Transfer function of a second order system

In summary, the conversation revolved around a question involving G(s) in two different questions. The person had successfully completed question 1.18 and understood it, but was confused about G(s) in question 2.5. They had asked their lecturer, who initially spent 10 minutes trying to figure it out before concluding that it was a mistake and should have been the same as in question 1.18. The person was seeking confirmation on this issue.
  • #1
influx
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Homework Statement


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Homework Equations


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The Attempt at a Solution


I have done question 1.18 and I understand it completely. However, for question 2.5, I do not understand how they got G(s)? Why isn't the G(s) in question 2.5 the same as G(s) at the bottom of question 1.18? I asked my lecturer and she spent about 10 minutes trying to figure out and eventually said that the answer for question 2.5 is a mistake and that G(s) should've been as in question 1.18. I just want to make sure whether she is right in saying this? Is G(s) in the answer for question 2.5 indeed a mistake? She seemed a bit unsure hence why I am checking on here. The same method (like question 2.5) has been used to calculate transfer function in subsequent questions.

Thanks
 
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  • #2
It's obvious - G(s) should be the same in 1.18 and 2.5.
She probably seemed befuddled trying to figure out how she could have made the mistake.
 
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What is a transfer function and why is it important?

A transfer function is a mathematical representation that describes the relationship between the input and output of a system. In the context of a second order system, it is a ratio of the output to the input of the system, and it allows us to analyze the behavior of the system in terms of its frequency response. It is important because it helps us understand how a system will respond to different inputs and allows us to design and tune the system for desired performance.

How is the transfer function of a second order system derived?

The transfer function of a second order system is typically derived using the Laplace transform. The system's differential equation in the time domain is transformed into an algebraic equation in the s-domain, where s is a complex variable representing frequency. The transfer function is then obtained by taking the ratio of the output to the input in the s-domain.

What are the key parameters of a second order system's transfer function?

The key parameters of a second order system's transfer function are the natural frequency (ωn), damping coefficient (ζ), and gain (K). The natural frequency determines how quickly the system responds to a change in the input, the damping coefficient affects the amount of overshoot and settling time, and the gain determines the overall magnitude of the system's response.

What is the significance of the natural frequency and damping coefficient in a second order system's transfer function?

The natural frequency and damping coefficient are important because they determine the behavior of a second order system. A higher natural frequency results in a faster response, while a higher damping coefficient reduces the system's overshoot and settling time. These parameters can be adjusted to achieve specific performance goals for the system.

How can the transfer function of a second order system be used to analyze its stability?

The transfer function of a second order system can be used to analyze its stability by examining the location of its poles in the s-plane. If the poles are in the left half of the s-plane, the system is stable. If the poles are on the imaginary axis or in the right half of the s-plane, the system is unstable. Additionally, the damping coefficient can also provide information about stability - a higher damping coefficient results in a more stable system.

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