- #1
VinnyCee
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Homework Statement
Find the unit step response of the transfer function...
a) [tex]G(s)\,=\,\frac{4}{s\,+\,4}[/tex]
b) [tex]G(s)\,=\,\frac{2}{0.2s\,+\,1}[/tex]
Homework Equations
General first order step response equation...
[tex]C(s)\,=\,R(s)\,G(s)\,=\,\frac{a}{s(s\,+\,a)}[/tex], where [tex]R(s)\,=\,\frac{1}{s}[/tex]
then do an inverse Laplace transform...
[tex]c(t)\,=\,1\,-\,e^{-at}[/tex]
The Attempt at a Solution
Part a) is simple enough. I just plugged into formula above and got [tex]c(t)\,=\,1\,-\,e^{-4t}[/tex]
However, part b) is where I am confused. To get the G(s) into the form needed (i.e. ~ [itex]\frac{a}{s\,+\,a}[/itex]), I divided both the numerator and denominator by 0.2...
[tex]G(s)\,=\,\frac{2}{0.2s\,+\,1}\,=\,\frac{10}{s\,+\,5}\,=\,2\left(\frac{5}{s\,+\,5}\right)[/tex]
But now the form is not exactly as needed in the first order system equations. What do I do?
I tried taking out a 2 from the numerator, and got an answer, just not sure if it's right though.
Is this right for part b)...
[tex]c(t)\,=\,2\,\left[1\,-\,e^{-5t}\right][/tex]
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