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G2 R (b) G1 H 1 Given above block diagram, we know that H1 = 1, G1 = 2, G2 = s+2 please determine the transfer function C/R

G2 R (b) G1 H 1 Given above block diagram, we know that H1 = 1, G1 = 2, G2 = s+2 please determine the transfer function C/R

Introduction to Chemical Engineering Thermodynamics
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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### Block Diagram Analysis #### Description: The block diagram displays a feedback control system consisting of several components: 1. **Inputs and Outputs:** - \( R \): Reference input - \( C \): Output 2. **Blocks:** - \( G_1 = \frac{1}{s+2} \): Transfer function for block \( G_1 \). - \( G_2 = \frac{1}{s} \): Transfer function for block \( G_2 \). - \( H_1 = 1 \): Gain for block \( H_1 \). 3. **Operation:** - The signal \( R \) enters a summing junction where it is added to the feedback from \( H_1 \). - The sum is then processed by \( G_1 \). - The output from \( G_1 \) is split; one path goes through \( G_2 \) and re-enters the summing junction at the output side, while the other path is fed back through \( H_1 \) to the input summing junction. - The final summing junction combines the output from \( G_2 \) and the signal from \( G_1 \) to produce the output \( C \). #### Task: Given this block diagram, determine the overall transfer function \( \frac{C}{R} \). #### Solution: To find the transfer function, consider the loop structure and input/output relationships. Utilize block diagram reduction techniques to simplify and solve for the constant terms and functions. --- This educational explanation serves as a foundation for understanding feedback control systems, enabling the derivation of the transfer function using mathematical tools and techniques.
Transcribed Image Text:### Block Diagram Analysis #### Description: The block diagram displays a feedback control system consisting of several components: 1. **Inputs and Outputs:** - \( R \): Reference input - \( C \): Output 2. **Blocks:** - \( G_1 = \frac{1}{s+2} \): Transfer function for block \( G_1 \). - \( G_2 = \frac{1}{s} \): Transfer function for block \( G_2 \). - \( H_1 = 1 \): Gain for block \( H_1 \). 3. **Operation:** - The signal \( R \) enters a summing junction where it is added to the feedback from \( H_1 \). - The sum is then processed by \( G_1 \). - The output from \( G_1 \) is split; one path goes through \( G_2 \) and re-enters the summing junction at the output side, while the other path is fed back through \( H_1 \) to the input summing junction. - The final summing junction combines the output from \( G_2 \) and the signal from \( G_1 \) to produce the output \( C \). #### Task: Given this block diagram, determine the overall transfer function \( \frac{C}{R} \). #### Solution: To find the transfer function, consider the loop structure and input/output relationships. Utilize block diagram reduction techniques to simplify and solve for the constant terms and functions. --- This educational explanation serves as a foundation for understanding feedback control systems, enabling the derivation of the transfer function using mathematical tools and techniques.
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