blockLowpassButterworth
Extends from Modelica.Blocks.Interfaces.SISO (Single Input Single Output continuous control block).
Information
This block defines the transfer function between the input u and the output y as an n-th order low pass filter with Butterworth characteristics and cut-off frequency f. It is implemented as a series of second order filters and a first order filter. Butterworth filters have the feature that the amplitude at the cut-off frequency f is 1/sqrt(2) (= 3 dB), i.e., they are always "normalized". Step responses of the Butterworth filter of different orders are shown in the next figure:
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).
Parameters
| Type | Name | Default | Description |
|---|---|---|---|
| Integer | n | 2 | Order of filter |
| SI.Frequency | f | Cut-off frequency | |
| Initialization | |||
| Modelica.Blocks.Types.Init | initType | Modelica.Blocks.Types.Init.NoInit | Type of initialization (1: no init, 2: steady state, 3: initial state, 4: initial output) |
| Real[m] | x1_start | zeros(m) | Initial or guess values of states 1 (der(x1)=x2) |
| Real[m] | x2_start | zeros(m) | Initial or guess values of states 2 |
| Real | xr_start | 0.0 | Initial or guess value of real pole for uneven order otherwise dummy |
| Real | y_start | 0.0 | Initial value of output (states are initialized in steady state if possible) |
Connectors
| Type | Name | Default | Description |
|---|---|---|---|
| RealInput | u (from SISO) | Connector of Real input signal | |
| RealOutput | y (from SISO) | Connector of Real output signal |
Components
| Type | Name | Default | Description |
|---|---|---|---|
| Real[m] | x1 | States 1 of second order filters (der(x1) = x2) | |
| Real[m] | x2 | States 2 of second order filters | |
| Real | xr | State of real pole for uneven order otherwise dummy |