Transfer Functions (General Question)

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Discussion Overview

The discussion revolves around the manipulation of a Laplace-transformed differential equation to derive the transfer function Y/X. Participants explore various approaches to isolate the transfer function while addressing the challenges posed by the presence of a constant term.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant presents a differential equation in the s-domain and expresses difficulty in isolating the transfer function Y/X due to the presence of a constant term g.
  • Another participant suggests moving the term g/s to the left side of the equation as a potential step towards isolating Y/X.
  • A further clarification indicates that the participant is not looking to revert to the time domain but rather to express Y/X solely in terms of g and s, highlighting a struggle with the manipulation of the equation.
  • One participant questions whether the constant term can be disregarded when deriving a useful transfer function, suggesting it may represent an initial condition.

Areas of Agreement / Disagreement

The discussion reflects uncertainty and differing opinions regarding the treatment of the constant term in the context of deriving the transfer function. There is no consensus on the best approach to isolate Y/X or the implications of the constant term.

Contextual Notes

Participants express limitations in their understanding of how to manipulate the equation effectively, particularly in relation to the role of the constant term and the need for partial fraction expansion.

Who May Find This Useful

Students or individuals studying control systems, transfer functions, or Laplace transforms may find this discussion relevant.

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Homework Statement



Just a generic question. If you have Laplace-transformed differential equation like s3Y + sY = g/s + X, where g is a constant, how do you handle manipulating the equation to get the transfer function Y/X? I feel like I've done this before, but I'm having a severe mental block.

2. The attempt at a solution

I've had some thoughts, but can't get anywhere with them. The constant g has nothing to do with X, so any attempts at factoring have been unsuccessful. I thought about some kind of superposition, but am not sure how that would work. Any guidance or hints would be greatly appreciated. Thanks!
 
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try move the g/s over to the left side of the equation. s3Y + sY - g*s-1 = X. Then do the transformation(use the table).
 
Thank you, but let me try to clarify a bit.

I don't require getting it back into the time domain. I'm just trying to find the transfer function with an output Y for an input X (in the s domain). To illustrate the problem I am encountering, simplifying you'll get Y(s4 + s2) = g + sX. The problem is that I need the quantity Y/X in terms of only g and s, and dividing both sides by X doesn't quite get the job done.

My thought is that there might be a partial fraction expansion or something I am missing.
 
Correct me if I'm wrong, but after a bit more reading and thinking: For the purposes of a useful transfer function, the constant term can be dropped because it is representative of an initial condition, right?
 

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