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Consider system shown in Fig. 2. Show the equivalent transfer function T(s) = ( 2 Sketch every intermediate diagrams. And indicate how you move every block.

Consider system shown in Fig. 2. Show the equivalent transfer function T(s) = ( 2 Sketch every intermediate diagrams. And indicate how you move every block.

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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**Problem Statement:** Consider the system shown in Fig. 2. Show the equivalent transfer function \( T(s) = \frac{C(s)}{R(s)} = \frac{s^3 + 1}{2s^4 + s^3 + 2s^2} \). **Instruction:** Sketch every intermediate diagram and indicate how you move every block. **Block Diagram Explanation:** - The diagram is a feedback control system with multiple blocks. - **Forward Path:** - The system starts with an input \( R(s) \). - The first block in the forward path is a gain block with transfer function \( s \). - The output of the first block is connected to a second gain block with transfer function \( s \). - This output is then added with feedback using a summing junction. - The result is passed through another gain block with transfer function \( \frac{1}{s} \). - **Feedback Path:** - The output \( C(s) \) is fed back through a gain block with transfer function \( s \). - This output is then fed back into the summing junction, completing the feedback loop. **Summing Junctions:** - There are two summing junctions: - The first junction adds the system input \( R(s) \) with the feedback signal. - The second junction adds the output from the final gain block to complete the feedback loop. This setup is used to determine the overall transfer function by analyzing the signal flow and adjusting block positions if necessary.
Transcribed Image Text:**Problem Statement:** Consider the system shown in Fig. 2. Show the equivalent transfer function \( T(s) = \frac{C(s)}{R(s)} = \frac{s^3 + 1}{2s^4 + s^3 + 2s^2} \). **Instruction:** Sketch every intermediate diagram and indicate how you move every block. **Block Diagram Explanation:** - The diagram is a feedback control system with multiple blocks. - **Forward Path:** - The system starts with an input \( R(s) \). - The first block in the forward path is a gain block with transfer function \( s \). - The output of the first block is connected to a second gain block with transfer function \( s \). - This output is then added with feedback using a summing junction. - The result is passed through another gain block with transfer function \( \frac{1}{s} \). - **Feedback Path:** - The output \( C(s) \) is fed back through a gain block with transfer function \( s \). - This output is then fed back into the summing junction, completing the feedback loop. **Summing Junctions:** - There are two summing junctions: - The first junction adds the system input \( R(s) \) with the feedback signal. - The second junction adds the output from the final gain block to complete the feedback loop. This setup is used to determine the overall transfer function by analyzing the signal flow and adjusting block positions if necessary.
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