In my class I'm in, our lecturer presented frequency response methods such as the nyquist plot and bode diagrams. Then when designing a lead compensator later, he said one of the specifications should be a steady state error to a step response below a certain value. Why do we consider step responses? I have been reading ogata's book and the first sentence in the frequency response chapter says that frequency response is specifically for the case of sinusoidal inputs.
It doesn't make sense to me to analyse the frequency response over a large range of $\omega$ either since a non repeating signal has an infinite frequency anyway?
If someone could explain this it would be helpful, I can't post my lecture slides here, but I hope I was clear enough.