# A control system described by a differential equation?

A system is described by the differential equation

y^(4)+y^(3)+ 5y^(2)+ 7y^(1)+y=u^(3)+ 2u^(2)+ 3u^(1)+ 7u.

Find the transfer function Y(s)/U(s) (Assume zero initial conditions).

Update:

I just realized that the equation is a little confusing and should read

y^(IIII)+y^(III)+ 5y^(II)+ 7y^(I)+y=u^(III)+ 2u^(II)+ 3u^(I)+ 7u

### 2 Answers

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- VamanLv 71 year agoFavourite answer
Use the Laplace transforms. I guess the answer will be

y(s)(s^4+s^3+5s^2+7s+1)=u(s)(s^3+2s^2+3s+7)

This gives

y(s)/u(s)=(s^3+2s^2+3s+7)/(s^4+s^3+5s^2+7s+1)

- rotchmLv 71 year ago
This doesnt require any maths really. Its just "plug & play"; Just evaluate the Laplace transform of each side (a recipe, no calculations) to get Y(s) & U(s) and divide them.

For instance, whats the Laplace of y^(4) ?

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