## Frequency Response Data (FRD) Models

### Frequency Response Data

In the Control System Toolbox™ software, you can use frd models to store, manipulate, and analyze frequency response data. An frd model stores a vector of frequency points with the corresponding complex frequency response data you obtain either through simulations or experimentally.

For example, suppose you measure frequency response data for the SISO system you want to model. You can measure such data by driving the system with a sine wave at a set of frequencies ω1ω2, ,...,ωn, as shown:

At steady state, the measured response yi(t) to the driving signal at each frequency ωi takes the following form:

${y}_{i}\left(t\right)=a\mathrm{sin}\left({\omega }_{i}t+b\right),\text{ }i=1,\text{\hspace{0.17em}}\dots ,\text{\hspace{0.17em}}n.$

The measurement yields the complex frequency response G at each input frequency:

$G\left(j{\omega }_{i}\right)=a{e}^{jb},\text{ }i=1,\text{\hspace{0.17em}}\dots ,\text{\hspace{0.17em}}n.$

You can do most frequency-domain analysis tasks on frd models, but you cannot perform time-domain simulations with them. For information on frequency response analysis of linear systems, see Chapter 8 of [1].

### Commands for Creating FRD Models

Use the following commands to create FRD models.

Command

Description

frdCreate frd objects from frequency response data.

### Create Frequency-Response Model from Data

This example shows how to create a single-input, single-output (SISO) frequency-response model using frd.

A frequency-response model stores a vector of frequency points with corresponding complex frequency response data you obtain either through simulations or experimentally. Thus, if you measure the frequency response of your system at a set of test frequencies, you can use the data to create a frequency response model:

1. Load the frequency response data in AnalyzerData.mat.

This command loads the data into the MATLAB® workspace as the column vectors freq and resp. The variables freq and resp contain 256 test frequencies and the corresponding complex-valued frequency response points, respectively.

Tip

To inspect these variables, enter:

whos freq resp
2. Create a frequency response model.

sys = frd(resp,freq);

sys is an frd model object, which is a data container for representing frequency response data.

You can use frd models with many frequency-domain analysis commands. For example, visualize the frequency response data using bode.

Tip

By default, the frd command assumes that the frequencies are in radians/second. To specify different frequency units, use the TimeUnit and FrequencyUnit properties of the frd model object. For example: