In the figure, are the two processes described by G1 and G2 interacting processes? Why or why not?
In the figure, are the two processes described by G1 and G2 interacting processes? Why or why not?
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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![**Title: Interaction of Processes in Control Systems**
**Question:**
6. In the figure, are the two processes described by \( G_1 \) and \( G_2 \) interacting processes? Why or why not?
**Description:**
This is a block diagram illustrating the interaction between control processes. The system features:
- **Block \( G_1(s) \):**
\[
G_1(s) = \frac{K_1}{\tau_1 s + 1}
\]
Input: \( U_1(s) \)
Output: \( Y_1(s) \)
- **Block \( G_2(s) \):**
\[
G_2(s) = \frac{K_2}{s}
\]
Input: \( U_2(s) \)
Output: \( Y_2(s) \)
- **Block \( G_3(s) \):**
\[
G_3(s) = \frac{K_3}{\tau_2^2 s^2 + 2\zeta \tau_2 s + 1}
\]
Input: \( U_3(s) \)
Output contributes to \( Y_2(s) \)
- The final output, \( Y_f(s) \), is the sum of \( Y_1(s) \) and \( Y_2(s) \):
\[
Y_f = Y_1 + Y_2
\]
**Analysis:**
To determine if the processes are interacting, we consider how the outputs \( Y_1(s) \) and \( Y_2(s) \) are generated. If \( G_1 \) and \( G_2 \) operate independently with no mutual influence, they are non-interacting processes. If some parameters or outputs of one process affect the other, they are interacting processes. In this diagram, \( G_1(s) \) and \( G_2(s) \) are arranged in parallel and supply signals directly to the summation point without affecting each other internally, indicating no interaction at this level.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe5d528f6-f704-4253-8470-44f2fbc0de86%2F4e57bae9-db7a-4e8a-b000-5e3ebec81491%2F2gdvky_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Interaction of Processes in Control Systems**
**Question:**
6. In the figure, are the two processes described by \( G_1 \) and \( G_2 \) interacting processes? Why or why not?
**Description:**
This is a block diagram illustrating the interaction between control processes. The system features:
- **Block \( G_1(s) \):**
\[
G_1(s) = \frac{K_1}{\tau_1 s + 1}
\]
Input: \( U_1(s) \)
Output: \( Y_1(s) \)
- **Block \( G_2(s) \):**
\[
G_2(s) = \frac{K_2}{s}
\]
Input: \( U_2(s) \)
Output: \( Y_2(s) \)
- **Block \( G_3(s) \):**
\[
G_3(s) = \frac{K_3}{\tau_2^2 s^2 + 2\zeta \tau_2 s + 1}
\]
Input: \( U_3(s) \)
Output contributes to \( Y_2(s) \)
- The final output, \( Y_f(s) \), is the sum of \( Y_1(s) \) and \( Y_2(s) \):
\[
Y_f = Y_1 + Y_2
\]
**Analysis:**
To determine if the processes are interacting, we consider how the outputs \( Y_1(s) \) and \( Y_2(s) \) are generated. If \( G_1 \) and \( G_2 \) operate independently with no mutual influence, they are non-interacting processes. If some parameters or outputs of one process affect the other, they are interacting processes. In this diagram, \( G_1(s) \) and \( G_2(s) \) are arranged in parallel and supply signals directly to the summation point without affecting each other internally, indicating no interaction at this level.
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