Second-Order System Transfer Function
8 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the damping ratio of the second order system in the given example?

  • 0.25
  • 0.5 (correct)
  • 1
  • 0.75
  • What is the un-damped natural frequency of the second order system in the given example?

  • 4 rad/sec
  • 3 rad/sec
  • 1 rad/sec
  • 2 rad/sec (correct)
  • What is the general transfer function of a second order system?

  • C(s) = R(s) / (s + 2ζωn s + ωn2)
  • C(s) = R(s) / (s + 2ζωn + ωn2)
  • C(s) = R(s) / (s + ζωn + ωn2)
  • C(s) = R(s) / (s + ζωn s + ωn2) (correct)
  • What are the two poles of the second order system in the given example?

    <p>-ωnζ + ωn√(ζ2 - 1) and -ωnζ - ωn√(ζ2 - 1)</p> Signup and view all the answers

    What does the damping ratio (ζ) represent in a second order system?

    <p>The degree of resistance to change in the system output</p> Signup and view all the answers

    What is the characteristic of an overdamped second order system?

    <p>Two real distinct poles</p> Signup and view all the answers

    What is the physical significance of ωn in a second order system?

    <p>The frequency of oscillation of the system without damping</p> Signup and view all the answers

    What is the condition for a second order system to be overdamped?

    <p>ζ &gt; 1</p> Signup and view all the answers

    Study Notes

    Second-Order System Transfer Function

    • A general second-order system is characterized by the transfer function: C(s) = ωn² / (s² + 2ζωn s + ωn²)

    Un-damped Natural Frequency (ωn)

    • ωn is the un-damped natural frequency of the second-order system
    • ωn is the frequency of oscillation of the system without damping

    Damping Ratio (ζ)

    • ζ is the damping ratio of the second-order system
    • ζ is a measure of the degree of resistance to change in the system output

    Example: Determining ωn and ζ

    • Given a second-order system transfer function: C(s) = 4 / (s² + 2s + 4)
    • By comparing with the general 2nd order transfer function, we can determine: ωn² = 4 => ωn = 2 rad/sec, and 2ζωn = 2 => ζωn = 1 => ζ = 0.5

    System Poles

    • The two poles of the system are: -ωnζ ± ωn √(ζ² - 1)

    System Categorization Based on ζ

    • According to the value of ζ, a second-order system can be categorized into four types:
    • Overdamped: when the system has two real distinct poles (ζ > 1)

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Related Documents

    Second Order System PDF

    Description

    Understand the characteristics of a general second-order system through its transfer function, including undamped natural frequency and damping ratio.

    More Like This

     Állapotmodell és átviteli függvény
    18 questions
    Klasyfikacja układów regulacji
    11 questions
    Control Systems and Z-Transforms Quiz
    34 questions
    Use Quizgecko on...
    Browser
    Browser