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C(s) Reduce the block diagram to a single transfer function, G(s) = R(S) 16 R(S) + 50 s+1 s+2 S ¹0 2 C(s)

C(s) Reduce the block diagram to a single transfer function, G(s) = R(S) 16 R(S) + 50 s+1 s+2 S ¹0 2 C(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
Section: Chapter Questions
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**Title: Reducing a Block Diagram to a Single Transfer Function** **Objective:** To convert the given block diagram into a single transfer function, represented as \( G(s) = \frac{C(s)}{R(s)} \). **Block Diagram Description:** 1. **Input Signal:** - The system begins with the input \( R(s) \). 2. **Summing Junction 1:** - Subtracts feedback from the loop, proceeding to the block with \( \frac{1}{s} \). 3. **Block 1:** - Transfer function of \( \frac{1}{s} \). 4. **Summing Junction 2:** - Combines the output from Block 1 with feedback from later in the system before entering the next block. 5. **Block 2:** - Transfer function of \( \frac{50}{s+1} \). 6. **Branching Points:** - Outputs from Block 2 branch into two pathways. - Pathway 1 enters the block with transfer function \( \frac{1}{5} \). - Pathway 2 enters a series of two blocks with transfer functions \( \frac{1}{s+2} \) and \( 2 \). 7. **Output Summing Junction:** - The outputs of both pathways combine, with feedback, leading to the next stage. 8. **Feedback Loop:** - Connects back to both Summing Junction 1 and the summing point between Pathway 1 and the feedback path. **Objective Conclusion:** The aim is to simplify this configuration to a single transfer function \( G(s) = \frac{C(s)}{R(s)} \), encompassing all the dynamic responses of the system into one relation.
Transcribed Image Text:**Title: Reducing a Block Diagram to a Single Transfer Function** **Objective:** To convert the given block diagram into a single transfer function, represented as \( G(s) = \frac{C(s)}{R(s)} \). **Block Diagram Description:** 1. **Input Signal:** - The system begins with the input \( R(s) \). 2. **Summing Junction 1:** - Subtracts feedback from the loop, proceeding to the block with \( \frac{1}{s} \). 3. **Block 1:** - Transfer function of \( \frac{1}{s} \). 4. **Summing Junction 2:** - Combines the output from Block 1 with feedback from later in the system before entering the next block. 5. **Block 2:** - Transfer function of \( \frac{50}{s+1} \). 6. **Branching Points:** - Outputs from Block 2 branch into two pathways. - Pathway 1 enters the block with transfer function \( \frac{1}{5} \). - Pathway 2 enters a series of two blocks with transfer functions \( \frac{1}{s+2} \) and \( 2 \). 7. **Output Summing Junction:** - The outputs of both pathways combine, with feedback, leading to the next stage. 8. **Feedback Loop:** - Connects back to both Summing Junction 1 and the summing point between Pathway 1 and the feedback path. **Objective Conclusion:** The aim is to simplify this configuration to a single transfer function \( G(s) = \frac{C(s)}{R(s)} \), encompassing all the dynamic responses of the system into one relation.
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Step 1: Simplifying the block diagram

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