Step response and peak response of a transfer function

In summary, the conversation discusses a problem involving a unity negative feedback system with a given open loop transfer function. The system input is a step function and the goal is to determine the damping factor. The document attached shows the necessary equations and how to solve for the damping constant, with the use of Matlab. It is mentioned that 10 cannot be used as the damping constant as it would result in an overdamped system. The correct damping constant is determined with the aid of software.
  • #1
mattbrrtt
11
0

Homework Statement



The open loop transfer function to a unity negative feedback system is given as:

G(s)=50/s(s+10)

Homework Equations



Unity feedback is used in this problem, and the system input is a step function.

Y(s)=50/s(s^2+10s+50)

The Attempt at a Solution



I have attached my work.

I think the difficulty I am having is determining the damping factor. 10 doesn't work.

Thank you.
 

Attachments

  • transfer.doc
    74 KB · Views: 238
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  • #2
In the document provided it shows you how to solve for dampening and natural frequency:

[tex] s^2 + 2 \zeta \omega_ns + \omega_n^2[/tex] and [tex] s^2 + 10s + 50[/tex]

simply match the coefficients.
 
  • #3
I was able to solve this problem with the aid of Matlab, but 10 can not be used as a damping constant, or the system would be overdamped, and not have the response that was needed. I was able to conclude the damping constant with the use of the software I have, but would like to be able to figure it out. I have corrected everything else in the attachment except the damping constant.

Thank you.
 

What is a step response of a transfer function?

A step response of a transfer function is the output of a system when a sudden change, or step, is applied to the input. This change is usually from zero to a steady-state value and the response is a plot of how the system reacts over time.

What is a peak response of a transfer function?

A peak response of a transfer function is the maximum output of a system in response to a step input. It can be represented as a single value or a peak-to-peak amplitude, depending on the type of system and input signal.

How are step and peak responses related in a transfer function?

The peak response of a transfer function is often used to determine the performance of a system, as it indicates how quickly and accurately the system reaches its steady-state value. The step response, on the other hand, shows the overall behavior and stability of the system.

What factors can affect the step and peak response of a transfer function?

The step and peak response of a transfer function can be influenced by various factors, such as the system's physical properties, input signal characteristics, and external disturbances. The design and parameters of the transfer function itself can also play a significant role in shaping the response.

How can the step and peak response of a transfer function be improved?

The step and peak response of a transfer function can be improved by optimizing the system's design and parameters, such as increasing the gain or bandwidth, reducing the settling time, and minimizing the effects of external disturbances. Feedback control systems can also be used to improve the overall performance of a system.

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