The Critical Damping component models an $n^{\mathrm{th}}$ order filter with critical damping characteristics and a cut-off frequency $f$. It is implemented as a series of first-order filters.

This filter type is especially useful to filter the input of an inverse model because the filter does not introduce any transients.

If the normalized parameter is $\mathrm{true}$ (the default), the filter is normalized such that the amplitude of the filter transfer function at the cut-off frequency $f$ is 3dB. Otherwise, the filter is not normalized, that is, it is unmodified. A normalized filter is usually much better for applications because filters of different orders are comparable, whereas non-normalized filters usually require the cut-off frequency to change when the order of the filter is changed.

Figures of the filter step responses are shown below.

$y\left(s\right)\=\frac{u\left(s\right)}{{\left(\frac{s}{\mathrm{\omega }}\+1\right)}^n}$

$\mathrm{\alpha }\=\{\begin{array}{cc}\sqrt{2^{\frac{1}{n}}-1}& \mathrm{normalized}\\ 1& \mathrm{otherwise}\end{array}$

$\mathrm{\omega }\=2\pi \frac{f}{\mathrm{\alpha }}$

The component described in this topic is from the Modelica Standard Library. To view the original documentation, which includes author and copyright information, click here.