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