CriticalDampingOutput the input signal filtered with an nth order filter with critical damping 
This information is part of the Modelica Standard Library maintained by the Modelica Association.
This block defines the transfer function between the input u and the output y as an nth order filter with critical damping characteristics and cutoff 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 cutoff 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 nonnormalized filters usually require to adapt the cutoff 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 nonnormalized 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
n 
Value: 2 Type: Integer Description: Order of filter 

f 
Value: Type: Frequency (Hz) Description: Cutoff frequency 
normalized 
Value: true Type: Boolean Description: = true, if amplitude at f_cut is 3 dB, otherwise unmodified filter 
initType 
Value: Modelica.Blocks.Types.Init.NoInit Type: Init Description: Type of initialization (1: no init, 2: steady state, 3: initial state, 4: initial output) 
x_start 
Value: zeros(n) Type: Real[n] Description: Initial or guess values of states 
y_start 
Value: 0.0 Type: Real Description: Initial value of output (remaining states are in steady state) 
x 
Type: Real[n] Description: Filter states 

u 
Type: RealInput Description: Connector of Real input signal 


y 
Type: RealOutput Description: Connector of Real output signal 
Modelica.Blocks.Examples Demonstrates the construction of an inverse model 

Modelica.Mechanics.MultiBody.Examples.Loops V6 engine with 6 cylinders, 6 planar loops and 1 degreeoffreedom 

Modelica.Mechanics.MultiBody.Examples.Loops V6 engine with 6 cylinders, 6 planar loops, 1 degreeoffreedom and analytic handling of kinematic loops 