# Problems with inverse laplace transform

I'm having a problem getting an inverse laplace transofrm with what, I think, is a PD controller.
I have a function H(s)P(s), where H(s) is known and P(s) is the input
signal.
I have to get [h(t) CONVOLUTION p(t)], but I'm not able to do
InvLaplace [ s P(s)/((s+1)(s+50))]
because P(s) is unknown. The idea is to have the result in terms of p(t), p'(t), p''(t), etc.. Does Anyone know how to do this?
Thanks for any help
Jorge Guzman -------- al912912
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snipped-for-privacy@gmail.com wrote:

You don't need to involve P(s) to find h(t) -- you just need to get the inverse laplace transform of H(s).
Whose idea is it to get it in terms of p(t) and its derivatives?
--

Tim Wescott
Wescott Design Services
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the
Well, as I understood my professor, to solve the PD controller, you have to get the value of some mius (u0, u1, u2, ...), which you get from solving the equations
h(t) * p(t) = p(t) u0 + (-T) p'(t) u1 + ((-T)^2/2!) p''(t)u2 + ... + ((-T)^k/k!) p(kth)(t)uk
where p(t) is a kth degree polinomial.
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wrote:

My guess would be some differential equation prof who's trying to teach the relationship between laplace operators and differential equations. It's usually taught near the end of the semester.
Y/P=(s/[(s+1)(s+50)]). Multiply out the denominator, then cross multiply. Take it back to the time domain, knowing that X(s) transforms to x(t), sX(s) transforms to dx(t)/st, and s^2X(s) transforms to the second derivative. If you need to carry through initial conditions, the OP should go look it up in a diffeq text.
Scott
Scott
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oops, typo.
sX(s) <---> dx(t)/dt