### Analyzing Feedback Control System Stability Using the Routh-Hurwitz Criterion**Problem Statement:**Given the following feedback control system, apply the Routh-Hurwitz criterion of stability to:a) Find the range of \( K \) that keeps the system stable.b) Find the value of \( K \) that makes the system oscillate.**System Block Diagram:**1. **Forward Path Transfer Function:** - The signal \( R(s) \) enters a summing junction (+), and then passes through a block containing the gain \( K \). - The output from this block then goes through another summing junction (+), and the result is input to a block with the transfer function \( \frac{10}{s(s^2 + 5s + 6)} \). The output of this block is the system output \( C(s) \).2. **Feedback Path:** - The output \( C(s) \) is passed through a block with the transfer function \( \frac{s}{5} \). - The output from this block is fed back to the second summing junction (-), where it is subtracted from the input signal.3. **Explanation of Transfer Functions in the System:** - The signal travels from \( R(s) \) to the first summing junction. - From the summing junction, the signal is amplified by a factor of \( K \). - The amplified signal is then processed by the transfer function \( \frac{10}{s(s^2 + 5s + 6)} \) before reaching the output \( C(s) \). - Part of the output \( C(s) \) is fed back through the transfer function \( \frac{s}{5} \), and the resulting signal is subtracted from the original input signal in the feedback loop.### Steps to Analyze Using Routh-Hurwitz Criterion:1. **Establish the Characteristic Equation:** - Simplify the block diagram and derive the characteristic equation of the closed-loop system.2. **Form the Routh Array:** - Construct the Routh array from the coefficients of the characteristic polynomial. - Ensure all elements in the first column of the Routh array are positive for stability.3. **Determine Ranges of \( K \):** - Solve the inequalities resulting from the Routh array analysis to determine the range of \( K \

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Given the following feedback control system, apply the Routh-Hurwitz criterion of stability to, a) Find the range of K that keeps the system stable, b) Find the value of K that makes the system oscillate. C(s) R(s) + K 10 s(s²+5s + 6)

Given the following feedback control system, apply the Routh-Hurwitz criterion of stability to, a) Find the range of K that keeps the system stable, b) Find the value of K that makes the system oscillate. C(s) R(s) + K 10 s(s²+5s + 6)

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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