solve parts d and e and f d in the picture, e and f are: e) The value of K when the root loci intersect the imaginary axis f) Ples the root loci for the closed loop system
solve parts d and e and f d in the picture, e and f are: e) The value of K when the root loci intersect the imaginary axis f) Ples the root loci for the closed loop system
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
Chapter6: Power Flows
Section: Chapter Questions
Problem 6.59P
Related questions
Question
solve parts d and e and f
d in the picture, e and f are:
e) The value of K when the root loci intersect the imaginary axis
f) Ples the root loci for the closed loop system
![**Q.3 For closed loop control system**
Given:
\[ G(s) = \frac{K(s+9)}{s(s^2 + 4s + 11)} \]
\[ H(s) = 1 \]
Tasks:
a) Determine the zeros and poles of the system
b) Determine the root loci on the real axis
c) Determine the asymptotes of the root loci
d) Find the value of \( K \) to keep the system stable
Instructions:
1. **Determine Zeros and Poles:**
- Zeros are the values of \( s \) that make \( G(s) = 0 \).
- Poles are the values of \( s \) that make the denominator of \( G(s) = 0 \).
2. **Determine Root Loci on the Real Axis:**
- Root loci are the paths that the roots of the characteristic equation follow in the s-plane as a single system parameter (typically \( K \)) varies from 0 to ∞.
3. **Determine Asymptotes of the Root Loci:**
- Asymptotes give the direction in which the root loci move as they tend to ∞.
- The formula for asymptotes is given by the centroid \( \sigma_a \) and angle \( \theta_a \):
\[
\sigma_a = \frac{\sum \text{poles} - \sum \text{zeros}}{n-m}
\]
where \( n \) is the number of poles and \( m \) is the number of zeros.
4. **Find the Value of \( K \) for System Stability:**
- The value of \( K \) should be such that all poles of the closed-loop system have negative real parts.
These tasks will help understand the stability and response characteristics of the given closed-loop control system.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Facf42901-461c-4318-866a-72a73aa9949c%2Faee92b52-dc91-44f7-8534-6ed151df5a31%2Fppxnb5o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Q.3 For closed loop control system**
Given:
\[ G(s) = \frac{K(s+9)}{s(s^2 + 4s + 11)} \]
\[ H(s) = 1 \]
Tasks:
a) Determine the zeros and poles of the system
b) Determine the root loci on the real axis
c) Determine the asymptotes of the root loci
d) Find the value of \( K \) to keep the system stable
Instructions:
1. **Determine Zeros and Poles:**
- Zeros are the values of \( s \) that make \( G(s) = 0 \).
- Poles are the values of \( s \) that make the denominator of \( G(s) = 0 \).
2. **Determine Root Loci on the Real Axis:**
- Root loci are the paths that the roots of the characteristic equation follow in the s-plane as a single system parameter (typically \( K \)) varies from 0 to ∞.
3. **Determine Asymptotes of the Root Loci:**
- Asymptotes give the direction in which the root loci move as they tend to ∞.
- The formula for asymptotes is given by the centroid \( \sigma_a \) and angle \( \theta_a \):
\[
\sigma_a = \frac{\sum \text{poles} - \sum \text{zeros}}{n-m}
\]
where \( n \) is the number of poles and \( m \) is the number of zeros.
4. **Find the Value of \( K \) for System Stability:**
- The value of \( K \) should be such that all poles of the closed-loop system have negative real parts.
These tasks will help understand the stability and response characteristics of the given closed-loop control system.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 3 images
Knowledge Booster
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 …
Electrical Engineering
ISBN:
9781305632134
Author:
J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:
Cengage Learning
Power System Analysis and Design (MindTap Course …
Electrical Engineering
ISBN:
9781305632134
Author:
J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:
Cengage Learning