# Control Systems and Laplace Transformations

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What is the step response of a system whose transfer function has a zero at -1, a pole at -2 and a gain factor of 2?

Determine the time response y(t) for the following transformed equation:

Y(S) = (s + 4)/(s(s + 1)(s + 2))

What is the unit step response of a system whose transfer function is given by:

P(s) = (S + 2) / (S + 0.5)(S + 4)

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Basically, to find unit response you have to multiply each of the transfer functions (unless otherwise specified) by the Laplace domain unit step response 1/s. Then you need to split this into its partial fractions from which you can find the inverse response in the time domain as you get a series of fractions which have unique inverse Laplace transforms.

a) A general transfer function can be written as

(please see the attached file).

Where (please see the attached file) is transfer gain and (please see the attached file) represent the zero's and represent the poles of the transfer function, (please see the attached file) represent the number of zero's and poles respectively

(please see the attached file)

As we are told that ...

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