frd (Control System Toolbox)

frd	Examples See Also

Create a frequency response data (FRD) object or convert another model type to an FRD model

Syntax

sys = frd(response,frequency)
sys = frd(response,frequency,Ts)
sys = frd
sys = frd(response,frequency,ltisys)

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 Table 1-14, "Data Format for the Argument response in FRD Models,".

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" in the manual and "Model-Specific Properties" in the manual). 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.

**Table 1-14: 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" in the manual for more information on single FRD models, and "Building LTI Arrays Using tf, zpk, ss, and frd" in the manual for information on arrays of FRD models.

Example

Type the commands

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

to create a SISO FRD model.