3?
5. Assuming K1, K2,T1 > 0 in the figure below, what qualitative
features do you anticipate in the response of Y1 to a unit step change
in U1 (s) = 1/s? By qualitative features, comment on whether you
expect oscillations, an approach to a new steady state or a return to
the old steady state, exponential divergence, etc.

Expert Solution

Answer

1. No it can not show oscillatory behavior because when step change occurs the value of output reaches its ultimate value that is 63.2% when the time elapsed is equal to one time constant.

The response of 1 order system to step-change in the input is Y(t) = A(1 - e^{-t/ $τ$}) when t is greater than or equal to zero.

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