# Thread: determining the unit ramp response of a transfer function

1. ## determining the unit ramp response of a transfer function

Hello so I have a question about determining some values analytically for the response of a transfer function or a lag of the form: 1/(ts+1) where t is just a variable. I know what the response will look like. I know its initial value will be 0 but I am having a problem figuring out what its final value will be and also where the pole will be in terms of the variable. I know for instance that I can take the limit of that same transfer function at inf and 0 to find initial and final values for its step response. Also I know that t will be roughly at the location of the pole of the transfer function. Can I use the same principles with a ramp response?

2. ## Re: determining the unit ramp response of a transfer function

if I understand you have have a system transfer function

$H(s) = \dfrac{\alpha}{s+\alpha},~\alpha = \dfrac 1 u$

(I changed $t$ to $u$ to avoid confusion with the time variable $t$ )

you input a unit ramp and wish to determine the output in the time domain.

Is this correct?

$X(t) = t,~0 \leq t$

$X(s) = \dfrac {1}{s^2}$

$Y(s) = \dfrac{\alpha}{s^2(s+\alpha)}= \dfrac{1}{s^2}-\dfrac{1}{\alpha s}+\dfrac{1}{\alpha (\alpha +s)}$

by inspection we can see the output is a unit ramp minus a unit step scaled by $\dfrac{1}{\alpha}$ plus a damped exponential scaled by $\dfrac{1}{\alpha}$

$y(t) = t + \dfrac{1}{\alpha}\left(e^{-\alpha t}-1\right)$

It should be easy enough to plug some values of $t$ in

Have I misunderstood the question?

3. ## Re: determining the unit ramp response of a transfer function

No you haven't misunderstood. Thanks for making the substitution that helped. Thanks for the help! Assuming that 1/s^2 is the Laplace of the ramp function?

4. ## Re: determining the unit ramp response of a transfer function

Originally Posted by vysero
Assuming that 1/s^2 is the Laplace of the ramp function?
yes

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# ramp response of a transfer function

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