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I am implementing a second order filter. It simulates hydraulic servo on an airplane. Its about 35-40 years old.

Second order filter to simulate servo

What confuses me is the notation. Like "2(.7)(52)S", what does it mean? If its just products, why then not write the resulting number?

I tried with doing 2704/(S^2+72.8S+2704), but it seem a bit slow.

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It might be written that way because the transfer function of a second order system is written as:

$$ h(s) = \frac{\omega_n^2}{s^2 + 2\zeta \omega_n s + \omega_n^2} $$

where $\zeta$ is the relative damping ratio and $\omega_n$ is the natural frequency.

So in your system

\begin{align} \zeta &= 0.7 \\ \omega_n &= 52 \end{align}

It's easy to see what the parameters are when it's written with $\zeta$ and $\omega_n$ factored out.

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