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I'm looking for good online resources for 2nd order system dynamics. Any recommendations?

I'm looking for stuff that ideally includes discussion of Q, damping ratio, overshoot, bode plots, for systems with transfer functions of

$$ H_1(s) = \frac{1}{\tau_2^2 s^2 + \tau_1 s + 1} $$

$$ H_2(s) = \frac{\tau_1 s + 1}{\tau_2^2 s^2 + \tau_1 s + 1} $$

and

$$ H_3(s) = \frac{s}{\tau_2^2 s^2 + \tau_1 s + 1} $$


edit: I've done change of variables to rewrite as

$$ H_1(\sigma) = \frac{1}{\sigma^2 + 2\zeta\sigma + 1} $$

$$ H_2(\sigma) = \frac{2\zeta\sigma + 1}{\sigma^2 + 2\zeta\sigma + 1} $$

and

$$ H_3(\sigma) / \omega_0 = \frac{\sigma}{\sigma^2 + 2\zeta\sigma + 1} $$

where $\sigma = \tau_2 s = s / \omega_0$, $\omega_0 = 1 / \tau_2$, and $\zeta = \tau_1 / 2\tau_2$ to normalize out the time scaling factor and end up with a transfer function of the single variable $\zeta$ (damping factor) which I think is the conventional treatment.

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  • $\begingroup$ Community Wiki. $\endgroup$
    – anonymous
    Commented Oct 1, 2010 at 18:00
  • $\begingroup$ done. (.......) $\endgroup$
    – Jason S
    Commented Oct 1, 2010 at 18:20

1 Answer 1

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Searching in Google itself gives you a great deal of information. I got this link which explains has the content which you need.

Next, [redacted: inappropriate link to pirated content] is an excellent source for those who are in need of books online.

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  • $\begingroup$ the problem is there are a lot of mediocre pages out there, and I'm looking for a good one; most of the sources of this type of information just have the transfer function with 1 in the numerator and something in the denominator. (having said that, the one you posted isn't too bad) $\endgroup$
    – Jason S
    Commented Oct 1, 2010 at 18:23

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