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 ω₁, ω₂, ,...,ω_n, as shown:

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

$$y_i\left(t\right)=a\sin \left({\omega }_{i}t+b\right),i=1,\dots ,n.$$

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

$$G\left(j{\omega }_i\right)=a{e}^{jb},i=1,\dots ,n.$$

You can do most frequency-domain analysis tasks on frd models, but you cannot perform time-domain simulations with them.

Commands for Creating FRD Models

Use the following commands to create FRD models.

Command	Description
frd	Create frd objects from frequency response data.
frestimate (Simulink Control Design)	Create frd objects by estimating the frequency response of a Simulink® model. This approach requires Simulink Control Design™ software. See Offline Frequency Response Estimation (Simulink Control Design) for more information.

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. Therefore, 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.

Load the frequency response data in AnalyzerData.mat.

load AnalyzerData

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.

Create a frequency response model.

sys = frd(resp,freq);

sys is an frd model object that represents frequency response data.

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

bode(sys)

By default, the frd function 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, set the frequency units to radians/minute.

sys = frd(resp,freq,...
    "TimeUnit","min","FrequencyUnit","rad/TimeUnit");