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The system given below is to have the following specifications: Kv = 10, = 0.5. Find the value of k₁ and kf required for the specifications to be met. R(S) kı 10 s (s+1) k+s C(s)

The system given below is to have the following specifications: Kv = 10, = 0.5. Find the value of k₁ and kf required for the specifications to be met. R(S) kı 10 s (s+1) k+s 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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The system given below is to have the following specifications: \( K_v = 10 \), \( \zeta = 0.5 \). Find the value of \( k_1 \) and \( k_f \) required for the specifications to be met. **Block Diagram Description:** - The input to the system is \( R(s) \). 1. **Summing Junction 1:** - The incoming signal \( R(s) \) and feedback are summed here. - Positive input from \( R(s) \). - Negative feedback path from the output. 2. **Gain Block \( k_1 \):** - The output of the first summing junction is multiplied by \( k_1 \). 3. **Summing Junction 2:** - Takes the output from the \( k_1 \) block. - Has a negative feedback input from the output. 4. **Transfer Function Block:** - The signal is passed through a transfer function \(\frac{10}{s(s+1)}\). 5. **Output:** - The output of the transfer function is \( C(s) \). 6. **Feedback Path:** - The output \( C(s) \) is fed back through a gain block \( k_f \) multiplied by \( s \), creating a feedback loop to the second summing junction.
Transcribed Image Text:The system given below is to have the following specifications: \( K_v = 10 \), \( \zeta = 0.5 \). Find the value of \( k_1 \) and \( k_f \) required for the specifications to be met. **Block Diagram Description:** - The input to the system is \( R(s) \). 1. **Summing Junction 1:** - The incoming signal \( R(s) \) and feedback are summed here. - Positive input from \( R(s) \). - Negative feedback path from the output. 2. **Gain Block \( k_1 \):** - The output of the first summing junction is multiplied by \( k_1 \). 3. **Summing Junction 2:** - Takes the output from the \( k_1 \) block. - Has a negative feedback input from the output. 4. **Transfer Function Block:** - The signal is passed through a transfer function \(\frac{10}{s(s+1)}\). 5. **Output:** - The output of the transfer function is \( C(s) \). 6. **Feedback Path:** - The output \( C(s) \) is fed back through a gain block \( k_f \) multiplied by \( s \), creating a feedback loop to the second summing junction.
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