Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
Which polynomial related to a pair of poles would yield a 2% settling approximately 0.5 seconds? (a) (s+8)² (b) (s+4)² (c) (s+4)² + (4)² (d) (s+12)² + (8)²

Which polynomial related to a pair of poles would yield a 2% settling approximately 0.5 seconds? (a) (s+8)² (b) (s+4)² (c) (s+4)² + (4)² (d) (s+12)² + (8)²

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
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
See similar textbooks
icon
Related questions
Question
The image presents two questions related to control systems and polynomial functions. Here is a transcription and analysis for educational purposes: --- **Question:** Which polynomial related to a pair of poles would yield a 2% settling time of approximately 0.5 seconds? **Options:** a) \((s + 8)^2\) b) \((s + 4)^2 + (8)^2\) c) \((s + 4)^2 + (4)^2\) d) \((s + 12)^2 + (8)^2\) --- **Question:** Which polynomial related to a pair of poles would yield a percent overshoot of approximately 5%? **Options:** a) \((s + 8)^2\) b) \((s + 4)^2 + (8)^2\) c) \((s + 4)^2 + (4)^2\) d) \((s + 12)^2 + (8)^2\) --- ### Explanation for Educational Context: In control systems, polynomial functions are used to describe the behavior of poles, which directly influence the system's response characteristics such as settling time and overshoot. 1. **Settling Time**: The time it takes for a system to settle within a certain percentage of the final value. Poles located closer to the origin in the s-plane generally lead to faster system responses. 2. **Percent Overshoot**: This is a measure of how much the peak level of the response exceeds the final steady-state value, relative to that value, expressed as a percentage. Understanding the placement and effects of poles can help in designing systems with desired dynamic properties. When analyzing the given polynomials, one should consider the real and imaginary parts of the poles and how these relate to damping, frequency, and system response.
Transcribed Image Text:The image presents two questions related to control systems and polynomial functions. Here is a transcription and analysis for educational purposes: --- **Question:** Which polynomial related to a pair of poles would yield a 2% settling time of approximately 0.5 seconds? **Options:** a) \((s + 8)^2\) b) \((s + 4)^2 + (8)^2\) c) \((s + 4)^2 + (4)^2\) d) \((s + 12)^2 + (8)^2\) --- **Question:** Which polynomial related to a pair of poles would yield a percent overshoot of approximately 5%? **Options:** a) \((s + 8)^2\) b) \((s + 4)^2 + (8)^2\) c) \((s + 4)^2 + (4)^2\) d) \((s + 12)^2 + (8)^2\) --- ### Explanation for Educational Context: In control systems, polynomial functions are used to describe the behavior of poles, which directly influence the system's response characteristics such as settling time and overshoot. 1. **Settling Time**: The time it takes for a system to settle within a certain percentage of the final value. Poles located closer to the origin in the s-plane generally lead to faster system responses. 2. **Percent Overshoot**: This is a measure of how much the peak level of the response exceeds the final steady-state value, relative to that value, expressed as a percentage. Understanding the placement and effects of poles can help in designing systems with desired dynamic properties. When analyzing the given polynomials, one should consider the real and imaginary parts of the poles and how these relate to damping, frequency, and system response.
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Root Locus
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.
Similar questions
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,
SEE MORE TEXTBOOKS