Critical Damping

nth order filter with critical damping

 Description 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.
 Equations $y\left(s\right)=\frac{u\left(s\right)}{{\left(\frac{s}{\mathrm{\omega }}+1\right)}^{n}}$ $\mathrm{\alpha }=\left\{\begin{array}{cc}\sqrt{{2}^{\frac{1}{n}}-1}& \mathrm{normalized}\\ 1& \mathrm{otherwise}\end{array}$ $\mathrm{\omega }=2\pi \frac{f}{\mathrm{\alpha }}$

Connections

 Name Description Modelica ID $u$ Real input signal u $y$ Real output signal y

Parameters

 Name Default Units Description Modelica ID n $2$ Order of filter n f $1$ $\mathrm{Hz}$ Cut-off frequency f normalized $\mathrm{true}$ True (checked) means the filter is normalized such that the amplitude of the filter transfer function at the cut-off frequency f is 3dB normalized Initial Values No initialization Type of initialization initType ${x}_{0}$ $\mathrm{zeros}\left(n\right)$ Initial or guess values of states x_start ${y}_{0}$ $0$ Initial value of output (remaining states are in steady state) y_start

 Modelica Standard Library 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.