Output the input signal filtered with an n-th order filter with critical damping
This block defines the transfer function between the input u and the output y as an n-th order filter with critical damping characteristics and 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, since the filter does not introduce any transients.
If parameter normalized = true (default), the filter is normalized such that the amplitude of the filter transfer function at the cut-off frequency f is 1/sqrt(2) (= 3 dB). Otherwise, the filter is not normalized, i.e., it is unmodified. A normalized filter is usually much better for applications, since filters of different orders are "comparable", whereas non-normalized filters usually require to adapt the cut-off frequency, when the order of the filter is changed. Figures of the filter step responses are shown below. Note, in versions before version 3.0 of the Modelica Standard library, the CriticalDamping filter was provided only in non-normalzed form.
If transients at the simulation start shall be avoided, the filter should be initialized in steady state (e.g., using option initType=Modelica.Blocks.Types.Init.SteadyState).
The critical damping filter is defined as
α = if normalized then sqrt(2^(1/n) - 1) else 1 // frequency correction factor ω = 2*π*f/α 1 y = ------------- * u (s/w + 1)^n
|u||RealInput||Connector of Real input signal|
|y||RealOutput||Connector of Real output signal|
|n||Integer||2||Order of filter|
|normalized||Boolean||true||= true, if amplitude at f_cut is 3 dB, otherwise unmodified filter|
|initType||Init||Modelica.Blocks.Types.Init.NoInit||Type of initialization (1: no init, 2: steady state, 3: initial state, 4: initial output)|
|x_start||Real[n]||zeros(n)||Initial or guess values of states|
|y_start||Real||0.0||Initial value of output (remaining states are in steady state)|
|alpha||Real||if normalized then sqrt(2^(1/n) - 1) else 1.0||Frequency correction factor for normalized filter|
|Modelica.Mechanics.MultiBody.Examples.Loops.EngineV6_analyticV6 engine with 6 cylinders, 6 planar loops, 1 degree-of-freedom and analytic handling of kinematic loops|
|Modelica.Mechanics.MultiBody.Examples.Loops.EngineV6V6 engine with 6 cylinders, 6 planar loops and 1 degree-of-freedom|
|Modelica.Blocks.Examples.InverseModelDemonstrates the construction of an inverse model|