LowpassButterworth
Output the input signal filtered with a low pass Butterworth filter of any order
Library
Modelica/Blocks/Continuous
Description
This block defines the transfer function between the input uand the output y as an n-th order low pass filter with Butterworthcharacteristics and cut-off frequency f. It is implemented asa series of second order filters and a first order filter.Butterworth filters have the feature that the amplitude at thecut-off frequency f is 1/sqrt(2) (= 3 dB), i.e., they arealways "normalized". Step responses of the Butterworth filter ofdifferent orders are shown in the next figure:
If transients at the simulation start shall be avoided, the filtershould be initialized in steady state (e.g., using optioninitType=Modelica.Blocks.Types.Init.SteadyState).
Parameters
| Name | Label | Description | Data Type | Valid Values |
|---|---|---|---|---|
mo_n | n | Order of filter | Scalar | |
mo_f | f | Cut-off frequency | Scalar | |
mo_m | m | Scalar | ||
mo_evenOrder | evenOrder | Scalar | true | |
mo_w | w | Scalar | ||
mo_initType | initType | Type of initialization (1: no init, 2: steady state, 3: initial state, 4: initial output) | Structure | |
mo_initType/choice1 | Modelica.Blocks.Types.Init.NoInit | Number | 0 | |
mo_initType/choice2 | Modelica.Blocks.Types.Init.SteadyState | Number | 0 | |
mo_initType/choice3 | Modelica.Blocks.Types.Init.InitialState | Number | 0 | |
mo_initType/choice4 | Modelica.Blocks.Types.Init.InitialOutput | Number | 0 | |
mo_x1_start | x1_start | Initial or guess values of states 1 (der(x1)=x2) | Vector | |
mo_x2_start | x2_start | Initial or guess values of states 2 | Vector | |
mo_xr_start | xr_start | Initial or guess value of real pole for uneven order otherwise dummy | Scalar | |
mo_y_start | y_start | Initial value of output (states are initialized in steady state if possible) | Scalar | |
mo_x1 | x1 | x1 | Structure | |
mo_x1/fixed | fixed | Cell of vectors | true | |
mo_x1/start | start | Cell of vectors | ||
mo_x2 | x2 | x2 | Structure | |
mo_x2/fixed | fixed | Cell of vectors | true | |
mo_x2/start | start | Cell of vectors | ||
mo_xr | xr | xr | Structure | |
mo_xr/fixed | fixed | Cell of scalars | true | |
mo_xr/start | start | Cell of scalars |
| Name | Label | Description | Data Type | Valid Values |
|---|---|---|---|---|
mo__nmodifiers | Number of Modifiers | Specifies the number of modifiers | Number | |
mo__modifiers | Modifiers | Add new modifier | Structure | |
mo__modifiers/varname | Variable name | Cell of strings | 'z' | |
mo__modifiers/attribute | Attribute | Cell of strings | 'start' | |
mo__modifiers/value | Value |
Ports
| Name | Type | Description | IO Type | Number |
|---|---|---|---|---|
u | implicit | Connector of Real input signal | input | 1 |
y | implicit | Connector of Real output signal | output | 1 |