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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.

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We consider step responses because that's often a close approximation to the real-world behavior that we're designing for.

We consider frequency response because that makes the design easier -- doing design in the frequency domain is a nicely structured process that translates reasonably well to the time-domain world that we live in.

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  • $\begingroup$ concise and helpful. -NN $\endgroup$ Oct 17 '19 at 7:11
  • $\begingroup$ Thanks for the answer! Am I correct in assuming that a step response is simply a frequency response analysis for frequency = 0 since the frequency of a step input aperiodic signal is infinite? $\endgroup$
    – Jeygopi
    Oct 17 '19 at 9:45
  • $\begingroup$ @Jeygopi No, the frequency spectrum of a step response contains all frequencies. The Laplace transform of the step function is $1/s$. $\endgroup$
    – alephzero
    Oct 17 '19 at 12:37
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In linear analysis, any real input can be decomposed into a set of step inputs, and the response is just the superposition of the step responses.

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