Transfer Functions (General Question)

1. Apr 11, 2010

Burner

1. The problem statement, all variables and given/known data

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!

2. Apr 11, 2010

kentigens

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).

3. Apr 11, 2010

Burner

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.

4. Apr 11, 2010

Burner

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?