Designing a Cruise Control System Controller with Root Locus Method | Coursework

[Altairs]

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 doesn't work..Any approximation ? I don't want to go for any tedious method...

 

[CEL]

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 doesn't work..Any approximation ? I don't 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.