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Given the following feedback control system, use block diagram algebra to reduce the system to a single block, this is, find the overall transfer function G(s) = C(s)/R(s)

Given the following feedback control system, use block diagram algebra to reduce the system to a single block, this is, find the overall transfer function G(s) = C(s)/R(s)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Given the following feedback control system, use block diagram algebra to reduce the system to a single block. This is, find the overall transfer function G(s) = C(s)/R(s). ![Control System Diagram] The diagram represents a complex feedback control system, comprised of several blocks and summing junctions, which are detailed as follows: 1. The system has an input R(s) on the left side. 2. The first block has a transfer function of \(\frac{1}{s}\). 3. The output of the first block is fed into a summing junction where it is combined with the feedback signal. 4. The resultant signal is then processed by a block with a transfer function of \(\frac{K}{s^2}\). 5. The output from this block is fed into another summing junction. 6. One path from this summing junction leads to a block with a transfer function of \(3\), whose output is the system output \(C(s)\). 7. The other path from the summing junction goes into a feedback loop that includes a block with transfer function \(\frac{2}{5}\). 8. The feedback signal is further processed through a block with transfer function \(\frac{1}{s+1}\) before it is fed back to the first summing junction. The goal is to use block diagram algebra to reduce this complex feedback control system to a single block, thereby finding the overall transfer function G(s) = C(s)/R(s). This entails combining the individual transfer functions and properly accounting for the feedback elements of the system.
Transcribed Image Text:Given the following feedback control system, use block diagram algebra to reduce the system to a single block. This is, find the overall transfer function G(s) = C(s)/R(s). ![Control System Diagram] The diagram represents a complex feedback control system, comprised of several blocks and summing junctions, which are detailed as follows: 1. The system has an input R(s) on the left side. 2. The first block has a transfer function of \(\frac{1}{s}\). 3. The output of the first block is fed into a summing junction where it is combined with the feedback signal. 4. The resultant signal is then processed by a block with a transfer function of \(\frac{K}{s^2}\). 5. The output from this block is fed into another summing junction. 6. One path from this summing junction leads to a block with a transfer function of \(3\), whose output is the system output \(C(s)\). 7. The other path from the summing junction goes into a feedback loop that includes a block with transfer function \(\frac{2}{5}\). 8. The feedback signal is further processed through a block with transfer function \(\frac{1}{s+1}\) before it is fed back to the first summing junction. The goal is to use block diagram algebra to reduce this complex feedback control system to a single block, thereby finding the overall transfer function G(s) = C(s)/R(s). This entails combining the individual transfer functions and properly accounting for the feedback elements of the system.
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