Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
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)

Power System Analysis and Design (MindTap Course List)
Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Chapter12: Power System Controls
Section: Chapter Questions
Problem 12.2P
See similar textbooks
icon
Related questions
Question
100%
### 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 \
Transcribed Image Text:### 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 \
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Mason’s Rule & Block Diagram Reduction
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Power System Analysis and Design (MindTap Course …
Power System Analysis and Design (MindTap Course …
Electrical Engineering
ISBN:
9781305632134
Author:
J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS