# What filter is this?

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.

\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.