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# 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)

https://brainmass.com/engineering/electrical-engineering/control-systems-laplace-transformations-503799

#### Solution Preview

** Please see the attached file for the complete solution response **

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