I need to identify two systems. Those are their Unit Step responses:

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I don't know, what order of the system that is. It could be second order system with zero in 0. Lecturer told me it was third order system, but then told me to solve it as second order system, so I'm a bit confused. More over we don't have materials for those systems, which would show us how to idnetify them. Lecturer told me to search it on the internet.

So I wonder whether anyone could give me some hint or better, if anyone could explain how to solve this or what kind of system those systems are.

I would welcome some good materials for this task.

  • $\begingroup$ Looks more like a system with a pole in the LHP rather than a system with a zero. $\endgroup$ Commented Mar 10, 2014 at 19:04
  • $\begingroup$ ok. If that is 1st order system with pole in LHP, it wouldn't oscilate. If that is 2nd order system with no zeros, only poles in LHP, it would have non zero signal in infinity. I didn't find any system, that would have value in infinity equal 0 and wouldn't have zero in 0. But then again, I didn't see much systems. So which for example would behave like that? $\endgroup$
    – user50222
    Commented Mar 10, 2014 at 21:32
  • $\begingroup$ I think a voltage regulator or any DC-DC converter can produce those signals. Try 3 poles and 1 zero first. $\endgroup$
    – user23972
    Commented Sep 30, 2016 at 8:48

1 Answer 1


Hint: It's a system with a damped oscillation of a single frequency sine wave, which also starts with an arbitrary phase. That should give you amplitude curve (damping), oscillation component (sinusoidal wave) and phase (starting point of the wave). If you can figure out the general form this system takes mathematically, it's a matter of plugging in the right values for those three.

Another hint: Don't overthink the system order. Think about what a first order system could look like. Do you need to go further? What could a second order system look like? Do you need to go further, etc. I guarantee you will stop pretty early.

Perhaps a more important hint: You're given a step response, not an impulse response, but there's a way to go from one to the other (what is it). Once you find the expression to describe this curve, going to impulse response should be very easy.

One last hint: Depending on how your subject is taught, this may help or this may hinder your attempts, so take this one with a grain of salt. If it confuses you, ignore it. My Linear Systems professor said this and made us repeat this out loud in class almost every lecture: Solutions to linear systems are always exponentials!


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