Control System Toolbox™

frd - Create or convert to frequency-response data models

Syntax

sys = frd(response,frequency) sys = frd(response,frequency,Ts) sys = frd sysfrd = frd(sys,frequency) sysfrd = frd(sys,frequency,'Units',units)

Description

sys = frd(response,frequency) creates an FRD model sys from the frequency response data stored in the multidimensional array response. The vector frequency represents the underlying frequencies for the frequency response data. See Data Format for the Argument Response in FRD Models for a list of response data formats.

sys = frd(response,frequency,Ts) creates a discrete-time FRD model sys with scalar sample time Ts. Set Ts = -1 to create a discrete-time FRD model without specifying the sample time.

sys = frd creates an empty FRD model.

The input argument list for any of these syntaxes can be followed by property name/property value pairs of the form

'PropertyName',PropertyValue

You can use these extra arguments to set the various properties of FRD models (see the set command, or LTI Properties and Model-Specific Properties). These properties include 'Units'. The default units for FRD models are in 'rad/s'.

To force an FRD model sys to inherit all of its generic LTI properties from any existing LTI model refsys, use the syntax

sys = frd(response,frequency,ltisys)

sysfrd = frd(sys,frequency) converts a TF, SS, or ZPK model to an FRD model. The frequency response is computed at the frequencies provided by the vector frequency.

sysfrd = frd(sys,frequency,'Units',units)converts an FRD model from a TF, SS, or ZPK model while specifying the units for frequency to be units ('rad/s' or 'Hz').

Arguments

When you specify a SISO or MIMO FRD model, or an array of FRD models, the input argument frequency is always a vector of length Nf, where Nf is the number of frequency data points in the FRD. The specification of the input argument response is summarized in the following table.

Data Format for the Argument Response in FRD Models

Model Form	Response Data Format
SISO model	Vector of length `Nf` for which `response(i)` is the frequency response at the frequency `frequency(i)`
MIMO model with `Ny` outputs and `Nu` inputs	`Ny`-by-`Nu`-by-`Nf` multidimensional array for which `response(i,j,k)` specifies the frequency response from input `j` to output `i` at frequency `frequency(k)`
`S1`-by-`...`-by-`Sn` array of models with `Ny` outputs and `Nu` inputs	Multidimensional array of size [`Ny` `Nu` `S1` `...` `Sn]` for which `response(i,j,k,:)` specifies the array of frequency response data from input `j` to output `i` at frequency `frequency(k)`

Remarks

See Frequency Response Data (FRD) Models for more information on single FRD models, and Creating LTI Models for information on building arrays of FRD models.

Example

Type the commands

freq = logspace(1,2);
resp = .05*(freq).*exp(i*2*freq);
sys = frd(resp,freq)