Homework Help: Open Loop Response

Have you studied Laplace Transforms?

if so, then you can get the Laplace transform of the response by multiplying the transfer function of the system - which you have - with the LT of your input - a unit step, which has transform 1/s.

Then you need to take the inverse transform of this, which will yield the response (with respect to time). To do this you'll probably need to make use of a partial fraction expansion.

I don't know any good websites with examples of this though, sorry.

 

I got:

[tex]c(t) = u(t-T) - u(t-T)e^{-5(t-T)}[/tex]

where u(t) is the Heaviside step function, and the T is the constant 't' in your transfer function (I changed it to a big T since it's a bit dodgy to use the same symbol for two different things)

i.e. I took:

[tex]G(s) = e^{-Ts}\frac{5}{s+5}[/tex]

Though I didn't take much care over it, so I'm not sure I'm correct. The Heaviside function will almost certainly be in your answer though, since there's a time delay in the transfer function.

I'd recommend going and looking up the t-shifting theorem for Laplace Transforms.