Coursework : Root Locus

 Quote by CEL When is$$Ke^{-\alpha t}$$ equal to 0.01K or 0.02K?
$$\frac{-ln(0.01)}{\alpha}$$

 Quote by CEL Obtain the time response and verify how long does it take from 10% to 90% of ss.
I have got the steady state value but how do I get the time response ? Laplace Transform ? Isn't there some shorter method ? This is because I have got a zero as well in the PI controller so the general formulae doesnt work..Any approximation ? I dont want to go for any tedious method...

 Quote by Altairs I have got the steady state value but how do I get the time response ? Laplace Transform ? Isn't there some shorter method ? This is because I have got a zero as well in the PI controller so the general formulae doesnt work..Any approximation ? I dont want to go for any tedious method...
You must take the inverse tarnsform of the response Y(s). Don't forget that the transform of the step is 1/s, so the s in the denominator cancels the s in the numerator.

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