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Obtain the transfer function of the block diagram below

Obtain the transfer function of the block diagram below

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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Obtain the transfer function of the block diagram below
The image depicts a block diagram representing a control system, with various transfer functions. Here's a detailed transcription and explanation: 1. **Inputs and Outputs:** - **R(s):** The input to the system. - **C(s):** The output of the system. 2. **Components and Connections:** - The input **R(s)** goes through a block with a gain of **4**. - A summation junction follows, where the output from the gain block is summed with feedback from the later stages of the system (negative feedback). - The result enters a block with the transfer function \(\frac{1}{s+1}\). - This output is then sent to another block with the transfer function \(\frac{s}{s^2+2}\). - It proceeds to a summation point where it is both added to a feedback loop and connected to the next block. - The subsequent block has a transfer function \(\frac{1}{s^2}\). - This is followed by another summation junction that adds feedback through a gain block of 50. - The system output is denoted by **C(s)**. 3. **Feedback Loops:** - A branch from the first summation junction sends the signal through a block with the transfer function \(\frac{4s+2}{s^2+2s+1}\), feeding back into the initial summation point. - Another feedback loop originates after the block with the transfer function \(\frac{s}{s^2+2}\), passing through a block with the transfer function \(\frac{s^2+2}{s^2+14}\) and returning to the second summation junction before the \(\frac{1}{s^2}\) block. This diagram illustrates a complex feedback control system with nested feedback loops and distinct transfer functions that collectively determine the system's behavior.
Transcribed Image Text:The image depicts a block diagram representing a control system, with various transfer functions. Here's a detailed transcription and explanation: 1. **Inputs and Outputs:** - **R(s):** The input to the system. - **C(s):** The output of the system. 2. **Components and Connections:** - The input **R(s)** goes through a block with a gain of **4**. - A summation junction follows, where the output from the gain block is summed with feedback from the later stages of the system (negative feedback). - The result enters a block with the transfer function \(\frac{1}{s+1}\). - This output is then sent to another block with the transfer function \(\frac{s}{s^2+2}\). - It proceeds to a summation point where it is both added to a feedback loop and connected to the next block. - The subsequent block has a transfer function \(\frac{1}{s^2}\). - This is followed by another summation junction that adds feedback through a gain block of 50. - The system output is denoted by **C(s)**. 3. **Feedback Loops:** - A branch from the first summation junction sends the signal through a block with the transfer function \(\frac{4s+2}{s^2+2s+1}\), feeding back into the initial summation point. - Another feedback loop originates after the block with the transfer function \(\frac{s}{s^2+2}\), passing through a block with the transfer function \(\frac{s^2+2}{s^2+14}\) and returning to the second summation junction before the \(\frac{1}{s^2}\) block. This diagram illustrates a complex feedback control system with nested feedback loops and distinct transfer functions that collectively determine the system's behavior.
Expert Solution
Step 1: Parameter needs to be calculated

For the given block diagram the transfer function of the system needs to be calculated by using the block diagram reduction technique.

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