Y(s) U(s) Зе-2s 1. Consider the transfer function: G(s) 8s+1 (a) What is the steady-state gain? (b) What is the time constant? (c) If U(s) = 2.5/s, what is the value of the output y(t) as t → 0? (d) For the same input, what is the value of the output y(t) when t=10? What is the output when expressed as a fraction of the new steady-state value? (e) If U(s) = (1-e*)/s (the expression for a rectangular pulse), what is the value of the output y(t) as t → 0?
Y(s) U(s) Зе-2s 1. Consider the transfer function: G(s) 8s+1 (a) What is the steady-state gain? (b) What is the time constant? (c) If U(s) = 2.5/s, what is the value of the output y(t) as t → 0? (d) For the same input, what is the value of the output y(t) when t=10? What is the output when expressed as a fraction of the new steady-state value? (e) If U(s) = (1-e*)/s (the expression for a rectangular pulse), what is the value of the output y(t) as t → 0?
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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i need help withh all the parts of this question
![1. Consider the transfer function:
\[
G(s) = \frac{Y(s)}{U(s)} = \frac{3e^{-2s}}{8s+1}
\]
(a) What is the steady-state gain?
(b) What is the time constant?
(c) If \(U(s) = \frac{2.5}{s}\), what is the value of the output \(y(t)\) as \(t \to \infty\)?
(d) For the same input, what is the value of the output \(y(t)\) when \(t=10\)? What is the output when expressed as a fraction of the new steady-state value?
(e) If \(U(s) = \frac{(1-e^{-s})}{s}\) (the expression for a rectangular pulse), what is the value of the output \(y(t)\) as \(t \to \infty\)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8ed819a1-7cc7-4b35-b605-cdaaef8761fd%2Fadda5a45-d2c9-4ae6-8301-8656c6797008%2Fe51t0a9_processed.png&w=3840&q=75)
Transcribed Image Text:1. Consider the transfer function:
\[
G(s) = \frac{Y(s)}{U(s)} = \frac{3e^{-2s}}{8s+1}
\]
(a) What is the steady-state gain?
(b) What is the time constant?
(c) If \(U(s) = \frac{2.5}{s}\), what is the value of the output \(y(t)\) as \(t \to \infty\)?
(d) For the same input, what is the value of the output \(y(t)\) when \(t=10\)? What is the output when expressed as a fraction of the new steady-state value?
(e) If \(U(s) = \frac{(1-e^{-s})}{s}\) (the expression for a rectangular pulse), what is the value of the output \(y(t)\) as \(t \to \infty\)?
Expert Solution
Step 1
The given transfer function of the process is,
...... (1)
(a)
Comparing equation (1) with the transfer function, , where is steady state gain and is time constant of the system
Therefore, steady state gain,
(b)
Time constant of the system is,
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