WOLFRAM SYSTEMMODELER

CriticalDamping

Output the input signal filtered with an n-th order filter with critical damping

Wolfram Language

In[1]:=
SystemModel["Modelica.Blocks.Continuous.CriticalDamping"]
Out[1]:=

Information

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 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-normalized 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

CriticalDampingNormalized.png

CriticalDampingNonNormalized.png

Parameters (6)

n

Value: 2

Type: Integer

Description: Order of filter

f

Value:

Type: Frequency (Hz)

Description: Cut-off 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)

Outputs (1)

x

Type: Real[n]

Description: Filter states

Connectors (2)

u

Type: RealInput

Description: Connector of Real input signal

y

Type: RealOutput

Description: Connector of Real output signal

Used in Examples (3)

InverseModel

Modelica.Blocks.Examples

Demonstrates the construction of an inverse model

EngineV6

Modelica.Mechanics.MultiBody.Examples.Loops

V6 engine with 6 cylinders, 6 planar loops and 1 degree-of-freedom

EngineV6_analytic

Modelica.Mechanics.MultiBody.Examples.Loops

V6 engine with 6 cylinders, 6 planar loops, 1 degree-of-freedom and analytic handling of kinematic loops